Gels and other soft amorphous solids 9780841233157, 0841233152, 9780841233164

Table of contents :
Content: Preface1. Polymer Gels: Basics, Challenges, and Perspectives2. Competitive Solvation Effects in Polyelectrolyte Solutions3. Computationally Driven Design of Soft Materials with Tissue-like Mechanical Properties4. Probe Diffusion Dynamic Light Scattering of Polymer solutions and Gels5. Nanostructure Evolution of Biomimetic Hydrogel from Silk Fibroin and Poly(N-Vinylcaprolactam): A Small Angle Neutron Scattering Study6. Model Polymer Thin Films To Measure Structure and Dynamics of Confined, Swollen Networks7. Effect of Solvent Quality and Monomer Water Solubility on Soft Nanoparticle Morphology8. The Design and Applications of Beta-Hairpin Peptide Hydrogels9. Self-Assembly and Mechanical Properties of a Triblock Copolymer Gel in a Mid-block Selective Solvent10. Mechanics of Disordered Fiber Networks11. Elastic Relaxation and Response to Deformation of Soft Gels12. Structure-Property Comparison and Self-Assembly Studies of Molecular Gels Derived from (R)-12-Hydroxystearic Acid Derivatives as Low Molecular Mass Gelators13. The Importance of Phase Behavior in Understanding Structure-Property Relationships in Crystalline Small Molecule/Polymer Gels14. A Nanoindentation Approach To Assess the Mechanical Properties of Heterogeneous Biological Tissues with Poorly Defined Surface Characteristics15. Gels for the Cleaning of Works of Art16. Polymeric Nanoparticles Explored for Drug-Delivery Applications17. Using Polymer Science To Improve Concrete: Superabsorbent Polymer Hydrogels in Highly Alkaline Environments18. Heterogeneity in Cement HydratesEditors' BiographiesAuthor IndexSubject Index

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Gels and Other Soft Amorphous Solids

ACS SYMPOSIUM SERIES 1296

Gels and Other Soft Amorphous Solids Ferenc Horkay, Editor Section on Quantitative Imaging and Tissue Sciences NICHD National Institutes of Health Bethesda, Maryland

Jack F. Douglas, Editor Materials Science and Engineering Division National Institute of Standards and Technology Gaithersburg, Maryland

Emanuela Del Gado, Editor Department of Physics and Institute for Soft Matter Synthesis and Metrology Georgetown University Washington, DC

Sponsored by the ACS Division of Polymeric Materials: Science and Engineering

American Chemical Society, Washington, DC Distributed in print by Oxford University Press

Library of Congress Cataloging-in-Publication Data Names: Horkay, Ferenc, editor. | Douglas, Jack F., 1956- editor. | Del Gado, Emanuela, editor. | American Chemical Society. Division of Polymeric Materials: Science and Engineering. Title: Gels and other soft amorphous solids / Ferenc Horkay, editor (Section on Quantitative Imaging and Tissue Sciences NICHD National Institutes of Health Bethesda, Maryland), Jack F. Douglas, editor (Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland), Emanuela Del Gado, editor (Department of Physics and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC); sponsored by the ACS Division of Polymeric Materials: Science and Engineering. Description: Washington, DC : American Chemical Society, [2018] | Series: ACS symposium series ; 1296 | Includes bibliographical references and index. Identifiers: LCCN 2018030058 (print) | LCCN 2018036667 (ebook) | ISBN 9780841233157 (ebook) | ISBN 9780841233164 Subjects: LCSH: Soft condensed matter. | Condensed matter. | Elastic solids. | Gelation. | Matter--Properties. Classification: LCC QC173.458.S62 (ebook) | LCC QC173.458.S62 G45 2018 (print) | DDC 530.4/1--dc23 LC record available at https://lccn.loc.gov/2018030058

The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI Z39.48n1984. Copyright © 2018 American Chemical Society Distributed in print by Oxford University Press All Rights Reserved. Reprographic copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Act is allowed for internal use only, provided that a per-chapter fee of $40.25 plus $0.75 per page is paid to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. Republication or reproduction for sale of pages in this book is permitted only under license from ACS. Direct these and other permission requests to ACS Copyright Office, Publications Division, 1155 16th Street, N.W., Washington, DC 20036. The citation of trade names and/or names of manufacturers in this publication is not to be construed as an endorsement or as approval by ACS of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission to the holder, reader, or any other person or corporation, to manufacture, reproduce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. Registered names, trademarks, etc., used in this publication, even without specific indication thereof, are not to be considered unprotected by law. PRINTED IN THE UNITED STATES OF AMERICA

Foreword The ACS Symposium Series was first published in 1974 to provide a mechanism for publishing symposia quickly in book form. The purpose of the series is to publish timely, comprehensive books developed from the ACS sponsored symposia based on current scientific research. Occasionally, books are developed from symposia sponsored by other organizations when the topic is of keen interest to the chemistry audience. Before agreeing to publish a book, the proposed table of contents is reviewed for appropriate and comprehensive coverage and for interest to the audience. Some papers may be excluded to better focus the book; others may be added to provide comprehensiveness. When appropriate, overview or introductory chapters are added. Drafts of chapters are peer-reviewed prior to final acceptance or rejection, and manuscripts are prepared in camera-ready format. As a rule, only original research papers and original review papers are included in the volumes. Verbatim reproductions of previous published papers are not accepted.

ACS Books Department

Contents Preface .............................................................................................................................. ix 1.

Polymer Gels: Basics, Challenges, and Perspectives ............................................ 1 Ferenc Horkay and Jack F. Douglas

2.

Competitive Solvation Effects in Polyelectrolyte Solutions ................................ 15 Alexandros Chremos and Jack F. Douglas

3.

Computationally Driven Design of Soft Materials with Tissue-like Mechanical Properties ........................................................................................... 33 Heyi Liang, Mohammad Vatankhah-Varnosfaderani, Sergei S. Sheiko, and Andrey V. Dobrynin

4.

Probe Diffusion Dynamic Light Scattering of Polymer solutions and Gels ...... 51 Mitsuhiro Shibayama and Xiang Li

5.

Nanostructure Evolution of Biomimetic Hydrogel from Silk Fibroin and Poly(N-Vinylcaprolactam): A Small Angle Neutron Scattering Study ............. 71 Rajkamal Balu, Jasmin Whittaker, Jitendra P. Mata , Naba K. Dutta, and Namita Roy Choudhury

6.

Model Polymer Thin Films To Measure Structure and Dynamics of Confined, Swollen Networks ................................................................................. 91 Sara V. Orski, Kirt A. Page, Edwin P. Chan, and Kathryn L. Beers

7.

Effect of Solvent Quality and Monomer Water Solubility on Soft Nanoparticle Morphology ................................................................................... 117 Halie J. Martin, B. Tyler White, Huiqun Wang, Jimmy Mays, Tomonori Saito, and Mark D. Dadmun

8.

The Design and Applications of Beta-Hairpin Peptide Hydrogels .................. 139 Peter Worthington and Darrin Pochan

9.

Self-Assembly and Mechanical Properties of a Triblock Copolymer Gel in a Mid-block Selective Solvent ................................................................................ 157 Santanu Kundu, Seyed Meysam Hashemnejad, Mahla Zabet, and Satish Mishra

10. Mechanics of Disordered Fiber Networks ......................................................... 199 Xiaoming Mao 11. Elastic Relaxation and Response to Deformation of Soft Gels ........................ 211 Mehdi Bouzid and Emanuela Del Gado

vii

12. Structure-Property Comparison and Self-Assembly Studies of Molecular Gels Derived from (R)-12-Hydroxystearic Acid Derivatives as Low Molecular Mass Gelators ..................................................................................... 227 V. Ajay Mallia and Richard G. Weiss 13. The Importance of Phase Behavior in Understanding Structure-Property Relationships in Crystalline Small Molecule/Polymer Gels ............................. 245 Kevin A. Cavicchi, Marcos Pantoja, and Tzu-Yu Lai 14. A Nanoindentation Approach To Assess the Mechanical Properties of Heterogeneous Biological Tissues with Poorly Defined Surface Characteristics ...................................................................................................... 265 Preethi Chandran, Emilios K. Dimitriadis, Peter J. Basser, and Ferenc Horkay 15. Gels for the Cleaning of Works of Art ............................................................... 291 D. Chelazzi, E. Fratini, R. Giorgi, R. Mastrangelo, M. Rossi, and P. Baglioni 16. Polymeric Nanoparticles Explored for Drug-Delivery Applications .............. 315 Heba Asem and Eva Malmström 17. Using Polymer Science To Improve Concrete: Superabsorbent Polymer Hydrogels in Highly Alkaline Environments ..................................................... 333 Kendra A. Erk and Baishakhi Bose 18. Heterogeneity in Cement Hydrates .................................................................... 357 K. Ioannidou Editors’ Biographies .................................................................................................... 373

Indexes Author Index ................................................................................................................ 379 Subject Index ................................................................................................................ 381

viii

Preface Gels are ubiquitous both in materials science and biology. Interest in the behavior of this class of soft materials has increased significantly in the last decades as new experimental approaches have been developed to synthesize and characterize gels, and as theoretical and computational methods have advanced to model the structure and properties of these complex materials. For example, molecular simulation is now an essential tool to investigate gels and other types of soft matter where experimental measurements are not possible. The growth of this field to include applications in biology and medicine as also provided much impetus to gels research. The goal of this volume is to discuss recent progress in gel science. The chapters cover a wide variety of topics from polymer chemistry, physics, materials science and engineering, reflectiong the interdisciplinary character of this field. A knowledge of the physical and chemical behavior of gels is essential for understanding, designing, and controlling material properties and performance. Gels can be synthesized with either flexible or stiff chains, linear or branched, and their length can also be tailored, etc. The network chains can be bonded to each other by chemical crosslinks or physical bonds involving van der Waals interactions, dipole-dipole interactions, hydrogen or ionic bonds, or pi-pi or pi-charge interactions. In addition to traditional polymer gels, this volume also focuses on low molecular mass organic gelators, relatively new, but rapidly growing, research direction in gel science. Special attention is devoted to the diverse applications of gels; using hydrogels for cleaning the painted surface of artwork (conservation of cultural heritage such as paintings and sculptures), developing advanced drug delivery systems, investigating the mechanism of setting of cement and hardening of concrete, etc. We hope the book will provide a valuable resource for researchers and students in developing their interest in synthetic and biological gels, biomaterials, and functional soft materials, and for advanced researchers in broadening their knowledge and appreciation of this field of research. We note that some chapters of this book are based on invited lectures presented at the Symposium “Gels and Other Amorphous Solids” (254th ACS National Meeting, August 20-24, 2017, Washington, D.C.). The symposium focused on all areas relevant to the formation, structure, properties and applications of synthetic and natural polymer networks and gels, including materials science, nanotechnology, surface science, rheology, tissue engineering, and modeling. These papers are intended to illustrate the central place of gel physics in modern materials science, biomedical research, biotechnology, medicine, etc.

ix

The editors of this book greatly enjoyed working with the authors, and would like to thank all authors for their excellent contributions to this exciting volume. We also acknowledge the colleagues who reviewed the chapters, as well as the staff of the ACS for making this volume possible. Our special thanks go to Ms. Sara Tenney, Ms. Amanda Koenig, Ms. Tracey Glazener, and Mr. Chris Moffitt for their excellent work.

Ferenc Horkay, Ph.D. Section on Quantitative Imaging and Tissue Sciences NICHD, National Institutes of Health 49 Convent Drive Bethesda, Maryland 20892, United States

Jack F. Douglas, Ph.D. National Institute of Standards and Technology Materials Science and Engineering Division 100 Bureau Drive Gaithersburg, Maryland 20899, United States

Emanuela Del Gado, Ph.D. Department of Physics and Institute for Soft Matter Synthesis and Metrology Georgetown University 37th and O Streets NW Washington, DC 20057, United States

x

Chapter 1

Polymer Gels: Basics, Challenges, and Perspectives Ferenc Horkay*,1 and Jack F. Douglas 1Section

on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, United States 2Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States *E-mail: [email protected]. E-mail: [email protected].

Recently, there has been a sharp increase in the number of theoretical and experimental studies made on gels to address various aspects of chemistry, physics, and applications of these structurally complex ‘soft’ materials. In this introductory chapter, we briefly discuss the classification of gels with an emphasis on the unique structural features and properties of this class of materials. Recent advances in emerging areas are also addressed, along with challenging unsolved problems, and possible future research directions are identified. Our personal perspective on this vast scientific field is mainly intended to convey the many potential opportunities for advancing our understanding of gels through advanced experimental, and theoretical investigations to enable the design of novel gel materials with rationally engineered physical, chemical and biological properties.

© 2018 American Chemical Society

Introduction Gels are a common form of soft matter that arises from diverse associating small molecules, polymeric, and particle components. However, the utilization of gels in numerous industrial and medical applications requires a better understanding of the process of gel formation, factors that influence gel stability, and relations between the structure and the unique rheological properties of this class of materials. Gelation encompasses diverse processes in which molecules or particles mutually interact with each other and the solvent in such a way as to become localized in space, leading to the emergence of macroscopic rigidity. Amorphous solidification process can occur either as an equilibrium thermodynamic transition or a non-equilibrium dynamical transition, and as thermally reversible or irreversible processes. Although many gels involve chemical cross-links, as in the case of rubbery materials, the constraints that lead to molecular and particle localization can also imply dynamic associations and topological interactions between extended anisotropic molecules and particles. Polymeric gels created through the introduction of cross-links between polymers in solution are perhaps the most familiar type of gel material in manufacturing applications. Cross-linked gels are often relatively robust when subjected to large deformations, and capable of absorbing a large amount of solvent when the polymer and solvent have a high affinity. The properties of cross-linked gels can be tailored by controlling the polymer chemistry and the chemical synthesis conditions. The mechanical strength of these materials is often augmented by incorporating filler particles and other additives that can form their own network with the polymer gel matrix. Although gel behavior has been studied for many decades, the rational engineering of the properties of these complex materials requires a better understanding of the relationship between the molecular structure and the physical properties. This chapter briefly reviews the classification of gels with an emphasis on ‘classical’ cross-linked polymer gels, although we also discuss various types of physical gels where association or topological interactions are responsible for the gelation or amorphous solidification. We also mention some recent advances in the field of gels, along with unsolved problems and suggest possible future research directions.

Classification of Gels As mentioned before, the bonding in gels can be either physical or chemical in nature (1, 2). Physical cross-links include hydrogen bonding, hydrophobic interaction, inter-chain entanglement interactions of topological nature, and local crystallite formation. Although physical cross-links are not permanent, they are sufficiently strong to link together chain segments over a long timescale to influence the mechanical response of the network to an imposed perturbation. The lifetime of physical bonds normally depends on the temperature and other thermodynamic variables, making these systems thermally reversible and self-healing. 2

In Table 1 the major classes of gels are listed.

Table 1. Typical gels Type of cross-link Chemical gels

Procedure

Example

Cross-linkig of existing polymer chains in random (vulcanization) or end-linking process

rubber poly(vinyl alchol) gel

Cross-linking polymerization

poly(acryl amide) gel

Addition polymerization

silicone gel (addition cure)

Condensation polymerization Physical gels

silicone gel (condensation cure)

Formed by physical (e.g.. hydrogen) bonds

‘jello’ agarose gel

Formed by crystallization

cellulose gel

Formed by ionic bonds

gelatin gel

Formed by self-assembly of small molecules (e.g., organogelators)

steroid gel

Formed by mechanical dispersion of carbon nanotubes in polypropylene

carbon nanotube entanglement network

Chemically Cross-Linked Gels Chemically cross-linked gels are formed by covalent cross-linking of polymer chains. Chemical gels are typically made by free radical polymerization, electromagnetic radiation (light, gamma, x-ray, electron beam), and by addition or condensation polymerization. Cross-linking by both free radical polymerization and electromagnetic irradiation involves three major steps: initiation, propagation, and termination. After initiation, the free radical site propagates and forms a network beyond the critical gelation point. Electromagnetic radiation can produce gels without the addition of a cross-linker. A further advantage of the latter cross-linking method is that it can be used at room temperature and at physiological pH. In addition and condensation polymerization processes, a multifunctional cross-linking agent reacts with the monomer units initiating chain growth. Anionic and cationic polymerization can also be used to make gels; however, these methods are sensitive to water, and therefore, their application is limited to non-polar monomers, i.e., cannot be used to synthetize hydrogels. The formation of covalent cross-links alters the chemical structure of the polymer, which has significant consequences on the physical properties of the system on both molecular and supramolecular levels. The type and degree of cross-linking influence many network properties, such as swelling, elastic, and transport properties. Cross-linking makes the polymer insoluble, independent of 3

the thermodynamic quality of the solvent. However, polymer networks are able to absorb solvent molecules. The driving force of the swelling process is the osmotic mixing pressure of the polymer Πmix. In a particular solvent, the degree of swelling is governed by the cross-link density of the polymer. Uncross-linked polymers can be diluted infinitely. Cross-links prevent infinite swelling because IImix is counter-balanced by the elastic pressure IIel generated by the cross-links. At equilibrium the solvent transport stops, and the swollen network coexists with the solvent. In other words, the swelling pressure IIsw becomes zero (3–5),

Equation (1) is based on the concept of additivity of the elastic and mixing free energies (4), and this assumption is widely used to analyze the swelling behavior of cross-linked polymer gels. The validity of this separability approximation is an important question, along with the nature of IIel when the polymer concentration is high so that mutual interparticle interaction effects are large (6). ‘Weak’ and ‘Strong’ Gels Many materials exhibit a highly compliant ‘jelly-like’ consistency rather than a fully solid like ‘gel’ character. This ‘squishy’ rheological response, so useful in so many applications and found in diverse common materials, is evidently intermediate between the ideal Newtonian fluid and Hookean elastic solid. In viscoelastic fluids, the elastic response is observed as a transient phenomenon, as first modeled by Maxwell, and the material flows after long times- ‘long’ often being a matter of human patience. Even crystalline solids will ‘flow’ given enough time so that stress relaxation with time t in viscoelastic materials does not in itself ensure the existence of a finite fluid viscosity η. This phenomenon is not exceptional, but is rather typical in everyday materials. Such materials may be termed ‘weak gels’ since they have an infinite viscosity, while at the same time they have a vanishing equilibrium shear elastic modulus. An infinite viscosity only requires the stress to decay sufficiently slowly. Given the ubiquity of this intermediate form of matter, some technical discussion is helpful to appreciate its nature and origin. The standard rheological characterization of gel materials is normally performed in the frequency domain by subjecting the material to a small oscillatory deformation and measuring the stress response to this perturbation. The most commonly measured properties are the ‘elastic modulus’ or ‘storage modulus’ G′ and the ‘viscous modulus’ or ‘loss modulus’ G″ obtained from the Fourier transform of the shear relaxation function, G(t). A ‘fully developed gel’ or ‘strong gel’ has the property G′ > G″, where both moduli (especially G′) are nearly independent of frequency ω over a large ω range. As noted before, such an elastic response to shear deformation ultimately derives from the presence of localized particles or molecules that store the deformation energy over long timescales. The existence of a linear stress-strain relation (Hooke’s law) implies that the material has a finite equilibrium modulus G. 4

The transition between a viscous fluid to a solid gel with a non-zero shear modulus Go is a progressive rheological transition and many equilibrium materials that we classify as being ‘gel-like’ exist in a state in which both G’ and G” are strongly frequency dependent. We term this type of intermediate material state a ‘weak gel’. These materials exhibit univeral properties associated with the emergence of the solid state that are rather distinct from ordinary Newtonian liquids and Hookean solids. The differece between the rheological behavior of weak and strong gels is illustrated schemitacally in Figure 1.

Figure 1. Schematic representation of the frequency dependence of the elastic modulus G’ and viscous modulus G” for strong and weak gels. It has been shown (7) that stress relaxation in systems undergoing amorphous solidification exhibits a universal power-law form, reflecting emergence of power correlations in the strain field of the gel material that often reflects the underlying hierarchical structure of the system. Specifically, the onset condition for forming a gel requires that the stress relaxtion function takes a power-law form,

so that the Fourier-transformed counterparts, G’ and G”, are likewise power laws in frequency, ω. In Eq. (2) S is a material constant and t is the time. Winter and coworkers (8, 9) have appropriately emphasized the emergence of power law scaling in G(t) as the defining condition for the emergence of the gel state. The shear viscosity is obtained from the integral of G(t) over finite times and this 5

quantity is divergent when G(t) takes the form of Eq. (2) so that η of a ‘weak gel’ is infinite. An infinite viscosity is a necessary condition for the solid state and this property provides a rationale for calling such materials “gels”. On the other hand, the power-law form of G(t) means that an applied stress will eventually decay to 0 at long times so that these materials ultimately relax as liquids. Thus ‘weak gels’ are a form of matter that is ‘intermediate’ between Newtonian liquids and Hookean solids (10–13). The exponent μ quantifies the precise degree of rheological ‘intermediacy (14, 15)’ and appears to vary with the type of the gel forming material. The determination of μ is presently phenomenological and research should be directed towards its better molecular understanding. While weak gels are arguably only a transitionary condition on the way to ‘proper’ gel state in which the material acquires a non-zero equibrium shear modulus G, this physical state is a prototypical condition for numerous everyday forms of ‘soft matter’ in living systems and soft materials encountered in manufacturing applications. From a practical standpoint, to estimate η and G raises issues since neither of these quantities are strictly speaking defined for weak gels. In practice, the frequency dependent extensions of η and G depend strongly on the measurement frequency so that a wide range of η and G values may be reported for gels if they are inappropriatly treated as Hookean solids or Newtonian liquids. Instead of η and G, these materials are characterized by the prefactor in Eq. (2), denoted by S by Winter and coworkers (8, 9), which has units involving fractional powers of time which characterize both the capacity of the material to store and dissipate energy. More theoretical and experimental work is needed to understand this important material property which is presently treated as purely a phenomenological parameter. The high degree of ‘softness’ of weak gels makes them susceptable to material change by perturbation. Some of their most characteristic and useful properties derive from this sensitivity and their self-healing when the perturbations are removed and the equilibrium state is recovered. In the next section, we discuss the nature of this highly non-linear response to describe property changes in these ‘susceptable’ materials. Responsive Gels A hydrogel is considered stimuli responsive, when minute changes in the environmental conditions (e.g., pH, ionic strength, temperature, solvent composition) induce a dramatic change in its properties (e.g., swelling degree, elastic modulus). In biomedical applications, stimuli responsive hydrogels are frequently called smart or intelligent gels, because response to different stimuli is a common feature of living systems. In smart gels, the structural changes must be fast and reversible, which make these systems of great interest in medical/biomedical applications (16, 17). Early studies on stimuli-responsive gels focused on the construction of artificial muscle-like materials. More recent studies aim to develop sensors, drug delivery, systems, scaffolds for tissue engineering, etc. Many applications require not only short response time (e.g., swelling-shrinking) but also the capability of the system to undergo large number of cycles without significant structural 6

destruction. Only relatively limited number of stimuli-responsive gel systems are available that exhibit optimized properties. Stimuli sensitive gels are based on the principle that polymer chains undergo conformational changes resulting in gel volume changes. This process reflects the change in the interactions between the components within the gel. For example, in pH and ion responsive gels volume transition is induced by changing the ionization of the polyelectrolyte chains. Decreasing the degree of ionization, the electrostatic interaction between the charged groups on the polymer chains is gradually reduced, and ultimately leads to the collapse of the network. In temperature sensitive systems the strength of polymer-solvent contacts varies relative to the polymer-polymer contacts. In a polymer solution, the polymer separates into a concentrated and a diluted phase at the critical temperature. When the polymer is cross-linked the gel undergoes a volume transition. Poly-N-isopropylacrylamide (PNIPAAM) is the most extensively studied temperature sensitive gel system. As the temperature increases PNIPAAM chains undergo conformational changes and the gels shrink at 40 °C. The swelling-shrinking process is reversible in these materials. Responsive gels are widely used as drug delivery devices to carry drugs to a specific site in the body. There is also strong interest in the application of responsive gels as biosensors in the medical field. A broad range of biomolecules of medical significance has been investigated. For example, glucose sensors are successfully used in insulin delivery systems (18). Work in this area is intense; trying to overcome challenges such as poor stability, hysteresis and long response time. In biomedical applications, a further critical requirement is to make the hydrogels biocompatible. An important emerging application of smart gels is tissue engineering (19). Smart hydrogels are well suited materials for scaffolds because (i) they provide the required aqueous environment for the cells, and (ii) they can release the cells in response to a stimulus. For example, it has been reported that PNIPAAm gels are capable to bind chondrocytes (cartilage cells) above the critical temperature and release them below the critical temperature (20). In tissue engineering application biodegradability of the gel scaffold and lack of cytotoxicity are also important requirements. Natural and Synthetic Polyelectrolyte Gels Biomacromolecules are naturally occurring polymers which are essential components of all living systems (21, 22). There are three major types of biopolymers: polysaccharides, proteins, and polynucleotides. Cellulose is the most abundant polymer in living systems. Many biopolymers, such as polypeptides, polynucleic acids, and certain polysaccharides are polyelectrolytes, i.e., charged macromolecules. In general, biological tissues are highly swollen polyelectrolyte gels. For example, the major component of cartilage extracellular matrix (ECM) is the negatively charged aggrecan/hyaluronic acid complex. The microgel-like aggrecan/hyaluronic acid assemblies provide the osmotic resistance of cartilage to external load (23). In other biological systems, e.g., in the nervous system, 7

Na+, K+, and Ca2+ ions regulate the excitability of neurons (21). Intracellular Ca2+ ions play important role in a variety of physiological processes such as muscle contraction, hormone secretion, synaptic transmission, gene expression, etc. Synthetic polyelectrolyte gels have a variety of applications in materials science and engineering, including materials for energy storage, separation, and drug delivery (24). The precise control of the molecular and supramolecular architecture of polymer gels makes it possible to design novel polyelectrolytebased materials in which the constituents are organized across multiple length scales to address a wide range of technological challenges. Since water is the medium of living systems, most biophysical gels are also polyelectrolyte gels, this class of gels heavily overlaps with those described in the previous sections. Polyelectrolyte gels have a great potential not only for designing new functional biomaterials (e.g., artificial muscle) but also understanding the principles of complex biological systems. Progress in the field requires an interdisciplinary effort to accomplish a better understanding of the structure and interactions of polyelectrolyte gels over multiple length and time scales. Gels Formed by Self-Assembly from Low Molecular Mass ‘Gelator’ Molecules Gels made from low molecular mass organic gelators (LMOGs) represent a relatively new class of soft materials (25, 26). In these gels, the monomer units self-assemble into fibrillar networks that entrap solvent molecules. The aggregation of gelator molecules is driven by a combination of directional non-covalent interactions (e.g., hydrogen bonding, π-π stacking, dipolar, quadrupolar) and non-specific and isotropic van der Waals interactions, rather than chemical cross-links (27). Often the directional interactions lead gelator molecules to self-assemble into chain-like structures glued together laterally by van der Waals interactions, resulting in the formation of highly extended fiber structures. The bundles, in turn, often form higher order secondary structures such as fibers, ribbons, sheets, etc. Although these gels commonly exhibit branching associated with defect formation in the fiber growth process, gelation can also arise from the extremely slow relaxation of disorganized suspensions of long uncrossable fibers, illustrating the phenomenon of gel formation without any cross-links (28). An outstanding question is what controls the diameter of these fibers. which is typically on the order of 10 nm (29). The physical factors governing the fiber branching is another basic feature that is not well understood and which greatly influences the mechanical properties of the resulting gel. Typically, gels from LMOGs are made by warming the material in a carefully selected solvent until the solid component completely dissolves and then cooling the resulting solution below the gelation temperature. During the cooling process, the gelator molecules start to phase separate. Three different scenarios may occur: (i) an ordered phase develops (e.g., crystals are formed), (ii) an amorphous phase develops due to random aggregation of the primary molecules, and (iii) a gel is formed. Gel formation depends on the interactions between the gelator and solvent molecules. It is known that a stable gel requires high melting temperature of the 8

gelator and low solubility in the liquid at room temperature. Gelators with higher solubilities are less suitable for network formation, and therefore they should be applied at higher concentrations. Furthermore, both gelator structure and solubility modulate the self-assembly process. A significant research effort has been devoted to identifying potential gelators by screening a variety of molecules using an Edisonian or ‘combinatoric’ approach, as well as by testing solvents that may be suitable to form gels using solubility parameters of the gelator as a guide (30–32). Although large number of LMOGs have been investigated (e.g., steroids, ureas, peptides, saccharides), a fundamental understanding of the molecular self-assembly and gelation processes is still limited (33, 34). For example, the structural requirements for small molecules to gel a liquid are still unclear. It is recognized that assembly often involves a combination of directional interactions leading to chain structure formation and lateral isotropic van der Waals interactions between chains that lead to the formation of bundles of chains. Correlative expressions have been found useful for gel forming ability based on measures of the solvent and gelator-solvent cohesive interaction (31, 32, 34). However, despite numerous chemical and physical studies have been made on many LMOG gels, important questions remain unanswered (35–42). The early stages of fiber formation are particularly unclear. Further research is needed to better understand what molecular factors govern the strikingly regular diameter of self-assembled fibers, the thermodynamic nature of the assembly transition, the frequency of fiber branching, the effect of the solvent and inherent molecular properties that influence the propensity of formation and stability of LMOG fiber gels (43). There is also a need to better understand how fiber formation influences the viscoelastic properties of solutions in the course of the gelation process.

Modeling There is a long history of modeling electrolyte and polyelectrolyte solutions starting from the seminal analytic theory of Debye and Huckel on electrolyte solutions (44) and its extension to polymers by Manning (45, 46). These works introduced the concept of screening of ionic interactions and charge condensation of counterions on the chain backbone. Many recent modeling works have been based on Monte Carlo (47–49) and molecular dynamics simulations (50, 51) where the ions are described as charged spheres and polyelectrolytes are modeled as chains of hard spheres dispersed within a continuum background fluid having a constant dielectric constant. Molecular dynamics simulations have been performed on networks of polyelectrolyte chains based on this type of ‘restricted primitive model’ of ionic solutions (52). These studies have given important insights into the coupling of charge interactions of the polymer segments with the counter-ions and the ions of the added salt. Despite all efforts, it is apparent that many aspects of polyelectrolyte solutions are not well understood such as how simple salts affect the viscosity of the solutions (53), how basic thermodynamic properties (density, surface tension, isothermal compressibility) depend on the salt concentration, and why highly 9

charged polyelectrolytes aggregate in solution, as directly observed by small angle neutron scattering and optical microscopy (54). Recent experimental (55) and computational studies (56, 57) have suggested that many of these problems can be traced to the importance of ion, interfacial and polymer hydration, etc. These studies have confirmed that ion and polymer solvation leads to qualitatively new effects such as the emergence of long range attractive interactions between highly charged polymer chains and ion-specific changes in the viscosity and water diffusion coefficient of aqueous salt solutions even without the polyelectrolyte. We may expect that this type of modeling will provide new insights into specific ion effects typical of polyelectrolyte solutions and gels in the future based on a more realistic treatment of solvation on the properties of electrolyte and polyelectrolyte solutions. Advances in high performance computation make this type of simulation possible since a significant part of the computation involves the treatment of the solvent which was neglected in former theoretical and computational studies. The development of analytical methods for treating solvation effects in ionic solutions and polyelectrolyte solutions provides a significant challenge for the future.

Summary The physics and chemistry of polymer gels is a rapidly developing field owing to the significance of these materials in both medical and materials science. However, there are still many challenging problems that should be addressed in the future in order to rationally design materials of this kind and to understand their properties from a more fundamental perspective. In this chapter, we briefly discussed some defining features of gels and brief taxonomy of the different kinds of gels. It is expected that synergetic advances in both theory and the development of new experimental methods will lead to deeper understanding of this ubiquitous form of soft matter to enable new avenues to design for novel materials with tailored physical and chemical properties and biological function.

Acknowledgments This work was supported by the Intramural Research Program of the NICHD, NIH.

References 1. 2. 3. 4.

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40. Babu, S. S.; Praveen, V. K.; Ajayaghosh, A. Functional p-gelators and their applications. Chem. Rev. 2014, 114, 1973–2129. 41. Ghosh, S.; Praveen, V. K.; Ajayaghosh, A. The chemistry and applications of p-gels. Annu. Rev. Mater. Res. 2016, 46, 235–262. 42. Awhida, S.; Draper, E. R.; McDonald, T. O.; Adams, D. J. Probing gelation ability for a library of dipeptide gelators. J. Colloid Interface Sci. 2015, 455, 24–31. 43. Douglas, J. F. Theoretical Issues Relating to Thermally Reversible Gelation by Supermolecular Fiber Formation. Langmuir 2009, 25, 8386–8391. 44. Debye, P.; Hückel, E. Zur Theorie der Electrolyte. Phys. Z. 1923, 24, 185–206. 45. Manning, G. S. Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties. J. Chem. Phys. 1969, 51, 924–933. 46. Manning, G. S. Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions III. An Analysis Based on the Mayer Ionic Solution Theory. J. Chem. Phys. 1969, 51, 3249–3252. 47. Orkoulas, G.; Kumar, S. K.; Panagiotopoulos, A. Z. Monte Carlo study of coulombic criticality in polyelectrolytes. Phys. Rev. Lett. 2003, 90, 048303. 48. Yan, Q.; de Pablo, J. J. Hyper-parallel tempering Monte Carlo: Application to the Lennard-Jones fluid and the restricted primitive model. J. Chem. Phys. 1999, 111, 9509–9516. 49. Dobrynin, A. V.; Obukhov, S. P.; M. Rubinstein, M. Cascade of Transitions of Polyelectrolytes in Poor Solvents. Macromolecules 1996, 29, 2974–2979. 50. Liao, Q.; Dobrynin, A. V.; M. Rubinstein, M. Molecular Dynamics Simulations of Polyelectrolyte Solutions: Nonuniform Stretching of Chains and Scaling Behavior. Macromolecules 2003, 36, 3386–2298. 51. Carrillo, J.-M. Y.; Dobrynin, A. V. Polyelectrolytes in Salt Solutions: Molecular Dynamics Simulations. Macromolecules 2011, 44, 5798–5816. 52. Yin, D. W.; Horkay, F.; Douglas, J. F.; De Pablo, J. Molecular Simulation of the Swelling of Polyelectrolyte Gels by Monovalent and Divalent Counterions. J. Chem. Phys. 2008, 129, 154909. 53. Kim, J. S.; Wu, A.; Morrow, A.; and Yethiraj, A. Self-diffusion and viscosity in electrolyte solutions. J. Chem. Phys. B 2012, 116, 12007–12013. 54. Zhang, Y.; Douglas, J. F.; Ermi, B. D.; Amis, E. J. Influence of counterion valency on the scattering properties of highly charged polyelectrolyte solutions. J. Chem. Phys. 2001, 114, 3299–3313. 55. Collins, K. D. Why continuum electrostatics theories cannot explain biological structure, polyelectrolytes or ionic strength effects in ion–protein interactions. Biophys. Chem. 2012, 167, 43–59. 56. Andreev, M.; Chremos, A.; de Pablo, J.; Douglas, J. F. Coarse-Grained Model of the Dynamics of Electrolyte Solutions. J. Phys. Chem. B. 2017, 121, 8195–8202. 57. Chremos, A.; Douglas, J. F. Communication: Counter-ion solvation and anomalous low-angle scattering in salt- free polyelectrolyte solutions. J. Chem. Phys. 2017, 147, 241103.

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Chapter 2

Competitive Solvation Effects in Polyelectrolyte Solutions Alexandros Chremos and Jack F. Douglas* Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States *E-mail: [email protected]. E-mail: [email protected].

An understanding of the solution properties and phase behavior of natural and synthetic polyelectrolyte requires an understanding of the competitive association of water (“hydration”) and ion association to the polymer backbone and the consequences of large scale clustering of counter-ions around highly charged polymers and associated chain clustering due to the high polarizability of this diffuse counter-ion cloud. We investigate the influence of counter-ion affinity for polyelectrolyte segments on the conformational properties of individual highly charged flexible polyelectrolyte chain using molecular dynamics simulations that include both ions and an explicit solvent. We find that an increase in the affinity of the counter-ions for polyelectrolyte segments leads to a significant increase in the average number of interfacial counter-ions. For a constant charge interaction defined by a fixed Bjerrum length and Debye screening length, this increase in the number of interfacial counter-ions with an increased strength in counter-ion affinity for the polyelectrolyte segments decreases the size of the polyelectrolyte chain and the average polyelectrolyte shape becomes less extended. We also calculate and quantify the distribution of counter-ions around solvated polyelectrolyte chains, where we find that a strong affinity of the counter-ions for the polyelectrolyte segments results in a decrease in the spatial extent of the diffuse counter-ion cloud around highly charged polymers. Not subject to U.S. Copyright. Published 2018 by American Chemical Society

I. Introduction Polyelectrolytes are complex ionic molecules in which charged groups are distributed along the backbone of a polymer chain and counter-ions are released to varying degrees into highly dielectric solvents, such as water, normally resulting in good polymer solubility (1, 2). Many biological molecules such as DNA, RNA, proteins, and synthetic polymers such as sulfonated polystyrene and polyacrylic acid are polyelectrolytes and due to their unique rheological and thermodynamic properties they are widely used as rheology modifiers, adsorbent materials, coatings, biomedical implant materials, encapsulating materials for pharmaceutical drug delivery systems (3–5). It is generally appreciated that this ionization process leads to a charged chain backbone in aqueous solution and results in long-range repulsive Coulomb interactions between the polymer segments that cause the polymer to swell. These interactions are greatly influenced by counter-ions that remain in the general proximity of the polyelectrolyte backbone and these interfacial counter-ions exchange with the counter-ions in the solution at a reasonably high rate so that the state of the bounded counter-ions is highly dynamic (6–8). It is these weakly bound counter-ions and their effect on chain conformation that make the modeling of polyelectrolytes challenging (6, 7, 9–12). Although it has long appreciated from the Manning model (13, 14) of polyelectrolyte solutions, and numerous experimental studies (6, 7, 9–12), that the counter-ions of highly charged polyelectrolytes tend to be localized near the chain backbone in which the average concentration is enriched, even though the ion-polymer as sociation is highly dynamic. Conventional modeling of polyelectrolyte solutions (15–21) does not address the solvation of ions within the chain backbone and the uncharged species of the polymer, a phenomenon that greatly influences thermodynamic and dynamic properties of ionic solutions (22, 23) and recent work has shown that counter-ion solvation can lead to long range attractive interactions between polyelectrolyte chains (24) that can also greatly influence thermodynamic and dynamic properties of polyelectrolyte solutions. In the present paper, we are concerned with the particular problem of how competitive association between ions and solvent influence conformational properties of charged polyelectrolyte chains in the limit of infinite polymer dilution where interchain coupling effects can be neglected. Without hydration, highly charged polymer chains naturally adopt rod-like conformations as Manning assumed, but recent simulations have indicated that hydration makes even highly-charged polymers to adopt molecular conformations closer to that of a random coil and the persistent length is highly sensitive to the counter-ion valence (25) as observed experimentally (26). We have found that these phenomena derive from a tendency of the solvated counter-ions to remain localized in a diffuse domain around the polyelectrolyte, in addition to being bound to the chain backbone as Manning’s model suggests, and strong reduction of the persistence length is found to that is caused by the tendency of the polyelectrolyte to chains “wrap” around the higher valent counter-ions (25, 27). To highlight the significance of solvation in polyelectrolyte solutions, we first summarize the effects of solvation in the “simple” case of electrolyte solutions (with no polyelectrolyte chains). Electrolyte solutions having different salts 16

exhibit a wide range of variation in solution properties, such as the density, viscosity, and surface tension; these changes in solution properties typically classified in terms of the Hofmeister series (28). Observations of Collins (29, 30), and theoretical arguments by Ninham (31), suggest the importance of ion-size on the extent of ion-solvation and the dispersion interaction between ions and water, respectively, in understanding the trends of polymer solubility, i.e., the Hofmeister series. Indeed, the ion solvation energy effectively reflects a combination of Coulombic and dispersion interaction contributions between the ions and the solvent particles surrounding the ions (32). Motivated by these observations, we explored an explicit electrolyte solvent model in which the water-ion dispersion interaction parameter was determined by the ion solvation energy through the application of Born theory of ionic solvation (22). We found that molecular dynamics simulations utilizing this model captured semi- quantitatively observed changes in solution viscosity and water diffusion coefficient on ion type (22), an effect that classical coarse-grained pair-potential models fail to reproduce (33). Recent calculations of the same model reveal that several other thermodynamic properties, including the density, isothermal compressibility, and surface tension, can be understood via the solvent-ion interactions, suggesting that the Hofmeister series is closely related to ion solvation (23). Thus, if the solvent interactions with the ionic species play such a crucial role in modulating the electrolyte solution properties, then it is logical to expect analogous effects in polyelectrolyte solutions. The present paper explores the relatively large parameter space governing the competitive binding of solvent and counter-ions to the polymer backbone in the infinite polymer dilution limit. In particular, we calculate the average number of interfacial counter-ions with variation of the counter-ion affinity for the polyelectrolyte segments. These results are compared to different solvent affinities for the charged species in the polyelectrolyte solution. We also calculate the radius of gyration of the polyelectrolyte chain and its average molecular shape with variation of the strength of the different affinities. Finally, we calculate the charge distributions of the different ions surrounding the polyelectrolyte chain and we rationalize the resulting effects of the competitive solvation on the polyelectrolyte chain flexibility. Our paper is organized as follows. Section II contains details of the model and simulation methods. Results of the conformational properties of the polyelectrolyte chain and the characterization of the spatial distribution of the counter-ions surrounding the polyelectrolyte chain are presented in Section III. Section IV concludes the paper.

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II. Model and Methodology We employ a bead-spring model of Lennard-Jones (LJ) segments bound by stiff harmonic bonds suspended in explicit LJ solvent particles, some of which are charged to represent counter-ions (34–37). The system is composed of a total of N = 64 000 particles in a periodic cube of side L and volume V. The system includes a single polyelectrolyte chain having a molecular mass of Mw = 41 and a total charge −Zp e is distributed uniformly along the molecular structure, where e is the elementary charge. For the purposes of our investigation, we focus on systems having Zp / Mw = 1. The bonds between polymer segments are connected via a stiff harmonic spring, VH (r) = k (r −l0)2, where l0 = σ is the equilibrium length of the spring, and k = 1000 ε / σ2 is the spring constant. The system also includes N− co-ions of charge −e and N+ = N− + Zp counter-ions of charge +e so that the system of interest has neutral total charge. All macro-ion segments, dissolved ions, and solvent particles are assigned the same mass m, size σ, strength of interaction ε. We set ε and σ as the units of energy and length; the cutoff distance for LJ interaction potential is rc = 2.5 σ. The size and energy parameters between i and j particles are set as σii = σjj = σij = σ and εii = εjj = εij = ε), except for three energy interaction parameters: the first interaction parameter is between the polyelectrolyte segments and the counterions εpc, the second interaction parameter is between the solvent particles and the polyelectrolyte segments εps, and the third one is between the solvent particles and the positive ions εcs. Variation of the interaction energy parameters between different types of particles reflect the degree of chemical incompatibility between the polymer repeating units (38). The primary focus of this study is on influence of εpc parameter on the conformational properties of the poyelectrolyte chain, while the other two parameters have been studied previously (39) and used here as points of reference. All charged particles interact via Coulomb potential (with a cut-off distance 10 σ) and a relatively short range Lennard-Jones potential of strength ε, and the particle-particle particle-mesh method is used (40). The systems were equilibrated at constant pressure and constant temperature conditions, i.e., reduced temperature kBT / ε = 0.75 (where kB is Boltzmann’s constant) and reduced pressure < P > ≈ 0.02, and the production run were performed at constant temperature constant volume, maintained by a Nosé-Hoover thermostat. The Bjerrum length was set equal to lB = e2 / (εs kBT ) ≈ 2.4 σ, where εs is the dielectric constant of the medium. The Debye screening length: λD = −1 / 2 [ 4 π lB (ρ+ + ρ−)]-1/2 ≈ 2.2, where ρ± = N± / L3 are the ion densities. Typical simulations equilibrate for 4000 τ and data is accumulated over a 10 000 τ interval, where τ = σ ( m / ε)1/2 is the MD time unit and the time step δt = 0.005 τ. Typical screenshots for different types of solvent affinities are presented in Figure 1. For comparison, we also consider an implicit solvent model at the some volume and temperature as our explicit solvent model, except that there is no solvent and all LJ interactions are described by Weeks-Chandler-Andersen potential.

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Figure 1. (a) Schematic of the different energetic interactions between three species in polyelectrolyte solutions namely, the polyelectrolyte segments, the counter-ions, and the solvent. The parameters at the corners of the outer and inner triangles correspond to the self-interaction energy and the cross-energy interaction parameters, respectively. Screenshots of typical molecular conformations of the polyelectrolyte chains (beads in red color) surrounded by counter-ions (beads in blue color) and co-ions (beads in light orange color) are also presented. (b) Screenshots of the charged species in the simulation box with the solvent rendered invisible on the top and visible (beads having green color) on the bottom.

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III. Results and Discussion We initiate our discussion with the characterization of the interfacial layer around the polyelectrolyte backbone. We set the interfacial layer based on an arbitrary distance criterion in which any counter-ion that is located at shorter distances than 1.1 σ are taken to be part of the interfacial region. This particular value, i.e., 1.1 σ, is chosen in order to discriminate between the counter-ions that are in contact with the polyelectrolyte from the remaining counter-ions. Based on our model, we find that the interfacial counter-ions exhibit a rich spectrum of behaviors for the different molecular topologies (27) and counter-ion valance (25). Now that we have defined the interfacial region for our model based on a precise geometric picture, we calculate the time average number of interfacial counter-ions, < ninter >, for different values of εpc. As seen in Figure 2, < ninter > significantly increases as εpc increases and quickly reaches a saturation point at about εpc / ε ≈ 3.8. This trend is in the opposite direction compared to the trends of other two interaction parameters (εcs and εps) since an increase in the affinity of the solvent particles for counter-ions or polyelectrolyte segments leads to “kicking out” the counter-ions from the polyelectrolyte backbone. Based on these observations, we find that an increased affinity of the counter-ions for the polyelectrolyte segments leads to “kicking out” the solvent particles from the polylectrolyte backbone. Due to their close proximity to polyelectrolyte, these interfacial counter-ions screen a significant portion of the bare charge of the polyelectrolyte. We calculate the effective polyelectrolyte charge as Qmacro = Zp − < ninter >. As seen at the inset of Figure 2, the effective charge can change significantly over the range of εpc / ε values, i.e., for small εpc / ε values Qmacro ≈ Zp. However, as εpc / ε increases Qmacro progressively decreases becomes nearly zero beyond the saturation point (εpc / ε ≈ 3.8). To better understand how the interfacial counter-ions organize along the polyelectrolyte backbone, we calculated the time average number of contacts these interfacial counter-ions have with the polyelectrolyte segments, < ncont >, as can be seen in Figure 3. If every interfacial counter-ion has exactly one polyelectrolyte segment contact then ninter = ncont, but as we have seen in previous studies (25, 27, 41) the polymer chain is more closely resembling a worm-like chain, meaning that the chain can “wrap” around counter-ions. This effect contributes to the inequality ninter < ncont. Evidently, there is a substantial increase in the number of contacts per interfacial counter-ion as εpc increases. A similar trend is found with increasing the valence of the counter-ions from monovalent to trivalent. Specifically, in the case of the trivalent counter-ions the polyelectrolyte chain collapses by wrapping around the counter-ions. These close similarities mean one thing: the polyelectrolyte chain is coiling around the interfacial counter-ions even in the case of monovalent counter-ions provided the affinity of the counter-ions is stronger among the other competitive solvation interactions. This is also supported from the screenshots in Figure 1 and by the calculations of polyelectrolyte size and shape, as we discuss below.

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Figure 2. Number of interfacial counter-ions < ninter > as a function of the cross energy interaction parameter between different species in polylectrolyte solutions. Specifically, εpc (circles), εps (squares), and εcs (diamonds) correspond to the cross interaction energy between the polyelectrolyte segments and counter-ions, counter-ions and the solvent particles, and the polyelectrolyte segments and solvent the particles, respectively. The dashed line corresponds to the implicit solvant model. Inset: Effective polyelectrolyte charge, Qmacro = Zp − < ninter >, as function of the strength of the cross energy interactions. The uncertainty estimates are smaller than the symbol size.

Having quantified the number of interfacial counter- ions along the polyelectrolyte backbone, we shift our focus on the conformational properties of the polymer. Specifically, we calculate the radius of gyration Rg of the polyelectrolyte chain for different values of εpc and the results are presented in Figure 4. An increase in εpc leads to a significant decrease in Rg. In the case of higher valent counter-ions, the interfacial counter-ions tend to increase the flexibility of the polymer chain by bending the chain around the higher valence ions (25). An increased number of interfacial counter-ions along the polyelectrolyte backbone evidently has effect as in the introduction of higher valent ions. Indeed, for εpc / ε > 2.7 the polyelectrolyte chain has collapsed and the overall size of chain is similar to the size of a polyelectrolyte chain in similar conditions, but having trivalent counter-ions. The conditions at which the polyelectrolyte chain collapses seems coincide with the condition at which 21

the saturation occurs for the number of interfacial counter-ions and the average number of segmental contacts per counter-ion compare Figures 2 and 3 with Figure 4. The contrast between the other types of cross energy interaction parameters is obvious. As εcs and εps increase the interfacial counter-ions are “kicked-out” of the interfacial layer leading for the polyelectrolyte chain to maintain its extended worm-like polymer over a wide range of εcs and εps values; see Figure 4.

Figure 3. Average number of contacts between the counter-ions and the polyelectrolyte segments, < ncont > as a function of the strength of cross interaction parameters. Specifically, εpc (circles), εps (squares), and εcs (diamonds) correspond to the cross interaction energy between the polyelectrolyte segments and counter-ions, counter-ions and the solvent particles, and the polyelectrolyte segments and solvent the particles, respectively. The dashed line corresponds to the implicit solvent model and the uncertainty estimates are smaller than the symbol size.

To determine to what degree a polyelectrolyte chain resembles a rod-like polymer or a random coil, we compare its average molecular shape to a chain with stiff bending potential and to other reference objects namely, a smooth sphere and self-avoiding walks. We use the ratio of the hydrodynamic radius over the radius of gyration, Rh / Rg, which is use ful descriptor to quantify the shape of polymers (42, 43); the calculation of Rh is based on the friction coefficient of an arbitrary shaped Brownian particle. The values of Rh / Rg for a smooth sphere is 22

1.29, for a random walk is 0.79, and this ratio approaches to zero for infinite long rod-like objects (44, 45). Unlike rigid rods, polymers exhibit coiled molecular conformation, meaning that we need to calculate the time average molecular shape, i.e., < Rh > / < Rg >. As we have shown in previous studies (25, 27), polyelectrolyte chains have a relatively stretched “worm-like” configuration somewhat stiffer than chains having no charges. Their shape is thus quite different from a rod.

Figure 4. Radius of gyration, Rg, of a polyelectrolyte chain as function of the strength of cross interaction parameters. Specifically, εpc, εps , and εcs correspond to the cross energy interaction between polyelectrolyte segments and counter-ions, counter-ions and solvent particles, and polyelectrolyte segments and solvent particles, respectively. The dashed line corresponds to the implicit solvant model and the error bars correspond to two-standard deviations.

The impact of a strong affinity between the monovalent counter-ions and the poyelectrolyte segments is presented in Figure 5. An increase in εpc leads less coiled conformations, see also typical screenshots at Figure 1a. For example, for counter-ion affinity for the polyelectrolyte segments εpc / ε ≈ 2.6 the resulting average molecular shape is approximately that of a random walk, meaning that there is a sufficient number of interfacial counter-ions that “screen” the repulsive electrostatic interactions between the polyelectrolyte segments, resulting in an average shape equivalent to that of polymer chains in θ-solvent. For εpc / ε > 23

2.6, the average molecular shape becomes more compact respect to a random coil in ideal conditions, but less symmetric than a sphere. However, we cannot characterize the molecular conformations as “collapsed”, as this would indicate that the shape would be close to a smooth sphere when Rg / Rh ≈ 1.29. Why would the polyelectrolyte chain contract in size resulting in to a more compact molecular conformation for higher counter-ion affinity for the polyelectrolyte segments? While the propensity of the persistence length to be reduced by the counter-ion valence has been noted in previous theoretical work (46, 47), there is little understanding on how the competitive van der Waals type of interactions between the different species in polyelectrolyte solutions influence the persistence length of the polyelectrolyte chains, these effects are not captured by conventional theoretical frameworks (48, 49). This phenomenon must be freshly addressed now that the importance of polymer and ion solvation effects on chain conformation have been established.

Figure 5. Ratio of the average hydrodynamic radius over the average radius of gyration Rh / Rg as as function of the strength of cross interaction parameters. Specifically, εpc, εps, and εcs correspond to the cross energy interaction between polyelectrolyte segments and counter-ions, counter-ions and solvent particles, and polyelectrolyte segments and solvent particles, respectively. The dot-dashed lines correspond to the reference values of reference objects, for a smooth sphere is 1.29 and self-avoiding walks in θ-solvent equals 0.79 (44, 45); we also include the value of Rh / Rg for a finite size rod having the same molecular mass Mw = 41 as for our polyelectrolyte chains, Rh / Rg ≈ 0.42 (25). The error bars correspond to two-standard deviations. The dashed line corresponds to the implicit solvant model. 24

We now focus on the spatial distribution of counter-ions in relation to the position of the polyelectrolyte segments. Previously, we developed an approach for quantifying the spatial distribution of the counter-ions surrounding a polyelectrolyte chains and we briefly outline this approach (25, 27). In particular, we calculate the average net charge q(r) as function of distance from the polyelectrolyte segments. As shown in Figure 6a, q(r) is simply the difference of the counter-ion distribution q+(r) and the co-ion distribution q−(r), meaning that q(r) contains information for both the counter-ions that are located in the interfacial layer (defined as any particle being at a distance r / σ ≤ 1.1 from any polyelectrolyte segment) as well as in the diffuse counter-ion cloud. This approach (25, 27) allows us to determine the size of the cloud of the diffuse counter-ions (Rcloud) associated with the polyelectrolyte chain, since the boundary between this cloud and the bulk is at q(r = Rcloud) = q+ (r) − q−(r) = 0. An example illustrating these charge distributions is presented in Figure 6a. For a weak dispersion interaction strength, εpc / ε = εcs / ε = εpc / ε = 1, a fraction of counter-ions have a small tendency to “condense” along the polyelectrolyte backbone. However, as we increase the counter-ion affinity for polyelectrolyte segments, we increase the number of interfacial counter-ions along the polyelectrolyte backbone along with the overall polyelectrolyte size and shape, thus significantly influencing the q(r) distribution, as illustrated in Figure 6b. The difference in the impact with the other two cross energy interaction parameters is clear. Increasing εcs or εps leads to the counter-ions to be dissolved and continue to interact with the polyelectrolyte chain at relative large distances 2 < r / σ < 10, leading to an enrichment of the diffuse counter-ion cloud surrounding the polyelectrolyte chain. An increase in εpc, on the other hand, leads to a counter-ion enrichment at relative short distances 1 < r / σ < 5, see Figure 7. We next consider the cumulative net charge, at a distance r from polyelectrolyte segments to better quantify the net ionic distribution around a polyelectrolyte chain (25, 27). Q(r) starts from 0 at short distances r / σ < 1 and progressively increases at long distances until it saturates, i.e., Q(r) / Zp ≈ 1, see Figure 8. The rate at which Q(r) / Zp reaches unity follows the approximately universal functional form:

where α and μ are fitting parameters. The most important parameter is α, since it determines the overall size of the diffuse counter-ion cloud. From previous studies, we know that the functional form of Eq. 1 holds for polyelectrolytes having different molecular architectures (27) and for different counter-ion valence (25), suggesting that the rate of charge saturation is coupled to the structure of the polyelectrolyte chains and the charge carried by the counter-ions. Moreover, for monovalent counter-ions, the size of ionic cloud is directly coupled to the size of the polyelectrolyte chain, as quantified by the 25

radius of gyration, Rg (27). However, deviations from the monovalent counter-ion behavior were found for divalent and trivalent counter-ions, where the trend was amplified due to the stronger coupling between the counter-ions with the conformational properties of the polyelectrolyte chain, leading to a non-trivial dependence between the size of the ionic cloud and Rg (25). Here, we extend this type of calculation to polyelectrolyte chains having different degrees of counter-ion affinity for the polyelectrolyte segments. By plotting the parameter Rg as function of α, we find that the average size of the polyelctrolyte chain is again found to scale with the α-parameter as we vary with the solvent affinity for the ionic species; see Figure 9. This finding agrees with our observations from our previous studies where we examined the role of molecular architecture on the size of the counter-ion cloud (27) and for different solvent affinities (39), i.e., εcs and εcs. We emphasize this simple relation between α and Rg only exists for monovalent counter-ions (25). Here we see that Eq. 1 only holds when the polyelectrolyte chain is sufficiently swollen, εpc / ε < 3.5, Q(r) / Zp starts from zero at short distances and progressively reaches saturation Q(r) / Zp = 1 at longer distances. In the case of a strong affinity εpc /ε > 3.5, Q(r) exhibits a maximum (Q(r) / Zp > 1) at an intermediate scale and then progressively decreases (Q(r) / Zp = 1) at longer distances. The maximum occurs near to the minimum observed in q(r) distributions, see Figure 7. This feature is associated with the formation of negatively charged layer of co-ions. A similar behavior was observed for the trivalent counter-ions (25), suggesting that the formation of a maximum in the Q(r) curves is an indication of a charge inversion and collapse. Equivalent behavior has been observed in experiments of aqueous polyaspartate with multivalent cations (50). Evidently, the solvation layer around different charged species exhibits a non-universal dependence on the relative strength of these competing interactions.

26

Figure 6. (a) Distribution of the ionic net charge, q(r), as well as the relevant distributions of the counter-ions q+(r) and co-ions q−(r), and the distribution of the polymeric segments, qpol(r), as function of distance from the polyelectrolyte segments. (b) Distribution of the net charge q(r) for four different types of solvent affinity namely, no solvent affinity (εcs / ε = εps / ε = 1), strong counter-ion solvent affinity(εcs / ε = 8), strong polyelectrolyte solvent affinity (εps / ε = 8), and strong affinity between the polyelectrolyte segments and the counter-ions (εpc / ε = 8).

27

Figure 7. Net charge q(r) as function of distance from the polyelectrolyte segments. Results for different values of the cross energy interaction parameter between polyelectrolyte segments and counter-ions are also presented.

Figure 8. Cumulative net charge Q(r) normalized by the total bare charge of the polyelectrolyte chain Zp as function of distance from the polyelectrolyte segments. Results for different values of the cross energy interaction parameter between polyelectrolyte segments and counter-ions are also presented. 28

Figure 9. Size of the counter-ion cloud, α, surrounding the polyelectrolyte chain as function of the radius of gyration, Rg. Each data point corresponds to different strength of cross energy interaction parameter between the counter-ions and the polyelectrolyte segments, εpc; see also Figure 4 for comparison. The error bars correspond to two-standard deviations.

IV. Conclusions In summary, we have investigated the conformational structure of an isolated polyelectrolyte chain and counter-ion distribution based on molecular dynamics simulations that include both ions and an explicit solvent. We particularly focus on the influence of the counter-ion affinity for the polyelectrolyte segments on the chain conformational properties. We find that an enhancement of the counter-ion affinity for polyelectrolyte segments results in significant increase of the average number of interfacial counter-ions. Moreover, the polyelectrolyte chains contract in size by “wrapping” around the interfacial counter-ions, thus greatly increasing the average number of the segmental contacts of the interfacial counter-ions. The contraction of the polymer size also makes the overall molecular shape of the polyelectrolyte chain more compact compared to a random coil. We also examined the net ionic distribution around the polyelectrolyte chain with variation of the counter-ion affinity for the polyelectrolyte chain and thus quantify the size of the diffuse counter-ion cloud surrounding the polyelectrolyte chain. The results are compared with two type of solvent affinities for the charged species, i.e., counter-ions and polyelectrolyte segments, where the trends in the conformational properties occur in opposite direction of the counter-ion affinity for the polyelectrolyte segments. We conclude that the competitive solvation of the polyelectrolyte backbone by solvent and counter-ions leads to a range of 29

distinct polymer conformational behaviors in solution, underlying the need to include an explicit solvent in the modeling of polyelectrolyte solution properties.

Acknowledgments We gratefully acknowledge the support of the NIST Director’s Office through the NIST Fellows’ postdoctoral grants program. Official contribution of the U.S. National Institute of Standards and Technology – not subject to copyright in the United States.

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Chapter 3

Computationally Driven Design of Soft Materials with Tissue-like Mechanical Properties Heyi Liang,1 Mohammad Vatankhah-Varnosfaderani,2 Sergei S. Sheiko,2 and Andrey V. Dobrynin*,1 1Department

of Polymer Science, University of Akron, Akron, Ohio 44325, United States 2Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3220, United States *E-mail: [email protected]. E-mail: [email protected].

Mimicking the mechanical properties of soft materials and biological tissues is crucial for novel materials development for medical implants, tissue engineering, soft robotics, and wearable electronics. Unfortunately, the required combination of softness, strength, and toughness is difficult to replicate in synthetic materials. Modern design strategies are predominantly Edisonian in nature and are based on exploratory mixing of assorted polymers, variation in cross-linking schemes, and solvents. However, it was recently demonstrated that it is possible to encode mechanical properties of soft tissues in solvent free synthetic elastomers by varying architecture of the network strands. This approach is based on the theoretical and computational studies of correlations between mechanical properties and architecture of networks with brush-like strands. Different types of graft polymers such as combs and bottlebrushes were modeled as ideal chains or filamets with effective Kuhn length. This representation of graft polymers allows for a precise mapping of network’s mechanical properties in both linear and nonlinear deformation regimes into molecular architecture of the network strands.

© 2018 American Chemical Society

This approach to materials design was tested by reproducing mechanical properties of assorted biological gels and tissues using poly(dimethylsiloxane) (PDMS) and poly(n-butyl acrylate) (PBA) graft polymer elastomers. This technique lays the foundation for a computationally driven materials design that will be capable of encoding mechanical properties of soft materials in solvent free elastomers.

Introduction Materials (synthetic and biological) (1–7) demonstrate an astounding variety of the mechanical properties which is reflected in different shapes of their stress-deformation curves (see Figure 1a). Polymer gels like jellyfish are soft and highly deformable while bone is rigid and brittle. Biological tissues (8) like heart and skin demonstrate unique strain adaptability manifested in a sharp increase in their instantaneous modulus, dσ/dλ, with deformation. However, despite this variety of mechanical responses, there is a general trend correlating the value of the Young’s modulus at small deformations E0 with an elongation-at-break λmax or strain-at-break εmax = λmax − 1 for materials undergoing uniaxial deformation (see Figure 1b) (1). This relationship is known as a “Golden rule” of the materials science and identifies a general trend that more rigid materials are less deformable. For synthetic elastomers or rubber both the modulus and elongation-at-break are uniquely determined by the degree of polymerization between cross-links nx. This results in a universal relationship, , confining a large fraction of polymeric networks into a single trend line with a lower bound imposed by the entanglements of the network strands, ne (9–11). For solvent free elastomers an entanglement modulus is on the order of Eent ~ 1 MPa and elongation-at-break λmax ~ 5 if no specific routes in network preparations are undertaken (12–16). In the case of brittle materials the universal follows from the fact that for a material to break it scaling relation . requires to store a particular amount of the energy density, However, there is a large class of biological and soft composite materials that occupy space below the “Golden rule” trend – referred to as the “Biological triangle” in Figure 1b. This poses a challenge of how to create synthetic replicas that will be capable of reproducing mechanical properties of materials from the “Biological triangle”. The conventional approach is to use multicomponent systems by utilizing Edisonian approach thorough exploratory mixing of assorted polymers, cross-linking schemes, and solvents. However, this approach is imperfect in property control (8, 17–23). For example, solvent can leak under applied stress or evaporate when the environmental conditions are changed. Furthermore materials properties are matched only in the linear deformation regime thus restricting synthetic materials design to the range of small deformations. 34

Figure 1. Diversity in materials mechanical properties is illustrated by uniaxial tensile stress-strain curves. b) “Golden rule” of materials science establishes an inverse relationship between elongation-at-break λmax and modulus E0. To display materials with different λmax in a single plot, E0/ρ is shown as a function of

, where ρ is the mass density. Data replotted from ref (1).

A new approach to the design of a wide class of polymeric materials capable of mimicking mechanical properties of tissues is based on variation of architecture of the network strands such as graft polymers (see Figure 2a) (1). This allows replication of materials’ (tissue or composite) mechanical properties in solvent free elastomers. For example, changes in the degree of polymerization (DP) of the side chains, nsc, and their grafting density, 1/ng, provides flexibility in control over the concentration of the stress supporting backbones (dilution of the backbone monomers). In addition to the dilution effect, by varying 1/ng and nsc one can change the effective Kuhn length of the graft polymers, making a network strand more rigid or flexible (1, 9, 24). The following strategy for replication of the mechanical properties of a soft material or tissue using graft polymer elastomers was outlined (1) (see Figure 2b): (i) fitting of the entire stress-strain curve to the macroscopic network model expressed in terms of the network modulus and elongation-at-break; (ii) using established correlations between macroscopic network parameters and chemical structure of graft polymers defined by architectural triplet [nsc, ng, nx] to determine feed ratios for network synthesis; (iii) synthesis of the polymer network with a given chemical structure of the network strands; and (iv) measurement of the mechanical properties of the replica and verification of the replication procedure. In the rest of the chapter we overview steps of the materials design and replication process. To put this approach on solid footing we begin our discussion with solution of the forward problem and establish relationships between mechanical properties of the networks of graft polymers and their chemical structure.

35

Figure 2. a) Schematic representation of the network made of graft polymer strands. b) Flow chart for replicating mechanical properties of a selected tissue in graft polymer elastomers.

A Model of Polymeric Networks and Gels A starting point of the replication procedure is fitting the materials stress-strain curve in the linear and nonlinear deformation regimes to a network deformation model (see Figure 2b). In our approach we use a network model which bridges a network deformation with the deformation of the individual network strands (25, 26). In particular, this model takes advantage of universality in individual strands’ deformation by representing them as worm-like chains with the effective Kuhn length bK (27). In the framework of this model the true stress generated in a network undergoing uniaxial elongation with elongation ratio λ at a constant volume is equal to

where G is the structural shear modulus, β is the strand extension ratio, and the first strain invariant for network undergoing a uniaxial deformation is I1(λ) − (λ2 + 2/λ). These two parameters G and β uniquely determine a network’s stress-deformation curve. In particular, the structural modulus G controls material stiffness and β parameter is responsible for the onset of strain-stiffening due to finite extensibility of the network strands and is related to the elongation-at-break. The strand extension ratio is defined as a ratio of the mean square end-to-end distance of the undeformed network strands in as-prepared networks, square of the contour length of a fully extended strand, length l, as follows

36

, and

, with a bond

For network strands described by worm-like chains with the effective Kuhn length bK,

is written as (11)

It is convenient to express the strand extension ratio β in terms of the number of the Kuhn segments per strand α−1 ≡ Rmax/bK

Two limiting cases are clearly identified. For flexible strands with bK >Rmax, β ~1. This is usually the case for biological networks and gels (28, 29). Structural shear modulus of the network, G, is proportional to the number density of the stress-supporting strands ρs

where C1 is a numerical constant that depends on the functionality of the crosslinks and network topology, kB is the Boltzmann constantan and T is the absolute temperature. It is important to point out the difference between the structural modulus G and the shear modulus at small deformations

used to characterize stiffness of linear chain networks (11). It follows from eq 6 that these two moduli G and G0 are only equal in the case of flexible networks strands for which β 1 (30). It is important to point out that the value of the crowding parameter Φ > 1 corresponds to a hypothetical system, where bottlebrush macromolecules maintain ideal conformations of side chains and backbones even at infinitely (unreasonably) large grafting density. In real systems, however, in the range of system parameters with Φ > 1, the backbone and side chains will stretch to maintain the melt density (ρ ≈ ν−1). The explicit expression for location of the crossover between combs and bottlebrushes given by Φ ≈ 1 is obtained by solving eqs 8 and 9 for a composition parameter

Figure 6. Diagram of states of graft polymers in a melt with bond length l, Kuhn length of the backbone and side chains b, and monomer excluded volume v. SBB – stretched backbone regime, SSC- stretched side chain regime, and RSC – rod-like side chain regime. Logarithmic scales. Adapted with permission from ref (30). Copyright 2017 American Chemical Society.

This parameter describes partitioning of monomers between a side chain and backbone spacer between two neighboring side chains and characterizes “dilution” of the backbone. 41

Figure 6 shows diagram of states of graft polymers as a function of their chemical structure and composition (30). There are two main regimes: (i) Comb regime, where both side chains and backbones of graft polymers interpenetrate and remain ideal and (ii) Bottlebrush regime, where excluded volume interactions between densely grafted side chains expel monomers of the neighboring macromolecules from the pervaded volume of a given graft polymer. In a Bottlebrush regime, bottlebrush backbones or side chains have to stretch to maintain a constant monomer density in a melt. Bottlebrushes with extended backbones are in the Stretched Backbone (SBB) regime and those with stretched side chains belong to the Stretched Side Chain (SSC) regime. Bottlebrushes with fully stretched side chains define the Rod-like Side Chain (RSC) regime. Table 1 presents the effective Kuhn length, bK, in terms of the degree of polymerization of the side chains nsc and the number of bonds between grafting points of the side chains, ng, and system molecular parameters (30, 32).

Table 1. Effective Kuhn Length of Graft Polymers in Different Regimes and Regime Boundaries (30)

Scaling relations for dependence of the effective Kuhn length on the macromolecular architecture summarized in Table 1 have been verified in the coarse-grained molecular dynamics simulations (33, 34) of the graft polymers in a melt (30). Figure 7 combines simulation data for the reduced effective Kuhn length bK/b as a function of the crowding parameter, Φ. In a comb regime the effective Kuhn length saturates at b. With increasing value of the crowding parameter, Φ, the interactions between side chains result in stiffening of macromolecules. This leads to increase of the effective Kuhn length bK. In the range of the values of the crowding parameter Φ>1, simulation data confirm a scaling dependence for the effective Kuhn length of the bottlebrushes, bK ≈ bΦ. 42

Figure 7. Dependence of the normalized Kuhn length, bK/b, of the graft polymers (see eq 8) for graft polymers with degree of on the crowding parameter polymerization of the side chains nsc varying between 2 and 32 and number of bonds on the backbone between side chains ng in the interval 0.5 and 32 (ng=0.5 corresponds to two side chains attached to each backbone monomer). See ref 30 for symbol notations. Thin solid lines show scaling predictions in comb and bottlebrush regimes. Adapted with permission from ref (30). Copyright 2017 American Chemical Society.

Model of the Graft Polymer Networks The next step is to use results for the dependence of the effective Kuhn length bK on the graft polymer architecture to develop a model of the graft polymer networks (31, 32, 35). Consider graft polymer networks made by cross-linking precursor macromolecules with the backbone degree of polymerization nbb in a melt with the monomer number density ρ. This cross-linking procedure produces two dangling ends of varying length per chain reducing the number of stress supporting strands (32)

Substituting eq 11 into eq 5, one obtains the following general expression for the structural shear modulus of graft polymer networks

43

The explicit form of eq 12 in terms of the architectural parameters of the graft polymers is derived by using corresponding expressions for the Kuhn length bK in different regimes of diagram of states shown in Figure 6 and listed in the Table 1. The results of such derivation are summarized in Table 2 (32).

Table 2. Structural Shear Modulus, G, and Inverse Number of Effective Kuhn Segments Per Network Strands, α, in Different Conformation Regimes (32)

The scaling expression for structural modulus and number of effective Kuhn segments per network strand have been tested in the coarse-grained molecular dynamics simulations of the graft polymer networks. In these simulations, the graft polymers have been cross-linked through the end monomers of the side chains, which corresponds to the experimentally studied systems (1, 9). This cross-linking scheme results in a hybrid network composed of brush-like and linear network strands and requires explicit consideration of the elastic response of both strands’ populations. However, in a wide range of the strands’ architectures, the elastic response of graft polymer networks is dominated by the deformation of the graft polymer strands. Thus, such networks can be approximated by graft polymer networks cross-linked through their backbones (see for detailed discussion ref (32)). The stress-deformation curves of graft polymer networks of different chemical sructures are shown in Figures 8a-c. As evident from Figures 8a and 8b, the decrease in the side chain length or strand length between cross-links both leads to the higher shear modulus and lower strand extensibility. However, we can achieve both shear modulus and strand extensibility increase with the decrease of grafting density as shown in Figure 8c. The linear relationships (see Figures 8d-f) between network parameters α, β, and G describing its mechanical properties and structural parameters [nsc, ng, nx] of the network strands allows for a simple calibration procedure for creation of libraries of the graft polymers for replication of soft materials and biological tissues using soft solvent free networks with predetermined stress-deformation curves. 44

Figure 8. Dependence of the tensile stress σxx on the deformation ratio λ for networks of graft polymers (a-c). (a) Illustration of the increase in the network structural modulus G and decrease in network extensibility with increasing DP of side chains nsc for networks with ng = 8, nx ≈ 16. (b) Decrease in network structural modulus G and increase in network extensibility with increasing DP of backbone between crosslinks nx for networks with ng = 2 and nsc = 8. (c) Nonlinear deformation of the networks with nsc = 8, nx ≈ 16 and different values of ng. The dashed lines are the best fit to eq 1 with structural modulus G and extension ratio β as fitting parameters. Correlations between network mechanical properties and strand architecture illustrated by linear relationship between reduced shear modulus and reduced density of stress supporting strands (d) for networks shown in (a), (e) for networks shown in (b), and (f) for networks shown in (c). Dashed lines in figures (d-f) illustrate linear correlation between αG/β and φ/nx. Adapted with permission from ref (32). Copyright 2018 American Chemical Society. 45

Figure 9. Breaking the “Golden rule” of the materials design, . The values of the λmax for this plot are calculated as λmax = β−1/2. The “Golden Rule” is shown as the dash line with a slope -2 in logarithmic scales. Data for linear chain networks are shown by brown symbols: nx ≈ 4 (rhombs), nx ≈ 5 (triangles), nx ≈ 6 (inverted triangles), and nx ≈ 9 (squares). Filled blue symbols show correlations between G and λmax for data sets from Figure 8 a for which DP of side chains nsc = 2, 4, 8, 16, 32 and ng = 8, nx ≈ 16. Filled green triangles represent correlations for data shown in Figure 8 b and corresponds to graft polymer networks with DP of backbone between crosslinks nx= 8, 11, 16, 20, 34, ng = 2 and nsc = 8. Open triangles of different colors show correlations for data in Figure 8 c. Adapted with permission from ref (32). Copyright 2018 American Chemical Society. (see color insert)

Figure 9 shows correlations between structural modulus and elongation-atbreak defined in terms of the strand extension ratio β as λmax ≈ β−1/2 (32). For networks made of comb-like strands, their structural modulus is φ times smaller than the corresponding modulus of the networks of linear chains with the same degree of polymerization between cross-links. In the case of bottlebrush strands, there is an additional contribution to the structural modulus G due to stiffening and finite extensibility of the network strands. Interplay between the dilution and stiffening effects results in simultaneous increase of stiffness and extensibility. , demonstrating This is manifested in a new scaling relation, an increase of the structural modulus with elongation-at-break (open symbols). This scaling corresponds to a crossover from the Bottlebrush regime to the Comb of the side chains keeping regime through variation of the grafting density the degree of polymerization between crosslinks nx almost constant. Thus the 46

graft polymer networks can break the “Golden rule” and occupy the “Biological triangle” (see Figure 1b). This feature is crucial for soft materials and tissue replication. In the next section we discuss implementation of the procedure for replication of the mechanical properties of soft and tissue-like materials in solvent-free graft polymer elastomers.

Experimental Implementation of the Replication Procedure The outlined approach for replication of tissue properties was successfully tested by synthesizing poly(dimethylsiloxane) (PDMS) and poly(n-butyl acrylate) (PBA) graft polymer elastomers with accurately controlled sets of [nsc, ng, nx] (1). The mechanical properties of such networks were obtained in the broad range of strains to verify correlations between structural triplet [nsc, ng, nx] and resultant network mechanical properties. Analysis of stress-strain curves of the network samples has confirmed that graft polymer networks violate the “Golden rule” populating the “Biological triangle” (see Figure 10a). The synthesized libraries of PDMS and PBA graft polymer elastomers prime the way for replication of tissues in this class of polymeric materials through calibration of relationships between network parameters α, β, and G (or E) describing its mechanical properties and structural parameters [nsc, ng, nx] (see for detail ref (1)). These correlations are used in the synthesis step of the protocol outlined in Figure 2b to create mechanical replicas of representative tissues.

Figure 10. a)Combined (λmax) plot for comb and bottlebrush elastomers. Eent entanglement modulus. b) Stress-strain data (□) for alginate gel, jellyfish tissue, and poly(acrylamide-co-urethane) gel are shown together with fitting analysis of the data by eq. 1 (dashed lines), and curves for PDMS bottlebrush and comb mimics synthesized via the fitting analysis with the corresponding architectural triplets [nsc, ng, nx] as indicated (solid lines). Adapted with permission from ref (1). Copyright 2017 Nature. Figure 10b displays successful replication of the stress-strain curves of alginate gel, jellyfish tissue, and composite poly(acrylamide-co-urethane) gel, with [nsc, ng, nx] combinations of [14, 1, 67], [28, 2, 100], and [14, 4, 1200] . 47

Conclusions and Outlook We overview a universal materials design platform that accurately encodes targeted physical properties in network architecture. This approach eliminates the current disconnect between material formulation and function which is compounded by imprecise control of network architecture and empirical descriptions of hierarchic structure-property relations. It employs the closed-loop integration of chemistry, physics, and biology to decode the structure-property relations of targeted networks and then program them in precise molecular architectures. Since the resultant materials are solvent-free, they will neither freeze in the Arctic nor dry in the Sahara. No liquid components will exist to be squeezed out in subsurface environments or to evaporate. However, despite of all these advantages the library of the graft polymers limits the types of the biological tissues for replication. It is currently impossible to replicate materials with extension ratio β > 0.3 (1). The tissues with such values of the parameter β are heart tissues, arteries, and skin. The required combination of the initial materials’ softness and strong strain hardening can be achieved in thermoplastic elastomers composed of liner-bottlebrush-linear ABA triblock copolymers (1). This additional complexity in the chemical structure of the network building blocks can provide additional degree of freedom for tissue mimicking. Furthermore, self-assembly of the linear blocks creates moldable physical networks that could be reprocessed on demand. We hope future studies will explore the full potential of this class of copolymers for tissue replication.

Acknowledgments The authors are grateful to the National Science Foundation for the financial support under the Grants DMR-1407645, DMR-1624569 and DMR-1436201.

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50

Chapter 4

Probe Diffusion Dynamic Light Scattering of Polymer solutions and Gels Mitsuhiro Shibayama* and Xiang Li Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan *E-mail: [email protected].

Probe diffusion dynamic light scattering technique is a powerful tool to investigate the dynamics of polymer chains in polymer solutions and gels. Not only the local dynamics and/or local viscosity but also the gel point and the post-gel dynamics can be investigated. In this chapter, we discuss (1) a conventional probe diffusion of radical polymerization of poly(N-isopropylacrylamide) (PNIPAM) aqueous system, (2) an in-situ isorefractive probe diffusion of tetra-arm poly(ethylene glycol) (Tetra-PEG) undergoing sol-gel transition via cross-end-coupling, and (3) of PNIPAM radical polymerization. It is demonstrated that the gel point is determined as a function of the reaction conversion, which is a more universal measure than the reaction time. The post-gel dynamics explored by the probe particles illuminates the local dynamics in a “pool” of the sol phase surrounded by a gel network. Furthermore, comparison in dynamics is made between well-controlled uniform networks (Tetra-PEG gels) and randomly cross-linked more heterogeneous networks (PNIPAM gels) from the viewpoints of the probe size dependence and scattering angle dependence.

Introduction Polymer gels have been useful matter for centuries because of their unique properties, such as soft and wet substances carrying a large amount of solvent and, if necessary, with small amount of ingredients, such medicine, flavor, condiment. © 2018 American Chemical Society

They have been used as glues and foods for centuries. In order to further develop the applications of gels, it is of importance to understand the chemistry of gels, gelation kinetics, the structure, and physical properties of polymer gels. Among various methods used for the structure and dynamics investigations of polymer gels, dynamic light scattering (DLS) is an easily-handled but powerful method. When light is incident to polymeric systems, light scattering is commonly observed as a result of concentration fluctuations in the system, which are ascribed to thermal motions of the solute, such as polymer segments. By monitoring the light scattering as a function of scattering angle, static light scattering intensity containing the structural information is obtained (1, 2). On the other hand, by taking time correation of the scattering intensity at a given angle, the time-correlation function (TCF) of scattered intensity is obtained, which contains the information of the dynamics of the scattering objects. This is called dynamic light scattering (DLS) (3, 4). A pioneering DLS work on polymer gels was carried out by Prins et al. and they observed a syneresis in a gelatin gel (5). Though this work illuminated the usefulness of DLS, the information was very limited. The dynamics of polymer gels is much more complicated than that of polymer solutions and molten polymers. This is due to the complexity of the network structure in polymer gels, such as polydispersity of subchains between neighboring cross-links, loops and entanglements, defects, and so on. In addition, the dynamics is collective because each chain is connected via chemical and/or physical cross-links. DLS studies on polymer gels have accomplished a long walk owing to the theoretical and experimental work by Tanaka-Hokker-Benedek (6). However, details of the network structure and the dynamics of gels have not been unveiled. Probe diffusion technique is a powerful method to explore the details of the structure and dynamics of polymeric systems because the scattering from probes, such as not only nanoparticles but also small molecules, polymer chains, or dendrimers, provides rich information about the local envirionment surrounding the probe. One of the advantages of the probe diffusion scattering method is to make use of strong scattering from the probe. Since the probe scattering is very sensitive to the local environment around the probe particles, it has been quite successful to discuss the quality of polymer solutions and the interaction among the solvent, the polymers, and the probes. Probe diffusion technique was also used to study polymer gels (7–11). However, by introducing probes, the sytem becomes a ternary system. As a result, the scattering contains both probe scattering (desired information) and matrix scattering (undesired information). In order to suppress the latter, isorefractive scattering methods have been employed. For example, Martin employed isorefractive diffuse scattering DLS and investigated the dynamics of polystyrene (PS) chains in a ternary system consisting of a solvent (toluene), PS chains in an isorefractive matrix polymer (poly(vinyl methyl ether)), and PS chains with a large refractive index increment to the solvent (12). As a matter of fact, isorefractive scattering has been often used in several studies for probe diffusion in polymer solutions and gels (13–15). However, this technique has not been used for investigating in in-situ gelation process. In this chapter, a brief review is presented for isorefractive probe diffusion DLS studies on two gelation systems having very different network archtectures. 52

Theoretical Background The time correlation function (TCF) for the scattered intensity, g(2)(τ), is given by (3, 4)

where τ is the time lag with respect to the reference time, 0. Since g(2)(0) = / 2 = 2 and g(2)( ∞) = /2 = 1, g(2)(0) – 1 is more commonly used rather than g(2)(τ) for TCF. For a monodisperse dispersion system, such as a polystyrene (PS) latex, g(2)(τ) is simply given by

Here, we assumed the instrument coherence factor being unity. Γ is the relaxation rate given by

where D is the (translational) diffusion coefficient (D = Dtr) and q is the magnitude of the scattering vector. By using the Stokes-Einstein equation, the hydrodynamic radius, Rh, is evaluated from D by

Here, k is the Boltzman constant, T is the absolute temperature, η is the solvent viscosity. In general, the dispersoid (solute) is not monodisperse but polydisperse. In such case, eq. (2) is generalized to

Here, H(Γ) is the decay rate distribution function. It should be noted that eq. (5) shows that g(2)(τ) is obtained by Laplace transform of H(Γ), and H(Γ) is often obtained by CONTIN (a constrained regularization method for inverting data program) (16). Dynamics of Polymer Solutions The dynamics of polymer chains in solutions depends greatly on the concentration. In dilute regime (C pc, A gradually decreases with p. This suggests that the probe particles are able to undergo Brownian motion even for p > pc but the movable space for the probe particles becomes smaller with p. The movable space seems to have the particle size dependence, i.e., the larger movable space for the smaller particles. The parameter, τ*, the characteristic relaxation time, is directly related to the local viscosity around the proble particles. It exhibits an interesting behavior with p. That is, τ*, rapidly increases with p for p < pc, but decreases with p for p > pc. The increase in τ* is understandable because the local viscosity steeply increases 61

by approaching the gel point. It was confirmed that the local effective viscosity evaluated by using the Stokes-Einstein equation, , together , is almost the same as with the assumption of its diffusive mode, the macroscopic zero-shear viscosity, η0, evaluated by rheological measurements as shown in Figure 8.

Figure 7. Reaction conversion, p, dependence of the fitted parameters evaluated eq. (11) for Tetra-PEG/DMSO systems undergoing gel point. The gold probe sizes were 28, 42, and 57 nm. The gel point, pc, obtained by viscoelastic measurements is shown with the dashed line. Reproduced with permission from ref (27). Copyright 2017 American Chemical Society.

Figure 8 shows the log-log plot of the effective (microscopic) viscosity, ηeff, and zero-shear (macroscopic) viscosity, η0, as a function of the relative distance of for p < pc. As shown the reactive conversion from the gel point, in Figure 8, all the data evaluated with different sizes of proble particles (Rh = 28, 47, and 57 nm) are collapsed to a single line together with η0. The critical exponent evaluated from the slope of the log ηeff vs log ε plot, was s = -1.13, which is reasonably in agreement with the values for randomly branched polyester in the critical percolation class, s = 1.36 ±0.09 (33), and to other gelling systems s ≈ 1.3 (34). This fact strongly indicates the validity and applicability of isorefractive probe diffusion DLS for the study of dynamics of gelling systems. 62

Figure 8. Effective viscosity, ηeff, evaluated from the probe diffusion DLS (circles, squares, and triangles) and the macroscopic viscosity (crosses), η0, as a function of the relative distance of reaction convertion from the gel point, ε. Reproduced with permission from ref (27). Copyright 2017 American Chemical Society.

Above pc, the probe particles trapped by the network are not observed, while those in “sol pools” are still observed. Hence, the decrease in τ* for p > pc suggests that the viscosity in the sol pools inside a gel decreases with p. This experimental observation is supported by computer simulations of gel point which suggest a decrease in the weight-averaged molecular weight of the polymer clusters in the sol region in postgel regime decreases with the reaction progress (35, 36). The stretched exponent, β, is close to unity for p tc. Note that the intensity fluctuations observed here are not due to nonergodicity of the 65

PNIPAM gels but to the result of non-random fluctuations of the probes. This figure clearly demonstrates that the ergodic-to-nonergodic transition of gelling system can be also detected by probe diffusion by simply measuring the scattering intensity from probes. Figure 11 shows the variations of the fraction of the fluctuating component to the total scattering intensity, X, the characteristic decay time, τ*, and the stretched exponent, β, as a function of ε , monitored with three different sizes of nanogold probes (Rh = 56, 37, and 25 nm). The solid Gaussian curves on the plots of τ* are guides for the eyes. The DLS experiments were conducted at three scattering angles (60°, 90°, and 120°) by scanning the goniometer. Hence, not only probe size denedence but also scattering angle dependence can be discussed from this figure. First, let us discuss the probe size, Rh, dependence of the dynamics. The parameter, X, indicating the fraction of movable component (sol fraction), suddenly drops from unity at ε ≈ 0 (gel point) irrespective of Rh. On the other hand, τ* has strong Rh dependence. The smaller Rh, the broader the distribution of τ*(ε) and the lower of τ*max. Both features suggest that smaller probes are still movable to some extent even after gel point. This tendency is more pronounced by observing at a lower scattering angle (60°), i.e., at a larger scale (2πq-1 ≈ 433 nm) than at a larger scattering angle (120°; at a smaller scale, 2πq-1 ≈ 251 nm), where q is the magnitude of the scattering vector defined by (n; the refractive index of the solvent, λ; the wavelength of the light in vacuum, θ; the scattering angle).

Figure 12. Transition point of ε(τmax*) as a function of q for different particle sizes. ε(τmax*) was estimated by fitting τ* near the gel point with a Gaussian function. ε(τmax*) of PNIPAM is corrected by removing the delay time from the calculation. Reproduced with permission from ref (37). Copyright 2017 American Chemical Society. 66

Figure 12 shows the q dependence of the value of ε at τ =τ*max, ε(τ*max), for Tetra-PEG/DMSO and PNIPAM/DMSO systems. As expected and indeed as shown in Figure 11, ε(τ*max) increases by increasing q. The larger in ε(τ*max), the more movable the probes are even in post-gel state (ε > 0). This effect can be more pronounced by observing at a larger q (at a smaller scale). By comparing Tetra-PEG/DMSO and PNIPAM/DMSO systems, ε(τ*max) of PEG/DMSO system is much smaller than that of PNIPAM/DMSO system, suggesting that the TetraPEG/DMSO system is more sensitive to the probes around at the gel point than the PNIPAM/DMSO system. This is because the mesh size of the former is more uniform than than latter as schematically shown in Figure 9. The mesh sizes of the PNIPAM/DMSO system are widely distributed because the gels are formed from NIPAM monomers by radical polymerization, while the network of the TetraPEG/DMSO system is formed by cross-end-coupling of well defined Tetra-PEG macromers. In addition, it can be also learned from Figure 12 that PNIPAM/ DMSO gels prepared at 60 °C are more heterogeneous than those prepared at 55°C, i.e., the larger in ε(τ*max) for the gels prepared at higher temperature. These differences in the network structures can be well characterized by the isorefractive probe diffusion DLS. More details discussions are reported by Watanabe et al. (37)

Concluding Remarks Recent topics on probe diffusion dynamic light scattering (DLS) of polymer solutions and gels are discussed. Here, in-situ isorefractive probe diffusion DLS experiments were conducted to investigate the gelation process of well-defined polymer networks, Tetra-PEG gels whose gelation kinetics of Tetra-PEG gels was well characterized by UV and dynamic viscoelastic measurements. Because the refractive index of the Tetra-PEG networks was matched to that of the solvent (DMSO), the scattering due to the polymer network dynamics was significantly suppressed and the probe dynamics of gold nanopartics was sololy extracted. As a result, the dynamics of gelation process was quantitatively monitored in-situ as a function of the reaction conversion, p. To our knowledge, this is the first time to investigate a complete gelation process across the gel point with DLS under isorefractive condition. The dynamics of the probes was successfully analyzed with the stretched exponential function. The fitted parameters suggested that the probe particles are able to undergo thermal motion to some extent even after gel point. Surprisingly, the local effective viscosity does not increase, but decreases with p before complete structural freezing occurs. Furthermore, a comparison of probe dynamics between uniform networks and random networks provides the details of local structure and dyamics around gel point. As demonstrated here, the probe diffusion DLS is a quite powerful method to study polymer gels, particularly the structure and dyamics near gel point. Extended works to more irregular polymer networks, such as, coarse Tetra-PEG gels prepared at a much lower concentration than C*, are on going.

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Chapter 5

Nanostructure Evolution of Biomimetic Hydrogel from Silk Fibroin and Poly(N-Vinylcaprolactam): A Small Angle Neutron Scattering Study Rajkamal Balu,1 Jasmin Whittaker,2 Jitendra P. Mata, 3 Naba K. Dutta,1,2 and Namita Roy Choudhury*,1,2 1School

of Engineering, RMIT University, Melbourne, VIC 3000, Australia Industries Institute, University of South Australia, Mawson Lakes, SA 5095, Australia 3Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW 2234, Australia *E-mail: [email protected]. E-mail: [email protected]. 2Future

The nanostructure of biomimetic hydrogels fabricated using regenerated silk fibroin (RSF) protein and thermoresponsive poly(N-vinylcaprolactam) (PVCL) polymer via physical and chemical crosslinking methods have been studied using Small Angle Neutron Scattering (SANS) technique. RSF showed no gelation and/or secondary structure (Gaussian coil) change at temperatures between 12 °C and 35 °C, whereas PVCL formed physical hydrogels by molecular self assembly exhibiting swollen coil to Gaussian coil structure change above a lower critical solution temperature (LCST) of ~32 °C. RSF-PVCL blend solutions were also observed to form physical hydrogels above this LCST. However, RSF-PVCL hybrid system exhibited swollen coil to collapsed coil structure change, suggesting relatively increased gelation compared to PVCL. Contrast variation SANS experiments demonstrate that in RSF-PVCL hybrid system, RSF provokes the intrinsic structural changes in PVCL without undergoing any structural change of its own. Unlike PVCL and other biomimetic © 2018 American Chemical Society

polymer hydrogels, RSF hydrogels exhibited ordered structures containing hydrophobic domains which exhibit sharp interfaces with hydrophilic domains and/or amorphous protein matrix. Further, photochemically crosslinked RSF and RSF-PVCL hybrid hydrogels showed variation in the order of secondary structures in hydrophilic domains, which can be associated to their reported difference in water uptake behavior.

Introduction Biomimetic hydrogels are three-dimensional macromolecular network structures formed by physical crosslinking (hydrogen bonding, ionic or hydrophobic interactions) or chemical crosslinking (covalent bonding) of synthetic polymers and/or natural proteins that are biocompatible in nature. Biomimetic hydrogels mimic biological extracellular matrix structures and absorb large amount of water without disintegrating (1). Notable examples of biomimetic hydrogels include: poly(acrylic acid), poly(ethylene oxide), poly(N-vinylcaprolactam), collagen, alginate and silk fibroin (1–7). In particular, hydrogels of poly(N-vinylcaprolactam) (PVCL) and silk fibroin have been extensively studied in the field of biomedical and tissue engineering (8, 9). PVCL is a nonionic thermoresponsive synthetic polymer widely synthesized by free radical polymerization, which exhibits lower critical solution temperature (LCST) characteristics in the physiological temperature range (~32-35 °C) (8). Though PVCL is widely applied in drug delivery and cosmetics, it is a relatively soft material, which limits its applications in tissue engineering (10). On the other hand, silk fibroin is a fibrous natural protein produced by silk worms such as Bombyx mori and can be extracted from their cocoons by chemical regeneration methods (11). The extracted silk fibroin, commonly known as regenerated silk fibroin (RSF), has been widely applied in tissue engineering for its high mechanical strength, excellent biocompatibility, controlled biodegradability and ability to support cellular interactions (12). Unlike PVCL and other thermoresponsive proteins (eg. Resilin), RSF does not show any critical solution temperature characteristics, which limits its applications in drug delivery (13–15). Developing hydrogels that exhibit combined properties of stimuli responsiveness and mechanical properties is of significant interest in the biomedical field. It has been reported that RSF and PVCL form stable hydrogen bonding interactions, which have been applied to fabricate capsules and coatings (16, 17). Recently, we reported a facile fabrication of RSF-PVCL hybrid hydrogels by a photochemical crosslinking method (18). However, the effect of RSF on the phase behaviour of PVCL and their resultant hybrid hydrogel nanostructure has not been studied. Fundamental understanding of the nanostructure of RSF-PVCL hybrid hydrogel is crucial to optimize their physicochemical and biological properties for desired applications. In this chapter, we study the intrinsic structure and assembly of RSF and PVCL molecules in both physically and chemically crosslinked RSF-PVCL hybrid hydrogels using small angle neutron scattering (SANS) technique. 72

SANS is an experimental technique which uses elastic neutron scattering at small scattering angles to provide structural information of various nanomaterials at a length scale of about 1-1000 nm (19). SANS is complimentary to small angle X-ray scattering (SAXS) and provides information from both bulk and surfaces/interfaces of materials which is not possible with other techniques (19). Thefore, SANS is advantageous in studying the structure and assembly of macromolecules in concentrated solutions and gel phases (20, 21). Moreover, SANS/SAXS is the only technique which provides nano to microstructure information of hydrogels in their native and swollen state without compromising structures by sample preparation that are common in other techniques such as electron microscopy and atomic force microscopy (19). Advantages of SANS over SAXS include its sensitivity to lighter elements such as hydrogen and the possibility of isotope labeling (22). In particular, the unique interaction of neutrons with hydrogen and its isotope deuterium provides contrast-variation capability, where water (H2O), deuterium oxide (D2O) and their mixtures can be used as solvent/background medium to contrast match one component and study the structure of other in a multi-component system such as RSF-PVCL hybrid hydrogels (22).

Experimental Materials Bombyx mori silk fibers were purchased from Beautiful Silks, Australia. N-vinylcaprolactam (VCL), 2,2’-azoisobutyronitrile (AIBN) and Tris(2,2′bipyridyl)dichlororuthenium(II) hexahydrate (Ru(bpy)3) were purchased from Sigma Aldrich, Australia. Dialysis tube and syringe filters were purchased from ThermoScientific, Australia. Deuterium oxide (D2O) was supplied by the Australian Nuclear Science and Technology Organisation (ANSTO). All other chemicals were purchased from Chem-Suppy, Australia. Preperation of RSF Solution For preparation of RSF aqueous solution, the silk fibers were first degummed by boiling in 0.5 N sodium carbonate. The degummed fibers were then washed with water, air-dried and dissolved in calcium chloride-ethanol-water mixture (1:8:2 mole ratio) at 70 °C for 3 h (7). The dissolved solution was then centrifuged at 10,000 rpm for 30 min to remove any precipitates, dialysed (using 3.5 MWCO dialysis tube) against D2O for 4 days, and filtered using 1.2 μm syringe filter. The molecular weight of prepared RSF was measured to be approximately 30 to 200 kDa using gel electrophoresis (7). Synthesis of PVCL PVCL was prepared via free radical polymerisation of the VCL monomer with AIBN as the initiator and toluene as the solvent at 70 °C for 24 h under nitrogen atmosphere (18). The polymer was recovered through precipitation in diethyl ether 73

and purified by dissolving in a mixture of acetone and water (3 : 7) followed by precipitation by heating the solution to 80 °C and drying in vacuum at 50 °C for 3 h (18). The molecular weight of synthesized PVCL was measured to be ~35.4 kDa using viscosity measurements (18). Fabrication of RSF-PVCL Blend Solutions and Hybrid Hydrogels For RSF-PVCL blend solution preparation, a predetermined amount of aqueous solution of PVCL dissolved in D2O was added slowly into RSF solution under gentle stirring followed by sonication for several minutes to allow adequate distribution of molecules. For physically crosslinked RSF-PVCL hybrid hydrogel fabrication, solution blends of RSF and PVCL was equilibrated at 35 °C for 1 hr. For chemically crosslinked RSF-PVCL hybrid hydrogel fabrication, predefined amount of PVCL was first mixed with RSF solution followed by the photo-catalyst Ru(bpy)3 and the electron acceptor ammonium persulfate. The mixed solution was then poured into Teflon moulds and exposed to a 250 W white light for 2 minutes. The gels formed were then turned over and exposed for a further 30 seconds to ensure complete crosslinking (18). The excess reactants from crosslinked hydrogels were removed by dialysing against ultra-pure water and vacuum dried. Small Angle Neutron Scattering SANS analysis was performed on RSF, PVCL and PVCL-RSF solution blends and crosslinked hydrogels using the ANSTO Quokka SANS instrument (23). The scattering profiles of samples were recorded against the scattering vector, q (equation 1) in the range of 0.006-0.36 Å-1 (24).

where 2θ is the angle of scattering and λ is the wavelength of the neutron beam (5 Å). Source to sample aperture distances of 2 m and 8 m were employed to cover the q range. The solutions prepared in D2O and hydrogels equilibrium swollen in D2O (cut into discs of ca. 15 mm) were loaded into demountable Quokka cell assembly of 20 mm diameter and 2 mm path length along with excess D2O. The neutron scattering length density (SLD) of D2O (6.36 × 10-6 Å-2) provides good contrast against RSF (~3.2 × 10-6 Å-2), PVCL (~1.1 × 10-6 Å-2), and also limits the incoherent background scattering from hydrogen in the system (25, 26). For contrast matching SLD of PVCL, the gels were equilibrium swollen in D2O/H2O mixture (22% D2O) prior to loading in Quokka cells with excess of respective medium. All measurements were performed with a sample aperture diameter of 12.5 mm, and the obtained data were reduced using NCNR SANS reduction macros (modified for the QUOKKA instrument) using the Igor software package with data corrected (considering detector sensitivity) for empty cell and cadmium scattering (27). Further, the data were transformed to absolute scale using an 74

attenuated direct beam transmission measurement. The solvent/medium scattering were subtracted from the respective sample data using the PRIMUS computer program (28). The incoherent background scattering was determined with a power law fit at the very high-q region using the SasView computer program (http:/ /www.sasview.org/) and the constant value was subtracted from the respective sample data for analysis (29). The structural parameters of the fabricated hydrogels were determined by fitting the neutron scattering data with different functions/ models using the SasView computer program.

Results and Discussion Intrinsic Structure of RSF, PVCL and Their Blend Solutions as a Function of Temperature In small angle scattering (SAS), the overall neutron scattering intensity, I(q) of polymer solutions are generally analysed by a function of both the form factor, P(q) which is an intra-scattering event and the structure factor, S(q) which is an inter-scattering event, as given in equation 2 (19).

where φ is a scaling factor related to the difference in SLD and the volume of scatterers. The intra-molecular scattering (high-q and mid-q) contains information about the distribution of inter-atomic distances within a molecule and can be interpreted in terms of its size and shape, whereas the inter-molecular scattering (low-q) provides information about the orientation-averaged polymer–polymer interactions and can be interpreted in terms of aggregate size or spatial distance (30). At low concentrations of protein and polymer solutions, the scattering data is highly dominated by the intra-molecular events, i.e. S(q) = 1 (24). Figure 1A, 1B and 1C shows the double logarithmic SANS intensity profile of RSF, PVCL and their solution blends, respectively at a low concentration of 2 wt%. The curves show two distinctive regions: a high-q Porod region (0.03 < q < 0.36 Å-1) and a mid-q Guinier region (0.006 < q < 0.03 Å-1). In general, the small angle scattering intensity probing to the local structure of tested system can be determined from Porod slope (n) measured from the Porod region (high-q) which yields information about the fractal dimension of the scattering objects, and the Guinier approximation at the Guinier region (mid-q) which allows for estimation of the radius-of-gyration (Rg) of scattering object (30). The scattering pattern of RSF was observed to show no noticeable difference across the tested temperature range of 12 °C to 35 °C, which suggests the RSF to be non thermoresponsive at tested temperatures. Conversely, PVCL and RSF-PVCL blend solutions showed increase in scattering intensity and Porod slope with increase in temperature, which supports the thermoresponsive property of PVCL reported in literature (31). The Porod slope was obtained from the high-q scattering data through a powerlaw fit using SasView computer program. The estimated Porod slopes of samples are given in Table 1. 75

Figure 1. (A), (B), (C) are SANS curves, and (D), (E), (F) are respective Kratky plots of RSF, PVCL and RSF-PVCL solution blend as a function of temperature. (G) and (H) are distance distribution functions of RSF and PVCL, respectively as a function of temperature. (I) is the polymer excluded volume model fit of RSF-PVCL solution blend as a function of temperature.

The RSF exhibited a Porod slope of ~2 at all tested temperatures, which is a signature of Gaussian coil in dilute environment and suggests the RSF structure to be largely unordered in solution (32). On the other hand, the PVCL exhibited a Porod slope of 1.56 ± 0.02 at 12 °C, which increased to 1.82 ± 0.02 at 25 °C and 2.00 ± 0.02 at 35 °C subsequently, suggesting changes in the intrinsic structure of PVCL molecules with temperature. In general, a Porod slope of ~1 corresponds to a rigid rod like structure, ~5/3 for a fully swollen coil, ~2 for Gaussian coil and between 2 and 3 for “mass fractals” such as branched systems (gels) or networks (33). Therefore, PVCL exhibiting swollen coil to Gaussian coil structure change occurs above a lower critical solution temperature (LCST) of ~32 °C. Moreover, the PVCL solution was observed to turn turbid at 76

35 °C and exhibits slight upturn at low-q scattering suggesting molecular self assembly, aggregation or occurance of gelation in the system. Interestingly, the RSF-PVCL blend solutions exhibited a Porod slope of 1.72 ± 0.02 at 12 °C, which increased to 2.0 ± 0.02 at 25 °C and 2.27 ± 0.02 at 35 °C, suggesting RSF induced/enhanced further structural changes (swollen coil to collapsed coil) in the blend system with temperature. Further, the turbidity of solution was observed to be more prominent for RSF-PVCL blend system at 35 °C with a strong scattering upturn observed at low-q suggesting increased gelation compared to PVCL. This structural change could also be associated with RSF induced tuning of LCST of PVCL, reported previously (13); where the onset of LCST of PVCL decreased from ~32 °C to ~25 °C in the presence of RSF. The structural change can be attributed to strong hydrogen bonding interactions between RSF and PVCL (16, 17). Further, the unfolded-ness of RSF and PVCL was qualitatively assessed by means of Kratky plot (Figure 1D, 1E and 1F). The Kratky plot divides-out the decay of the scattering and clearly shows any structural differences in the sample (33). The Kratky plot of RSF and PVCL displayed initial monotonic increase in mid-q followed by a plateau or slight increase in high-q, which is characteristic of an overall random coil secondary structural conformation of macromolecules in solution (33). However, at 35 °C, PVCL showed increased scattering intensity at low-q region, which further confirms the existence of larger structural assembly in the system. The RSF-PVCL blends showed scattering trend similar to that of PVCL at 12 °C and 25 °C, however, with a well pronounced feature in mid-q region, which further establishes larger structural assembly of molecules in the system leading to co-accervation or gelation. In SAS data analysis, Guinier’s approximation is commonly used for estimation of particle/molecular size such as radius-of-gyration (Rg). However, the approximation is very sensitive to scattering intensities at small q-values and has been reported to underestimate the Rg for structurally unordered protein and polymer coils (34). On the other hand, the pair-distance distribution function, P(r) is a model independent function that calculates the Rg by inverse Fourier transform of the entire scattering spectrum with a histogram of all of the inter-atomic distances (r). Therefore, here we estimated the Rg of RSF and PVCL systems using P(r) function (Figure 1G and 1H) (30, 35). However, for RSF-PVCL blend system that showed mass fractal Porod exponent at 35 °C, the Rg was estimated using polymer excluded volume model fit to scattering data using SasView computer program (Figure 1I). The polymer excluded volume model describes the scattering from polymer chains subject to excluded volume effects and has been used as a template for describing mass fractals or collapsed polymer chains, therefore chosen for estimating Rg of RSF-PVCL blend system (36). The form factor, P(q) is presented in the following integral form (37):

77

where ν is the excluded volume parameter (which is related to the Porod exponent/ slope n as ν = 1/n), a is the statistical segment length of the polymer chain, and n is the degree of polymerization (37). The estimated structural parameters of samples are given in Table 1. The Rg of RSF (~11 nm) was observed to be consistent between tested temperatures of 12 °C and 35 °C, whereas the Rg of PVCL was observed to decrease with increase in temperature. The decrease in Rg along with increase in Porod slope suggests occurrance of change in structure of PVCL in the molecular level leading to self assembly and aggregation. On the other hand, in RSF-PVCL blend system, with increase in temperature, the Rg was observed to increase along with Porod slope. This is due to the mid-q scattering of RSFPVCL blend system observed to be dominated by low-q scattering with increase in temperature. At 35 °C, the RSF-PVCL blend system showed Rg of 23.09 ± 0.06. A strong upturn at low-q intensity observed towards low-q suggests presence of structural co-assemblies on a range of length scales in the sample, extending beyond the measured SANS range (> 100 nm). To further validate and assess the reliability of estimated Porod exponent and Rg, Guinier-Porod model was fit to SANS data of prepared macromolecules (Figure 2) (38). Guinier-Porod model is a shape-independent model which calculates scattering for a generalized Guinier/power law object and can be used to determine the size and dimensionality of scattering objects (38). Considering the structure of macromolecules in solution to be three-dimensional (3D), a dimension variable of zero (used for 3D objects) was used to obtain the structural parameters Porod exponent and Rg (38), and given in Table 1. The Porod exponent of samples obtained using Guinier-Porod model fit was observed to be consistent with values obtained using power law fit. The Rg of RSF obtained using Guinier-Porod model fit was also in good aggrement with values obtained using P(r) function fit suggesting the prepared RSF to be in monomeric form at a concentration of 2 wt%. However, the Rg of PVCL and RSF-PVCL blend solution obtained using Guinier-Porod model fit was observed to be less than that obtained using P(r) function fit, which suggests possibility of inter-molecular interaction in PVCL and RSF-PVCL blend solutions that may have contributed to higher Rg estimated using P(r) function fit. In order to obtain an in-depth understanding of the intrinsic structure of RSF in the RSF-PVCL blend solution system, experiments were performed by contrast matching neutron SLD of PVCL (masking PVCL scattering). Figure 3 shows the PVCL contrast matched SANS intensity profile of RSF-PVCL blend system. The contrast matched data showed that the scattering intensity profile of RSF-PVCL blend system did not change with temperature, which indicates intrinsic structure of RSF in the RSF-PVCL blend solution system to be unaffected by the presence of PVCL and temperature. The RSF in RSF-PVCL blend system exhibited a Porod slope of ~2 (Gaussian coil) (33). This is also consistent with Kratky plot showing initial monotonic increase in mid-q followed by a plateau or slight increase in high-q (33). Therefore, in RSF-PVCL blend system it is evident that the observed structural change is dominated by change in intrinsic structure of PVCL rather than RSF.

78

Table 1. Structural Parameters of Solution Samples Estimated from SANS Data Sample

RSF

PVCL

79 RSF-PVCL

Temperature (°C)

Power law fit

P(r) function fit

Polymer excluded volume fit

Guinier-Porod fit

Porod slope

Rg (nm)

Rg (nm)

Rg (nm)

High-q Porod slope

12

2.00 ± 0.02

11.30 ± 0.35

-

10.39 ± 0.07

2.00 ± 0.10

25

2.00 ± 0.02

11.00 ± 0.35

-

10.34 ± 0.07

2.00 ± 0.10

35

2.00 ± 0.02

11.03 ± 0.33

-

10.35 ± 0.07

2.00 ± 0.10

12

1.56 ± 0.02

8.25 ± 0.16

-

5.39 ± 0.01

1.56 ± 0.01

25

1.82 ± 0.02

8.07 ± 0.21

-

5.24 ± 0.01

1.82 ± 0.01

35

2.00 ± 0.02

6.89 ± 0.29

-

4.29 ± 0.01

2.00 ± 0.01

12

1.72 ± 0.02

-

13.01 ± 0.06

7.65 ± 0.01

1.72 ± 0.01

25

2.00 ± 0.02

-

16.48 ± 0.04

10.77 ± 0.01

2.00 ± 0.01

35

2.27 ± 0.02

-

23.09 ± 0.06

25.78 ± 0.01

2.27 ± 0.01

Figure 2. Guinier-Porod model fit to SANS data of (A) RSF, (B) PVCL and (C) RSF-PVCL blend system as a function of temperature. The individual data curves have been transposed for clarity.

Figure 3. (A) SANS curves and (B) respective Kratky plots of RSF-PVCL blend system as a function of temperature and contrast matched to PVCL. 80

Supramolecular Structure of RSF Hydrogels Although RSF does not form quick gels with temperature like PVCL, hydrogels of RSF can be formed by aging (physically crosslinked) and photocrosslinking (chemically crosslinked) (7, 39). From our previous experiments, a minimum of 15 wt% RSF was observed to get a free standing gels by photocrosslinking (7). Figure 4A compares the scattering profile of 15 wt% RSF in solution, physically crosslinked hydrogel and photochemically crosslinked hydrogel at 25 °C. Compared to 2 wt%, the 15 wt% RSF solution showed relatively lower Rg (7.51 ± 0.06) as increase in concentration of proteins reduces the available aqueous volume and elevates the osmotic pressure relative to pure water, thereby causing them to adapt to more compact conformations (32). RSF in solution exists in α-helix and random coil conformations (soluble form), which upon aging transitions to crystalline β-sheets and is rendered insoluble (physically crosslinked gel) (26, 29, 40). On the other hand, in photocrosslinked RSF hydrogel, the RSF molecules are crosslinked by covalent dityrosine crosslinks (7). The tyrosine crosslinking is anticipated to form crystalline β-sheets (due to crosslinking between tyrosine residues in regular sequences of RSF as well as amorphous structures (random coil) in RSF hydrogel (41). Therefore, RSF hydrogels are anticipated to contain hydrophobic domains (predominantly containing β-sheet) in the system, which can be observed by a Porod slope of ~4 exhibited by hydrogels (42). A Porod slope of ~4 is a characteristic of sharp interface of structures formed with the surrounding environment, which in this case can be attributed to β-sheet structures (crystalline) that exhibit sharp interface with D2O and/or amorphous protein matrix (19, 43). Further, the hydrophobic domains in the hydrogel system can be clearly seen in Kratky plot with a distinct high-q correlation peak (Figure 4B). The size of hydrophobic domains was estimated to be around 6 nm from correlation peak q value of ~0.1 using the relation d = 2π/q (19). On the other hand, the difference in mid-q scattering intensity observed between physically and chemically crosslinked RSF hydrogel can be attributed to their difference in the order of secondary structures. The order of secondary structure in gels affects the voids which inturn influences water uptake capacity. To put it simply, higher the order of secondary structure, higher the crosslink density, lower water uptake, lower mid-q scattering, whereas higher mechanical properties (13, 44). Compared to physically crosslinked RSF hydrogel, the photocrosslinked RSF hydrogel demonstrated higher mechanical strength, lower water uptake, lower mid-q scattering intensity and therefore lower the order of secondary structure (13). Moreover, an increased trend in mid-q region intensity observed towards low-q suggests presence of structural assemblies on a range of length scales in the sample, extending beyond the measured SANS range.

81

Figure 4. (A) SANS curves and (B) respective Kratky plots of RSF solution and hydrogels. (C) and (D) are shape-independent model function fits to physically crosslinked and photocrosslinked hydrogels, respectively. (see color insert)

Table 2. Structural Parameters of Gel Samples Estimated from SANS Data Sample

DAB (mid-q) + Guinier-Porod (high-q) fit Correlation length (nm)

Rg (nm)

High-q Porod slope

Physically crosslinked RSF hydrogel by aging

7.14 ± 0.24

3.49 ± 0.01

4.00 ± 0.01

Photocrosslinked RSF hydrogel

4.78 ± 0.36

2.29 ± 0.01

4.00 ± 0.01

Photocrosslinked RSF-PVCL hybrid hydrogel

18.01 ± 1.55

2.91 ± 0.04

3.50 ± 0.04

82

In order to obtain in-depth structural information and to further our understanding of RSF hydrogels the SANS data were fit to shape-independent form factor function (Figure 4C and 4D) combining Guinier-Porod model, A(q) at high-q and Debye Anderson Brumberger (DAB) model, B(q) at mid-q, as given in equation 4 (42).

The structural parameters estimated from the fits are given in Table 2. The DAB model calculates the scattering from a randomly distributed two-phase system characterized by a single scale correlation length (L), which is a measure of the average spacing between regions of the two phases (45). The DAB model also assumes smooth interfaces between the two phases and hence exhibits Porod behavior (I~q-4) at high-q (45). From Table 2 it can be observed that the average hydrophobic domain size in physically crosslinked RSF hydrogel was estimated to be ~3.5 nm, which is randomly distributed in the amorphous matrix containing hydrophilic domains of silk fibroin with a correlation length (average spacing between β-sheets) of ~7.1 nm. Photocrosslinked RSF hydrogel demonstrated relatively smaller hydrophobic domain size (Rg ~2.3 nm) and correlation length (~4.8 nm) due to restriction in co-localization of tyrosine residues by dityrosine crosslinks, which is anticipated to give rise to its higher mechanical properties (42, 46). A schematic of RSF hydrogel nanostructure is given in Figure 5.

Figure 5. A schematic of RSF and RSF-PVCL hybrid hydrogel nanostructure. Reproduced with permission from reference (42). Copyright (2018) Elsevier. 83

Figure 6. (A) SANS curves and (B) respective Kratky plots of RSF-PVCL hybrid hydrogels. (C) Shape-independent model function fits to photocrosslinked RSF-PVCL hybrid hydrogel. (see color insert)

Supramolecular Structure of RSF-PVCL Hybrid Hydrogels Applying the photochemical crosslinking method, double network RSF-PVCL hybrid hydrogel with a highly crosslinked rigid phase (RSF) and a physically entrapped soft component (PVCL) have been fabricated (18). Figure 6A compares the scattering profile of physically and photochemically crosslinked RSF-PVCL hybrid hydrogels. It can be observed that the physical hydrogel obtained by equilibrating the solution blends above LCST temperature of PVCL demonstrated collapsed polymer network structure (less ordered secondary structure) with a measured Porod slope of ~2.27, whereas photocrosslinked hydrogel demonstrated partially ordered/crystalline hydrophobic structures with a Porod slope of ~3.5 (33). The difference in Porod slope observed between photocrosslinked RSF hydrogel and photocrosslinked RSF-PVCL hybrid hydrogel can be attributed to the increased contribution from the uncollapsed PVCL chains (exhibiting power law behaviour of q-2) (42). Further, Kratky plot shows the characteristic of less ordered structure for physical hydrogel in the nanoscale, whereas highly ordered structure for photochemically crosslinked hydrogel with correlation peak observed around q value of 0.08 Å-1 (Figure 6B). Therefore, the SANS data of photocroslinked RSF-PVCL hybrid hydrogel was fit (Figure 6C) with shape-independent form factor function (equation 4), and 84

the obtained structural parameters are given in Table 2. From Table 2 it can be observed that the average hydrophobic domain size and correlation length of photocrosslinked RSF hydrogel showed 26% and 275% increase, respectively with PVCL substitution and subsequent photocrosslinking. The physically croslinked RSF-PVCL hybrid hydrogel was not fit with DAB function as it did not show a distinctive hydrophobic and hydrophilic structure. The PVCL forms strong hydrogen bonding with RSF thereby affecting its secondary structural arrangement during crosslinking or gelation. This is also in correlation with measured decrease in crosslink density of photocrosslinked RSF hydrogel with PVCL (18). Moreover, an increased trend in mid-q region intensity observed towards low-q suggests presence of structural assemblies on a range of length scales in the sample, extending beyond the measured SANS range. A schematic of RSF-PVCL hybrid hydrogel nanostructure is given in Figure 5.

Conclusions In summary, the evolution of nanostructure of biomimetic hydrogels fabricated using RSF and PVCL solutions has been studies using contrast variation SANS. At 12 °C, PVCL exhibited swollen coil secondary structure in solution, whereas RSF exhibited Gaussian coil structure. With increase in temperature, PVCL exhibited swollen coil to Gaussian coil secondary structure change above a transition temperature of ~32 °C and the solution turned to physical hydrogel. However, no change in secondary structure and solution to gel transition was observed for RSF solution. RSF-PVCL blend solutions exhibited Gausian coil to collapsed coil secondary structure change above ~25 °C and the solution turned to physical hydrogel. Contrast variation SANS further revealed that the RSF molecules without undergoing any structural change of its own induced/enhanced the intrinsic structural changes of PVCL in RSF-PVCL blend solution, which caused gelation of RSF-PVCL blend solution to occur at relatively lower temperature. Photocrosslinked RSF hydrogel exhibited ordered structures comprising hydrophobic and hydrophobic domains. Photocrosslinking RSF in the presence of PVCL caused decrease in the order of RSF secondary structure in hydrophilic domains, whereas increase in the size of hydrophobic domains. The study provides further insight into the nanostructure of RSF-PVCL hybrid hydrogel systems and benefits in understanding their structure-property realations.

Acknowledgments This research has been financially supported by the Australian Research Council (ARC) through Discovery Grant funding. The SANS experiments were supported through an ANSTO beam time award (P3550). 85

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Chapter 6

Model Polymer Thin Films To Measure Structure and Dynamics of Confined, Swollen Networks Sara V. Orski, Kirt A. Page, Edwin P. Chan, and Kathryn L. Beers* Materials Science and Engineering Division, The National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, United States *E-mail: [email protected]. E-mail: [email protected].

In this chapter, we discuss applying X-ray reflectivity to study the structure and dynamics of dense and ultrathin polymer films upon exposure to solvent vapors. These vapor swelling studies permit the measurement of thermodynamic parameters using established mean-field models such as Flory-Huggins, Flory-Rehner, and Painter-Shenoy to understand the elastic contributions to swelling, as well as the polymer solvent interaction parameter of these confined films. This chapter describes the various experimental approaches to leverage mean-field theories towards describing and understanding swelling behavior of thin film networks and brushes, the applications, and their limitations.

Introduction Polymer thin films over the last several decades have advanced beyond conventional, passive coatings and filters to active semi-permeable membranes that have a delicate interplay between analytes, the solvent or gas environment, the thin film support surface, and neighboring polymer chains. Thin film membranes have developed a broad application space, from acting as environmental absorbents or biological scaffolds, to controlling fouling or separating large and small molecules in the liquid or gas phase (1–5). Development of these Not subject to U.S. Copyright. Published 2018 by American Chemical Society

advanced polymer thin film membranes have been largely empirical as material optimization is generally tailored to improving performance, such as selectivity of one analyte over a small list of competing species, for practical and commercial uses. Fundamental metrology of membrane molecular structure, chain morphology, thermodynamics and (ultimately) correlation to performance of these materials have also been limited, especially for in situ measurements, as films are often sub-100 nm in thickness, which limit the tools available to measure these parameters. The design of next-generation films requires accurate structure/property relationships and a fundamental understanding of critical structural and thermodynamic parameters that affect performance such as analyte diffusivity, solubility, pore size, pore size distributions, stability, and service life. Using two case studies – polymer membranes for water purification and grafted polymer brushes for tailored surface chromatography separation methods – we demonstrate major advances in metrology designed to support basic research into characterization of ultra-thin polymer networks (6–8). This chapter covers recent advances in the synergistic approach to understanding swelling behavior in these films by combining synthetic design of controlled, homogeneous model thin films, with X-ray reflectivity measurements to measure changes in film thickness, roughness, and material density when exposed to solvent vapor. These changes upon swelling can be applied to mean field thermodynamic models to understand when the enthalpic and entropic contributions to swelling agree with established theoretical models or when new models need to be developed to account for additional parameters that may not be incorporated into existing theories.

X-ray Reflectivity To Study Thin Film Structure Overview Swelling is a classic approach used to interrogate the structure of a crosslinked polymer network. This approach measures the amount of solvent uptake as a function of solvent activity and then applies the appropriate equation-of-state to determine the thermodynamic parameters of the polymer network. Swelling measurements are straightforward for macroscopic specimens since it simply relates swelling to solvent activity by measuring the change in specimen mass or specimen dimensions. Measuring the swelling behavior is non-trivial for ultrathin films because of the diminishingly small changes in mass and volume due to solvent uptake, as well as adsorption that can occur at the interface between the ultrathin film and its supporting layer (9–11). This chapter describes the application of specular X-ray reflectivity (XR) to measure the dimensional change of polymer thin film networks due to vapor swelling. XR is a high-resolution measurement technique for studying the interfaces of materials possessing different electron densities with resolution of approximately 0.1 nm (12, 13). XR has been widely used to study soft materials such as photoresists (14), polymer glasses (15–17), nanoimprinted polymers (18, 19), polymer bilayers (20), polymer brushes (21), gel layers (22, 23), polyelectrolyte multilayers (24, 25) and membrane layers (26) over 92

the past two decades. XR is particularly suited for conducting polymer thin films thermodynamic studies, as repeated measurements of a specimen area can be conducted, limiting uncertainty due to batch to batch variation of thin film samples.

Vapor Swelling of Polymer Thin Films A typical XR measurement of a polymer thin film is illustrated in Figure 1a. An X-ray beam is directed onto the polymer film that is supported by a substrate in a vacuum or air environment. Typically, the incident X-ray is directed at a glancing angle from ≈0.1° to 1° and then the scattered beam is measured at the specular condition, i.e. where the incident angle equals the reflected angle. Several properties of the substrate-supported polymer film can be quantified with an X-ray reflectivity measurement. These properties include the thickness (h), the roughness (σ), and the electron density (Qc2). For more complex films such as polymer multilayers, XR can also quantify the thickness, roughness and density for each layer if there is sufficient electron contrast between layers and they are sufficiently smooth. The reflectivity curve is typically presented as a plot of reflectivity (R(Q)) versus the incident angle (θ) or the scattering vector (Q). Below the critical angle or the critical scattering vector (Qc), R(Q) remains constant at the maximum value, as the incident irradiation is completely reflected. Above Qc, when the incident radiation penetrates into the film thus resulting in scattering at the various interfaces, oscillations or interference fringes occur. As a result, R(Q) drops abruptly and decays with increasing Q. Film thickness is determined by successive minima or maxima (ΔQ) of the fringes, which is equivalent to 2π/h. Real material interfaces are not infinitely sharp and display a gradient in density from the surface into the bulk of the material. We will not go into detail about the effects of roughness on reflectivity as many others have already discussed this topic (13, 27). All XR measurements described in this chapter were performed using a Phillips X’PERT X-ray diffractometer with a Cu Kα source (λ=0.154 nm. The X-ray beam was focused using a curved mirror into a quadruple bounce Ge [220] crystal monochromator. The specular condition was obtained for the reflected beam using a triple bounce Ge [220] crystal monochromator. The scattering vector was calculated from:

where θ is the incident angle and λ is the wavelength of the X-ray beam. Specular reflectivity curves were collected from 0.1° up to a maximum angle of 1.5° for each film, depending on the largest angle where additional fringes were not discernable due to surface roughness. 93

Figure 1. Studying the swelling behavior of commercial PA NF membrane selective layer via XR. a) Sample geometry of XR. b) Reflectivity versus scattering vector curves as a function of relative humidity illustrating the PA layer expansion. The solid black curves are the best fits of the reflectivity data. c) Electron density change as a function of relative humidity. d) Thickness swelling ratio as a function of water activity measured using 3 separate PA samples. The curve is a fit to the data as defined by the Flory-Rehner theory for one-dimensional swelling (28). The inset figure shows the linear relationship between thickness change and mass change, thus indicating that the selective layer swells only along the thickness direction. Reproduced with permission from reference (28). Copyright 2013 John Wiley & Sons.

Vapor swelling experiments were performed at 25 °C using an aluminum chamber sealed over the target substrate with X-ray transparent beryllium windows. A dual mass flow controller system to control vapor mixing and thus vary the partial pressure of solvent was assembled according to literature procedures (29). All films were allowed to equilibrate at each activity until reflectivity curves were identical between successive scans. This protocol was used to ensure the chamber was temperature equilibrated at each vapor concentration before measurement. Calibration of the actual activity within the chamber relative to the mass flow controller settings was performed by using either a humidity sensor for water vapor, or by flowing the vapor through a quartz cell in a UV-vis spectrometer and using the integrated absorption area of the solvent peak normalized to the area measuring from the saturated vapor attained using a solvent reservoir, in the case of organic vapors. For the highest 94

solvent activities measured (as ≥ 0.95), an open reservoir of solvent was allowed to equilibrate in the closed chamber until vapor saturation was reached. Data reduction for each reflectivity curve was performed using a MATLAB routine that consisted of footprint correction and conversion of the scattering angle into scattering vector. Theoretical reflectivity curves were modeled using NIST Reflfit software (30), which uses Parratt’s formalism for given layer thickness and scattering length densities. Fitting the model to experimental data yielded film thickness, scattering length density, roughness, and linear absorption coefficient; the quality of fit was indicated by Pearson’s chi-squared test. Initial predictions of Qc2 for each solvent, polymer thin film, and bulk silicon were calculated from the NIST NCNR website (31).

Determination of Thin Film Swelling Ratios and Dimensionality The thickness information about each layer obtained from the reflectivity curves at each solvent activity (as) can be used to determine the thickness swelling ratio, α, The thickness swelling ratio at each activity was calculated using equation 2:

where hd and hs are the film thickness in the dry and swollen state. Evaluating the thickness increase alone is insufficient in understanding the complete swelling behavior of the layer since lateral expansion of the layer cannot be determined. The volumetric swelling of the selective layer is determined by comparing the change in the measured Qc2 at a given as (Qc2x) with known or measured Qc2 in the dry film (Qc2dry) and the solvent (Qc2solvent). Since the electron density is directly related to the mass density, this parameter can be used to estimate the volume fraction of the polymer (φp) relative to the solvent volume fraction (φs) in the swollen layer by:

The polymer volume fraction was then converted to a volume fraction swelling ratio (S) and compared with the thickness swelling ratio,

Swelling dimensionality (n) is needed to derive proper theromdynamic models based on whether the chains swell isotropically (n=3) or unidirectionally (n=1). All experiments in this chapter have displayed 1D swelling based on dimensionality calculations. It is important to note that while the polymer volume fraction can be used to calculate the volumetric swelling of the PA, the uncertainty of Qc2 is significantly greater than h, meaning that α should be used over φ whenever swelling dimensionality is consistent across all measured activities. 95

Another issue is that calculating the polymer volume fraction requires a density difference between the polymer and the solvent, which is not always possible.

Thermodynamic Models Once swelling ratios and the corresponding dimensionality of the swollen polymer thin film have been established, mean field models can be applied to characterize swelling thermodynamic parameters in the polymer thin film networks. Solvent uptake with systematic change of the chemical potential are described by equations 6 and 7, beginning with conventional Flory-Huggins (32) theory ((δΔG/δns)el = 0) as well as adaptations for entropic, elastic contributions to the chemical potential change in the networks ((δΔThe elastic contribution to G/δns)el) via Flory-Rehner (33) and Painter-Shenoy (34) models. The Flory-Rehner and Painter-Shenoy models share two fundamental assumptions about the thermodynamics of the system, 1) that the free energy of swelling can be separated into distinct contributions from mixing and elastic energies (equation 6) and 2) that the mixing contribution to the energy (and therefore chemical potential) change upon swelling of the network follows Flory-Huggins theory of mixing.

Flory-Rehner and Painter-Shenoy models differ in their final assumption of the system. Flory Rehner makes the assumption that swelling is affine, which implies that the solvent distribution within the network is homogeneous (28, 35, 36). The elastic contribution to the free energy change for 1D swelling for the Flory-Rehner model has been derived (28) and is shown in equation 8, where N is the number of monomer units between crosslinks. Substituting equation 8 into equation 2 yields the full chemical potential change of the swollen network and is shown in the full Flory-Rehner equation (equation 9).

Since the chemical potential was derived in terms of the change in the number of solvent molecules, N must be in terms of the solvent molar volume equilvent, which is denoted as Ns. In the Painter-Shenoy model, the swelling of the network is not affine and consists of polymer chain expansion with topological rearrangement of the network junctions, which results in heterogeneous solvent distribution where there are solvent-rich regions devoid of polymer chains. The degree of cross-linking can affect the χ parameter as well (37), as different mechanisms to make a 96

cross-linked thin film can result in different molecular masses between crosslinks that can interact with different amounts of absorbing solvent, yielding different solvated properties (38). The elastic contribution to the free energy change for Painter-Shenoy 1D swelling has been derived and is shown in equation 10, where f is the functionality of the network junctions, or the number of chains tethered at a single crosslink location in the network. The full Painter-Shenoy expression for the chemical potential change is shown in equation 11.

One must take great care in choosing a thermodynamic model with which to analyze the reflectivity data. It is important that the model has a physical basis and that the scattering model is consistent with a real-space image obtained from microscopy. While scattering techniques have been used for the last two decades to study these materials, there remain many challenges and opportunities to develop comprehensive models and techniques to elucidate the structure-property-performance relationships in these functional materials.

Model Polyamide Networks for Water Desalination XR has been used to understand the structure of water desalination membranes. Water desalination, based on pressure-driven membrane separations such as reverse osmosis (RO) or nanofiltration (NF), is currently the most widely used commercial technology for providing clean and sustainable water supplies (39), as they are considered the most energy efficient and high-throughput technologies over methods such as distillation and forward osmosis. An ideal desalination membrane is one that has 1) the highest selectivity between water molecules and salt ions, and 2) the highest water permeability. To date, such an ideal membrane does not exist. Current water desalination membranes either have high selectivity or high water permeability but not both, which is an empirical observation commonly referred to as a performance tradeoff (40). Over the past several decades, the search for an ideal desalination membrane has been largely empirically driven via development of new polymer selective layers with modified or entirely new chemistries. To efficiently develop an ideal membrane requires an understanding of the intimate relationships between polymer chemistry, resultant structure and membrane performance. Addressing this challenge necessitates measurements that enable the development of the structure-property relationships relevant to transport. The state-of-the-art membrane material used in RO and NF is a polyamide (PA) thin film composite (TFC). It is a multi-component polymeric laminate consisting of three different classes of polymers: the semi-permeable layer that separates salt from water is a PA ultrathin film with a thickness ≈100 nm. It is a highly crosslinked polymer network with a mesh size 99% MP Biomedics, Inc.), dodecyl trimethylammonium bromide (DTMAB, TCI, >98%), potassium persulfate (KPS, >99%, Across Organics), butyl acrylate (BA, >99%, Acros Organics), ethylene glycol dimethacrylate (EGDMA, >98%, Sigma Aldrich), tetrahydrofuran (THF, BDH HPLC grade), methanol (BDH, ACS grade), deuterated tetrahydrofuran (THF-d8, Cambridge), and deionized water (BDH) were used as received. Styrene (Aldrich, 99.9%) and divinylbenzene (DVB, Aldrich 90%, 80 para content, technical mixture) were de-inhibited by passing through alumina prior to use. 119

Synthesis of Nanoparticles Two soft poly(butyl acrylate) (PBA) nanoparticles were synthesized using a semi-batch nano-emulsion polymerization technique (6, 11). In this procedure, sodium dodecyl sulfate (SDS) was dissolved in deionized water and was charged into a 250 mL round-bottom flask with magnetic stir bar. The flask was equipped with a condenser and sealed with a rubber septum. The solution was then bubbled with Argon gas for 20 minutes and put into an oil bath at 70 °C for 1 hour with constant stirring. Initiator, potassium persulfate (KPS), was added into the flask to dissolve in the SDS solution under Argon protection and the system was stabilized for 20 minutes. The monomers, butyl acrylate and ethylene glycol dimethacrylate (EGDMA) crosslinker, were fed into the SDS solution continuously at 12 mL/hour using a syringe pump. The reaction was continued for one hour after monomer feeding was completed. A transparent latex with a slight blue reflection was formed. The nano-emulsion was quenched by cooling down the system to room temperature. The PBA polymer nanoparticles were recovered by precipitation in large excess of methanol. The polymers were filtered and extracted with methanol using a Soxhlet extractor for 24 hours. The resulting nanoparticle were dried in a vacuum oven at 40 °C for 24h. For each nanoparticle, 4.60 mol % of EGDMA crosslinker was used. Nanoparticle PBA_10c used 10 weight % SDS surfactant (surfactant to monomer ratio 1:1) while nanoparticle PBA_15c used 15 weight % surfactant (surfactant to monomer ratio 1.5:1). The soft polystyrene nanoparticles were synthesized using a semi-batch nano-emulsion polymerization technique (11), in which the styrene monomer and divinylbenzene (DVB) crosslinker were added simultaneously into the water/dodecyl trimethylammonium bromide solution. It is important to emphasize in this nanoparticle synthesis that an excess of surfactant was used ( 27 weight%) with a surfactant to monomer ratio of 4:1. This synthesis method produces soft nanoparticles with a homogeneous crosslinked core with a fuzzy interface comprised of polystyrene chain ends and loops. Two sets of polystyrene nanoparticles were examined in this experiment including monomer rates of addition of 1 mL/h and 2 mL/h. The rate of monomer addition into the polymerization has a direct effect on the molecular weight of the polystyrene nanoparticle. For each set of nanoparticles, four distinct amounts of DVB crosslinker were added to the styrene monomer which included 0.81 mol %, 1.91 mol %, 4.60 mol %, and 10.7 mol% DVB. For the nanoparticles synthesized with 1mL/h rate of monomer addition, the amount of crosslinker has no direct effect on the topology of the nanoparticle where each nanoparticle results in the same effective nanoparticle “fuzziness”, i.e. the ratio of the half width of the fuzzy interface to total nanoparticle radii or the degree of nanoparticle fuzziness with respect to the nanoparticle size. For the 2 mL/h rate of styrene addition, the amount of DVB crosslinker has a direct effect on the width of the fuzzy interface where the higher amount of crosslinker results in a nanoparticle with a smooth interface (11).

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Small-Angle Neutron Scattering Deuterated tetrahydrofuran (d8-THF) and deuterated cyclohexane (C6D12) were purchased from Fischer Scientific and were used without further purification. Small-angle neutron scattering (SANS) experiments on 1 weight % solutions of the PS nanoparticles in d8-THF and C6D12 and 1 weight % of PBA nanoparticles in d8-THF were conducted at Oak Ridge National Laboratory (ORNL) at the High Flux Isotope Reactor (HFIR) using the General Purpose SANS (CG-2) and at the National Institute of Standards and Technology (NIST) Center for Neutron Research NGB 30m SANS beamlines. For the two experiments at ORNL, two separate scattering configurations were used. For the 1 weight % PS nanoparticles in d8-THF, three separate detector distances of 18, 2.7, and 0.3 meters with a wavelength of 12 Å was used and for the 1 wt % PS nanoparticles in C6D12 and PBA nanoparticles in d8-THF, the detector distances were 19.2, 2.7, and 1 meters with a wavelength of 4.75 Å to characterize the nanoparticles. This allowed , λ is for a Q range of 0.0038 Å-1 to 0.7 Å-1 where the neutron wavelength, and Θ is the scattering angle. The instrument at NIST, the three detector distances were 13 m, 4 m, and 1 m with a wavelength of 6 Å resulting in a Q range of 0.0034 to 0.46 Å-1. The nanoparticles in d8-THF were characterized at room temperature, while the PS nanoparticles in C6D12 were characterized in 2 mm wide quartz banjo cells at 38.5 °C, the nominal theta temperature of polystyrene in deuterated cyclohexane (19). The raw data was reduced using SPICE ORNL reduction protocol macros and NCNR macros in Igor Pro and corrected for empty cell scattering, dark current, and blocked beam (20). Absolute coherent scattering was obtained through the elimination of contributions from background incoherent scattering and thermal fluctuations and normalized to an absolute standard. Scattering length densities were calculated from the measured densities of the PS nanoparticles (11), as well as the densities of the solvents, and the density of PBA from literature using the NIST Center for Neutron Research Neutron activation and scattering calculator (20). The fitting of the SANS data to models was performed using SASView software.

Results SANS of Nanoparticles The low-Q scattering data of the scattering data from the PBA nanoparticle solutions was analyzed as a Guinier plot (lnI(Q) vs Q2) to determine the forwardscattering intensity, I(Q=0), and radius of gyration, Rg, of the PBA nanoparticles using Equation (1). This procedure determines the radius of gyration of the

121

nanoparticle without assuming any specific shape of the scattering particles. Moreover, the molecular weights of the two PBA nanoparticles are determined from their forward-scattering intensity, I(Q=0), where the relationship between the weight average molecular weight of the nanoparticle, Mw, and I(Q=0) is given in Equation (2). In Equation (2), ρ is the density of PBA from literature (21), NA is Avogrado’s Number, φ is the volume fraction of the nanoparticle in the scattering solution, and Δη is the difference in scattering cross sections of the nanoparticle and solvent.

To characterize the structure and topology of the nanoparticles, through the long wavelength relation, a combined scattering model (Equation (3)) was used to fit

the scattering data to a suitable form factor (11). This is primarily due to the unique shape of these nanoparticles which exhibit two distinct length scales: scattering from the nanoparticle shape and size (P(Q)), and the scattering from the correlations among crosslinks within the nanoparticles (INetwork). The scattering model in Equation (3) accounts for a fuzzy sphere form factor model (Equation (4)) that describes the radius of the

crosslinked core, Rc, and the half-width of the fuzzy interface, τfuzzy. In Equation (4) the half-width of the fuzzy interface is directly related to where the scattering length density has diminished to half of the core value. The total nanoparticle radius is calculated from the radius of the crosslinked core, Rc, and two times the half width of the fuzzy interface, τfuzzy, as Rp=Rc+2τfuzzy. The effective nanoparticle “fuzziness” is the ratio of the fuzzy interface to the total nanoparticle radius calculated as σ=τfuzzy/Rp. To account for the polydispersity of the nanoparticles we used a Gaussian distribution. The crosslinked network is described using the Gaussian Lorentz gel model (Equation (5)) which accounts for the static correlation length, Ξ, the “frozen-in” crosslinks within the nanoparticle as well as the dynamic correlation length, ξ, or the fluctuations between crosslinked polymer chains. Due to the dilute nanoparticle concentrations in solution the structure factor, S(q), in Equation (3) can be neglected from negligible inter-particle interactions, i.e. S(Q)=1. 122

The SANS data of the solutions of PBA nanoparticles in deuterated THF as well as the fits of the data to the Fuzzy Gel model are shown in Figure 1. A summary of the structural properties of the soft PBA nanoparticles of interest as determined from these analyses are provided in Table 1. The only difference in the synthesis of the two PBA nanoparticles is the concentration of SDS surfactant that was used within the reaction vessel. We note that PBA_10c has a smaller crosslinked core and larger fuzzy interface than PBA_15c. The measured radii of gyration from the Guinier Analysis are very similar for the two nanoparticles. It is also interesting to note that the effective nanoparticle “fuzziness” of the nanoparticle decreases as the SDS surfactant concentration increases. Moreover, comparing the structure of the PBA and PS nanoparticles shows that the effective nanoparticle “fuzziness” decreases as the amount of surfactant in the synthesis increases, even though the PBA nanoparticles are larger. Similarly, the small angle neutron scattering data of the polystyrene nanoparticles dispersed in a good solvent, d8-THF, and a theta solvent, C6D12, are presented in Figure 2 for nanoparticles synthesized with 1ml/h rate of monomer addition and in Figure 3 for nanoparticles synthesized with 2 mL/h rate of monomer addition. For the 1mL/h polystyrene nanoparticles in d8-THF and C6D12, there is a very good agreement for the forward scattering intensity, I(Q=0), of all samples, which correlates to similar nanoparticle molecular weight. This low-Q agreement is also seen for the 2mL/h rate of styrene monomer addition nanoparticles with a 4.60 mol % and 10.7 mol% DVB crosslinker. These agreements indicate that these nanoparticles are individually dispersed in these solutions. However, the low-Q scattering data for the 0.81 mol % and 1.91 mol % PS NPs at 2mL/hr rate of monomer addition in C6D12 exhibit a sharp upturn, which is consistent with possible nanoparticle aggregation in these solutions. Table 2 lists a summary of the important characteristics from the neutron scattering fits with the Fuzzy Gel model for these nanoparticles in d8-THF and C6D12. Most interestingly, the radii of gyration as determined from the Guinier plots are between 5 and 9 nanometers for these nanoparticles in C6D12. Also, the core radius of the PS nanoparticles appears to collapse in the theta solvent C 6D12 relative to the internal morphology of the nanoparticles in a good solvent d8-THF. Moreover, the effective nanoparticle “fuzziness” ratio of all nanoparticles in C6D12 is between 0.3-0.4 and does not change with crosslink density, which is contrary to the structure of the nanoparticles in a good solvent d8-THF, which shows a decrease in the “fuzziness” with crosslink density.

123

Table 1. Summary of the Molecular Properties for PBA Nanoparticles Prepared through Semi-Batch Nanoemulsion Polymerization Using 4.60 mol% of Crosslinker and the PS Nanoparticle Using Similar Polymerization Characteristics from Ref (11) Sample

S

Mwa (g/mol)

Rgb (nm)

Rcc (nm)

PD Rcd

τfuzzye (nm)

PD τfuzzyf

Rpg (nm)

σh

PBA_10c

1:1

164,000

7.99 ±0.12

3.41 ±0.22

0.25

6.02 ±0.22

0.44

15.5 ±0.49

0.38

PBA_15c

1.5:1

296,000

8.94 ±0.08

6.15 ±0.04

0.22

4.81 ±0.06

0.35

15.8 ±0.13

0.30

PS_NP

4:1

725,000

8.50 ±0.11

9.76 ±0.29

0.10

1.03 ±0.94

0.17

11.8 ±1.9

0.09

a molecular weight calculated from forward scattering intensity (I(Q=0) from SANS using Equation (2) b Guinier radius determined from SANS c Core radius of the nanoparticle determined from SANS d The Gaussian distribution of the polydispersity of the nanoparticle radii e Half-width of the fuzzy interface f The Gaussian distribution of the polydispersity of the nanoparticle fuzzy interface g Total nanoparticle radius =

Rc+2τfuzzy

h

Effective nanoparticle “fuzziness”,

.

Figure 1. The small angle neutron scattering fits of PBA_10c (circles) and PBA_15c (triangles) to the combined Fuzzy Gel Model. 124

Figure 2. Small angle neutron scattering fits for PS NPs with 1mL/h monomer rate of addition in deuterated tetrahydrofuran, d8-THF, (triangles) and deuterated cyclohexane, C6D12, (squares) using the combined Fuzzy Gel Model.

Figure 3. Small angle neutron scattering fits for PS NPS with 2mL/h monomer rate of addition in deuterated tetrahydrofuran, d8-THF, (circles) and deuterated cyclohexane, C6D12, (triangles) using the combined Fuzzy Gel model. 125

Table 2. The Results of the Fuzzy Gel Model Fitting of the Polystyrene Soft Nanoparticles in Deuterated THF and Deuterated Cyclohexane Rate of Add’n (mL/h)

Mol% DVB

0.81

1.91 1 4.60

10.7

0.81

1.91 2 4.60

10.7

Solvent

Rg (nm)

Rc (nm)

τfuzzy (nm)

Rp (nm)

σ

d8-THF

8.86±0.1

3.67±1.5

6.36±0.6

16.4±1.9

0.39

C6D12

8.50±0.09

2.52±1.2

5.13±2.2

12.8±4.3

0.40

d8-THF

8.43±0.06

3.30±0.9

3.76±0.4

10.8±1.2

0.39

C6D12

8.28±0.07

2.00±0.3

5.20±1.2

12.4±2.4

0.42

d8-THF

6.14±0.02

1.95±1.7

2.73±0.2

7.42±1.7

0.37

C6D12

5.85±0.04

1.57±0.2

3.43±0.1

8.43±0.3

0.40

d8-THF

6.21±0.03

3.51±1.4

3.44±0.3

10.8±1.6

0.32

C6D12

6.99±0.07

2.15±0.3

4.32±1.3

11.2±2.6

0.36

d8-THF

10.1±0.05

3.46±0.1

4.62±0.1

12.7±0.2

0.36

C6D12

8.81±0.2

2.41±0.3

6.12±0.3

14.7±0.7

0.42

d8-THF

6.83±0.03

6.15±1.7

2.48±1

11.1±2.6

0.22

C6D12

8.18±0.2

2.22±0.5

4.25±0.8

10.7±1.7

0.40

d8-THF

7.00±0.02

5.99±0.2

1.39±0.1

8.79±0.1

0.16

C6D12

8.52±0.1

2.50±0.8

5.83±0.2

13.1±0.9

0.39

d8-THF

6.46±0.01

7.13±0.1

----

7.13±0.1

----

C6D12

8.82±0.1

2.28±0.1

5.15±0.2

12.5±0.4

0.40

Discussion Micro-emulsion polymerization has been employed to prepare latex nanoparticles with various hydrophobic monomers for well over 20 years. Simply defined, the emulsion is a thermodynamically stable, transparent dispersion of monomer droplets in an immiscible liquid (22, 23). The influence of many aspects of the typical micro-emulsion polymerization have been investigated to determine their influence on the final nanoparticle latex including the importance of surfactant-to-monomer ratio, the rate of monomer addition, the solubility and polarity of monomer in either the oil or water phase, reaction temperature, as well as the polymerization initiator (24, 25). For instance, the effects of monomer addition rate and crosslink density on the formation and topology of PS nanoparticles in a monomer-starved, nano-emulsion polymerization have been studied when the polymerization uses excess surfactant to control the overall 126

nanoparticle size (11). The current experiments extend these studies to document the importance of monomer solubility in water on the size, morphology, and topology of the soft nanoparticle in the nano-emulsion polymerization of butyl acrylate. Effect of Surfactant Concentration In nano-emulsion or micro-emulsion polymerizations, it is well established that the monomer micelle sizes are controlled by the surfactant concentration, where it is possible to produce nanoparticles with radii between 10 and 60 nm in size (26). Initially, surfactant forms micelles when the concentration rises above the critical micelle concentration. These micelles are highly fluid and have low rigidity (23). Antonietti et al. investigated the relationship between the amount of surfactant and final size of PS nanoparticles (26). As the surfactant to monomer ratio, S, was increased from 0.2 to > 1 the hydrodynamic radii systematically decreased from approximately 60 nanometers at low surfactant loadings to less than 15 nanometers when the surfactant to monomer ratio became greater than 1. However, they witnessed deviations from the systematic radii decrease when the nanoparticles were very small, under 20 nanometers (26). The surfactant to monomer ratio of the PBA nanoparticles investigated in this study varies from 1 to 1.5, while the total particle radius remains fairly constant between 15 and 16 nanometers. It has been established that in some nano-emulsions that the size of the monomer micelles does not change during the polymerization (23). This is primarily because the increased surfactant to monomer ratio creates smaller micelles with decreased pliability (26). This appears to be the case in the synthesis of the PBA nanoparticles, where the addition of new monomer to the reaction vessel does not swell the monomer micelles. Therefore, in the synthesis of the PBA nanoparticles, it is more probable that the slow rate of monomer addition combined with high surfactant concentration limits the swelling of monomer micelles and the addition of additional monomer creates new monomer micelles. The increased surfactant concentration also likely decreases the rate of polymerization and thus increased the nucleation period of the monomer micelles (27). The solubility of the monomer in water increases the difficulty of controlling the size and topology of the nanoparticles during nano-emulsion polymerizations. The polydispersity that emerges from the fit of the data to the model, providing a measure of heterogeneity of crosslinked core radius and the fuzzy interface in the synthesized PBA nanoparticles. As the polydispersity increases towards 1, the scattering objects become less uniform. Previous studies have shown that, the size of the nanoparticles become more uniform by increasing the surfactant concentration in nano-emulsion polymerizations (26). In Figures 4 and 5, the distribution of the core radius and fuzzy interface of the PBA nanoparticles and PS nanoparticle are presented. Comparing the distributions of the PBA_10c and PBA_15c, which differ in the amount of surfactant in the reaction flask, shows that increasing the surfactant concentration decreases the polydispersity of both the fuzzy interface and the radius of the PBA nanoparticles. The polydispersity is further decreased when the monomer has limited water solubility, as is true for styrene. The limited water solubility of the styrene monomer results in further 127

control of the nano-emulsion polymerization where the radicals formed during the polymerization likely remain in the monomer micelles controlling the propagation of the polymer chains thus always growing the nanoparticle.

Figure 4. The Gaussian distribution of the polydispersity of the nanoparticle radii.

Figure 5. The Gaussian distribution of the polydispersity of the fuzzy interface of the soft nanoparticles. 128

Influence of Monomer Water Solubility on Nanoparticle Formation The solubility of the monomer in water has been shown to affect the polymerization of nanoparticle latexes in micro- or nano-emulsions (10, 14, 25, 27). When the solubility of the monomer in water is too high, often a co-surfactant must be incorporated into the polymerization for stability (28). If a co-surfactant is not used, control of the micro- or nano-emulsion degrades and results in the nanoparticles precipitating out of the reaction before the reaction reaches completion. For a nano-emulsion polymerization, the desired location for polymer initiation is within the monomer-swollen micelles. However, if the monomer is slightly soluble in water, free radicals can be generated in the continuous aqueous phase and polymerize within this phase until exceeding their solubility and thus precipitating early (14). It is then likely for those precipitated oligomers to absorb surfactant and undergoing “homogeneous nucleation” (14). It is also known that the monomer solubility in water has a direct effect on the number of nanoparticles and the size of nanoparticles produced by emulsion polymerization (29, 30). For a hydrophobic monomer such as styrene, which has an extremely low solubility in water, the size of the monomer micelles in the polymerization constantly increases with growing nanoparticles until the completion of the polymerization (29). Styrene monomers will either immediately form new monomer micelles or will enter previously formed monomer micelles, which results in continuous growth of the nanoparticles. However, for a monomer that is slightly soluble in water, such as butyl acrylate, it is likely that activated butyl acrylate monomers will form new monomer micelles instead of adding to already formed monomer micelles. This creates micelles that do not change much throughout the polymerization, depending on the surfactant concentration (29). The solubility of the monomer within the water also allows the monomer free radical to move from micelle to micelle and therefore decreases the control of the polymerization that is possible when using an insoluble monomer (14). The PBA nanoparticles exhibit distinctly different effective nanoparticle “fuzziness”, σ, with a change in surfactant concentration. As the surfactant concentration varies from 10 to 15 % in the polymerization, the effective nanoparticle “fuzziness” decreases from 0.41 to 0.27. Comparison of the “fuzziness” of the PBA nanoparticles to that of a PS nanoparticle that was polymerized under similar conditions shows that the effective nanoparticle “fuzziness” decreases to 0.09. Thus, the precise control of topology in the monomer starved semi-batch nano-emulsion polymerization of polystyrene nanoparticles is limited when the monomer is slightly soluble in water. For the PBA nanoparticles themselves, an increase in the surfactant to monomer concentration translates to an increase in fuzzy interface. This is interpreted as the polymerization with less surfactant contains micelles that are more pliable, allowing monomer to enter and exit the micelle more easily, resulting in a larger fuzzy interface. An increase in surfactant concentration creates less pliable micelles that results in a more static micelle, where the polymerization resides in the center of the micelle growing the crosslinked core rather than at the surface. The PBA nanoparticles also have a larger total particle radius, Rp, compared to that of the PS nanoparticle. One interpretation is that the increased solubility of 129

the butyl acrylate in water increases the size of the nanoparticle due to enhanced monomer diffusion in the continuous aqueous phase (29).This is most likely due to the moderate rate of monomer addition resulting in more monomer available in the system, which supplies monomer micelles with more monomer initially to form larger nanoparticles than the polystyrene nanoparticles (14). Impact of Solvent Quality on Dispersed Nanoparticle Morphology The change in PS nanoparticle structure and morphology as the solvent quality changes from a good solvent to a theta solvent is relevant to understanding the structure of a soft nanoparticle morphology in a polystyrene matrix, which should mimic theta conditions. The nanoparticle is modeled as a highly cross-linked core with a “blurred” interface that is a result of decreasing crosslinking towards the outer surface of the nanoparticle. Towards understanding the impact of solvent quality on the structure of soft nanoparticles, the structures of PS nanoparticles are determined in d8-THF, a good solvent for PS and in C6D12 at 38.5 °C, a theta solvent for PS. Two sets of PS nanoparticles with different monomer rates of addition were chosen to investigate the behavior of the impact of effective nanoparticle “fuzziness” on the nanoparticle structure in these solvents. SANS of the 1 wt.% of PS nanoparticles in d8-THF exhibit a nanoparticle morphology that is completely swollen. For the PS nanoparticles synthesized with 2mL/h monomer addition, the size of the crosslinked core radius increases while the half-width of the fuzzy interface decreases as the amount of crosslinker increases in the semi-batch emulsion polymerization. The PS nanoparticles synthesized with 1 mL/h monomer addition rate in d8-THF exhibited no real correlation between the amount of DVB crosslinker and the size of the fuzzy interface. This is ascribed to the formation of new monomer micelles as the monomer is slowly added and the polymerization proceeds with little penetration of the crosslinker molecules into the micelles because the surfactant interfacial layer is highly concentrated and non-pliable (11). This essentially results in these nanoparticles exhibiting a constant effective nanoparticle “fuzziness” with increased crosslink density. The PS nanoparticles in 1 wt% solutions in C6D12 at 38.5 °C are expected to collapse relative to the nanoparticles in d8-THF due to the decreased solvent quality. The nanoparticles are only marginally soluble in this theta solvent for polystyrene, thus extreme diligence was taken when preparing the SANS samples to limit aggregation. The fact that the majority of the scattering curves exhibit similar forward scattering intensities, I(Q=0), (except for 0.81 and 1.91 mol % of DVB crosslinker at 2 mL/h monomer addition rate) to those in THF verify that these experiments are evaluating the structure of individually dispersed nanoparticles. The two samples with a modest increase in forward scattering is probably due to undesirable aggregation that occurred when the warm C6D12 solutions were transferred into cool quartz banjo cells. This phase aggregation of nanoparticles results in a slight increase in the I(Q=0) intercept resulting in skewed molecular weight calculations, but does not affect the determination of the nanoparticle size or structure, which is influenced by the complete scattering curve. 130

Using the fuzzy sphere form factor to fit the SANS data sets provides a pathway to probe the internal structure of the soft nanoparticles, including the change in the radius of the crosslinked core and the size of the fuzzy interface. It is interesting to note that for all nanoparticles, regardless of monomer rate of addition, the measured crosslinked core radius decreases with a decrease in solvent quality to the theta solvent (Figure 6 and Figure 7). A polymer chain dispersed in a good solvent will swell due to the penetration of the solvent into the polymer chain. However, a decrease in solvent quality leads to less favorable interactions between polymer and solvent, and the polymer conformation changes to increase monomer-monomer interactions reducing the less favorable monomer-solvent interactions. This results in a contraction or collapse of the overall polymer (31). Applying these principles to the PS nanoparticles dispersed in a theta solvent, the nanoparticles wants to eliminate the solvent from within the internal structure of the nanoparticle, and the nanoparticle goes from a swollen state to a more contracted state. Inspection of Table 2 shows that this contraction primarily manifests in the collapse of the core, which is accompanied by an increase in the fuzzy interface width for the clear majority of the nanoparticles (Figure 8 and Figure 9).

Figure 6. Impact of solvent quality, d8-THF (dots) and C6D12 (stripes), on the PS nanoparticles core radius, Rc, synthesized with a 1mL/h monomer rate of addition. 131

Figure 7. Impact of solvent quality, d8-THF (dots) and C6D12 (stripes), on the PS nanoparticles core radius, Rc, synthesized with a 2mL/h monomer rate of addition.

Figure 8. Impact of solvent quality, d8-THF (dots) and C6D12 (stripes), on the PS nanoparticles fuzzy interface half width, τfuzzy, synthesized with a 1mL/h monomer rate of addition. 132

Figure 9. Impact of solvent quality, d8-THF (dots) and C6D12 (stripes), on the PS nanoparticles fuzzy interface half width, τfuzzy, synthesized with a 2mL/h monomer rate of addition.

This translates to a relatively uniform half width of the fuzzy interface of the PS nanoparticles in theta conditions regardless of the synthetic conditions. This is in contrast to the structure of the nanoparticles synthesized with 2 mL/h monomer addition rate in a good solvent, which exhibit a steady decrease in the fuzzy interface with an increase in DVB crosslinker. It is likely that the increase of the half-width of the fuzzy interface in the theta solvent is due to the nanoparticle core becoming overly compact and the remaining polystyrene chain ends and loops are unable to coil and collapse any further into themselves. This results in a fuzzy interface that is similar to or larger than in the soft nanoparticles in the good solvent d8-THF. It is particularly interesting that the change in structure of the PS nanoparticle in a theta solvent is concentrated at the crosslinked core, and not the peripheral fuzzy interface. This means that if we envision these soft nanoparticles to mimic the behavior of hairy nanoparticles (solid nanoparticles with grafted polymer chains), the change in solvent quality decreases the more solid-like core, but retains the free chains at the surface (32, 33). Following this analogy further, the core radii of the nanoparticles in a theta solvent are less than half the tube diameter for linear polystyrene (≈ 8.3 nm) (34, 35) and approaching sizes where one might expect surprisingly large and qualitatively different changes in polymer nanocomposite structure and dynamics (35–37). In particular, Faraone and co-workers have reported an increase in the tube diameter with the addition of nanoparticles smaller than the entanglement mesh size (37). This may therefore 133

provide additional insight into the mechanism by which the presence of these soft nanoparticles increase the diffusion coefficient of the neighboring polymer chains (17) if these nanoparticles behave in a similar manner.

Conclusion SANS was used to investigate the structure and morphology of soft PBA nanoparticles as well as soft PS nanoparticles in both good and theta solvents. The water solubility of the monomer polymerized in a monomer starved semi-batch nano-emulsion polymerization is an important factor that impacts the structure of the produced soft nanoparticles. Using hydrophobic monomers, such as styrene, reduces the propensity of the monomer to reside in the continuous water phase, thus increasing the tunability of the morphology and topology of the nanoparticle as the monomer is sequestered into the micelles. When using a slightly watersoluble monomer, such as butyl acrylate, the topology of the nanoparticle is more difficult to control regardless of the surfactant concentration. However, as the surfactant concentration is increased, the pliability of the monomer micelle surface decreases and more control is possible. When PS nanoparticles are dispersed in a theta solvent, the radius of the crosslinked core of the nanoparticle decreases as the polymer collapses due to unfavorable interactions between the nanoparticle and the solvent. At the same time, the smooth decay of the scattering length density at the surface of the fuzzy sphere increases. It is interesting that the predicted contraction with decreased solvent quality is concentrated on the core of the nanoparticle, which provides insight into the structures of the nanoparticle that are present in an all polymer nanocomposite that consists of these soft nanoparticles and linear polymer chains. This relationship of soft nanoparticle structural behavior to a solvent quality provides insight that will guide future studies of soft nanoparticles dispersed into a bulk polymer matrix producing a stronger relationship for nanoparticles behaving as athermal fillers where the soft nanoparticles are more collapsed in a bulk polymer matrix than their swollen structure in a good solvent.

Acknowledgments This research was supported by the Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division. A portion of this research was also completed at ORNL’s High Flux Isotope Reactor, which was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing neutron research facilities used in this work. A portion of this research was also conducted at the Center for Nanophase Materials Sciences at ORNL, which is a DOE Office of Science User Facility. We thank Dr. Shiwang Cheng for fruitful discussions. 134

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Chapter 8

The Design and Applications of Beta-Hairpin Peptide Hydrogels Peter Worthington1 and Darrin Pochan*,2 1Department

of Biomedical Engineering, University of Delaware, Newark, Delaware 19716, United States 2Department of Material Science and Engineering and Delaware Biotechnology Institute, University of Delaware, Newark, Delaware 19716, United States *E-mail: [email protected].

This chapter reviews the history, development, and applications of the beta-hairpin peptide family of hydrogelators developed by the Schneider and Pochan laboratories. Peptide design provides for molecules that intramolecularly fold with consequent intermolecular assembly into a tightly defined fibrillar network in desired solution conditions. The resultant hydrogel network is described as an “injectable solid” due to the innate property of being able to flow under shear and immediately reheal back into a solid network on the cessation of shear. The ability to modify the peptide sequence confers a high degree of tunablility over the resultant hydrogel network properties and the solution conditions in which a gel is formed. This tunability leads to integration of the hydrogel within many applications such as drug delivery and complex cell culture.

Introduction Supramolecular gels are an important subclass of hydrogels formed from molecular self-assembly, both of high and low molecular weight compounds, that rely on non-covalent interactions to generate the highly hydrated, fibrous networks with desired material properties (1–3). The resulting supramolecular, physical (as opposed to covalent) networks tend to be easily modified due to the relative simplicity of their molecular building blocks and the ease with which © 2018 American Chemical Society

changes can be made in the molecular self-assembly pathway. With respect to changes in the molecular assembling molecules, slight alterations in chemical structure can result in targeted changes to the hydrogel nanostructure that have large implications in the resulting bulk material. With respect to alteration of the molecular self-assembly pathway, supramolecular hydrogel networks are highly dependent on their solution conditions; temperature, pH, and salt concentration can be used to trigger and either expedite or slow self-assembly in a number of ways. This combination of molecule and assembly pathway design results in tunable materials with a high degree of customization available. Biomolecules are particularly capable of functioning as the basic building block of a supramolecular gel, including DNA, RNA, proteins, synthetic polypeptides/peptides, and carbohydrates. While each group has its own advantages and disadvantages, amino acid-based molecules are of particular interest due to their natural ability to form higher order structures and potential cyto- and biocompatibility. Alpha-helical and beta-sheet secondary structures result in decidedly regular local structure. Hydrophobic collapse, hydrogen bonding, and electrostatic interactions can drive specific self-assembly from peptide backbone and side chain interactions. Put together, the above attributes allow proteins, polypeptides, and peptides to be designed in a biomimetic fashion for specific, desired self-assembly mechanisms. Peptides are a particularly useful class of amino acid-based hydrogelators due to their comparatively small size, ease of design and synthesis, and ease of solution processing. The ability to design peptide intra- and intermolecular interactions from the bottom up results affords a thorough understanding of the effect of each amino acid within a molecule and assembly pathway and the implications from changing an individual residue. There is a rich history of using peptide based hydrogels taking advantage of their propensity to self-assemble using secondary structure, hydrophobic collapse, and electrostatic interaction. Adams (4, 5), Gazit (6, 7), and Ulijn (8, 9) have taken advantage of the aromatic interaction of Fmoc-peptides to generate hydrogels. Collier (10, 11), Conticello (11), Hartgerink (12, 13), and Woolfson (5, 14) have used the alpha-helix secondary structure to great effect while Boden (15), Saiani (16, 17), and Zhang (18, 19) have relied on the beta-sheet as a building block for hydrogel formation. The beta-hairpin is a specific type of beta-sheet interaction that relies on the interaction of two covalently connected beta-sheet strands. This type of molecular structure is the result of a de novo designed peptide placing two amphiphilic amino acid strands with high beta-sheet propensity flanking a central turn sequence. The solution conditions can be altered to trigger the intramolecular folding of the molecule into a beta-hairpin conformation. Importantly for supramolecular assembly and hydrogel formation, only after the monomer folds does intermolecular assembly of the fibrillar network begin. The dependence of the intermolecular assembly on the intramolecular folding provides a high degree of control over hydrogelation, only occurring in desired solution conditions and with desired kinetics. This chapter will focus on the design and modification of the MAX family of beta-hairpin peptide hydrogels designed by Schneider and Pochan, the work within both the Schneider and/or Pochan laboratories to understand the basic self-assembly mechanisms and material properties, and resulting applications explored. 140

Structure The MAX family of peptides are designed around the motif of two locally amphiphilic arms flanking a central turn sequence. MAX1, the original peptide design is a 20 amino acid sequence ((VK)4-VDPPT-(KV)4-NH2) with the two amphiphilic arms being 4 sets of alternating valine and lysine around the central type II’ turn structure of valine, d-proline, proline, and threonine (20). The research concerning this class of peptides has spanned a number of small and large modifications to the amino acid sequence, both in the arms and the turn sequences, with large implications for the supramolecular assembly pathway, the nanostructures formed, and the hydrogel material properties and applications, all of which will be discussed herein. (Figure 1)

Figure 1. TEM of self-assembled nanofibrillar structures and the proposed self-assembled structure of the fibrils and dimension. Reprinted in part with permission from Phys. Rev. Lett. 2004, 93 (26 I), 1–4. Copyright 2004 American Physical Society (20). 141

Folding Mechanism The MAX1 amino acid sequence in pure pH 7 water exists in solution in the random coil confirmation. When the proper folding conditions (temperature, pH, salt concentration) are met the peptide is able to fold into its hairpin conformation. The charge state of the arm lysines is critical for controlling when this change occurs. The charges keep the arms from folding together into a parallel beta sheet. If the pH of the solution is increased the lysines can be deprotonated, if the salt concentration in the solution is increased the charges can be screened, and if the temperature of the solution increases the rate of hydrophobic collapse also increases (21–23). These three variables can be used together or independently tuned to control beta-hairpin folding and consequent hydrogelation. After the hairpin is formed it is stabilized by hydrogen bonding between the two arms of the peptide. The formation of the individual hairpins results in the beginning of the supramolecular assembly. (Figure 2) The hairpin is facially amphiphilic with a hydrophobic valine face and a hydrophilic lysine face. Two hairpins will stack burying the hydrophobic valine face between them. More hairpin pairs will assemble laterally continuing to bury the hydrophobic valines and stabilized by intermolecular hydrogen bonding. This process results in the formation of physically stabilized nanofibrils with a valine core sandwiched between two lysine faces. Recently, the molecular packing of the beta-hairpins within the fibrils has been well characterized. The two layers of hairpins within individual nanofibrils always have their turn sequences on opposite sides from each other (24). Also, the vertical hairpin pairs do not stack perfectly over one another but offset by half the width of a hairpin.(Figure 3) The hydrogel network forms as entanglement interactions between different fibrils occur and defects during the fibril self-assembly process result in nucleation points for a new fibril branch. An example of gelation occurs in phosphate buffered saline at pH 7.4 at 37 C with 150 mM NaCl-the assembly process of 0.75 wt% MAX1 takes approximately 30 minutes and results in a hydrogel with a stiffness of approximately 1 kPa. Modifications in the procedure and/or molecule that results in a faster gelation process (high concentration of peptide, higher salt concentration, higher temperature, alteration of the peptide design) would result in a stiffer overall hydrogel.

Material Properties Like most hydrogels MAX is a highly hydrated network, typically approximately < 97% water by weight. MAX is also a peptide based material, typically made from solid phase peptide synthesis. This results in a material that is highly tunable and cyto-. Biocompatible (26). Because of the self assembling nature of the hydrogel it is simple to encapsulate a number of different things inside the hydrogel, primarily cells or therapeutic compounds. The stiffness of typical hydrogels made from the assembly of beta-hairpins is between 10-10,000 Pa as measured by oscillatory rheology. The most exciting material property is its shear thinning behavior; after the hydrogel has formed into a solid, a shear force can be applied to the hydrogel resulting in the hydrogel flowing like a liquid 142

(27). As soon as the force is stopped the hydrogel immediately reheals back into a solid. The shear shinning is a result of the physical nature of the hydrogel; there are no covalent bonds, only physical interactions holding each individual hairpin together and the supramolecular gel network. So, the hydrogel can break into domains and flow without damaging the network.(Figure 4) When the hydrogel reaches its destination after flow, the domains immediately repercolate back together and form a stiff solid. This has implications for the delivery of various payloads encapsulated inside the hydrogel (28–30). Also, the amphiphilic nature of the hydrogel means that there are domains for both hydrophobic and hydrophilic molecules to be stored.

Figure 2. Cartoon schematic of peptides folding into the β-hairpin conformation under physiological conditions followed by self assembly into a fibrillar network. Reprinted in part with permission from Anal. Biochem. 2017, 535. Copyright 2017 ELSEVIER (25).

Modifications, Implications, and Applications The design history of the MAX peptides is one of modification, both small and large, to improve the hydrogel for a particular application, to further investigate a specific material property, and to study the self-assembly mechanism. This chapter will categorize these various alterations to the peptide sequence, give some context to the goals of the alteration, and show how the alteration affected the structure of the peptide, affected the self-assembly, and affected the ultimate hydrogel material properties. The two major applications in mind for the hydrogel are as a method of payload delivery; such as cells, small molecules, or biological therapeutics; and as a synthetic extracellular matrix to create advanced cell culture models. There are also potential uses of the materials for which both of the above applications are important hydrogel attributes. A recent application being investigated that does 143

just that is high throughput drug screening (25). High throughput drug screening is the process of designing disease models that can be tested many thousands of times to quickly screen very large compound libraries. Drug screening tends to rely on liquid handling due to the precision needed when working with such small volumes, and the inclusion of a solid scaffold can greatly complicate matters, However, a shear-thinning and rehealing hydrogel such as those made with betahairpins can be used for both cell encapsulation and culture with defined cell distribution as well as injected with HTS equipment.

Figure 3. Cartoon schematic of the specific packing of β-hairpins within the MAX nanofibril. Reprinted in part with permission from Proc. Natl. Acad. Sci. 2015, 112 (32), 9816–9821. Copyright 2015 National Academy of Sciences (24).

Assembly Early ideas for molecule design based on amino acids include an early study on diblock copolypeptide amphiphiles which tested the gelation ability of lysinexleuciney and lysinexvaliney, an alpha-helix and beta-strand former respectively (31). The resulting materials were able to gel at ~1 weight percent and displayed a rapid recovery of the gel stiffness following a breakdown of the structure by large amplitude oscillations in the rheometer. Although the conclusion was that alpha-helical gelators were slightly better than beta-strands in block copolypeptides, the need for new assembling peptides was clear, leading the way to create the much smaller beta-hairpin MAX peptide. Soon after, a 144

paper detailing the MAX1 peptide was published detailing the control of pH over self-assembly and proposed a mechanism for gelation where in a basic solution (pH 9) some of the lysines are neutral allowing the peptide to fold (21). The next study focused on the importance of temperature to the hydrogel system (22). MAX2 and MAX3 were synthesized substituting one (position 7) or two (position 7 and 13) threonines for valine respectively, making MAX2 more hydrophilic than MAX1 and MAX3 more hydrophilic than both. Holding pH at 9 MAX3 was shown to self-assemble at 75 C but unassembled when brought to 5 C, the behavior was shown to be repeatable.

Figure 4. The evolution of the hydrogel network before during and after shear. Reprinted in part with permission from Soft Matter 2010, 6 (20), 5143–5156. Copyright 2010 Royal Society of Chemistry (27).

The effect of salt on self-assembly and the idea of biological applications was a clear next step in the beta-hairpin study. At a solution pH of 7.4 (biological), MAX1 is not able to assemble without the addition of salt. At pH of 7.4 MAX1 has a positive charge from the lysines. Therefore, significant, additional counterions are required to screen those charges before self-assemble can occur. At 400 mM NaCl the peptide rapidly self-assembled to 2000 Pa, at 150 mM NaCl (biological) the peptide assembled to 200 Pa, and at 20 mM NaCl the peptide slowly assembled to 100 Pa. This study showed how salt can affect assembly 145

and introduces the idea of how the speed of assembly kinetics can affect the final hydrogel network structure. The faster the assembly kinetics, the more branch points are formed due to defective incomplete collapse of the hairpin hydrophobic faces, thus forming a more stiff hydrogel network even with the same concentration of peptide molecules (32). MAX4 and MAX5 were designed to test the importance of lateral hydrophobic interaction between neighboring molecules valines (33). In MAX1 the valines make both facial and lateral interactions, while MAX4 makes only facial interactions. TEM shows that MAX1 makes very consistent fibrils while MAX4 has many higher order assemblies. A deeper look into the hydrophobic face of the peptide and the importance of branching due to defective hydrophobic collapse focused on the 8 flanking valines of the beta-hairpin replaced by four napthylalanines side chains and four alanines to make LNK1 ((Nal)K(Nal)KAKAK-VDPPT-KAKAK(Nal)K(Nal)-NH2)) (34). The goal was to force the hairpins to stack across the fibrils in a specific manner matching the four bulky napthylalanine side chains from above with the four small alanine side chains from below, forming a lock and key-like steric packing in the hydrophobic core of the fibrils. The design was a success, and fibril branching was greatly reduced. The lack of branching also manifested in the inability of the hydrogels to recover following shear thus revealing that the branch points formed during self-assembly of the MAX family of peptides are critical to the inherent shear thinning and immediate rehealing properties. This work was further expanded with a study that replaced all 8 valines with a variety of other hydrophobic amino acids (35) including valine, aminobutyric acid, norvaline, norleucine, phenylalanine, and isoleucine as l replacements. The most important variable to assembly was found to be hydrophobic content with the more hydrophobic amino acids assembling at lower pH and temperature. The stiffness of the resulting hydrogel was harder to attribute specifically to the molecule structure, as it did not depend clearly with hydrophobicity or beta-sheet propensity. This is because the molecules were found to not simply assemble into a nanofibril with a bilayer of peptide and a hydrophobic core but to assemble in a hierarchical fashion into larger ribbons and fibers. An iterative study looked into the relationship between of the total charge of the molecule and the pH of solution (36). This was done by designing MAX1 modified peptides replacing a single lysine with a glutamic acid at each position, and designing MAX1 modified peptides with altered net charge. This was done to find a peptide that would assemble quickly at pH 7, an important pH for its biological relevance. MAX1 (K15E) was the resultant molecule later named MAX8 and will be discussed at length below. An in-depth study on the evolution of the nanostructure during self-assembly showed two distinct time scales. The first includes fibril cluster formation and intercluster overlap, while the second involves the percolation of fibrillar clusters (32). This has implications for when to include payloads that will be encapsulated in the gel; too slowly during the hydrogelation process and the payload may not be homogenously distributed. Further investigation into the kinetics of assembly comparing the faster assembling MAX8 to MAX1 using neutron scattering to probe the nanoscale networks showed that changing one amino acid to decrease total charge results in a higher storage modulus (stiffness) from increased fibrillar branching 146

and physical crosslinks, while the dimensions of individual fibrils did not change (37). The most exact information about the final fibrillar structure is from an NMR study that shows MAX1 assembles in a highly specific way resulting in monomorphic fibrils within a kinetically trapped hydrogel network (24). The resulting fibril can be defined as Syn/Anti with all of the hairpins in the same beta-sheet have their turns on the same edge, and the hairpin in the opposite beta sheet all have their turns on the opposite edge. This arrangement allows the turn sequences in the same beta-sheet to pack decreasing the solvent exposed area, and the terminal valines are able to interact with the turn sequence prolines of their vertical neighbor.

Figure 5. Neutron scattering of vincristine-laden hydrogel with the proposed drug-gel configurations. Reprinted in part with permission from Biomater. Sci. 2016,4, 839-848. Copyright 2016 Royal Society of Chemistry (30).

Antibacterial Properties While the MAX hydrogel was designed with biological applications in mind, it was discovered in the Schneider laboratory to have the fortuitous material property of inherent broad spectrum antibacterial activity. Following this discovery, the bulk hydrogel was challenged with a number of Gram positive, ex Staph, and Gram negative, ex E Coli, bacteria (38). The bacteria were killed so long as the amount of bacteria added did not pass above a certain threshold. The suggested mechanism of destruction is a mechanical tearing of the bacterial inner and outer membranes when the negatively charged bacteria interact with the positively charged hydrogel. This innate mechanism is effective until cellular debris from dead bacteria builds up to create a buffer, preventing new living bacteria from reaching the hydrogel, and overwhelming the antibacterial 147

properties. Cocultures of NIH 3T3 fibroblasts and bacteria did not show a negative effect on the fibroblasts proliferation while the bacteria were killed. To further explore antibacterial hydrogels, MARG1 was synthesized replacing lysine with arginine at position 6 and 17 to mimic other antimicrobial peptides and add the guanidinium functional group (39). MAX1 and MARG1 were challenged with MRSA. Both were able to kill the bacteria, but MARG1 was effective up to higher concentrations of the bacteria. Importantly, the bacteria still needed to make contact with the hydrogel for it to be effective. Mammalian mesenchymal stem cell proliferation was not inhibited by culture on MARG1. Cell Scaffolding, Delivery, and Culture With the basics of self-assembly understood, the focus turns more toward applications. The first major biological investigation looked at the cytocompatibility between MAX1 and NIH 3T3 fibroblast cells (40). First DMEM was shown to induce peptide self-assembly and not cause material degradation over time. Next the 3T3 cells were shown to readily attach to the hydrogel when added on top of the preformed gel. The cells were shown to successfully proliferate over 72 hours, even outperforming the control cells grown on polystyrene. Finally, the cells were shown to have almost no effect on the hydrogel stiffness following the 72 hours of growth. MAX8 was designed to improve the biological applicability of beta-hairpin peptides by increasing the speed of gelation at pH 7.4 (41). This was done by exchanging a lysine for a glutamic acid at position 15 lowering the peptides charge state by 2 and allowing the remaining lysine charges to be screened more efficiently (42). This change allowed the hydrogel to form fast enough to homogenously suspend encapsulated mesenchymal stem cells and provided evidence that the cells would remain suspended during injection through a syringe. Having established the MAX hydrogels as cytocompatible in vitro, the next goal was to look at the possibilities of in vivo. J774 mouse macrophages were cultured on MAX1 and MAX8 and their inflammatory response was measured (43). The macrophages were able to successfully proliferate, but displayed no inflammatory response providing evidence that MAX could be successfully implanted in vivo. Small angle neutron scattering and rheology was used to examine MAX1 and MAX8 restoration kinetics following a shear disruption of the network to prepare for delivering cell encapsulated in the hydrogel via syringe (27). The speed of the rehealing process was dependent on the rate and duration of the shear force as well as the stiffness of the hydrogel before shear, but there was no measurable change to the hydrogel nanostructure for any of the shear rates tested, suggesting that the hydrogel breaks into domains that can repercolate together following a secession of shear force. MG63 osteosarcoma cells were encapsulated in MAX8 and underwent a test injection to measure the effect of the injection on cell viability, 3 hours after the injection greater than 95% of the cells were still viable. Polystyrene spheres modified to fluoresce where encapsulated in MAX8 to visualize hydrogel flow through a capillary, mimicking flow in a syringe (26). It was discovered that the gel underwent plug flow; while there was a difference in the velocity of the gel close to the walls of the syringe, decreasing as it the gel 148

got close to the wall, the gel in middle area of the syringe flowed at a constant velocity, preventing it from experiencing shear, which has been shown to have a phenotypic effect on cells (44–46). The total cross-sectional area of the capillary that was at a constant velocity depended on the total flow-rate; with an increased flow-rate, the cross-section at constant velocity decreased. This information can be used to protect cells from shear during injection which has been shown to have phenotypic effects on cells. MAX8 was used as a cell scaffold as a part of a high throughput drug screen (25). The hydrogel was modified to include the cell binding motifs, RGDS IKVAV and YIGSR, to simulate extracellular matrix proteins. These modifications to the cellular microenvironment resulted in phenotypic change in the ONS76 medulloblastoma cells making them more invasive and improving stemness. These changes also resulted in the cells responding differently to the drugs when compared to 2D. Another modification that can be made to control the cellular microenvironment is the inclusion of sights susceptible to proteolysis by matrix metalloproteases (47). A series of susceptible hydrogels where designed and synthesized called DP1-4, they were shown to degrade specifically to MMP-13 dependent upon the susceptibility of the individual sequence and the stiffness of the bulk hydrogel. The inclusion of the MMP cleavage sequence was shown to improve cell motility through the hydrogel. Therapeutic Delivery The MAX hydrogels provide a number of useful material properties as a possible delivery vehicle. The ability to undergo triggered self-assembly prior to injection, flow like a liquid without experiencing a breakdown of the local hydrogel network, and immediate rehealing into a solid after a secession of the shear force are all useful properties. When combined with the biological compatibility as well as the tunable nature of the synthetic hydrogel, the material becomes an attractive delivery vehicle. A first delivery study in the Schneider lab looked at three dextran probes of increasing size and their ability to diffuse out of the MAX1 and MAX8 hydrogel networks (28). As expected the relationship between the probe size and the network mesh size had the greatest effect on diffusion rates, providing a way to control the rate via peptide design. A deeper investigation looked into the ability of MAX8 to perform as a delivery vehicle for a more varied selection proteins and how the nature of the encapsulated protein effected the gel network and the proteins diffusion (48). The first thing to note was that the hydrogelation of MAX8 was not impeded by the presence of the protein payloads nor did it have a measurable effect on the hydrogel bulk properties. The release of the positively charged and neutral proteins was largely governed by the size of the protein and its steric integration with the mesh size of the hydrogel network. The release of the negatively charged proteins was impeded by their electrostatic interaction with the positively charged peptide network. Diffusion was tested again on loaded gels following a syringe injection. There was a small effect lowering diffusion rates overall but releasing more of the loaded protein. Taking this information in a therapeutic direction, the neurotrophic growth factors NGF and BDNF were encapsulated in MAX8 to study the possibility of sustained 149

local delivery to spinal cord injuries (49). Release rates for both growth factors was shown to be dependent on the weight percent of the hydrogel and the amount of growth factor encapsulated. The rate was also measured to be consistent over 28 days. The loaded gel was used to deliver NGF to PC12 adrenal medulla cells, which responded by growing neurite like extensions. The cells continued to show this phenotypic response to the encapsulated NGF past 28 days of culture, considerably longer than the cells response to NGF in solution which lasted for 3 days. A targeted study was done encapsulating curcumin as a potential chemotherapeutic (29). Curcumin is a challenging therapeutic molecule because of its hydrophobicity and short half-life. The encapsulation of varying concentrations curcumin into the MAX8 hydrogel was shown to have minimal effects on the hydrogel bulk properties and released from the gel at a consistent rate over two weeks while and inducing cell death in DAOY medulloblastoma cells. A more conventional chemo therapeutic, vincristine, was also encapsulated in a later study to study release and effectiveness (30). The loaded vincristine was shown to release over 28 days and still be able to induce cell death in DAOY cells at day 28, considerably longer than its half-life of 4 days in aqueous solution would suggest possible.(Figure 5) This is another example of the protective benefit the amphiphilic hydrogel has for hydrophobic compounds. More recent delivery studies include the use of MAX1, MAX8, and HLT2, a peptide modified to have a lower net positive charge, to deliver DNA and stimulate an immune response in mice (50). It can be a challenge to deliver whole, undegraded DNA in a therapeutic application. It was hypothesized that a beta hairpin hydrogel would be able to protect its DNA cargo en route to its destination (51). All three gels were able to retain greater than 90% of the encapsulated DNA over two weeks. After injection into mice MAX8 and HLT2 gels each showed an increase in lymphocyte proliferation, but only HLT2 had large amounts of infiltrating cells, resorption of the hydrogel, and growth of new tissue. These results suggest that DNA was unable to be released from the highly charged MAX1. Major Modifications While the beta-hairpin conformation is robust to arm modification, the turn sequence and the hydrophobic face of the folded peptides are more fundamental to the existence of the hairpin structure. A study into the turn sequence focusing on the replacing the d-proline with an l-proline resulted in no hydrogel structure but instead the formation of twisted beta-sheet-rich ribbons with high stability to solution changes after assembly, a large change due to changing the chirality of one amino acid (52). MAX6 was designed to test the how the inclusion of a charged amino acid on the hydrophobic face would affect folding by exchanging a valine for a glutamic acid at position 16. MAX7 tested the effect of exchanging a valine with a cystine on folding, which had little effect. Both of these molecules were used to explore the addition of more molecular controls to triggering selfassembly (53). In particular, the cystine was used to create MAX7CNB through the addition of a photocage that has a negative charge under basic conditions. The molecule would not self-assemble until the photocage was removed by UV light. 150

The resulting hydrogel was also shown to support NIH 3T3 fibroblast proliferation. A similar peptide called MLD was designed by replacing a lysine at position 5 and 18 with a lysyl sorbamide and adding an extra lysine at the beginning and end of the peptide for a total of 22 amino acids. The sorbamide groups can be covalently crosslinked using UV following self-assembly of the hydrogel network. After the network physically self assembles, the UV induced polymerization increased the stiffness of the gel 2.5 fold, giving another tool to tune the hydrogel. Strand swapping peptides were designed by synthesizing hairpins with uneven sets of valine lysine pairs flanking the turn sequence (54). SSP1 (VK)2-VDPPT-(KV)6- NH2 had two sets of valine lysine pairs on one side and six pairs on the other, this meant that the resulting hairpin was two pairs long with a dangling four pair domain that could beta-strand swap with another peptide forming a facially amphiphilic dimer. SSP2 (VK)3-VDPPT-(KV)5NH2 was similarly designed with three pairs in the hairpin and two pairs dangling. The normal self-assembly pathway resulted in fibrils. However, the SSP1 fibrils twisted while SSP2 fibrils did not. A further study created SSP3 (VK)5-VDPPT-(KV)3- NH2, a peptide identical to SSP2 with the strand asymmetry switched to have the longer stand on the N-terminus (55). All three peptides made individual fibrils with a four peptide cross-section instead of the normal two peptide cross-section in the MAX peptides. This is because the extra beta strand length in a folded peptide requires a partner peptide on the same face of the nanofibril to satisfy the possible hydrogen bonds available in the extra beta-strand. After folding and hydrophobic collapse, the individual fibrils contain a four peptide cross-section. The fibrils either twisted, remained straight, or laminated, and each network had different stiffnesses. A three stranded peptide with two turn sequences called TSS1 was designed to make two hairpins during the folding process (56). It had similar material properties of triggered self-assembly, shear thinning, and rehealing, but the hydrogel had a greater stiffness than unmodified MAX1 giving a way to control stiffness not connected to weight percent or speed of assembly. A second method of stiffness control unrelated to kinetics or weight percent was found while studying the enantiomer of MAX1 called DMAX1 synthesized using d amino acids (57). It was originally of interest as a way to prevent enzymatic degradation, and when gelated alone, behaved nearly identically to MAX1 in terms of material property. But, when the two peptides were mixed together the resulting hydrogel was much stiffer. The greatest increase, a four fold increase, occurs when the two peptides were mixed one to one. If the ratio increased in favor of one peptide or the other the increase in stiffness was lessened. A final point on use of L or D amino acids, the DP found in the hairpin turn sequence, while a critical portion of the molecule design, makes bacterial expression of the peptides difficult. Three peptides were designed that would be expressible by bacteria with redesigned turn sequences called EX1 ((VK)4-VPDGT-(KV)4-C02H), EX2 ((VK)4-VPIGT-(KV)4-C02H), and EX3 ((VK)4-YNGT-(KV)4-C02H) (58). Each peptide was shown to be suitable for bacterial expression with all three peptides able to self-assemble, shear-thin and reheal with EX3 being the most stiff hydrogel. TEM of the fibrils showed that EX1 was more heterogenous than the other two, possibly from the negatively charged aspartic acid added to the hydrophobic face. MBHP 151

(VKVKVKV-CGPKEC-VKVKVKV-NH2) is also a peptide designed around a modified turn sequence. It relies on the binding of a heavy metal ion to form the individual beta-hairpins (59). The addition of the two cystines flanking the turn sequence provide a location for the metal ion to bind and force the peptide to fold. The nanostructure of the network depended on the type of metal bound, twisting or laminating fibrils with some making very stiff final networks.

Conclusion The development of the beta-hairpin peptide was one of careful choices and simultaneous serendipitous discovery. The hydrogels resulting material properties make it a powerful tool for both therapeutic delivery and complex cell culture. The growing list of peptide modifications and design tools means it can be tailored to fit many specific situations currently and in the future.

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Chapter 9

Self-Assembly and Mechanical Properties of a Triblock Copolymer Gel in a Mid-block Selective Solvent Santanu Kundu,* Seyed Meysam Hashemnejad, Mahla Zabet, and Satish Mishra Dave C. Swalm School of Chemical Engineering, 323 Presidents Circle, Mississippi State University, Mississippi State, Mississippi 39762, United States *E-mail: [email protected].

Polymer gels are used in many applications including in bioimplants, tissue scaffolds, oil recovery, and drug delivery. In these applications, gels often undergo mechanical deformation when subjected to tensile, compressive, shear, and mix-mode loading. At sufficiently large-strain, the gel deformation can be non-linear and can often lead to failure of the material. The mechanical responses of gels depend on their structure at various length scales. These structures form through the chemical bonding and/or physical assembly of constituting gelator molecules. Subjected to mechanical loading, the underlying structure of gels undergoes association, dissociation, and bond-breaking process, although macroscopic mechanical responses are often similar. To elucidate the link between the gel structure and mechanical properties, here we consider a self-assembled gel consisting of a triblock copolymer [ABA] in a mid-block selective solvent. The triblock copolymer is poly (methyl methacrylate)- poly (n-butyl acrylate)- poly (methyl methacrylate) [PMMA-PnBA-PMMA] with midblock length much longer than the end-blocks. 2-ethyl-1-hexanol and n-butanol have been selected as the midblock selective solvents. Below gelation temperature, as investigated by small-angle scattering, the end-blocks formed spherical aggregates. These aggregates were connected by the midblock bridges leading

© 2018 American Chemical Society

to a three-dimensional network. Altering the self-assembly process by incorporating graphene nanoplatelets resulted in a decrease of gelation temperature. During shear-deformation, the midblock bridges were stretched without being pulled out of the aggregates, as the end-blocks were strongly associated. As a result, a distinct strain-stiffening behavior has been observed for these gels and such behavior was successfully captured using large amplitude oscillatory shear (LAOS) experiments. To understand the failure behavior of these gels originated from a defect within a gel, a custom developed cavitation rheology technique was used. The pressure vs time responses from the cavitation experiments were analyzed using neo-Hookean and Gent constitutive equations. Although a cavitation or snap-through expansion like deformation behavior was observed, the critical pressure was higher than that predicted by the Gent and neo-Hookean constitutive equations. It was likely that the chain pull-out from the aggregates took place during the cavitation process, which contributed to the additional pressure.

Introduction Gels are a class of soft solids consisting of a large amount of solvent (1, 2). In these materials, the solvent molecules are entrapped /immobilized in a volume-spanning three-dimensional network. The network is formed by polymer or oligomer chains, low-molecular-weight gelators, etc. (1–3). To form the network, the constituting molecules are often physically or chemically crosslinked, however, topological interactions of the self-assembled structures can also display a gel-like behavior (1–7). In hydrogels, the solvent is water, whereas, in organogels, the solvent is an organic liquid. Physical properties of gels, including mechanical and interfacial properties can be altered in many ways, for example, by choosing suitable chemical structure of the gelators, adopting different synthesis strategies for forming chemically crosslinking networks, dictating the self-assembly processes for physically crosslinked gels, and incorporation of nanoparticles in the gels. Further, gels can be rendered responsive to external stimuli such as temperature, pH, electrical field, and light (1, 2, 8–15). Because of these attractive features of gels, these materials are being used or have potential applications in many areas including in bioimplants, tissue engineering, drug delivery vehicles, superabsorbent, gel-based sensors, soft robots/machines (1, 2, 8–21). In fact, gels are ubiquitous in daily used products, particularly, contact lenses, jello, hair gels, etc. (22, 23) Gels formed by the self-assembly of a block-copolymer segment in a specific solvent are of significant interest, as the association and dissociation of the structure can often be controlled by the application of stimuli such as temperature and pH (4, 5, 24–30). Similarly, for the low-molecular-weight gelators, the small molecules can associate to form fibers or other self-assembled structures leading 158

to gel formation through topological interactions (3, 6, 7, 31, 32). For polymeric systems, the choice of solvent plays an important role, as the individual blocks of a block copolymer can interact with the solvent differently (33). Thermoreversible gels can be obtained by harnessing the change of solubility of one or more blocks of a block copolymer in comparison to the other blocks as a function of temperature (34–37). In triblock copolymer gels, triblock copolymers can form a gel in end-block and mid-block selective solvents (5, 25, 27, 38, 39). In pluronic gels, one of the most commonly known triblock copolymer gels, poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) or PEO-PPO-PEO forms a gel in water, an end-block selective solvent (38, 39). In these gels, transition from sol to gel phase occurs with increasing temperature. With increasing temperature, the PPO blocks collapse forming a micellar structure. The gelation behavior of pluronic gels can be altered by adding other components, such as chitosan (38, 39). These gels are commonly used in pharmaceutical formulations and in cosmetics (39–41). In another system, the end-blocks of triblock copolymers associate to form a gel-like material in mid-block selective solvents. Here, the gelation takes place with decreasing temperature. The decrease in the solubility of the end-block resulting in a reduction of interaction between the end-blocks and solvents, and formation of aggregates due to the association of the end-blocks. The aggregates are connected by the mid-blocks forming a three-dimensional network. Many gels of this type have been reported, particularly, polystyrene-rubber-polystyrene [PS-rubber-PS] in oil, which is a good solvent for the rubbery block (26–28). Rubbery blocks such as poly(ethylene/propylene)(PEP), poly(ethylene/butylene) (PEB), and polyisoprene (PI) have been investigated (26, 27, 29, 42, 43). In addition to PS-rubber-PS systems, other systems that have been considered are acrylic block copolymers, such as poly (methyl methacrylate)–poly (tert-butyl acrylate)–poly (methyl methacrylate) [PMMA-PtBA-PMMA] and poly(methyl methacrylate)–poly(n-butyl acrylate)–poly(methyl methacrylate) [PMMA-PnBA-PMMA] in butanol and 2-ethyl-1-hexanol (5, 24, 25, 36, 44). Most of these gels are thermoreversible in nature, i.e., these gels can be converted into liquid and vice versa by changing temperature. Structure and mechanical properties of gels consisting of ABA triblock copolymers in mid-block selective solvents depend on many factors such as the absolute and relative copolymer block lengths, the copolymer concentration in solution, pH, and temperature, which affect the polymer-solvent interactions significantly. Many different types of gels have been reported in the literature and we do not aim to present a complete review of all those gels. Rather, we present the self-assembly process and mechanical properties of a self-assembled triblock copolymer gel consisting of PMMA-PnBA-PMMA triblock copolymer in two mid-block selective solvents, n-butanol and 2-ethyl-1-hexanol. If not otherwise mentioned, the triblock copolymer considered here has a PMMA end-block molecular weight of 9,000 g.mol-1, whereas the molecular weight of the PnBA mid-block is 53,000 g.mol-1. In this chapter, this polymer is referred as A9B53A9. As the average entanglement molecular weight of PnBA is about 20,000-30,000 g.mol-1 (45), where a significant entanglement is not expected. 159

For a self-assembled system, achieving a control on the self-assembly process is an important consideration. For triblock copolymer gels, homopolymers resembling one of the blocks can be added to alter the self-assembly process. Alternatively, the self-assembly process can be altered by adding graphene nanoplatelets, as reported here. However, how these nanoplatelets affect the self-assembly process is an open question, particularly, if the size of the nanoplatelets is bigger than the aggregates and the pore size of the gels. Most of the literature reports on these gels have been limited to a small temperature range, near the gelation temperature, mostly at the room temperature. However, as the solvent quality continues to change with decreasing temperature, the self-assembly process is expected to continue. This, in turn, can affect the properties of these gels. Although important for practical applications of these materials, such understanding is limited and will be presented here. Another important question for these self-assembled gels is how these gels fail subjected to a mechanical load. Failure in these gels can primarily take place through chain pull-out from the aggregates, rather than chain scission. Strength of association in the aggregates, solvent quality, and mid-block length in tandem dictate the fracture process. Nonlinear rheology is increasingly being used to characterize soft materials and can capture the large-strain deformation behavior of these gels leading to failure. Failure behavior of these gels can be further investigated using cavitation rheology, a simple yet powerful technique. Both nonlinear rheology and cavitation rheology can provide fundamental understanding regarding the gel failure mechanism.

Effect of Solubility Parameter on Self-Assembly Gelation of triblock copolymer takes place as a result of a change in the interaction between the polymer blocks and the solvent, i.e., the change of solvent quality with the changing temperature. The solvent quality can be interpreted by the Flory–Huggins interaction parameter (χ) (1, 46). To understand the gelation of PMMA-PnBA-PMMA in mid-block selective solvents, such as n-butanol and 2-ethyl-1-hexanol, the temperature dependency of the χ parameter for the individual homopolymers has been studied. Figure 1a represents the images of PMMA and PnBA, in n-butanol and 2-ethyl-1-hexanol at different temperatures. At 80 °C, PMMA was soluble in the above-mentioned solvents resulting in transparent solution, whereas, the turbidity of the samples at 4 °C illustrates the PMMA phase separation. With a further reduction of temperature, precipitation of polymer occurred demonstrating a strong temperature dependency of χ parameter. The solubility of PnBA did not change over the temperature range of -66 °C to 80 °C, as the solution remained transparent. χ parameter as a function of the temperature can be obtained experimentally. The χ parameter and θ temperature for the PMMA samples with various molecular weights in different alcohols have been reported by Llopis et al. (47) The θ temperature was found to be 85 °C and 83.2 °C in n-butanol and n-propanol, respectively. The χ parameter as a function of temperature, T (in K) has been given as (47) χMS = −2.82 + 1189.058/T. The subscripts “M” and “S” represent PMMA 160

and the solvents, respectively (Figure 1b). χ 0) or strain-softening (e3 < 0), and shear-thickening (υ3 > 0) or shear-thinning (υ3 < 0) behavior of a material. Figure 10 displays the experimental data and the results analyzed using LAOS framework for a 5 vol% triblock gel (A9B53A9) at 22 °C and at a frequency of 1 rad/ s (5). The first harmonic storage modulus, G′1, and loss modulus, G″1, are shown in Figure 10a. G′1 values were much higher than G″1, confirming the soft-solid like the behavior of the gel. At low strain, G′1 values were almost independent of strain but at large strain, G′1 values increased with increasing strain amplitude, indicating the strain-stiffening behavior of this gel. The corresponding stress-strain curves (Lissajous-Bowditch curves) are shown in Figure 10c. The evolution from an elliptical stress-strain curve to a distorted one with increasing strain-amplitude is clearly visible, indicating a transition from linear to the non-linear region. The third-order Chebyshev coefficients, e3, were estimated using MITlaos software and are shown in Figure 10b. The e3 values became positive in the non-linear region, confirming the strain-stiffening response of the gel. Both G′1 or e1, and e3 increased rapidly at large-strain. These results indicate that the strength of the physical association (PMMA aggregates) was significant. During the deformation process, it was possible to stretch the chains to near to their full length before being pulled out of the aggregates. This behavior resulted in distinct strain-stiffening responses observed here. During strain-sweep experiments, a fracture in the gel sample was observed at a strain value of ≈350%, as a result, a drop in modulus value was observed (point 19 on Figure 10a). Fracture of triblock gel subjected to simple-shear has been related to the strain-localization or non-homogeneous strain field (89). Note that the strain value for fracture was very close to the maximum strain value corresponding to the maximum chain extensibility.

175

Figure 10. Linear and non-linear viscoelastic responses of a 5 vol% gel consisting of A9B53A9 polymer in 2-ethyl-1-hexanol. (a) The symbols are G′1 and G″1 estimated by the rheometer software. The solid line is e1, predicted from Gent model (Eq. 9) considering maximum stretch ratio (λm) of 3.8. (b) Closed symbols are the third Chebyshev coefficients (e3) estimated from experimental data and the solid line is the prediction of Gent model (Eq. 10). (c) Lissajous-Bowditch curves as a function of strain. Adapted with permission from Ref. (5).. Copyright 2015 Royal Society of Chemistry. (see color insert) Although a strain-stiffening behavior was observed for this gel, no negative normal stress was observed in dynamic shear-oscillation (Figure 11) (109). For parallel-plate or cone-plate geometries, the normal stress is estimated as σN = 2Fz/ πR2, where R is the radius of the plate, and Fz is the normal force measured by the rheometer (83). For parallel -plate, σN = N1 – N2 , where, N1 is the primary normal (N1 = σθθ – σzz) and N2 is the secondary normal stress difference (N2 = σzz − σrr). The magnitude of N2 is often smaller than that of N1.83 In comparison, an alginate gel, which also displays strain-stiffening behavior, exhibits negative normal stress. For semi-flexible polymer gels, strain-stiffening behavior and negative normal stress appear in tandem (79, 110). Such behavior has not been observed for the triblock gels likely because of flexible nature of the mid-block chain. 176

Figure 11. Shear stress and corresponding normal stress as a function of time during an oscillatory shear experiment for 5 vol% gel consisting of A9B53A9 polymer in 2-ethyl-1-hexanol (a); (b) for an alginate gel with alginate concentration is 10 mg/mL and [Ca2+] ≈ 12.5 mM. Applied frequency was 0.5 rad/s both sample, For triblock gel, the applied strain amplitudes was 150%, whereas, for alginate gel the strain amplitude was 30%. A parallel plate geometry was used. Adapted with permission from Ref. (109). Copyright 2016 Wiley.

G′1 and G″1 as a function frequency are shown in Figure 12. G′1 values were found to be much higher than that of G″1 over the frequency-range investigated here. G′1 also had a very week frequency-dependency, and such dependency decreased with temperature (22 vs 6 °C). Both these observations are typical of gel-like materials (31). Changes in the stress-strain responses with increasing frequency and strain amplitude provide us some interesting insights. Figure 13 displays the stressstrain plots as the frequency (ω) was increased from 1 rad/s to 30 rad/s and strain amplitude (γ0) increased from 10 % to 200 %. For each curve, the corresponding 177

e3 and G′1 values are shown. As expected, in the linear viscoelastic region, the e3 values were zero at small strain and became slightly positive at a higher frequency. However, with increasing frequency and strain amplitude, a significant increase in e3 (as high as 3 times) was observed. This indicates that the strain-stiffening response became further important with increasing frequency. It is anticipated that at high frequencies there would not be enough time for the exchange of PMMA end-blocks in and out of the aggregates and the mid-block stretching at large-strain had been manifested by the enhancement of strain-stiffening behavior.

Figure 12. G′1 and G″1 as a function of frequency for a 5 vol% gel consisting of A9B53A9 polymer in 2-ethyl-1-hexanol at (a) 6°C and (b) 22°C. Adapted with permission from Ref. (5). Copyright 2015 RSC.

Effect of GNPs on the strain-stiffening behavior has been investigated and the results are shown in Figure 14. The strain-stiffening behavior was observed for the pristine and graphene containing gels at 22 °C and 6 °C. At 6 °C, the difference between G′ and G″ was relatively independent of the concentration of graphene, whereas, at 22 °C the G′ and G″ were slightly different for different graphene concentration. These results were similar to that presented in temperature sweep data (Figure 9), in which it has been shown that below 10 °C, moduli for both pristine and graphene containing gels were similar, likely due to the completion of self-assembly process at that temperature. Also, GNPs had no effect on the onset of the nonlinear elastic behavior at these two temperatures, as the strain-stiffening behavior became important beyond the strain value of ≈100%. 178

Figure 13. Lissajous-Bowditch curves as a function of frequency and strain amplitude for a 5 vol% gel consisting of A9B53A9 polymer in 2-ethyl-1-hexanol. Red dashed lines represent the pure elastic stress responses of the gel. The e3 and G′1 values are indicated for each oscillatory test. Reproduced with permission from Ref. (5). Copyright 2015 RSC.

179

Figure 14. G′ and G″ as a function of strain amplitude for a 5 vol% gel consisting of A9B53A9 polymer in 2-ethyl-1-hexanol with and without GNPs at (a) 22 °C and (b) 6 °C. The applied frequency was 1 rad/s. Adapted with permission from Ref. (4). Copyright 2015 RSC.

Relaxation Behavior The relaxation behavior of both pristine and GNPs containing gels was studied over a temperature range of 6 °C to 25 °C to achieve further understanding of the self-assembly process (4). Here, a step strain of 5%, which falls within the linear viscoelastic region was applied and the evolution of time-dependent modulus G(t) as a function of time was captured (Figure 15). The decrease in G(t) with time represented the relaxation of samples with time. For samples far away from the gelation temperature, the relaxation process was slower than that near the gelation temperature, where the sample was more viscoelastic. For the physical gels, the stress relaxation process involves end-blocks pull-out of the aggregates, and exchange between the neighboring aggregates. Hence, both temperature and graphene platelets can alter the relaxation process. 180

A stretched exponential function has been used to fit the stress-relaxation data. This model is given as (4, 31, 111):

Here, is the shear modulus at time zero, τ is the relaxation time, and β is the stretching exponent. β =1 represents the Maxwell model, whereas, fractional value of β represents a distribution of relaxation time.

Figure 15. Stress relaxation of pristine gels (a) and gels with 0.12 mg/mL GNPs (b) over a temperature range of 6 to 25 °C. 5 vol% polymer (A9B53A9) was used in these gels. The symbols are experimental data, whereas the lines are model fitting (Eq.5). Aadapted with permission from Ref. (4). Copyright 2015 RSC. (see color insert) The stretched-exponential function captures the relaxation data reasonably well. The G0, τ, and β values for the samples without and with graphene at various temperatures are shown in Table 3. At lower temperature, chain pull-out or exchange from the less swollen aggregates was slower than that from the more swollen aggregates at higher temperatures. As a result, the relaxation time increased significantly with decreasing temperature for both these gels. The β has been found to be in the range of 0.2 – 0.3. These results are slightly different than that obtained for β = 0.33 by Erk and Douglas for a pristine gel (111). The results obtained here are similar to β = 0.2 by Hotta et al. for a triblock gel consists of polystyrene-polyisoprene-polystyrene (112). Interestingly, Drzal and Shull obtained β = 0.53 for PMMa-PtBA-PMMA gel (36). The differences are likely related to the different instruments and experimental protocols used in different studies. Both these gels display a similar trend in the stress-relaxation behavior. However, at a lower experimental temperature such as at 15 °C and 20 °C, the τ values for the graphene-containing gels were slightly lower than the pristine gels. The difference in response at 25 °C, was likely due to the liquid-like behavior of the graphene-containing samples at that temperature. 181

Table 3. Fitted Parameters for Stress-Relaxation Data Shown in Figure 15 for the Pristine Gel (a) and for the Gel with Graphene Concentration of 0.12 mg/mL (b) a)

b)

T

G0 (Pa)

τ (s)

β

T

G0 (Pa)

τ (s)

β

6 °C

202± 11

223±33

0.23

6 °C

218± 7

198±3

0.27

10 °C

196±8

20±34

0.22

10 °C

186±20

60±14

0.29

15 °C

175±12

21±6

0.23

15 °C

161±10

15±6

0.27

20 °C

135±12

7±2

0.25

20 °C

119±15

3±2

0.27

25 °C

78±15

4±2

0.3

Figure 16. Creep compliance for a 5 vol% gel 5 vol% gel consisting of A9B53A9 polymer in 2-ethyl-1-hexanol . Adapted with permission from Ref. (4). Copyright 2015 RSC.

Creep experiments have also been conducted on these samples with a constant applied stress of 100 Pa. The creep compliance data for a pristine gel is shown in Figure 16. A distinct creep-ringing was observed initially and that faded out gradually. A stretched exponential function can be reasonably used to the longterm creep compliance data (t > 5 s), i.e., beyond the creep-ringing. The fitted values for τ, and β are similar to the ones from the fitting of stress-relaxation data (Table 3). 182

Modeling Stress-Strain Behavior Dynamic rheology data captures the mechanical properties of triblock gels. The results are then fitted different constitutive models such as Gent model, Fung model, etc. (5, 37) Here, results are shown for Gent model, which considers the finite chain extensibility (5).

Gent Model For elastic materials, strain energy density functions (W) relates the strain energy density of a material to the deformation gradient (1, 107, 113). For Gent model, W can be presented as (1, 107):

Where, E is Young’s modulus, J1 = λ12 + λ22 + λ32 – 3 (λis are the extension ratios in the principal stretch directions), Jm corresponds to the maximum extensibility or maximum chain extension, λm, Glin is the linear elastic modulus and is equal to E/3 for Poisson’s ratio = 0.5. If λm →∞, Jm →∞, i.e., if the chain extensibility approaching infinity, the Gent model approaches the neo-Hookean model (1, 107). Since the elastic modulus of the triblock gel was much higher than the viscous modulus, the viscous dissipation can be considered to be negligible. Therefore, the elastic shear stress is then approximately equal to the total stress (τelastic ≈ τ). In that case, Glin is equal to the first-harmonic storage modulus in the linear viscoelastic region. In a general term, the shear stress as a function of shear strain can be written as (92):

Where γ is the shear strain and f(γ) represents the functional dependence of shear modulus as a function of γ. At small strain, f(γ) approaches Glin. For simpleshear experiments, shear strain (γ) and extension ratio (λ) is related as γ = λ - 1/λ. For the Gent model:

Here, shear stress was obtained by taking the derivative of the strain energy function with respect to strain (Eq. 6) (1, 107). It has been shown that (92)

183

Using these relationships, the e1 and e3 for the Gent model can be presented as:

Note that the third-order Chebyshev coefficient for Gent model is always a positive number, predicting a strain stiffening behavior. The summation of e1 and e3 is equal to f(γ) in Eq. 8. The Eqs. 9, 10 were fitted to the experimental data and are shown in Figures 10a and 10b. The maximum extension ratio for the 5 vol% copolymer gel was estimated based on the scattering data (24, 25, 37). The fully stretched length of the PnBA mid-blocks with the molecular weight 53,000 g/ mol has been estimated as ≈ 105 nm and the unstretched length obtained from the scattering data is ≈ 28 nm. This gives maximum extensibility, λm ≈ 3.8, which was used to fit the data. As presented in Figure 10, the model captured the experimental data reasonably well. As shown in the Eqs. 9 and 10, the coefficient, e3 captures the non-linear response of the gel, whereas, e1 has both linear and nonlinear contributions.

Investigation of Mechanical Properties Using Cavitation Rheology Cavitation phenomena, caused by elastic instability, is observed in pressure sensitive adhesives during the peeling-off process, and in biological materials such as in human brain subjected to a shock wave (114, 115). This phenomenon has been harnessed in developing cavitation rheology technique towards investigating local mechanical properties of soft solids (5–7, 95–103). Schematic of a cavitation set-up is shown in Figure 17a, in which a needle is inserted at any arbitrary location within the gel. As the needle radius can be varied, using this technique the gel deformation behavior can be investigated over a length scale of ~ 10 µm to 1000 µm. This technique has been used to investigate the mechanical properties of triblock copolymer gels with different volume fractions and at two different temperatures. Effect of polymer volume fraction: The pressure vs time response obtained in cavitation experiments for three gels with polymer (A9B53A9) volume fractions (φ) of 0.05, 0.07, and 0.10, respectively. With pressurization, the system pressure increased to a maximum pressure, also defined as a critical pressure, Pc, before a rapid drop of pressure took place (Figure 17b). Pc values increased with increasing polymer volume fraction, i.e., with increasing modulus. Gel deformation at the tip 184

of the needle at the critical pressure and beyond the critical pressure are shown in Figures 17c-e. For φ≈0.05 and 0.07, a rapid spherical cavity growth at Pc was observed, whereas, a fracture like behavior was observed for φ≈0.1. With sudden increases in cavity volume or fracture like process, a decrease in system-pressure was observed. If the expansion ratio or stretch ratio is defined as λ = (Ac/Ac0)½, where, Ac is the surface area of the cavity at any instance and Ac0 is the inner cross-sectional area of the needle (the initial area), λ was found to be as high as 15. The maximum stretchability of the PnBA chains considered here has been shown to be ≈ 3.8. This indicates that during the cavity growth process the PnBA chains most likely have been pulled out of the PMMA aggregates.

Figure 17. Cavitation rheology experiments. (a) Schematic of the experimental set-up. (b) Pressure as a function of time for three polymer (A9B53A9) volume fractions, φ = 0.05, 0.07, and 0.10. (c-e) Photomicrographs of cavity growth at and after the critical pressure for (c) φ = 0.05, (d) φ = 0.07, (e) φ = 0.10. Needle radius, rs = 156 µm. Experimental temperature was 22 °C. Adapted with permission from Ref. (5). Copyright 2015 RSC. 185

Effect of Compression/Pumping Rate Mechanical response of a viscoelastic material depends on the applied strainrate. Cavitation experiments were conducted at different pumping/compression rates (μ) directly related to the different strain-rate gel deformation at the needletip. Pumping rate was varied from 0.01 to 25 mL/min. For a polymer volume fraction of φ = 0.05, Pc for μ = 0.01 mL/min was 850±50 Pa, which was lower than 1500±100 Pa observed for μ = 0.5 mL/min. Pc did not change significantly beyond that pumping rate. This difference in Pc resembled the weak frequency dependence observed in frequency sweep data (Figure 12).

Effect of Temperature To investigate the temperature dependence of cavitation process, experiments were conducted by cooling the sample in an ice bath corresponding to the sample temperature of ≈ 6 °C. Results for 6 and 22 °C for φ = 0.05 have been compared. As shown in Figure 12, G′ increased with decreasing temperature from 22 °C to 6 °C. Similarly, increase in Pc has also been observed. However, the increase in G′ was about two times, in comparison to 1.5 times increase in the Pc.

Model Prediction for Pressure Responses The pressure vs. time responses presented above can be captured analytically approach and finite-element model (FEM). In addition to Gent model, which captures the rheological data for triblock copolymer gels, the neo-Hookean model has also been considered. To obtain pressure response analytically, cavitation phenomena has been approximated as the growth of a spherical cap at the needle-tip. Here, the pressure at any instance can be given by, P =ΓdA/dV +σ (97), where Γ is the surface energy, σ is the mechanical stress the gel at the needle-tip is subjected to. A and V are the surface area and volume of the cap, respectively. The stress σ can be estimated based on various strain energy functions. For Gent strain energy function the critical pressure for cavitation (97, 107):

For neo-Hookean solid, i.e., for Jm → ∞, the critical pressure for cavitation is given by (97, 108, 109):

186

For neo-Hookean solid analytically it has been shown that

or in dimensionless form

In Eq 13b, the is defined as the elastocapillary number or ECN. The first term of the equation 13a represents the elastic contribution of the gel resisting the cavity growth and the second term represents the surface energy contribution, necessary to overcome the increasing surface area during cavity growth. As shown by Gent, for a cavity growth in dry rubber, where the surface tension is negligible, . Such relationship is also obtained for very small values ECNs (Eq 13b), that can be obtained, for example, if rs is large. FEM has been used to investigate cavitation phenomena for a neo-Hoookean solid (108). FEM results and that obtained for the analytical method are compared in Figure 18. Simulations have been conducted over a range of ECN = 0 to 100, capturing the cases without any surface tension to a significant surface tension present, respectively. In these simulations, pressure was increased in a step-wise manner, in pressure-control mode. FEM could only capture the deformation up to the maximum pressure but not beyond that. The maximum pressure, which was same as Pc for this case, was about 0.4E higher than that obtained from analytical prediction. A similar increase has also been observed by Hutchens and Crosby (99). Therefore, the needle has an effect on the critical pressure likely due to the stress concentration at the needle corner. The cavity shapes at the maximum pressure for different ECNs are shown in Figure 18b (108). No significant change in cavity shape has been observed although the pressure magnitude increased significantly. For ECN =0, no pressure maximum was observed, rather the pressure asymptotically reached a critical pressure. In this case, the pinning of the cavity at the needle tip has been observed. Figure 18c summarizes Pc and λc as a function of ECN. Note that λc was small at the critical pressure, except for the case where ECN is very small. Although a slight increase in critical pressure was observed for the presence of needle, such increase was not significant with respect to the contribution of the surface tension effect. The above equation captures the maximum or critical pressure, but not the pressure evolution. However, using the Eqs. 11, 12 and considering the closed volume confined by the syringe plunger and the gel at the tip of the needle filled with an ideal gas, and no diffusion of air into the gel during pressurizing, the following equations can be obtained (5, 108). For neo-Hookean solid:

187

For Gent gel:

where, P0 and the V0 represent the initial system pressure and system volume, respectively. µ is the pumping rate and t is the time. By solving the above equations for each time step, pressure vs time response can be obtained, as discussed in Ref (5). The results are summarized in Figure 19 displaying the pressure and extension/stretch ratio (λ) as a function of time for neo-Hookean and Gent gels (5). In the neo-Hookean gel, pressure increases to a critical (maximum) pressure followed by a rapid drop in pressure. λ increases slowly initially until a certain jump at the critical point (λc = 1.4) caused by elastic instability. For neo-Hookean gels, λm→∞ and the cavity volume can increase without any bound. This rapid increase in cavity volume or snap-through expansion results in a sudden drop of pressure. This phenomenon is defined as the cavitation phenomena. For Gent gels, because of finite chain extensibility (λm ≈3.8, for the present case), the increase of cavity volume is restricted at the instability point. As a result, the decrease in pressure is small at the instability point. The pressure continues to rise beyond that instability point with increasing compression. Both neo-Hookean and Gent models predict the similar response up to the critical pressure, but the polymer chain extensibility dictates whether a snap-through expansion is expected. In fact, cavitation in Gent gels is possible, if λm is very large. The increase of pressure in Gent gel cannot be unrestricted as the failure or fracture of the gel takes place beyond a certain pressure. Cavitation or snap-through expansion was observed for triblock gels, although the chain extensibility has been considered to be equal to of 3.8. Therefore, the cavity growth observed here likely involved the fracture process, where the chains were pulled out of the aggregates. The critical pressure corresponding to fracture is a function of elastic modulus, needle radius, and critical energy release rate (Gc) (5, 85, 97). For a first order approximation, if a linear elastic material is considered, the critical pressure for fracture scales as (5, 85, 97). For Gent gels, such functional relationship is not precisely known. This equation predicts Gc ~ 0.1 J/m2. This value is of the same order obtained by Seitz et al. for triblock gels (88). Further theoretical and computational studies are necessary to obtain a quantitative relationship between the critical pressure and the materials parameters of the gels.

188

Figure 18. Comparison of simulation and analytical results for a neo-Hookean solid. (a) Normalized pressure vs stretch ratio for different ECNs. Solid lines display the analytical prediction (Eq. 13b) and the symbols represent the FEA results. (b) Cavity shape at the maximum pressure obtained from FEA. For ECN = 0, cavity shape is plotted for λ= 4. (c) The critical pressure, Pc, and critical stretch, λc, plotted as a function of ECN. Adapted with permission from Ref. (108). Copyright Elsevier 2018. (see color insert)

189

Figure 19. Predicted pressure and extension ratio (λ) as a function of time for (a) a neo-Hookean gel with λm → ∞; (b) for a Gent gel with λm = 3.8; (c) the zoomed-in view of (b). Adapted with permission from Ref. (5). Copyright 2015 RSC.

Concluding Remarks and Future Directions Here, we have reported the structural evolution, and mechanical properties of a thermoreversible, triblock copolymer gel consisting of PMMA-PnBA-PMMA in mid-block selective solvents. The self-assembly process has been altered by adding GNPs, and such has been manifested by a decrease in gelation temperature. The gel displays strain-stiffening behavior and such behavior has been captured using a Gent constitutive equation with finite chain extensibility. Although a major understanding has been achieved in this gel system, many questions still need to be addressed. Based on the present literature, no other self-assembled triblock copolymer gels display strain-stiffening behavior, similar to the biological network. Interestingly, in most of these gels, the mid-block molecular weight is larger than the entanglement molecular weight. Therefore, a systematic study with the varying molecular weight of the blocks will provide further insights into the mechanical properties of these gels. Simulation studies indicate that that the size and the number of aggregates change with the applied frequency and strain (116, 117), however, the results from the experimental investigations are not conclusive (25). The fracture process of these gels needs to be further investigated, as this process is influenced by many factors such as the block-length, solvent quality, the strength of association, time and length scale associated with the gelation process. As graphene nanoplatelets have been successfully incorporated in these gels, these gels can be rendered responsive subjected to an electrical field. Such behavior can lead to new applications of these gels.

Acknowledgments The authors gratefully acknowledge the financial support from National Science Foundation through CAREER Award [DMR 1352572], and EPSCoRTrackII funding [IIA-1430364]. We also acknowledge supports from Mississippi State University. 190

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Chapter 10

Mechanics of Disordered Fiber Networks Xiaoming Mao* Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109, United States *E-mail: [email protected].

Disordered network models of fibers tied together by crosslinks capture the essential structure of many materials in nature, such as the cytoskeleton and the extracellular matrix as networks of biopolymers, and manmade materials such as paper and felt. In this chapter, we discuss fundamentals of mechanical properties of disordered fiber networks. A basic concept we introduce is the central-force isostatic point, where in the limit of ignoring fiber bending stiffness, the network is on the verge of mechanical instability. Networks with connectivity lower than this point are bending dominated when they are deformed, whereas dense networks with connectivity above this point are stretching dominated. Using this concept, we explain phase diagrams of linear elasticity of fiber networks, strain stiffening in the nonlinear elasticity regime, as well as unusual fracturing processes of these fiber networks.

Introduction Fiber networks are disordered networks composed of long fibers and crosslinks that tie the fibers together (Figure 1a). This simple conceptual model of fiber networks captures the essential structure of a wide collection of materials in nature, including various biopolymer network gels in the cytoskeleton and the extracellular matrix (1–4) (Figure 1b), and manmade materials, such as felt, paper, and buckypaper which shares a similar structure with regular paper but consist of carbon nanotubes instead of cellulose fibers (5). Many different types of gels, such as colloidal gels consisting three dimensional dilute networks of colloidal particles, hydrogels which are polymer networks swelled by water, and © 2018 American Chemical Society

aerogels composed of porous solid nanostructures with numerous air pockets, all share fibrous nature in their microscopic structure, and could be characterized as fiber networks.

Figure 1. Mechanics of fiber networks. (a) An illustration of the fiber networks model consisting long fibers tied by crosslinks. (b) Confocal reflectance image of collagen network (green) as an example of fiber network material. Three cancer cells (red) pull on the collagen network, driving it into nonlinear elasticity regime. Scale bar 20μm Adapted with permission from ref. (6). Copyright 2017 Springer Nature. (c) Storage (G′) and loss (G″) shear modulus of various fiber network gels as functions of shear strain γ showing strain stiffening. Adapted with permission from ref. (1). Copyright 2005 Springer Nature. (d) Storage modulus as a function of strain for collagen gels at different collagen concentration. Adapted with permission from ref. (2). Copyright 2009 PLOS. (see color insert)

Fiber networks display intriguing mechanical properties. A rather universal phenomenon among many fiber networks is “strain stiffening”, which means under shear strain, the shear modulus of the network greatly increases, often by more than an order of magnitude, before the network fails (Figure 1c). Even in the linear elasticity regime, shear modulus of fiber networks can also change very sensitively to parameters such as fiber density (Figure 1d). Such huge change of shear modulus as control parameters change indicates that there is a mechanical critical point underlying this phenomenon. In this chapter we will discuss this mechanical critical point, named “central-force isostatic point” (CFIP), and its profound implications to the elasticity of various fiber networks. 200

In Sec. 2 we introduce foundations of mechanics of fiber networks, the CFIP, and discuss its implications in the linear elasticity regime. In Sec. 3 we discuss implications of the CFIP for nonlinear elasticity, and In Sec. 4 we discuss interesting behaviors of these fiber networks when they fail under pressure, where the CFIP plays an important role again.

Maxwell Counting and Linear Elasticity of Fiber Networks To elucidate mechanics of fiber networks, let us start by considering a minimal model, where details of the actual fibers and crosslinks are ignored, and we focus on the essential physics of the mechanical properties of the network. In this minimal model, we have Nfiber fibers which are modelled as straight slender elastic rods. Each fiber i has ni crosslinks on it, which are modelled as free hinges connecting fiber i with other fibers. These crosslinks make sure the fibers cross but post no constraints on their rotation. The Hamiltonian of this minimal fiber network model can then be written as

where the first term is the stretching energy and the second term is the bending energy of the fibers. In the first term, is the position of crosslink m on fiber i, li,m and μi,m are the rest length and the stretching stiffness of segment m (defined as the segment between crosslinks m and m + 1 on fiber i. In the second term, the sum rums over all inner crosslinks on each fiber. θi,m is the bending angle of fiber i at crosslink m. Here we have discretized the bending energy of the fibers such that the fiber segments are straight between neighboring crosslinks and bend at finite angles at each crosslink. In Mao et al (7) we have carefully discussed this approximation from the full continuous bending energy of the fibers as elastic rods. Because fibers are long slender rods, it is straightforward to see that it’s much easier to bend than to stretch them, so (here we refer to general segments so we dropped the subscripts i, m). It is thus very interesting to consider the where the system becomes a central-force (CF) network. limit of “Central force” means that the Hamiltonian only depends on the distances between the crosslinks [keeping only the first term in Eq.(1)]. An example of taking this limit is shown in Figure 2a. 201

Mechanics of CF networks has been extensively studied since J. C. Maxwell, who wrote down the equation for the number of zero modes (normal modes of zero energy) of a CF network

where N is the number of sites (corresponding to crosslinks in the fiber network), d is the spatial dimension which gives the number of degrees of freedom per site as a point particle in d dimensions, and Nb is the number of bonds (corresponding to fiber segments in the fiber network model). This equation relates the number of zero modes of a CF network to the “unconstrained” degrees of freedom, and this follows directly from normal mode analysis of the equations of motion of the network (8). Maxwell’s counting rule [Eq.(2)] leads to a simple equation for the verge of mechanical instability in CF networks

where ázñ is the mean coordination number of the sites (mean number of arms from a site). This follows from Eq.(2) by considering degrees of freedom and averaged number of constraints per site. In general, when ázñ < 2d the CF network has more constraints than degrees of freedom and is stable, whereas when ázñ < 2d there must be zero modes. The special point where ázñ = 2d marks a mechanical critical point of a CF network separating stable and unstable phases, and is thus called the central-force isostatic point (CFIP) (9–12). Networks in the CF limit with ázñ < 2d are in general floppy and have vanishing elastic moduli. Interestingly, when we turn bending stiffness of the fibers, κ, back on, network elastic moduli are restored, because the zero modes bend the fibers and will now cost bending elastic energy. This regime is thus called “bending dominated.” Of course, the resulting elastic moduli in this regime are proportional to the fiber bending stiffness, G~κ and much smaller than elastic moduli of networks with ázñ > 2d (the “stretching dominated” regime), which is proportional to stretch stiffness of the fibers, G~μ. Mechanical phase transitions at the CFIP has been studied from the 1980s in the literature of glass transitions (10, 14–16). More recently this concept has been applied to understand fiber networks with bending stiffness (7, 9, 13, 17). Fiber network models based on diluted periodic lattices have been used to analytically study this mechanical critical point via effective medium theory. With good agreement between the effective medium theory and numerical simulations, phase diagrams were obtained for these fiber networks, as shown in Figure 2 b-e.

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Figure 2. The central force isostatic point and phase diagrams for fiber networks linear elasticity. (a) Mapping a fiber network to a CF network with the same geometry by turning off the bending stiffness. (b) An example of a diluted triangular lattice under shear deformation. Color shows deviation from affine (i.e. uniform) deformation: blue for small deviation and red for large nonaffine (non-uniform) deformations. (c) Linear elasticity phase diagram for lattice in (b). (d) An example of a diluted kagome lattice, the phase diagram of which is shown in (e). Note axes in (c) and (e) are related to one another by a 90° rotation. (b-c) Adapted with permission from ref. (9). Copyright 2011 Springer Nature. (d-e) Adapted with permission from ref. (13). Copyright 2013 American Physical Society. Labels in the phase diagram have been modified to follow the notation of this chapter. (see color insert) In particular, two types of two-dimensional lattices, the triangular (18) and the kagome lattices have been used. The main difference between these two lattices is that the maximum coordination number (the coordination number of the undiluted lattice), zm is zm = 6 > 2d for the triangular lattice (Figure 2 b-c) and zm = 4 = 2d for the kagome lattice (Figure 2 d-e). Bonds in the lattices are randomly removed with probability 1 − p so the mean coordination number is ázñ = pzm for a network. 203

This difference in zm makes a big difference in the resulting phase diagrams of the two types of lattices. For the triangular lattice the CFIP is a continuous transition in the middle of the ázñ axis, giving rise to a critical regime where bending and stretching effects are coupled in shear deformations (7, 9). On the other hand, for the kagome lattice, the CFIP is the maximum of ázñ (corresponding to p = 1) and features a discontinuous transition (13). For both lattices, there is also a rigidity transition at lower coordination zb = pbzm where fiber networks with κ > 0 loses rigidity. These two lattices show very similar behaviors in their bending dominated regimes, and can both be used to describe diluted fiber networks. The triangular lattice model has the extra regime where ázñ > 2d which can be applied to networks where crosslinks can tie more than two fibers together. In Broedersz et al (9), a three-dimensional diluted face-center cubic lattice was also studied, which displays a phase diagram similar to the triangular lattice. Besides these lattices, off-lattice disordered fiber networks models, such as the Mikado model, has also been extensively used in the literature to study mechanics of fiber networks (19, 20). Now let’s consider implications of the results from these diluted lattice models to real fiber networks. First, if the crosslinks in the network ties only two fibers together (which is the case for most fiber networks), we have zm = 4 which = 2d in two dimensions and < 2d in three dimensions. This puts these networks almost always in the bending dominated regime, where G~κ and the network is very soft in the linear elasticity regime. Second, in many experiments the control parameter is the fiber concentration (e.g., in Figure 1d). As analyzed in Sharma et al (21), the fiber concentration controls both the mesh size of the network and the bending stiffness of the fibers. For a fiber network in the bending dominated regime close to the CFIP, the shear modulus is very sensitive to the change of these parameters. This explains why the linear shear modulus of fiber networks displays big spreads at different fiber concentrations (Figure 1d).

Nonlinear Elasticity of Fiber Networks As we mentioned in the introduction, strain stiffening, i.e., shear modulus increases as strain increases in the nonlinear elasticity regime, is a ubiquitous phenomenon in most fiber networks (1). There are two main causes for strain stiffening. First, as discussed in Storm et al and Mackintosh et al (1, 22), fiber networks are often in a thermal environment and fiber segments experience thermal undulations. In other words, the equilibrium state we consider should be a state where fiber segments have excess length for thermal fluctuations. When the network is under strain, these fibers are being stretched. In the first stage, the thermal undulations are being stretched, and the shear modulus is controlled by entropic elasticity, G~kBT which is small (similar to rubber elasticity). As the strain progress, thermal undulations are stretched out and the fiber segments become straight. Any further strain will stretch the fibers directly, so the shear modulus is controlled by the stretching modulus G~μ which is much larger. 204

Figure 3. Strain stiffening of fiber networks. (a) An illustration of soft bending modes being exhausted by shear deformation and any further deformation will stretch fibers. Red dashed lines show fiber segments becoming aligned with the strain. Adapted with permission from ref. (25). Copyright 2015 American Physical Society. (b) Three-dimensional phase diagram for the diluted triangular lattice model in the space of probability of each bond to be present, p (which relates to network connectivity through ázñ zmp), bending stiffness κ and shear strain γ. The p − κ plane is the same as the linear elasticity phase diagram as shown in Figure 2, and the γ axis represents nonlinear strain. The yellow dot denotes the CFIP. As strain increases, bending dominated networks enters the nonlinear regime and eventually become stretching dominated (26). In the limit of κ = 0, the bending-dominated to nonlinear crossover becomes a continuous transition with a line of critical points (red solid curve starting from the CFIP), as pointed out in Sharma et al. (21) Point Ω represents κ = γ = 0 and p = pb (defined in the previous section). (c) Similar phase diagram for the kagome lattice, where the CFIP is at p = 1 and there is no critical regime. (b-c). Adapted with permission from ref. (26). Copyright 2016 Royal Society of Chemistry. (see color insert)

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The second cause, as first discussed in Onck et al and Wyart et al (23, 24), is an athermal scenario based on the geometry of the network. As the strain increases, bending modes become “exhausted” and fibers are becoming stretched so the shear modulus changes from G~κ to G~μ and greatly increases (see illustration of this effect in Figure 3a). The second scenario is easy to understand from the linear elasticity phase diagrams we discussed in the previous section: if a network start in the linear regime as bending dominated (because they have ázñ < 2d and small bending stiffness), they can crossover to stretching dominated in the nonlinear regime. Which of the two scenarios applies for a real fiber network depends on the network itself. One simple quantity to consider is the persistence length of the fibers in the network, lp which characterizes the length scale under which the fiber stays straight under thermal fluctuations. If the persistence length is much smaller than the mesh size, strong thermal undulations are present on fiber segments. In the linear elasticity regime, the network is soft due to both thermal undulations and bending modes, and in the nonlinear regime, both of these two effects need to be exhausted before the network enters the stretching dominated regime and shear modulus increases. On the other hand, if fiber segments are essentially straight between crosslinks, and strain stiffening is mainly caused by bending to stretching crossover. It is instructive to carefully investigate this strain-induced bending-tostretching crossover using the diluted lattice models again, which are convenient for theory and simulation (21, 25–27). Nonlinear elasticity of these lattice models (which captures essential physics of fiber networks) are characterized by the phase diagrams in Figure 3. In particular, the triangular lattice where the CFIP is a continuous transition displays a nonlinear regime between bending and stretching dominated regimes, whereas the kagome lattice does not. Moreover, in the limit of κ = 0, the lattices are completely floppy below the CFIP, and as strain increases, stiffness emerge as a continuous phase transition, as pointed out in Sharma et al. (21) Strain stiffening in fiber networks studied here shares a lot of similarities with nonlinear elasticity of colloidal gels (28). Another feature related to strain stiffening in fiber networks is the alignment of fibers in the strain direction (Figure 3a) as the bending modes are being exhausted. This alignment can be described be a nematic like order parameter as discussed in Vader et al and Feng et al (2, 25) and plays an important role in guiding cell motion in the extracellular matrix, a phenomena called “contact guidance” (2, 29–31).

Fracturing of Fiber Networks The interesting nonlinear elasticity of fiber networks governed by the crossover from bending to stretching dominated regimes, as discussed in the previous section, implies unusual phenomena when these networks fail under pressure.

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Figure 4. Fracturing of fiber networks. (a) Stress concentration near crack tips in dense fiber networks above the CFIP (using the diluted triangular lattice model), with the resulting Griffith crack shown in (b). (c) and (d) show force chains and distributed damage in dilute fiber networks below the CFIP. Bonds are colored according to force; broken bonds are also marked. Bonds with a larger force are thicker. Adapted with permission from ref. (32). Copyright 2017 American Physical Society. (see color insert)

Failure of conventional brittle materials is characterized by a long, straight crack, a phenomena called “crack nucleation”, due to stress focusing effect at crack tips, as explained by A. A. Griffith in 1921 (33). Surprisingly, it is found that fiber networks below the CFIP displays very different phenomena, where cracks do not nucleate and damages are distributed over a divergent length scale, even though microscopic breaking events of fiber segments are set to be brittle (32). The origin of this interesting phenomenon is the mechanism of how rigidity emerge as strain increases in these fiber networks. Let us first consider the CF network (κ = 0)), which has no rigidity (G = 0) below the CFIP. In a numerical 207

study in Zhange et al (32), a diluted triangular lattice model was used, and it is observed that as strain increases beyond a critical value γc (red line in Figure 3 b-c) the network starts to have rigidity as force chains emerge which bear stress. which means it will break If each fiber segment has an extension threshold when it is extended beyond (1 + λ) of its original length, fibers in the force chain will break first. Interestingly, after the first force chains break, new force chains will emerge, and their locations are not correlated with the previous ones. Thus, the network enters a “steady state” where new force chains replaces broken ones, and the damage is distributed over the whole sample with no crack nucleation, as shown in Figure 4. This phenomenon occurs for all fiber networks below the CFIP. On the other hand, for networks above the CFIP, crack nucleates at a length scale, which only diverge as the network approaches the CFIP from above (34). When a small bending stiffness κ is added, this phenomenon of distributed damage in fiber networks remains true, because the origin of this phenomenon, the steady state where force chains emerge-break-emerge, is robust against the addition of bending stiffness. It is only when the bending stiffness becomes comparable to the stretching stiffness, the network will enter the linear stretching dominated regime, and the Griffith scenario of stress focusing and crack nucleation is recovered (32).

Conclusion and Discussion In this chapter, we reviewed studies of fundamental mechanical properties of disordered fiber networks, which models a wide variety of materials, such as biopolymer gels and manmade porous media. A number of interesting mechanical properties, such as strain-stiffening, sensitive change of elastic moduli as a function of fiber concentration, distributed damage during fracturing process, can emerge from an underlying mechanical critical point, the CFIP, where the network is at the verge of mechanical stability in the central-force limit. Predictions based on the CFIP has been verified in experiments on biopolymer gels (21, 27). The comparison between theoretical predictions based on the CFIP and measured mechanical properties in various types of real gels can help elucidate the structures and mechanics at microscopic length scales of these gels. This also opens the door to a number of intriguing questions for future study, such as the cytoskeleton and the extracellular matrix as active fiber network under driving, as well as the design of mechanical metamaterials with well controlled nonlinear mechanical response and fracturing process (35).

Acknowledgments The author was supported by the National Science Foundation under grant DMR-1609051. 208

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20. Head, D.; Levine, A.; MacKintosh, F. Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks. Phys. Rev. E 2003, 68, 061907. 21. Sharma, A.; Licup, A. J.; Jansen, K. A.; Rens, R.; Sheinman, M.; Koenderink, G. H.; MacKintosh, F. C. Strain-Controlled Criticality Governs the Nonlinear Mechanics of Fibre Networks. Nat. Phys. 2016, 12, 584. 22. Mackintosh, F. C.; Kas, J.; Janmey, P. A. Elasticity of Semiflexible Biopolymer Networks. Phys. Rev. Lett. 1995, 75, 4425–4428. 23. Onck, P. R.; Koeman, T.; van Dillen, T.; van der Giessen, E. Alternative Explanation of Stiffening in Cross-Linked Semiflexible Networks. Phys. Rev. Lett. 2005, 95, 178102. 24. Wyart, M.; Liang, H.; Kabla, A.; Mahadevan, L. Elasticity of Floppy and Stiff Random Networks. Phys. Rev. Lett. 2008, 101, 215501. 25. Feng, J.; Levine, H.; Mao, X.; Sander, L. M. Alignment and Nonlinear Elasticity in Biopolymer Gels. Phys. Rev. E 2015, 91, 7569. 26. Feng, J.; Levine, H.; Mao, X.; Sander, L. M. Nonlinear Elasticity of Disordered Fiber Networks. Soft Matter 2015, 12. 27. Licup, A. J.; Münster, S.; Sharma, A.; Sheinman, M.; Jawerth, L. M.; Fabry, B.; Weitz, D. A.; MacKintosh, F. C. Stress Controls the Mechanics of Collagen Networks. Proc. Natl. Acad. Sci. U.S.A. 2015, 112, 9573. 28. Bouzid, M.; Del Gado, E. Network Topology in Soft Gels: Hardening and Softening Materials. Langmuir 2018, 34, 773–781. 29. Sander, L. M. Alignment Localization in Nonlinear Biological Media. J. Biomech. Eng. 2013, 135, 071006. 30. Riching, K. M.; Cox, B. L.; Salick, M. R.; Pehlke, C.; Riching, A. S.; Ponik, S. M.; Bass, B. R.; Crone, W. C.; Jiang, Y.; Weaver, A. M.; Eliceiri, K. W.; Keely, P. J. 3D Collagen Alignment Limits Protrusions to Enhance Breast Cancer Cell Persistence. Biophys. J. 2014, 107, 2546–2558. 31. Shi, Q.; Ghosh, R. P.; Engelke, H.; Rycroft, C. H.; Cassereau, L.; Sethian, J. A.; Weaver, V. M.; Liphardt, J. T. Rapid Disorganization of Mechanically Interacting Systems of Mammary Acini. Proc. Natl. Acad. Sci. U.S.A. 2014, 111, 658–663. 32. Zhang, L.; Rocklin, D. Z.; Sander, L. M.; Mao, X. Fiber Networks Below the Isostatic Point: Fracture without Stress Concentration. Phys. Rev. Mater. 2017, 1, 052602. 33. Griffith, A. A., VI The Phenomena of Rupture and Flow in Solids. Philos. Trans. R. Soc. London, Ser. A. 1921, 221, 163. 34. Driscoll, M. M.; Chen, B. G.-g.; Beuman, T. H.; Ulrich, S.; Nagel, S. R.; Vitelli, V. The role of rigidity in controlling material failure. Proc. Natl. Acad. Sci. U.S.A. 2016, 113, 10813. 35. Zhou, D.; Zhang, L.; Mao, X. Topological Edge Floppy Modes in Disordered Fiber Networks. Phys. Rev. Lett. 2018, 120, 068003.

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Chapter 11

Elastic Relaxation and Response to Deformation of Soft Gels Mehdi Bouzid1 and Emanuela Del Gado*,2 1LPTMS

- Université Paris Sud - Bâtiment 100 15 rue Georges Clémenceau 91405 Orsay Cedex, France 2Department of Physics and Institute for Soft Matter Synthesis and Metrology, Georgetown University, 37th and O Streets NW, Washington DC 20057, United States *E-mail: [email protected].

Soft amorphous solids such as gels made of particles or small aggregates form in a variety of soft matter systems. The complexity of the large scale organization of the gel network, its elasticity, and the mechanical heterogeneities that can be easily generated during the gel self-assembly have implications for the aging properties of those materials and their strongly nonlinear mechanical response. Here we review our recent work where we used 3D numerical simulations of a microscopic model to investigate how the competition between thermal fluctuations and elastic relaxation can qualitatively change the gel aging and how the network topology fundamentally determines the nonlinear response under shear. The insight gained through the numerical simulations helps us rationalize various experimental observations and identify new routes for material design.

Introduction Self-assembly and aggregation of soft condensed matter (proteins, colloids or polymers) into poorly connected and weakly elastic solids is very common and ubiquitous in nature (1–3). Phase separation, spinodal decomposition as well as externally driven self-assembly or aggregation often lead to gels, which display diverse structural and mechanical features (4–8).

© 2018 American Chemical Society

In most cases, the interaction energies and the size of the aggregating units make these structures quite sensitive to thermal fluctuations, with a rich relaxation dynamics associated to spontaneous and thermally activated processes. In addition to affecting the time evolution, or aging, of the material properties at rest, those dynamical processes interplay with an imposed mechanical load or deformation and may be hence crucial for the mechanical response of this class of solids (5, 9–15). Under deformation, soft gels typically display strongly nonlinear response and their structural complexity allows for a wide variety of different behaviors, ranging from softening to stiffening, ductility and brittleness, all of which have important implications for novel technological applications and smart material design (16, 17). Since a deeper understanding of the structure-mechanics relationship is needed to control material properties and achieve their design, microscopic numerical simulations that do not assume a specific constitutive model but provide space and time resolved insight into dynamical processes from which the overall constitutive behavior emerges have become a major investigation tool, especially in combination with experiments (18). Having recently developed a computational approach that has proven very effective in investigating the mechanics and rheology of complex network structures (which can or cannot restructure under deformation), here we would like to provide an overview of the insight gained, in particular with respect to the aging dynamics of soft gels and to the emergence of the strongly nonlinear response from the gel microstructure.

Computational Approach: Model and Numerical Simulations The idea is to obtain the gel structure via self-assembly of elementary units (particles, small aggregates, fibers…) through effective interactions that contain minimal, but crucial, information of the physical-chemistry of the material of interest. Starting from the self-assembled structures, we have used Molecular Dynamics (MD) and Non-equilibrium Molecular Dynamics (NEMD) type of simulations to analyze the structure and mechanics of large samples at rest or under deformations, and with different types of boundary conditions. Such approach allows for novel, more detailed insight into how the microstructure and the effective interactions among the structural units determine their mechanics and for a full description of the non-linear response (12, 19–22). We have developed a minimal 3D model for colloidal particles gels, considering particles (or small aggregates represented as particles) of diameter a that interact with a short range attraction (combined with a repulsive core) U2(rij), where rij is the distance between particles i and j. In particular for computational efficiency, for U2(rij) we use the form U2(rij) = A((a/r)18 − (1/r)16), where r is the distance rescaled by the particle diameter d, while a and A are dimensionless parameters that control the width and the depth of the potential respectively (19). Once particles start to aggregate, their mechanical contacts can be more complex than the simple geometric contact between two perfect spheres and, in particular, there may be an energy cost associated to rotation of particles 212

around each other in an aggregate made by more than two of them, due to surface interactions more complex than simply described by the short range, spherically symmetric attractive well U2(rij) (23, 24). We include therefore an additional short range repulsion U3(rij, rik, θijk), which depends on the angle between bonds and departing from the same particle i and introduce an angular rigidity to the particle connections. For U3(rij, rik, θijk), we use the computationally convenient form , where B,θ and u are dimensionless parameters that set the range of the angular rigidity and its relative strength with respect to the depth of the attractive well. The radial ensures that U3 vanishes modulation being the Heaviside function) (19). beyond a distance 2d (with The total potential energy of a system of N particles with coordinates is and then computed as used in simulations where we solve the equations of motion for all particles in presence of thermal fluctuations using Langevin dynamics. This potential energy depends parametrically on the five dimensionless quantities mentioned above, which are fixed to the following values: A = 6.27, a = 0.85, B = 67.27, θ = 65° and u = 0.3. Tuning these parameters leads to a variety of mechanically stable porous microstructures. The values chosen here are such that a disordered and thin percolating network starts to self-assemble for low particle volume fractions at ε ≈ 20kBT (19). The diameter d of the particles is determined by the distance at which two particles start to experience the short range repulsion and it is the unit lengthscale used in the simulations, while ε is the unit energy. For computational convenience we solve the Langevin equations of motion with inertia for each particle, with each particle having a unit mass m, but then fix the drag coefficient to obtain an overdamped dynamics, with the time scale associated to oscillations due to inertia and used as time unit. More details about the effective interactions, the parameters and protocols used in the simulations can be found in (12, 19–22, 25). In the simulations, the particle volume fraction φ is estimated as the fraction of the total volume V that is occupied by the N particles φ = πa3/6V and in the following we will mainy discuss (V is the volume of the simulation box). As just mentioned above, the particle spontaneously self-assemble into a disordered, persistent and interconnected network. In the remainder we will mainly refer to simulations performed using particles. In spite of its simplicity, our model gel captures several physical features of real soft gels: the heterogeneity of the gel structure is associated to mechanical inhomogeneities, and the simulations have revealed the coexistence of stiffer regions (where tensile stresses tend to accumulate) with softer domains, where, in presence of thermal fluctuations, most of the structural relaxation occurs (19, 20). In this type of simulations we can solve the many-body dynamics and compute the stresses due to the interparticle interactions through the network, with and without an imposed deformation, using the virial stress tensor in which α, β stand for the cartesian components {x, y, z} (26, 27). Hence we 213

can distinguish the contribution of particles located in different part of the gel structure (e.g., in the network strands or in the branching points) to the stresses. If we restrict the sum to a relatively small portion of the total volume we can compute the local stresses and their spatial distribution. Figure 1 shows a snapshot of a typical gel structure in the model just described, where the network has been colored to distinguish prevalently tensile or compressive contributions to local stresses.

Figure 1. Schematic of the model gel network at rest and at low volume fraction φ = 7%. The structure is represented by showing the inter particle bonds, each bond is represented by a segment and generated when the distance between two particles particles i and j is less than dij ≤ 1.3a, the color indicates the value of the contribution (per particle) to the component σxx of the stress tensor. (see color insert)

Aging and Elastic Relaxation Due to the complexity of gels microstructure and to the structural disorder always present, diffusive processes driven by thermal energy are expected, in general, to lead to slow cooperative motion with a subdiffusive microscopic dynamics, governed by a wide distribution of relaxation times and cooperative in nature. Such phenomena manifest themselves in the slow decay of time correlations in density fluctuations, displacements or structural rearrangements, typically measured in quasi-elastic scattering experiments or in numerical simulations (e.g., molecular or Brownian dynamics), typically slower than exponential and described by a stretched exponential decay with β < 1, akin to the slow dynamics close to a glass transition (28–31). Using the 214

computational approach described above we were able to show that in soft gels the consequences of local bond breaking propagate along the gel network over distances larger than the average mesh size and this long-range correlations are at the origin of the cooperative dynamics reported in the experiments (19, 20). Interstingly enough, time- and space-resolved scattering measurements have also detected, in gels and other soft materials, dynamics faster than exponential (so called compressed exponential dynamics), intermittency and abrupt microstructural changes. Such experiments have raised the question whether the aging may be controlled, instead, by stress relaxation through elastic rebound of parts of the material, after local breakages occur in its structure, challenging the generally accepted paradigm that the relaxation dynamics is always slow and glassy (i.e. similar to microscopic dynamics in supercooled liquids) in these soft materials (4, 32–40). While a mean field theoretical framework invoking elasticity has been proposed in (38) and successfully used to explain part of the experimental observations, a 3 dimensional, microscopic understanding of the intermittent dynamics and of its connection to faster than exponential relaxation of density fluctuations was still fundamentally lacking. We have combined the MD based computational approach described above with a MonteCarlo dynamics in which we periodically scan the local stresses in the gels and remove those connections whose contribution to the overall tension in the material is the largest. This process mimics the gel aging through micro-collapses in its structure and allowed us to analyse the dynamical processes that develop from the local ruptures and help redistribute the stresses over time. Figure 2 shows a cartoon of the aging process in our simulations. We note that our study does not necessarily cover all possible elementary aging events that can happen in different materials, e.g., we do not consider coarsening or compaction of initially loosely packed domains (41). As a matter of fact, in our simulations, recombinations of the gel branches are actually possible but just not observed at the volume fractions and for the time window explored here. One could extend our simple but effective approach to include also local micro-compaction events that would tend to favor an increase of the modulus over time, whereas the breaking events – micro-collapses considered here obviously weaken the gel over time. In spite of the different trend in the time evolution of the gel strength, the disruption of the elastic strain field due to the rupture of a branch of the gel is basically the same as the one induced by a recombination of the gel branches (42). Hence we do not expect qualitatively different results in the two cases. In our study, we were able to monitor the consequences of the aging process acting on the precise same gel structure in presence of different amount of thermal fluctuations, by solving the Langevin equations of motion for all particles in the gel for different values of kBT/ε as described in (21). The value of kBT/ε represents different amount of thermal fluctuations (i.e. Brownian stresses, whose order of magnitude is ~kBT) with respect to the enthalpic stresses (whose order of magnitude is ~ε) initially frozen-in in the network structure during the gel formation and processing. kBT/ε can be easily fixed as a tuning parameters in our simulations. Figure 3 shows the data obtained for the time-decay of the correlation of the density fluctuations (the coherent scattering function) at different wave vectors q and of the correlations of stress fluctuations for different values of kBT/ε. 215

Figure 2. Snapshots of the colloidal gel network showing the interparticle bonds before (left) and after (right) a bond rupture. On the left, the bond that will break is highlighted. On the right, the arrows indicate the displacement after the rupture. Reproduced with permission from Ref. (21). Creative Commons license available at https://creativecommons.org/licenses/by/4.0/. Copyright 2017 Nature Publishing Group.

Our key new findings are that the relaxation dynamics underlying the aging change dramatically if the enthalpic stress heterogeneities, frozen-in upon solidification, are significantly larger than Brownian stresses. The decay of the coherent (and incoherent) scattering functions over time change from stretched to compressed exponential as kBT/ε decreases (see Fig. 3, left). From the behaviour obtained at different wave vectors we can elucidate that, upon decreasing the strength of thermal fluctuations, the dynamics gradually changes from stretched to compressed exponential relaxation. The wave vector dependence well agrees with experimental observations: the exponent β decreases with increasing q and the relaxation time increases with decreasing q but becomes less sensitive to changes in q. By analysing the distribution of microscopic displacements following the micro-collapses, we show that the microscopic motion underlying the compressed exponential dynamics is of elastic origin since the PDF is fully captured by the prediction of continuum elasticity for the elastic strain (42). We elaborate that the timescales governing stress relaxation, respectively through thermal fluctuations and elastic recovery, are key. When thermal fluctuations are weak with respect to enthalpic stress heterogeneities, the stress can partially relax through elastically driven fluctuations. Such fluctuations are intermittent, because of strong spatio- temporal correlations that persist well beyond the timescale of experiments or simulations, and the elasticity built into the solid structure controls microscopic displacements, leading to the faster than exponential dynamics reported in experiments and indeed hypothesized by the theory (4, 32, 33, 37–40, 43). Thermal fluctuations, instead, disrupt the spatial distributions of local stresses and their persistence in time, favoring a gradual loss of correlations and a slow evolution of the material properties. The difference in the stress relaxation measured in the simulations with different amount of thermal fluctuations, while the same amount of connections have been removed, 216

and corresponding to stretched vs compressed exponential relaxation is shown in Figure 3 (right). In the simulations, we have been able to clearly demonstrate how the elastic nature of the partial stress relaxation affects the microscopic particle dynamics, when thermal fluctuations are too weak.

Figure 3. Stretched and compressed exponential dynamics in soft gels. Left: Time decay of the correlations of the density fluctuations as provided by the coherent scattering functions measured in the simulations for different wave vectors q and for different values of kBT/ε starting from exactly the same gel configuration. The decay changes from stretched to compressed exponential upon reducing the Brownian stresses with respect to the enthalpic stresses initially frozen-in in the gel structures. Right: Time correlations computed from the fluctuations of a representative component of the total stress in the gel during aging. Decreasing kBT/ε leads to strongly correlated, intermittent fluctuations, strongly reminiscent of the experimental findings. The time correlations show that the stress fluctuations are persistently correlated when only elastic relaxation of the network is at play. Modified with permission from Ref. (21). Creative Commons license available at https://creativecommons.org/licenses/by/4.0/ Copyright 2017 Nature Publishing Group. (see color insert) The study just described provided deeper understanding of the interplay between thermal fluctuations and elasticity in the aging of soft materials, and in particular of how stress relaxation, when driven essentially by elasticity, translates into qualitatively different microscopic dynamics due to the radically different nature of the stress spatio-temporal correlations. When elastic relaxation dominates, the stress fluctuations are strongly and persistently correlated over large distances, and this fact explains why experimental observations are often close to the prediction of the mean field theory, even if the materials are structurally heterogeneous (21). The insight gained here helps us identify the conditions for which the elastically driven intermittent dynamics emerge in different jammed solids. Close to ergodicity, enthalpic and thermal degrees of freedom may still couple and stress correlations decay relatively fast. When the material is deeply quenched and jammed, instead, recovering the coupling between the distinct degrees of freedom and restoring equilibrium through 217

thermal fluctuations requires timescales well beyond the ones accessible in typical experiments or simulations. If elastic degrees of freedom are the ones responsible for the stress relaxation, the associated stress fluctuations are strongly spatio-temporally correlated and the result will be intermittent dynamics and compressed exponential relaxations (33, 40).

Network Topology and Nonlinear Response So far we have analyzed the relaxation dynamics and the stress redistribution in soft gels at rest. Such dynamics are controlled by the nature of the microscopic fluctuations (spontaneous or driven by internal stress relaxation) for a fixed configuration. More generally, the stress redistribution is also strongly affected by, and can vary significantly with, the structural complexity and diversity. It can be very dramatically seen in presence of an external load, when the microstructural diversity leads to a rich variety of strongly nonlinear responses (10, 44–48). Being able to design the microstructure-process or microstructure-rheology interplay in this class of materials is essential to achieve smart rheology and mechanics that can be finely tuned and adjusted on the fly, such as in soft inks for 3D printing technologies (16, 17). Within this context in particular, being able to fine tune the interplay and feedback among deformation, deformation rate and microscopic restructuring of soft gels requires a deeper understanding of the role of the gel microstructure in its mechanical response. Our computational approach has the potential to provide unique insight thanks to the possibility to access the spatio-temporal microscopic dynamics and its link to the emerging rheological response of the material. We have used the model previously introduced to explore specifically the role of the topology of the gel networks in their linear and non-linear response. For these simulations, we have studied gels at different volume fractions and in athermal conditions, subjected to different type of mechanical tests (12, 22, 25). In the following, we highlight some of the outcomes of studies where we have imposed a deformation rate on the initially solid sample as in a start-up shear experiments by performing small deformation steps where a small affine shear strain step δγ is imposed on all particles. The affine strain step is followed by a relaxation step of duration δt during which the stresses accumulated under strain are relaxed by solving damped equation of motion, in which the damping coefficient represents the dissipation of the particle motion through the solvent ). We use Lees-Edwards (for the data discussed in the following boundary conditions that are compatible with the flow (49). Varying δt allows us to vary the shear rate to investigate the shear rate dependence (12), but here we will focus on mechanical tests performed at a fixed shear rate . By repeating the deformation and relaxation steps we can accumulate arbitrarily large shear strains γ and, at each step, compute local and global stresses as discussed above. To characterize the linear response of the gels we have also performed small amplitude oscillatory shear tests (described in (12) and (22)), to reconstruct the viscoelastic spectra and extract the low frequency storage modulus G0. 218

In the gel model briefly described above, varying the volume fraction between 5% and 15% changes the number of branching points in the gel network without changing the morphology of the branches. The self-assembly protocol and the effective interactions used are the same. Therefore, varying the volume fraction allows us to explore the role of one specific topological change in the structure (i.e., a change in the number of branching points) for the mechanics. The gels at 5% in particle volume fractions are very sparse, being composed of relatively long and semiflexible strands connected by a few branching points. Upon increasing the volume fraction, the strands become shorter (and hence less flexible) as more and more branching points form and distribute more homogenously in space (50).

Figure 4. Linear and non-linear response to a start-up shear test in simulations of soft gels. Load curve identifying the different regime of the gel response at intermediate volume fractions, where the initial linear regime is followed by stiffening and hardening. Figure 4 shows the typical load curve obtained in the shear start-up tests: a relatively narrow linear regime is followed by an extended regime where the dependence of the shear stress σ on the strain γ is nonlinear (22). The first part of the nonlinear regime can be associated to a stiffening of the gels, due to the straightening of large part of the structure, a typical nonlinear but elastic process (51). The nonlinear increase of the stress with the strain in denser and more densely connected gels tend instead to be due to hardening, a plastic process, because of the formation of additional branching points under shear (the hardening is absent in the very dilute gels and becomes more prominent upon increasing the volume fraction). From the load curve we can compute the differential moduus and use it to quantitatively characterize the nonlinear response. In Figure 5 we have plotted K = G0 as a function of the shear stress σ normalized by 219

the value of the stress σc at which the nonlinear response sets in, for a dilute gel at 5% in volume fraction. The stiffening in this case is preceded by a prominent softening of the material and, analyzing the microscopic deformation in the gel structure, we have been able to rationalize such phenomenon in terms of the bent strands produced during the gel self-assembly, when the gel is very sparse. In view of the semiflexible nature of the gel strands, their bending has an energy costs which favours its release under deformation. The following and clearly distinct nonlinear regime features a pronounced increase of the differential modulus that in these very soft gels is mainly ascribed to the stiffer response of large part of the structure that have been already straightened out, as proved by the degree of alignment of the microstructure in the direction of maximum elongation (12, 13, 22). The dependence of the differential modulus on the stress in the stiffening regime reported in Figure 5 is consistent with the stiffening predicted by theories for random networks of semiflexible filaments and typically observed experimentally in biopolymer networks (3, 51–54).

Figure 5. The response of a very soft gel (volume fraction 5%), displayed in terms of the differential shear modulus, normalized by the low frequency storage modulus, as a function of the stress. Such gels feature a pronounced softening followed by stiffening. By increasing the volume fraction and changing the gel topology towards more connected and spatially homogeneous networks, the tendency to softening progressively disappears and the stiffening is characterized by a different scaling of the differential modulus with the stress, akin to what typically predicted for networks of stiff rods. Increasing the volume fraction even further, the gels eventually have microstructure quite similar to cellular solids and their 220

mechanical response is hardly nonlinear, while they feature a less ductile damage accumulation, rapidly leading to a brittle failure. The results obtained prove that the network topology in soft gels plays a crucial role in how the stress can redistribute under deformation and hence in the emergence of the nonlinear rheological response of the material (55). Such findings suggest that topological control on gel microstructure could open interesting possibilities for smart material design that do not require changing the chemistry of the compounds.

Conclusions Three-dimensional microscopic simulations of soft gel networks provide unique access to the spatio-temporal dynamic underlying aging and non-linear rheology of these versatile materials. We have developed a computational approach based on a particle model and here have given an overview of the typeof insight that can be obtained. Our recent studies allowed us to disentangle the interplay between thermal fluctuations and elastic relaxation during the aging of soft gels and other amorphous solids, shedding new light into the compressed exponential, intermittent microscopic dynamics detected in experiments. We have shown that the nature of the fluctuations controls the type of aging dynamics for a given microstructure. Nevertheless, the microstructural complexity of these materials also plays an important role on stress redistribution, and our three-dimensional microscopic simulations have allowed us to elucidate this aspect as well. In particular, we have shown here how the network topology alone can radically change the stress-redistribution, and hence the nature of the non-linear response, in start-up shear experiments. On the basis of the results obtained, controlling the network topology could in principle allow for tuning the non-linear rheology from softening to stiffening and hardening to brittle rupture, without changing the gel components.

Acknowledgments The authors thank the Impact Program of the Georgetown Environmental Initiative and Georgetown University for funding and the Kavli Institute for Theoretical Physics at the University of California Santa Barbara for hospitality. This research was supported in part by the National Science Foundation under Grant No. NSF PHY17-48958.

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Chapter 12

Structure-Property Comparison and Self-Assembly Studies of Molecular Gels Derived from (R)-12-Hydroxystearic Acid Derivatives as Low Molecular Mass Gelators V. Ajay Mallia1 and Richard G. Weiss*,2 1School

of Science and Technology, Georgia Gwinnett College, Lawrenceville, Georgia 30043, United States 2Department of Chemistry and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC 20057-1227, United States *E-mail: [email protected].

This chapter summarizes the self-assembly, structure and properties of molecular gels derived from amide and hydrazide derivatives of (R)-12-hydroxystearic acid (HSA) while comparing them to those of the parent acid. The nature of the aggregates is discussed at different length scales, starting from single molecule structures and progressing to packing within the self-assembled fibrillar networks (SAFINs) of these gels. The structural properties of the gelators are correlated with the bulk properties of their gels. Of note is the observation that many of these gels exhibit thixotropic properties (i.e., they are converted to sols upon application of destructive strain and then return to their gel state when the strain is released). Analyses of the factors within the SAFINs leading to their viscoelastic properties and to the ability of another derivative of HSA to form self-supporting and self-healing gels are presented as well. The results demonstrate how small structural modifications of derivatives of HSA can cause very large changes in the properties of their gels, some of which have important potential consequences to their potential applications.

© 2018 American Chemical Society

Introduction Molecular gels are quasi-solid materials composed of small amount of a low molecular weight compound (a gelator) and a liquid (1–7). They are a subclass of a wide range of materials commonly called ‘soft matter’. In the appropriate temperature and concentration regimes, the gelator molecules self-assemble to form one-dimensional objects (e.g., fibers, strands, tapes or tubules), that further interact with each other and form 3-dimensional self-assembled fibrillar networks (SAFINs) (8, 9). The SAFINs are stabilized by weak intermolecular interactions such as H-bonding, π-π stacking, electrostatic interactions or London dispersion forces, and macroscopically entrap the liquid in which they reside (10). As such, they are sometimes referred to as ‘physical gels’ to differentiate them from ‘chemical gels’ in which the 3-dimensional networks are comprised of interacting polymeric chains (i.e., the ‘molecular gelators’ can be thought of as being covalently linked). Interest in molecular gels has increased significantly during the last two decades due to their fundamental importance to understand modes of molecular aggregation (11) and their potential applications (12). Many molecular gelators contain steroidal, aromatic, and other functional groups, or they may rely on ionic interactions between two molecules, neither of which is a gelator alone (1, 13, 14). Long n-alkanes are the simplest possible organic molecules that are gelators, and their SAFINs are stabilized by London dispersion interactions (15, 16).

Figure 1. Structures of(R)-12-hydroxystearic acid (1) and gelators based on it.

In this chapter, we summarize systematically some relationships between the properties of the gels and the structures of the molecular gelators and their aggregates at different distance scales that are derived from a molecule which is a di-substituted n-alkane, (R)-12-hydroxystearic acid (HSA; 1 Figure 1). It is obtained from a natural source—hydrolysis and hydrogenation of triglycerides found in the seeds of the castor plant. SAFIN structures of molecular gels of the parent molecule, HSA, have been studied extensively (17). X-ray and infrared studies, especially, have demonstrated that the carboxylic acid groups of HSA promote the formation of H-bonded sequences that stabilize SAFINs, and the 12-hydroxy groups participate in the stabilization as well—HSA is a much more efficient gelator than stearic acid (18–23). 228

As demonstrated by the large body of research with polypeptides, H-bonding interactions between primary or secondary amide groups can be even more effective than those between carboxylic moieties (24). Thus, the amide derivatives of HSA, 2 and 3 (R = alkyl), are efficient gelators. Also, H-bonding interactions of molecules with alkyl (25) and aryl hydrazide groups (26, 27) have been used to stabilize self-assembled structures. Thus, the gelating abilitiy of 4 and 5 (R = alkyl) have also been assessed as has the series of (R)-12-hydroxy-N-(ω-hydroxyalkyl)octadecanamides (6), in which an amide and a hydroxyl functional group are separated by an alkyl chain linker. SAFINs of the molecular gels of 6 are also stabilized by H-bonding involving the hydroxyl group at the C12 postion of the octadecanoyl chains, the terminal ω-hydroxyl groups on the N-alkyl chains, and the amide groups (28).

Gelation Studies and SAFIN Structure As noted above, HSA gelates many liquids, including n-hexane, toluene, silicone oil and acetonitrile (29). The gel melting temperature (Tgel) of these gels depends on the concentration of the gelator and the nature of the liquid being gelated (Table 1). As an example, at 2 wt % of HSA, Tgel ofthe gel in silicone oil is higher than that in n-hexane. However, as a result of the stronger H-bonding interactions between primary or secondary amide functional groups than carboxylic acid groups (30), Tgel values of molecular gels of the primary amide (2) in hexane, silicone oil, toluene and acetonitrile are higher than those of the corresponding HSA gels. Consistent with the importance H-bonding interactions at the head groups of HSA derivatives in controlling the stability of their molecular gels, the Tgel values of the secondary amides (3) are generally lower than those of 2; H-bonding interactions among the molecules with secondary amide groups are weaker than those of primary amides. As noted, hydrazide groups exhibit strong intermolecular H-bonding interactions as well (30). For that reason, (R)-12-hydroxystearic acid hydrazide (4) is able to gelate alkanes, alcohols, and aromatic liquids among others. However, critical gelator concentrations (CGCs; i.e., the lowest concentrations of a gelator at which gels can form at room temperature) values for 4 are larger than those of of HSA, primary or secondary HSA-derived amides (29); in this regard, the hydrazide gelators are less efficient. Based on the very low CGC values of their gels in silicone oil, acetonitrile, and toluene (0.5 wt%) (R)-12-hydroxy-N-(ω-hydroxyalkyl)octadecanamides are exceedingly effective gelators (28). CGC values of gels of 4 in n-hexane and in silicone oil are 3.9 and 1.5 wt %, respectively. Consistent with the observations with primary and secondary amide derivatives of the HSA gelators, the alkylated hydrazide, (R)-N-ethyl-12-hydroxyoctadecane hydrazide (5, R = ethyl), did not gelate hexane and decane or most of the alcohol liquids examined. However, 5wt % 5 (R = ethyl) was able to gelate aromatic liquids such as toluene and nitrobenzene (31). Also, (R)-12-hydroxy-N-(ω-hydroxyethyl)octadecanamide (6, n = 2) did not gelate n-hexane (28). 229

Table 1. Appearancesa and Tgel Values (°C, in Parentheses) of Gels Containing 2 or 5 wt % of HSA Derivatives in Various Liquids. See Figure 1 for Structures. Liquid /gelator

1b,d

2b,d

3b d R = C2H5

4c

e

5c,e R = C2H5

6b, f n=2

n-Hexane

OG (59-60)

OG (91-92)

OG (81)

OG (107108)

P

I

Silicone oil

OG (73-74)

OG (98-100)

OG (86-87)

CG (108109)

OG (99-103)

OG (107-108)

Toluene

CG (44-45)

CG (65-67)

OG (57-58)

CG (75-78)

TG (72-75)

CG (82-83)

1-Octanol

Soln

OG (27-34)

P

OG (53-55)

Viscous solution

P

Methanol

Soln

Soln

Soln

TG

P

Soln

Acetonitrile

OG (45-48)

OG (53-54)

OG (56)

P

P

OG (67-70)

Unless stated otherwise, all gels were prepared by a ‘fast-cooling’ protocol by placing hot sols/solutions of a gelator and liquid in the air or in a cold water bath until the sample reached room temperature: OG-opaque gel, TG-translucent gel, CG-clear gel, P-precipitate, I-insoluble, Soln-solution. b 2 wt % and c 5 wt %. d from reference (29), e from reference (31) and f from reference (28). a

As shown in Figure 2A, the hydroxyl groups on HSA are connected by an unidirectional H-bonding network in their SAFIN networks. The periodicity of the molecular packing arrangement of the HSA was interpreted as the distance between double planes with a monoclinic crystal lattice in one unit cell, similar to those observed in many fatty acids (32). Although more than one XRD crystal structure of racemic HSA has been reported (33, 34), to the best of our knowledge, no single crystal structure of the (R) enantiomer of HSA has been determined. In benzene and acetonitrile gels, SAFINs of HSA exhibit monoclinic crystalline packing within fibers of rectangular ribbon-like aggegates (32). Comparison of XRD diffractograms of neat powders and 5 wt % 2 in silicone oil gels show that 2 in silicone oil gel show similar morphology as in the neat gelator. The Bragg distances of the low-angle peaks, indicated lamellar packing arrangement shown in Figure 2B (29). The positions of the diffraction peaks of the silicone oil gel of 12-hydroxy-N-propyloctadecanamide correspond to those of the neat gelator, and are consistent with a monolayer arrangement as shown in Figure 2C.

230

Figure 2. A) Structural model of the ribbon-like aggregates of HSA in organic solvents. The parallel vertical lines represent the direction of the H-bonding network. Adapted from reference . Two proposed packing arrangement of gelator molecules in gel aggregates: B) Calculated length of a conformationally extended dimeric unit of 2 = 52.8 A °; C) Calculated molecular length 12-hydroxy-N-propyloctadecanamide = 31.1 A °. Adapted from reference (29).

231

Figure 3. (A) Possible molecular packing models for (R)-12-hydroxystearic acid hydrazide (4), (B) (R)-N-decyl-12-hydroxyoctadecane hydrazide (5, R = decyl), and (C) (R)-12-hydroxy-N-(2-hydroxyethyl)octadecanamide (6, n = 2). A and B are reproduced with permission from reference (31). Copyright 2016 Wiley-VCH Verlag GmbH & Co. (C) reproduced with permission from reference (28). Copyright 2015 The Royal Society of Chemistry.

XRD diffractograms of the organogels and neat solids of (R)-12hydroxystearic acid hydrazide (4) and (R)-N-decyl-12-hydroxyoctadecane hydrazide (5, R = decyl) were also compared. The Bragg reflections of the XRD diffractograms indicated lamellar spacing. The lowest angle reflection for (R)-12-hydroxystearic acid hydrazide (4) was twice the calculated molecular length, indicating bilayer packing (see Figure 3A) (31). The lowest angle reflection for (R)-N-decyl-12-hydroxyoctadecane hydrazide corresponds to a distance close to the length of an extended molecule; the suggested packing arrangement for two of the molecules is shown in Figure 3B. Figure 3C shows a possible head-to-tail packing arrangement for (R)-12-hydroxy-N-(2-hydroxyethyl)octadecanamide (6, n =2) based on the structurally similar methyl ester of HAS (28). Radially-averaged, 2-dimensional small angle neutron scattering (SANS) curves of a gel comprised of 2 wt% 6 (n = 2) in toluene-d8 gel exhibited a Bragg reflection peak at Q = 1.2 Å, corresponding to a distance of 52.0 Å. The SANS data were also consistent with a bilayer packing arrangement of 6 (n = 2) in its toluene gel. The overall fit of the SANS curve indicates flexible cylinders with poly-radii and a radius of (Figure 4) (28). 232

Figure 4. Log–log plot of SANS intensity (I) versus Q profile of a 2 wt% 6 (n = 2) in toluene-d8 gel (●). The black line is the theoretical curve for cylinders with poly radii and a radius of Å, The arrow shows the second oscillation peak at d = 52.0 Å. Reproduced with permission from reference (28). Copyright 2015 The Royal Society of Chemistry.

Polarizing optical micrographs (POMs) in Figure 5 show images of the SAFINs of gels of 2 wt % 2 in silicone oil and in toluene. Both show spherulites, and they were larger when the sols were cooled more slowly Also, spherulitic objects were observed for 5 wt % 4 and 5 (R = C2H5) in silicone oil gels (Figure 6). POM images of a 2 wt % 6 (n = 2) in silicone gel exhibited fibrillar textures and the corresponding AFM image showed rope-like bundled fibers with ca. 100 nm diameters (Figure 7).

Figure 5. Polarizing optical micrographs of gels 2 wt % 2 (A) in silicone oil and (B) in toluene. Adapted from reference (29). 233

Figure 6. Polarizing optical micrographs of 5 wt % silicone oil gels of 4 (A) and 5 (R = C2H5) (B). Reproduced with permission from reference (31). Copyright 2016 Wiley-VCH Verlag GmbH & Co.

Figure 7. (A) Polarizing optical micrograph and (B) AFM image of a gel comprised of 2 wt % 6 (n =2) in silicone oil. Reproduced with permission from reference (28). Copyright 2015 The Royal Society of Chemistry.

Thixotropic Properties Thixotropy can be defined as the shear thinning of a viscoelastic material upon the application of a destructive strain and the subsequent recovery of the viscoelasticity after cessation of the strain (36). Thixotropic properties arise in molecular gels when the changes in applied strain result in a loss and gain of intermolecular interations among SAFINs (37–39). A recent review has highlighted and summarized the correlations between thixotropic and structural properties of molecular gels with crystalline networks (40). In this chapter, we summarize the efforts to understand why some structurally-simple molecular gelators which are derived from HSA (Figure 1) can form gels which are thixotropic. We extend our discussion of how the morphologies of the SAFINs are contolled by the different head groups of the HSA-related derivatives to the rheological properties of their gels. 234

Figure 8. A) Elastic (G’) (●) and viscous (G”) (▴) moduli as a function of time and application of different levels of strain and frequency to a 2.0 wt % 2 in silicone oil gel at 25 ºC. Adapted from reference (29). B) Thixotropic studies of 5 wt% 4 in silicone oil gel (G’ (●) and G” (●)). Reproduced with permission from reference (31). Copyright 2016 Wiley-VCH Verlag GmbH & Co.

For the thixotropic studies, the viscoelastic the elastic (G’) and viscous (G”) moduli were measured sequentially within the linear viscoelastic regime (LVR), at a destructive strain, and finally at theoriginal LVR condi tions. In all cases, the values of G’ were taken as the measure of recovery. For example, a 2 wt % silicone oil gel of HSA was found to recover 70% of its initial G’ value in 99%, their recovery times, ~16.6 and 2.5 min, respectively, were very different and much longer than the recovery times of the shorter homologues. The results show 236

that addition or subtraction of one methylene unit on the hydroxyalkyl chain attached to the amide nitrogen atom of the series of 6 molecules affects both the eventual recovery of the viscoelastic properties of the gels and the time required for that recovery. These observations indicate that the conformational changes within the head groups of the 6 homologues have an important role in determining the degree of intra- and inter-molecular H-bonding within their SAFINs and the ability of the subunits present immediately after the cessation of destructive strain to reassemble and lead again to gels. A possible mechanism for these processes in the isostearyl alcohol gels with the 6 homologues is shown in Figure 10.

Figure 10. Cartoon representation of a possible mechanism to explain the thixotropic behavior of SAFINs of 6 in isostearyl alcohol gels. Reproduced with permission from reference (28). Copyright 2015 The Royal Society of Chemistry.

Self-Standing Gels and Diffusion Studies Many molecular gels are not sufficiently strong to be free-standing solids. Some have been strengthened by incorporating polimerizable groups, such as methacrylate, within the gelator structureand then polymerizing the SAFINs (43). After such treatments, the gels are no longer classified as molecular (physical); they are polymer (chemical). However, there are few reports of self-standing sorbitol-based molecular gels (44, 45), and Dastidar and coworkers have developed a broad selection of two component salt gelators (14), some of which form self-standing and self-healing gels (46). Of the HSA-derived gelators and their gels, those of ethylene glycol and 2 or 5 wt% (R)-12-hydroxystearic acid hydrazide (4) exhibit self-standing and selfhealing properties. The stiffness and the load-bearing force (Fb) of cylindrical blocks of the gels were measured using compression tests by decreasing the gap between parallel rheometer plates. Fb and rate of increase of force increased from 10 to 47 N and 1.23 to 1.95 Nm/m on increasing the gelator concentration from 2 to 5 wt% (Figure 11). 237

Figure 11. Compression curves of normal force versus gap distance for (R)-12-hydroxystearic acid hydrazide gels. a) gels at 2 and 5 wt% gelator in ethylene glycol and in ethylene glycol/DMF mixtures. b) 5 wt% gelator in ethylene glycol (black, 1) and repeated cycles of compression (squares, 2a-6a) and extension (circles, 2b-6b) below the load bearing force, Fb; red (2), blue (3), green (4), cyan (5), and magenta (6) are from the first, second, third, fourth, and fifth cycles, respectively. Note that the color in these figures will only be available in the online version. Compression (and extension) speeds were 1 mm/s. Reproduced with permission from reference (31). Copyright 2016 Wiley-VCH Verlag GmbH & Co.

Figure 12. Gel blocks of R)-12-hydroxystearic acid hydrazide in ethylene glycol: a) 5 wt% and b) 2 wt% gelator. ( c) Two 5 wt% gelator blocks placed in contact with each other; the lower one contains methylene blue. d) The two blocks in (c) after 17 h, showing their self-healing and the diffusion of methylene blue between them. Reproduced with permission from reference (31). Copyright 2016 Wiley-VCH Verlag GmbH & Co. 238

Self-standing gels based on (R)-12-hydroxystearic acid hydrazide (4) and mixtures of ethylene glycol and DMF exhibit similar stiffness, although they became weaker at higher DMF contents (Figure 11). However, none of the homologues of 5 examined yielded a self-standing gel in any of the liquids tested. Self healing of an (R)-12-hydroxystearic acid hydrazide in ethylene glycol gel was demonstrated as shown in Figure 12. First, a cylindrical gel block was divided into two and one part was submerged into a solution of methylene blue in ethylene glycol. After remaining in contact for 17 h, the two pieces had merged and some of the methylene blue had diffused into the undoped part. The diffusion of an anionic dye, methylene blue, and a cationic dye, erythrosine B, from a gel of 2 wt% (R)-12-hydroxystearic acid hydrazide in ethylene glycol into ethylene glycol liquid was determined quantitatively using Fick’s second law (eqn (2)) (47, 48).

Mt is the total amount of dye released during the measurement time t, M∞ is the total amount of dye that was in the gel phase at time = 0, λ is the gel thickness; and D is the diffusion coefficient. D was calculated from the slope of a plot of Mt2 as a function of time, t. The diffusion coefficients of methylene blue and erythrosine B at 25 °C were found to be 7.59x10-12 and 6.04x10-12 m2 s-1, respectively. These values are ca. 10% of the self-diffusion rate of neat ethylene glycol (49); The gel matrix slows diffusion. After ca. 2.5 days, 53% of the anionic and 48% of the cationic dye had been released into the ethylene glycol liquid. These results suggest that the gels may be useful in slowing the release of drugs.

Conclusions We have summarized the properties of molecules with simple structures derived from HSA as organogelators and the properties of their gels. The natures of the aggregates of the gelators, starting from the individual molecules and proceeding to SAFINs, have been described. Those results have been correlated with various properties and efficiencies of the gels, especially those related to thixotropy, self-standing, and self-healing. Specifically treated here are amide and hydrazide modifications of the head group of HSA and their effects on the ability of the molecules to attain H-bonding networks which promote SAFINs and gelation of liquids. An ultimate goal of this and related research is to devise predictive models for how and when a gelator molecule will be able to gelate a specific solvent. Although we are far from achieving that end, progress is being made, and results like those summarized here should aid in reaching it. 239

Acknowledgments We thank the U.S. National Science Foundation for its support of the portion of the research in this chapter conducted at Georgetown through grants CHE-1147353 and -1502856. We are also grateful to the researchers at Georgetown who have contributed to the results presented here.

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Chapter 13

The Importance of Phase Behavior in Understanding Structure-Property Relationships in Crystalline Small Molecule/Polymer Gels Kevin A. Cavicchi,* Marcos Pantoja, and Tzu-Yu Lai Department of Polymer Engineering, The University of Akron, Akron, Ohio 44325-0301, United States *E-mail: [email protected].

A wide-range of crystalline small molecules are able to self-assemble into three-dimensional solid networks in solvents and polymers producing organogels. The design of small molecule organogelators (SMOGs) is still largely empirical as gelation is a complex process dependent on both the thermodynamics and kinetics of crystallization and assembly. This chapter demonstrates how the underlying phase behavior of two example SMOG/polymer systems are useful to understanding the properties of the gels. The two systems discussed are SMOGs as clarifying agents for semi-crystalline isotactic polypropylene and fatty acid swollen, crosslinked natural rubber shape memory polymers.

Introduction Small molecule organogelators (SMOGs) are molecules that gel non-aqueous fluids through their supramolecular self-assembly into three-dimensional, load-bearing networks (1). A large class of SMOGs form gels through the nucleation and growth of anisotropic crystals (2–4). SMOGs of this type have been discovered with a wide-range of non-covalent interactions (van der Waals, hydrogen bonding, pi-pi interactions, metal coordination, and ionic bonding), and © 2018 American Chemical Society

network morphologies (platelets, fibers and spherulites) (5). This diversity in chemical structure and fluid compatibility has led to the development of SMOGs as viscosity modifiers and nanoscale templating agents across a range of fluids for cosmetics and personal care products (6, 7), food science (8, 9), pharmaceuticals (10–12), organic electronics (13), oil recovery (14, 15), separations (16, 17), and nanomaterials synthesis (18, 19). This ubiquity across different applications has driven the refinement of empirical design approaches and screening methods using combinatorial chemistry, crystal engineering and solvent parameters (20–22). In turn, the increased ability to design SMOGs has allowed researchers to develop new SMOGs that respond to stimuli beyond temperature including light, mechanical force, enzymes, and ions (23). Despite these advances in SMOG design, the synthesis and application of many SMOGs are still very empirical processes (5, 20). It is known that gel formation depends strongly on the kinetics of crystallization, which depends on thermodynamic properties such as the gel transition temperature and the extent of undercooling varied by step changes in temperature or the cooling rates through the gel transition (24, 25). Furthermore, significant variation in the gel morphology can occur as the solvent or gelation pathway (cooling rate, gelation temperature) are varied (26–28). However, the full phase diagram of SMOG solutions is rarely measured. A simple example of the utility of examining the phase behavior of a SMOG solution was recently shown by Crist et al. (29) They found that liquidliquid phase separation occurred at higher concentration in solutions of a bisamide SMOG in trans-decalin. This results in an invariant melting point below the liquidliquid miscibility gap and therefore a region where the gel transition temperature is invariant with concentration. While the behavior of the gel transition temperature vs. SMOG concentration had previously been observed, it had not been adequately explained (30, 31). The objective of this chapter is to further demonstrate the importance of the phase diagram of SMOG organogels to understanding their structure-property relationships and improving the design of gels. Two examples are discussed where a SMOG is used to modify the properties of a polymer. In the first example, the use of SMOGs to act as nucleating agents in isotactic polypropylene and modify its optical properties is discussed. Here measurement of phase diagrams was crucial to understanding the non-monotonic dependence of the optical properties on the SMOG concentration in the polymer (32, 33). This work is a beautiful example of the application of material science in soft matter systems. Their similarity to more classical problems in metallurgy, such as steel manufacturing and second phase hardening (i.e. Gunier-Preson zones) (34), first inspired the authors to delve into the field of SMOGs. The second example is from the authors’ own work, where fatty acids are used to convert crosslinked natural rubber, a commodity elastomer, into a shape memory polymer (35). The phase diagram was used to understand differences in the varation of the shape memory behavior with the fatty acid concentration among different fatty acids.

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Clarifying Agents for Isotactic Polypropylene It is known that soribitol derivaties and 1,3,5-benzene trisamides are able to act as clarifying agents for isotactic polypropylene (i-PP) (36–39). Clarifying agents are a specific type of nucleating agent that, in addition to raising the crystallization temperature of the melt, improve both the mechanical and optical properties by drastically reducing the spherulite size (40, 41). In particular, they are referred to as clarifying agents due to their ability to increase the clarity (light scattered at a small angle < 2.5°) of i-PP articles (32, 42). Thierry et al. noted that 1,3:2,4dibenzylidene sorbitol (DBS) is both an excellent clarifying agent and SMOG for polar solvents through their assembly into three dimensional fibrillar networks with sub-micron diameters (41). The ability of the fibers to act as an epitaxial nucleating surface and the high surface area of the fibrillar network leads to a high nucleation density and therefore a large number of small spherulites. While there are still differences among the refractive indicies of the amorphous and crystalline polymer and the fibrillar network, the small length scale of these entities limits the light scattering, resulting in materials with high optical transparency. It was known early on in the study of clarifying agents that there is an optimum concentration for maximum clarity (43). The variation in clarity and haze (scattered light at 2.5 - 90°C) is shown in Figure 1 for 1,3:2,4-bis(3,4-dimethyldibenzylidene) sorbitol (DMDBS) in i-PP as reported by Kristiansen et al. (32) The maximum clarity and minimum haze is observed at 1.0 wt% DMDBS with a rapid loss in transparency with increasing DMDBS content. The origin of the non-monotonic optical behavior was determined from the investigation of the phase behavior of i-PP/DMDBS. Figure 2 shows the phase diagram measured on heating and cooling by a combination of DSC, rheology, and optical microscopy. It is noted that liquid-liquid phase separation of the molten solution was observed above 2 wt% DMDBS. Therefore, on cooling from the homogenous liquid state through the miscibility gap, DMDBS droplets would form resulting in large DMDBS crystals. While the DMDBS fibrils would still form and act as nucleating sites, the presence of larger DMDBS crystals would scatter light reducing the clarity and increasing the haze. A schematic diagram relating the morphology and the phase diagram is shown in Figure 3. Region II shows the wt% DMDBS range where DMDBS forms fibrils directly from the homogeneous liquid, which results in both small DMDBS and i-PP crystals leading to high clarity and low haze. In addition to the liquid-liquid miscibility gap in region III, there is a eutectic point separating region I and region II. Below the eutectic composition, the i-PP would crystallize first on cooling reducing the ability of DMDBS to act as a clarifying agent to modify the morphology of the i-PP crystals.

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Figure 1. Optical properties of isotactic polypropylene (i-PP)/ 1,3:2,4-bis(3,4-dimethyldibenzylidene)sorbitol (DMDBS) for different compositions. Writing instruments viewed through injection-molded plaques containing 0.1, 0.5, 2, and 10 wt % of DMDBS (top) and measured values for haze (▴) and clarity (■) as a function of the DMDBS content (bottom). Reprinted with permission from ref. (32). Copyright 2003 American Chemical Society.

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Figure 2. Crystallization (top) and melting (bottom) temperature/composition diagrams of the binary system i-PP/DMDBS. In the diagrams the symbols refer to experimental data obtained by (●) DSC, (closed star/open star) rheology, and (Δ) optical microscopy. The denotation D refers to DMDBS, P to i-PP, L to liquid, and S to solid. Reprinted with permission from ref. (32). Copyright 2003 American Chemical Society.

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Figure 3. Proposed schematic, monotectic phase diagram of the binary system i-PP/DMDBS. Indicated are four relevant composition ranges I, II, III, and IV that divide the phase behavior below the eutectic point (I), along the lower liquidus (II), along the miscibility gap (III), and above the monotectic point (IV) and inserted are sketches and actual optical micrographs (crossed nicols) of the various states of matter of representative mixtures of compositions in those ranges. Adapted with permission from ref. (32). Copyright 2003 American Chemical Society.

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Figure 4. Temperature/composition diagrams for the (pseudo-)binary system i-PP/1 obtained in cooling (top) and heating (bottom) experiments. Symbols refer to data for different transitions: crystallization and dissolution/melting (▵, ▴) and solid-state transition of 1 (●), crystallization or melting of the polymer and eutectic (▪) and clearing point (?), respectively. Open symbols denote experimental data obtained from optical microscopy and solid symbols refer data obtained by thermal analysis. The denotation L refers to liquid and S to solid; subscripts ‘a1’ and ‘a2’ refer to the two solid-state structures of additive 1, and ‘p’ to i-PP. Reprinted with permission from ref. (33). Copyright 2006 Elsevier.

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Figure 5. Top: optical micrograph displaying liquid–liquid phase separation at 270 °C in a mixture containing 25 wt% of 1 in i-PP. Bottom: photomicrograph, taken between crossed polarizers at 80 °C, of the solid-phase structure of a 50/50 i-PP/1 wt%-mixture. The structures in the upper left corner crystallized from a droplet rich in 1. Reprinted with permission from ref. (33). Copyright 2006 Elsevier.

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Figure 6. Top: optical micrograph, taken in reflected light, of a sample produced with a ‘diffusion–screening’ method by placing powder of 1 in the center of a compression-molded film of i-PP and allowing the additive to radially diffuse at 220 °C, after which the sample was cooled down to room temperature. The clear ring is indicative of the clarifying ability of compound 1. Bottom: corresponding optical micrograph taken in transmittance with crossed polarizers and a λ/4 plate. A schematic of the i-PP/1 monotectic phase diagram is drawn onto the micrograph to approximate the different characteristic optical regimes and the corresponding composition ranges. Reprinted with permission from ref. (33). Copyright 2006 Elsevier.

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Further evidence of the influence of the phase behavior on the morphology and clarifying ability of SMOGs was reported by Kristiansen et al. for N,N’,N”tris-isopentyl-1,3,5-benzene-tricarboxamide (1) in i-PP (33). Qualitatively similar phase diagrams to the DMDBS/i-PP system were obtained and are shown in Figure 4. In the 1/i-PP system measurements were made over a much larger wt% 1 range compared the DMDBS/i-PP system. Quantitative measurement of the clarity and haze of the 1/i-PP samples vs. wt% 1 showed similar behavior to Figure 1. The reported optimum composition range and values for high clarity (98%) and low haze (ca. 27%) in injection molded plaques was 0.25 – 1 wt% 1, corresponding to the region where 1 solidifies directly from the liquid on cooling through the lower liquidus line. The haze and clarity display an upturn and downturn, respectively, in the composition region where the lower liquidus approaches the monotectic temperature at ca. 2 wt% 1. Figure 5 shows optical micrographs of 25 wt% 1 in i-PP in the liquid-liquid phase separated and solid states, where a 1-rich phase resulting from the crystallization in a phase separated droplet is clearly observed. Figure 6 shows a compression molded sample where 1 was placed in the center of the film and allowed to radially diffuse producing a composition gradient from high to low 1 concentration from the center of the film. The variation in the optical clarity of the film clearly shows that there is an optimal concentration range for 1 to act as a clarifying agent as schematically shown by the phase diagram overlaid on the micrograph under crossed polarizers in the bottom half of the figure. It should be noted that while the phase behavior is the key component in the function of clarifying agents in semi-crystalline polymers, other criteria must be met at the same time. In addition to establishing a region where the clarifying agent and semi-crystalline polymer sequentially crystalize from the homogeneous melt, the clarifying agent also must be able to crystallize into three dimensional fibrillar networks and act as an epitaxial nucleating agent for the surrounding polymer (44, 45). Given the many criteria that must be satisfied it is therefore crucial to examine the phase behavior of complex SMOG/semi-crystalline polymer systems which are instrumental in further developing high performance clarifying agents (46). While there has clearly been success in the design of clarifying agents in modifying the optical properties of i-PP, this research field is not complete as it is only one of many semi-crystalline polymers. For example, clarifying agents for polyethylene have recently been reported (47, 48). This field has a potentially broad future due to growing interest in other semi-crystalline polymers, such as bio-based polylactide (49), and conjugated polymers for organic electronics (50).

Shape Memory Polymer/Small Molecule Blends Shape memory polymers (SMPs) are a class of polymers where their elastic recovery can be turned on and off by the application of an external stimulus (51). This is accomplished by preventing the elastic retraction of a polymer network through vitrification, crystallization, or additional, reversible crosslinking (52). While many SMPs are composed of a single polymer, such as a polyurethane (53), there has been recent interest in decoupling the elastic network, providing shape recovery, and the reversible network, providing shape fixity, through blending 254

elastomers and small molecules (54). While this concept is analogous to SMOG/ solvent organogels there are a few key differences. First, the medium being gelled is not a liquid, but a viscoelastic solid, which produces the shape memory effect. Second, a much higher loading of the SMOG is typically used compared to SMOG/ liquid organogels. In SMOG/liquid organogels the fluid is immobilized above the percolation threshold of the SMOG network (i.e. at the minimum gelation concentration). In contrast, the SMOG network in an SMP must not only form a percolating solid network, but be able to resist the elastic contractive forces of the surrounding elastomer network. While there are numerous examples of polymer/small molecule SMPs (55–63), the systematic study of the mechanical properties of the SMOG/polymer network and the shape memory properties has only recently been reported by Pantoja et al. using fatty acid swollen, natural rubber bands (35). An example of the excellent shape memory property of fatty acid swollen natural rubber is shown in Figure 7. The sample was deformed and fixed to ca. 400% strain by heating the sample above the melting point of stearic acid; uniaxially stretching the sample and then cooling it to room temperature under load, allowing the stearic acid to crystallize into a ‘house of cards’ network that restricts the movement of the natural rubber chains (64); and recovered to the original shape by heating the unloaded sample above the melting point of stearic acid. The figures of merit characterizing the shape memory polymer are the fixity (F) and recovery (R). These are in turn calculated from the uniaxial strains in the sample during the shape memory cycle: the initial strain prior to stretching (εi), the applied strain during deformation (εa), the fixed strain after cooling and unloading the sample (εf), and the residual strain after heating and recovering the unloaded sample (εr). These strains are given by,

where lx is the length of the sample and the subscript (li, la, lf, or lr) is the same subscript as the particular strain (εx). From these strains, fixity (F) and recovery (R) are calculated as,

Figure 8 shows the fixity and recovery for a 2.94N load for natural rubber bands swollen with lauric (LA), myristi c (MA), palmitic (PA) and stearic acid (SA). An optimum loading is seen for high fixity and recovery around 50 wt% fatty acid. An interesting question from these results is, why do the LA swollen samples behave differently from the other fatty acids, which show very similar behavior? Specifically, in Figure 8 while the recovery and fixity overlap for the MA, PA, and SA samples, the LA samples shows significantly lower values than these three acids at less than 50 wt% fatty 255

acid. The fixity is dependent on the modulus and the yield strength of the fatty acid network, which should both scale with the wt% acid in the elastomer, similar to other cellular solids (65). Ultimately a high modulus of the fatty acid network is needed to reach ca. 100% fixity as any deformation of the solid acid network will allow the retraction and recovery of the elastic polymer network. Figure 9 shows the storage modulus of the fatty acid swollen rubber measured by constant frequency strain sweeps. Power law behavior is observed with a distinct change in the power-law exponent at intermediate fatty acid concentrations. This change in slope is assigned as the mechanical percolation threshold and is plotted as dashed vertical lines in Figure 8. A correlation between the mechanical percolation and the upturn in the fixity vs. wt% fatty acid in Figure 9 demonstrates how the mechanical properties of the solid fatty acid network drive the fixation of the deformed elastomer.

Figure 7. Shape memory cycle of natural rubber band swollen with 59% stearic acid strained to ca. 400% at 72 °C and fixed at room temperature with a fixity of 98% and a recovery of 98%.

Figure 8. (a) Fixity and (b) recovery vs. weight percent acid for 2.94 N applied load. Vertical lines correspond to fatty acid network percolation threshold from Figure 9. Adapted with permission from ref. (35). Copyright 2018 John Wiley & Sons, Inc. 256

Figure 9. Fatty acid network modulus vs. weight percent fatty acid. Horizontal dashed line represents the modulus of neat rubber. Reprinted with permission from ref. (35). Copyright 2018 John Wiley & Sons, Inc.

Similar to the fixity data, the modulus data also show that LA is different from the other three fatty acids, with a lower modulus at all wt% fatty acid, resulting in poor fixity. While this demonstrates the direct connection between mechanical properties of the fatty acid solid network and the shape memory properties, it does not explain why LA has a lower modulus than the other fatty acids at equivalent loading. Figure 10 shows the phase diagram of the four fatty acids in high molecular weight polyisoprene. It is clear that LA is more soluble at low temperature than the other three acids. To estimate the solubility limit at room temperature the liquidus line was fit to the Flory-diluent model,

where Tm is the melting temperature of the fatty acid vs. the volume fraction of fatty acid, φ2, A quantifies the Flory-Huggins interaction parameter (χ = A/T), and ΔHfo and Tmo are the standard enthalpy of formation and melting temperature, respectively, of the pure fatty acid, and R is the universal gas constant. Using the lever rule, the wt% of the solid fatty acid was calculated as a function of overall wt% fatty acid in the swollen natural rubber. From this calculation, the modulus data in Figure 9 were replotted as E’ vs. wt% solid acid in Figure 11. This adjustment shifts the LA data closer to the other fatty acids. There is likely also a vertical shift in the data due to the soluble lauric acid plasticizing the natural rubber and softening the network, shifting the curves down with respect to the other fatty acids. However, this effect is difficult to quantitatively calculate. 257

Figure 10. Experimental (circles) and modeled (lines) fatty acid-polyisoprene phase diagram. Reprinted with permission from ref. (35). Copyright 2018 John Wiley & Sons, Inc.

Figure 11. Fatty acid network modulus vs. weight percent solid fatty acid. Horizontal dashed line represents the modulus of neat rubber. Reprinted with permission from ref. (35). Copyright 2018 John Wiley & Sons, Inc. This work shows that the measurement of the fatty acid/polymer phase diagram was crucial to elucidate the variation in the properties of different fatty acid swollen, natural rubber, shape memory polymers. More generally, these results demonstrate that the efficiency of an SMOG to form solid networks in elastomers for shape memory is directly related to their solubility limit, even though the SMOG is used at significantly higher concentrations to achieve good shape memory. For example, it would be interesting to compare the efficiency of fatty acids with paraffin waxes, which also form similar platelet crystal structures, 258

but would have a different room temperature solubility, with the waxes being more soluble in polyolefins based on their solubility parameters (58, 66). Another important question for future research is, how does the efficiency of structure formation and mechanical percolation of different SMOGs ultimately affect shape memory? For example, Figure 12 shows the phase diagram of R-12hydroxystearic acid (12-HSA) and stearic acid (SA) in n-dodecane. In addition to having lower solubility in the alkane, 12-HSA is a more efficient organogelator where the difference between the minimimum gelation concentration (12-HSA: 0.019 vol%, SA: 2.1 vol%) and the solubility limit (12-HAS: ca. 0 vol%, SA: 0.2 vol%) are smaller for 12-HSA compared to stearic acid. This implies that 12HSA is able to achieve mechanical percolation more efficiently, likely due to two factors: first, its fibrillar structure, which fills space more easily than platelets and second, differences in the kinetics of crystallization due to the larger undercooling achievable in 12-HSA from the distinct low concentration plateau compared to the more parabolic shape of the stearic acid liquidus line. Assuming similar power law exponents for different SMOGs, achieving mechanical percolation at lower concentration would allow the critical modulus needed for good shape memory to be achieved at lower concentration. Unfortunately, 12-HSA is unable to swell natural rubber, preventing the direct comparison of these two materials, leaving the answers to these questions to future research.

Figure 12. Cloud-point curves of R-12-hydroxystearic acid (12HSA) and stearic acid (SA).

Conclusions This chapter has shown the measurement of phase diagrams is exteremly useful in understanding the structure-property relationships of SMOG/polymer gels. While the measurement of full phase diagrams can be an intensive process it is necessary to interpret complex systems, such as the semi-crystalline and 259

crosslinked polymer networks shown as examples. In general phase diagrams serve as an additional tool to aid in the study of gelation by crystalline small molecules, a complex thermodynamic and kinetic process.

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Chapter 14

A Nanoindentation Approach To Assess the Mechanical Properties of Heterogeneous Biological Tissues with Poorly Defined Surface Characteristics Preethi Chandran,*,1 Emilios K. Dimitriadis,2 Peter J. Basser,3 and Ferenc Horkay3 1Department

of Chemical Engineering, Howard University, Washington, DC 20059, United States 2Biomedical Engineering and Physical Science, National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, Maryland 20892, United States 3Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, United States *E-mail: [email protected].

Most living tissues are composite materials with highly nonuniform material properties. Their structure and composition vary from point to point. There are also changes in strength and stiffness, with age and disease condition, which affect the biological function of the tissue. Therefore, the knowledge of tissue mechanical properties on the nano/micro scales is critically important. We have developed an approach to extract the elastic moduli of highly inhomogeneous biological tissues with surface defects that cannot be well characterized. The robustness of our method is illustrated on the example of cartilage extracellular matrix. The tissue was mildly crosslinked to prevent proteoglycan loss due to diffusion occurring upon tissue slicing. Thin tissue slices (~12 μm) have a poorly defined surface layer due to the damage and stress release caused by sectioning. Under indentation forces, the tissue exhibits apparent strain-stiffening, an artifact of the presence of this layer. Therefore, this layer must be accounted for if © 2018 American Chemical Society

the properties of the intact, bulk matrix are to be correctly probed. To separate out the effect of this damaged layer, we used large indentations with the mechanics model for finite sample thickness and included an additional constant force contribution from the surface layer as well as the contact point of the underlying intact layer as fitting parameters. This in effect is equivalent to allowing for the existence of an effective\contact point that is computed as a best-fit parameter. By not forcing the fitted contact point to be on the force curve and by applying larger indentations, we obtain the elasticity of an equivalent material undergoing similar indentation but having a smooth, undamaged surface. Such an approach not only gave us an elasticity modulus that remained unchanged with indentation depth, but also had good correlation across length scales. This explains previous observations that the Hertz model cannot satisfactorily probe matrix mechanics and instead, large deformation models need to be employed (Lin et.al, Biomech. Model. Mechanobiol., 2009). Comparing the contributions from the intact matrix alone, we found that the cartilage stiffness increases towards the resting zone but decreases in the proliferative zone, even though the chemical composition does not change significantly between these regions.

1. Introduction The knowledge of the mechanical properties and structure of biological tissues is necessary for better understanding their physiological functions. In general, biological tissues are highly heterogeneous, composite materials containing macromolecules (proteins, polysaccharides, polynucleotides) small organic molecules, ions, water, etc. Tissue mechanical properties are closely connected to their physiological state. The main objective of biomechanical studies is to determine the mechanical response of the tissue and develop models to relate the chemical composition to the mechanical behavior, and the mechanical behavior to the biological function. The mechanical behavior of living tissues is significantly different from typical engineering materials. Biological tissues are gel-like materials that exhibit viscoelastic properties, i.e., the stress-strain relationship is a function of the rate at which the stress is applied on the material. Because of the composite nature of biological tissues their properties change from point to point. Elasticity measurements provide important information about structural changes and it is known that changes in the elastic modulus may be indicative of disease. It has been reported that the load bearing ability of osteoarthritic cartilage is about one order of magnitude lower than that of normal (healthy) cartilage (1). 266

Due to the heterogeneity of biological tissues, it is essential to develop high-resolution approaches that can accurately assess tissue elastic properties. In the present work, we illustrate our approach on mouse cartilage samples using the Atomic Force Microscope (AFM). We address several major experimental challenges which should be considered to make meaningful nanoindentation measurements on cartilage. We propose a robust approach to extract the elastic moduli from indentation data and construct the elastic modulus map of the tissue. We present a novel force curve fitting method to analyze the data. The results indicate that our procedure provides reproducible estimates for the elastic modulus of cartilage and can be potentially applied to investigate other heterogeneous tissue samples. Articular cartilage is a thin layer of tissue lining the apposed surfaces of joints preventing bone-to-bone hard contact and lubricating motion by maintaining a large swelling pressure (2, 3). Its microstructure consists of closely packed highly negatively charged aggrecan molecules confined within a collagen network (4, 5). The charge-repulsion and counter-ion influx due to the packing of negativelycharged entities within the collagen network produces a high swelling pressure in equilibrium with the matrix that is under tension (6, 7). The swelling pressure enables cartilage tissue to bear compressive loads. The relation between cartilage composition and mechanics is of considerable interest because the former changes with age and disease (8–11). The growth plate is a cartilaginous tissue present at the end of long bones. Positioned between the articular surface and the fully-developed bone region, the tissue is responsible for growth and lengthening of bones (12, 13). It provides a scaffold for a reservoir of chondrocytes that are recruited into dividing, growing, secreting matrix, and eventually calcifying into bone. The different stages of bone formation occur in the growth plate as a sequence of spatially-separated zones (Fig. 1) (12). At one end of the growth plate is the Articular Surface (AS), below which is a layer rich in dormant chondrocyte cells known as the ‘Reserve’ or ‘Resting’ zone (14). The section of cells towards the bone surface divides to form transverse stacks or columns of flat cells that are aligned along the long axis of the bone. This zone is known as the ‘Proliferative’ zone. The dividing cells increase in size 5 – 10 fold, secrete cartilage matrix, and become separated in the ‘Hypertrophic’ zone. Subsequent calcification of these cells in the ‘Calcified zone’ results in the formation of bone matrix. Because of the well-documented spatial changes in the tissue composition and architecture, the cartilage growth plate becomes an appropriate template for understanding the biophysical coupling between between nanoscale composition, microscale mechanics, and macroscale function of a tissue (15, 16). Defects in growth plate formation result in mild to severe forms of skeletal deformities (17). The composition of the cartilage matrix (distribution and type of collagen, proteoglycans and hyaluronic acid) varies between the zones of the growth plate. Previous studies have revealed the effect of this variability on local mechanics (18–20), but the results have been inconsistent due to the intrinsic challenges in obtaining local, bulk matrix mechanical properties from a hierarchical composite structure with several scales of organization (21, 22). For instance unconfined compression studies for millimeter-sized matrix regions show the stiffness 267

decreasing from the resting zone to the proliferative/hypertrophic zone (22). On the other hand, AFM nano-indentation of matrix regions in a rabbit growth plate shows the stiffness increasing from the articular to hypertrophic region, reflecting the calcium deposition pattern within the growth plate (23).

Figure 1. Growth Plate of Articular Cartilage with schematic of distinguishing cell features. Researchers observed that matrix elasticity changes by orders of magnitude depending on the contact area in indentation studies. Macroscale indentation experiments report elasticity on the order of MPa, whereas nanoscale indentations report values on the order of 10s of kPa (24). Park et al. demonstrated that the matrix elastic modulus increases with the size of the indenter (25). Indentations with nanoscale (sharp) probes appear to be picking up the mechanics of individual macromolecules; they produce a bimodal distribution of elasticity depending on whether collagen fibers or the much softer aggrecan molecule is indented (24, 26, 27). On the other hand, the matrix mechanics in macroscale indentation experiments could be dominated by the mechanical properties of the cells (28, 29). It has also been reported that the elastic modulus increases with indentation depth in the zones of the growth plate (25). Darling et al. reported a three-fold increase in elasticity when indentation forces were increased from 5 to 50 nN (30). While the depth-dependent changes might reflect a cartilage matrix that is nonlinearly stiffening, researchers have suggested that the initial low values of elastic moduli could be contributed from a damaged or collapsed layer present atop the tissue slice (30). Some of the reported variations in growth plate mechanics can be attributed to the age of the plate. Prein et al. reported that the stiffness of the proliferative zone in mouse growth plate increased with age (26). However in such samples it is challenging to separate the age-related changes in matrix composition from load-induced remodeling changes (31). For instance, rats that are temporarily exposed to gravity-free conditions (no load-induced remodeling) have different 268

calcification profiles, collagen morphology, and proteoglycan distribution in their growth plates (32). Recently Mertz et al. reported the matrix composition in different zones of the neonatal mouse cartilage in terms of its collagen, proteoglycans, proteoglycan sulfation, and non-collagenous protein contents (33). The measurements were obtained with μm-scale resolution using infrared hyperspectral imaging, and the tissue slices were kept in specialized chambers to prevent their collapse and loss of shape. Our goal is to correlate the compositional changes in the cartilage growth plate to changes in matrix micro-mechanics with a robust experimental methodology that addresses the common artifactual challenges faced when probing a heterogeneous microstructure with several scales of organization and with a damaged superficial layer. Our experimental methodology included the following features: We used neonatal wild-type mouse cartilage, because it has not been subject to weight bearing, i.e., variations in mechanical properties from load-induced remodeling can be discounted: •

• •

•

•

The tissue slice was depleted of calcium so that only the compressibility of the soft matrix components (collagen, proteoglycans, non-collagenous proteins) was probed. The μm-sized indentation probe was selected such that its contact area was larger than the high-frequency surface roughness due to individual macromolecules and slicing artifacts, while still small enough to resolve matrix and cell regions at μm-scale penetration depths. The penetration depth was selected to be large enough to extend beyond the superficial damaged layer and probe the underlying intact matrix. The neonatal cartilage is rich in cells and the matrix indentation points alone were selected by aligning the height and elasticity profiles against the optical images. Moreover, jointly examining the height and elasticity profiles allowed us to distinguish pure matrix regions from matrix regions containing cells or lacunae below. Elasticity was extracted by fitting the force curves to thin film indentation models. Thin film models were used to accommodate the large indentation depths in our experiments. These models require the film thickness at each indentation point as an input parameter. This thickness was obtained by always performing the indentations along a line extending from the base glass slide into the tissue, and subtracting the tissue contact point from that of the base. A modified Hertzian model was used to extract elasticity from the indentation force curves. The Hertzian model by itself describes the indentation of a hard, spherical probe into a homogenous material with smooth surface. However, the tissue surface exhibits significant surface roughness resulting from the slicing. This superficial layer has properties which cannot be simply characterized and differ significantly from the intact matrix below. Consequently, the experimentally-determined contact point (point where forces first appear), does not represent the 269

contact point as required by the Hertzian model (point where contact with a smooth surface is made). To avoid the uncertainties with determining the contact point (CP), we set it as a model fitting parameter that did not need to lie on the force curve. In effect the force curve was considered to be the sum of a constant force contribution from the surface layer of unknown characteristics, and an underlying intact layer with a smooth surface and whose elasticity we are interested in probing. We show that this approach not only corrects for the force contribution from the damaged layer, but also produces matrix contact points and elasticity that are independent of the indentation depth. The latter suggests that the cartilage matrix in each zone is in fact a linear elastic material.

2. Materials and Methods 2.1. Preparing Tissue Slices for AFM Experiments Proximal halves of femurs were dissected from newborn mouse. The tissue was first demineralized by immersion into 0.25 M EDTA solution for 2 hours before sectioning to facilitate uniform attachment to the glass substrate. The demineralized cartilage was then lightly fixed (0.4% formaldehyde for 24 hours) to minimize diffusional loss of glycosaminoglycans after sectioning. A typical cartilage slice was 12 μm thick and extended from the articular surface to the mineralized bone region in all the different regions of the growth plate shown in Fig. 2A. The tissue slices were directly deposited on glass slides (superfrost+, Daigger Scientific, IL) and immediately immersed in 1xPBS. All imaging and force spectroscopy were conducted on hydrated slices using the fluid cell of the Atomic Force Microscope (Bioscope Catalyst, Bruker).

2.2. AFM Imaging of Cartilage Surface To Optimize Spherical Indenter Size and Indentation Depth Based on the Surface Roughness Profile Nanoscale AFM imaging was performed in the “Peak-Force” tapping mode (Nanoscope v.8.15, Bruker-Nano) with sharp tips (7 nm nominal radius of curvature) of etched silicon probes (FESP, Bruker) having nominal stiffness of 2.8 N/m. The roughness was estimated from surface images of cartilage matrix in ~10 X 10 μm2 areas. The appropriate probe diameter was determined by measuring the average roughness over contact areas of different size and selecting that which gave contact areas larger than the individual matrix components (~100 nm) and larger than the typical surface (in-plane) roughness but were small enough to interrogate the matrix region between cells. The cantilever stiffness was chosen so that indentations much greater than the surface roughness can be achieved, to ensure that the bulk, intact matrix was being probed rather than the superficial damaged layer. 270

2.3. Nanoindentation along the Growth Line Indentation was performed using 5 μm diameter silica microspheres (Polysciences, Inc., Warrington, PA) attached to cantilevers of stiffness in the range of 3 to 5 N/m (NanoandMore, Watsonville, CA) using UV-curable epoxy. The stiffness of each cantilever was estimated using the thermal calibration method. The exact microsphere diameter was measured by comparing against a control length under a microscope. The ramp rate for indentations was typically 15-20 μm/sec. Deflection sensitivities were measured at the beginning and end of each experiment by indenting the glass surface. Indentations were performed along the growth line in the growth plate tissue (Figure 2B). These growth lines are the axis along which zonal changes occur between the articular and bone surface. The autoramp feature of the instrument software (Nanoscope v.8.15) was used to indent points along a straight line, which we call the indentation line (Fig. 2C). Each indentation line was 120 μm long with indentation points spaced 1 μm apart. To span the mm distance from the glass slide into the tissue along each growth line, the centers of successive indentation lines were offset by 100 μm (Fig. 2C). This produced an overlap of 10 μm on either side of the indentation lines, which was used for correcting errors in x- y- and z- displacements between consecutive lines (see below). The 1 μm resolution for the indentation points was necessary to obtain smooth profiles of tissue thickness and elasticity along the indentation lines, so that cell and matrix regions can be easily identified (Fig. 2D). 2.4. Extracting Elasticity and Contact Point from Indentation Force Curves with Three-Parameter Hertzian Model The material elasticity was initially estimated from AFM indentation force curves using the Hertz model where a spherical probe indents a homogenous elastic matrix that has infinite thickness and a smooth planar surface. The relation between force F and indentation δ is given as:

where E, v, and R are the matrix elastic modulus, Poisson ratio and the probe radius. The indentation, δ, is the difference between the AFM ramp, z – z0 , and the cantilever deflection d – d0, where z0, d0 are the coordinates of the contact point:

The force is determined from the cantilever deflection as

where k is the spring constant of the cantilever bending. We used a variation of the Hertz model equation proposed by Dimitriadis et al. (34) for a finite-thickness material that is bonded to a rigid substrate: 271

where,

and h is the thickness of the sample. Typically, the contact point is obtained from the force curve as the point where non-zero force appears or where the slope starts to increase nonlinearly. In our case, the probe is indenting a matrix with a rough, possibly collapsed surface caused by slicing. In such a case the cantilever force at low indentations may be due to incomplete contact and this early strain does not homogeneously transmit to the bulk, intact matrix underneath. Therefore, the point at which force is detected does not represent contact with the bulk material. To account for this indeterminate surface layer we introduce a correction to the contact point by searching for an “effective” Hertzian contact point (zH, dH) with scaled zero force FH = k (d-dH) that gives the best fit for the deeper indentations into the matrix

where

We solve the above equation for the three unknown parameters p = [E, zH, dH] , using the classical Least Square Minimization technique with a set of equations described below

where C is the residual that needs to be minimized, Fdata is the experimentally measured force at different z values and F is the best guess for different z, with the values of the parameter vector, p, determined to give the best fit. Because of the square root term in Eqs. 1 and 3, the forces for δ < 0 or δ < δH have only imaginary terms. Since the force values at these indentations are mathematical artifacts with no physical meaning (Hertz model is not valid for these negative indentation values), we neglect them in the calculation of the fitted force vector by taking only the real values of Δp. The Jacobian D for the residual function describes how the function changes when each parameter is changed. 272

Since D is not a square matrix,

The above equation is solved by Newton Raphson iteration to determine p. The convergence of the Newton Raphson method is determined by the goodness of the initial guess for p. We get the initial guess for the components z0 and E in p from the slope and intercept of a straight-line fit to the Hertz equation that is rearranged as

To summarize, there are three strategies that distinguish our method from other fitting strategies of Hertzian mechanics in literature. First, we float our contact point as a fitting parameter since, because of surface roughness and interactions, the slope CP cannot be equated to the idealized Hertz CP. Second, because the Hertz equation has a square root in the indentation term, the zero forces at indentations smaller than the Hertz CP will have imaginary terms. By deliberately updating p with only the real terms from the iteration solution (Eq. ), these non-physical imaginary terms are discarded. Finally, guessing initial values of the elasticity and Hertz CP from straight-line fits to the force vs. separation data ensure that the Newton Raphson solution procedure converges robustly.

2.5. Extracting Matrix Elasticity from Line-Indentation Profiles Each set of indentation data from across each tissue slice was analyzed twice. In the first round of analysis, the contact points of each force curve were determined using the 3-parameter model as described above. These CPs were subtracted from the average CP on the reference glass slide to obtain the tissue thickness at each indentation point. The thickness was then used as an input variable (Eqs. 3 and 4) in a second round of analysis where the thickness-corrected elasticity was determined at each indentation point. Profiles of height and elasticity at each indentation line were aligned against the corresponding optical image to find matrix regions that were uninterrupted by other features (cells, lacunae, pericellular matrix, etc.). These were used to construct a line profile showing how the matrix elasticity varied along the growth line. Matrix elasticity data from the different zones of 4 tissue slices were pooled together to generate a histogram summarizing the zonal variation in matrix mechanics. All analysis procedures, including file handling, model fitting, and matrix selection, were automated by writing MATLAB code. 273

Figure 2. Indentation sequence adopted for spanning a mm-scale growth line with □ overlapping micron-scale indentation areas. 274

3. Results and Discussion 3.1. Determining Probe Diameter and Indentation Depth from Surface Roughness Characteristics Figure 3A is an image of a 50 X 50 μm2 region of the cartilage surface showing a well-separated matrix region (boxed). The surface height along a line at this scale shows the roughness produced by matrix and cell regions. A 5 μm diameter bead is superposed on the plot to help visualize the typical contact areas that arise as the sphere indents into the material. Due to the 10X difference in the x and y scales the bead appears as an ellipse in the figures. For the cell density and cell sizes in the image, the 5 μm bead is able to resolve separate cell and matrix regions. Fig. 3B shows the zoomed-in, high-resolution height image of the matrix region (boxed region from Fig.3A). Several scales of height variation or roughness are seen in the image; the short wavelength variations are possibly due to the protruding macromolecules (GAGs or collagen fibers), whereas longer wavelength variations can be generated by tissue-slicing. Also shown for visualization purposes are the typical contact areas of a 5 μm diameter bead at 1 μm and 1.5 μm indentation depths. As the contact area of the indenter increases with indentation, the magnitude of roughness sampled is expected to increase. We define roughness at a point as the difference between its height and the average height of the surface in a contact area. Figure 3C shows a sample distribution profile for roughness within a contact area that has a contact diameter of 1 μm. In Fig. 3D we show how this roughness distribution varies with contact area by plotting the 50%, 75%, and 100% values of the distribution for different contact area diameters. The data for the plot were accumulated from multiple high-resolution scans of 100 μm2 matrix areas in three mm-size cartilage slices. The plot shows that the roughness distribution increases with contact area, stabilizes at contact area diameter between 0.4 and 0.5 μm, and then increases again to stabilize beyond 1 μm diameter. The plot captures the wavelength and amplitude of the two anticipated roughness sources. At the shorter length scale, 97% of the roughness amplitudes are below 50 nm and have wavelength below 250 nm. These roughness dimensions are consistent with protruding cartilage macromolecules. For instance, aggrecan length is about 100-200 nm, and aggrecan and collagen diameters are about 50 – 60 nm (7, 35). At higher length scales, 97% of roughness amplitudes fall below 120 nm and have wavelength below 1.2 μm.

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Figure 3. [A] AFM image of cartilage height showing separate matrix and cell regions. The height profile along the blue line is shown on the right, with a superposed image of a 5 μm sphere (blue circle). The sketch to the right shows the sphere approaching the matrix region. The difference in x and y scales cause the sphere to appear elliptical. [B] High-resolution image of the matrix region from Fig. 3A (box) with the contact areas of a 5 μm diameter bead at 1 and 1.5 μm indentations superposed. The sketch to the right shows typical roughness indented by the 5μm sphere. [C] Histogram of surface roughness sampled for areas with contact diameter of 1 μm within the matric region of cartilage. [D] The 50, 97, and 100 percentile values of cartilage roughness sampled in histograms such as C, shown plotted for different contact area diameters. Superposed on the plots are the contact areas for spherical probes of different diameters obtained at different indentation depths. To obtain meaningful force curves for the underlying matrix, we not only need to indent beyond the rough layer but also need to do so with a minimum probe diameter that exceeds the matrix roughness length scale. That is, the contact diameter must be greater than the largest roughness wavelength and the indentation depth must be larger than the largest roughness amplitude. Now the contact area (D) is related to the indentation depth (r) for a given probe diameter (d) as r ~ 0.5(D2/d). To determine a suitable probe diameter and minimum indentation depth, we superposed the indentation depth vs. contact area diameter plots for different probe diameters on the roughness amplitude vs. wavelength plot in Fig. 3D. From the combined plots, it can be inferred that a 2.5 μm diameter probe has to indent > 250 nm to achieve contact areas of diameter > 1.2 μm. However, by this indentation depth, the probe has penetrated well over the roughness depths. On the other hand, a probe of 5 μm diameter samples the 1.2 μm contact diameter at 150 nm indentation where the indentation is also 97% of the surface roughness. Probes larger than 5 μm achieve the desired contact area at lower indentations, but require larger contact areas to surpass the roughness amplitudes. The latter decreases the ability of larger probes to resolve cell and matrix regions. For this reason, we chose to work with a 5 μm probe where both the roughness wavelength and amplitudes were surpassed by 150 nm indentation. In order to indent the material beyond roughness depths, we choose AFM cantilevers with nominal stiffness in the range 3-5 N/m. Depending on the stiffness of the bulk matrix, such a cantilever can achieve 500 nm to 2 μm indentation into the tissue slice. 3.2. Extracting Elasticity by Fitting Three Parameters in the Hertzian Indentation Model The Hertz model of indentation mechanics is commonly used to extract elastic modulus from the force curves. The model describes the indentation of a spherical probe into a material with a smooth surface (Fig.4 left). The Hertz contact point (H-CP) is the point of zero indentation where the probe contacts a smooth surface and resistive forces appear. In experiments however, the sphere makes contact with a rough surface (roughness ~ 150 nm) and can indent further into the superficial 277

collapsed layer before sampling the intact layer beneath (Fig. 4 right) (36). The experimental CP, determined as the point where forces appear, is not suitable for extracting the elasticity of the underlying intact tissue using the Hertz idealization. In fact the Hertz-relevant CP for the intact layer is expected to lie somewhere between the experimental CP and the intact layer (Fig. 3). Since it is not known where the Hertz CP lies, we set it as an unknown variable in the Hertz equation and solve for it to get the best fit with the experimental data. The basal force at contact is also solved as a best-fit parameter. This is the extra force due to the damaged and rough layer that needs to be added to the Hertzian description of the intact layer mechanics. We fit the experimental force curves to the Hertz model (Eqs, 5-7) by solving for three parameters: the Hertz-relevant CP, the basal force at Hertz CP, and the elastic modulus.

Figure 4. Classic Hertz mechanics describes the indentation of a spherical probe into an intact homogenous layer with a smooth surface (left), whereas in experiments the surface of the tissue is rough and may contain a collapsed layer. As a result the contact point expected by the Hertz model is not equivalent to the slope contact point determined in experiments. The slope contact point in experiments is the point at which a surface is contacted and where a resistive force is first seen to arise. The Hertz contact point marks the beginning of the intact material which is underneath the collapsed surface layer and in whose material properties we are interested in probing.

Figure 5A(left) shows a typical force curve from the matrix region of the cartilage slice and its best fit with the conventional one-parameter Hertz indentation model where the elasticity alone is solved as a best-fit parameter. Here the contact point is the physical point of contact determined from the change in the slope of the deflection vs. displacement curve. The one-parameter fitting does not capture the experimental force curve well, giving the impression that the intact matrix has nonlinear and depth-dependent properties. On the other hand, the three-parameter model, where the Hertz CP is solved as a best-fit parameter and does not necessarily fall on the force curve, captures the matrix indentation force curve well (Fig. 5A, right). The difference between the two CPs, which is ~ 200 nm, is an estimate of the size of the damaged layer atop the intact tissue 278

and it is about the thickness of two to three collagen filaments (37). In fact, when the damaged layer is discounted for, the cartilage matrix in each zone appears rather linear with no depth-dependent variations. Shown in Fig. 5B are the best-fit Hertz-relevant CP and elasticity determined for force curves up to different indentation levels. As the indentation range increases, values of both the Hertz-relevant CP and elasticity stabilize, indicating that at depths beyond the collapsed layer the matrix is not strain-stiffening. This is in contrast to the observation of Park et al. (25) who used the one-parameter Hertz fit and reported that the elasticity does not stabilize as the indentation increases, except at small indentations. We observed that the elasticity calculated with the experimental CP shows a similar behavior in our case (Fig. 5B, dotted); it is nearly constant at small indentation, but increases monotonically with increasing indentation. Also shown in plot 5B is the elasticity vs. indentation curve without making the finite thickness correction. Using a floating Hertz CP leads to stabilized values, but they are 10-30% higher than the elasticity values with the finite thickness correction. We note that when using the Hertz CP, our results indicate that indentations > 400 nm are required to get consistent values of matrix elasticity (Fig. 5B). The higher indentations are necessary so that much of the force sampling comes from the intact region and not from the collapsed region (38). In Figure 5C we show that the Hertz CP is more representative of the surface feature of the tissue slice. Its height profiles show smooth changes that track the features in the optical image; cells appear taller and lacunae appear as pits. On the other hand, the height profiles from the Slope CP have a lot of fluctuations, which may be attributed to the rough/collapsed surface of the tissue and to spurious biomolecular and hydrodynamic interactions between the tip and surface. The latter especially are not easily quantifiable and not relevant to the determination of material mechanics.

3.3. Indentation Profiles of Growth Zones in Cartilage The elasticity and height profiles for each line indentation were aligned with the optical image. Examples from the four growth zones are shown in Figure 6. Cells appear at U-shaped troughs in the elasticity profile and as elevated regions in the height profile (Fig.6A). The pericellular matrix (PCM) shows up as narrow rings around the cell (Fig.6A). The PCM is the matrix in which cells are housed; it is rich in proteoglycans and type VI collagen rather than in type II. Extracellular Matrix (ECM) regions appear as spikes of increased moduli in the elasticity profiles (Fig.6A). The ECM region is much stiffer than the cell while the PCM is of intermediate stiffness. Fig. 7A shows representative force curves for complete indentation into a cell, PCM, and ECM regions from the Reserve zone. For these representative cases, the three-parameter Hertz fit yields elastic moduli of ~284 kPa, 667 kPa, and 1364 kPa, respectively. The ratio between the ECM, PCM, and cell moduli is about 1:3:5 , and it reflects reports by researchers of a two- to three- fold increase in elasticity between cell and PCM, and between PCM and ECM (30, 36, 39). Moreover, the matrix modulus is on the order reported for both micro- and millimeter scale indentation into cartilage (27, 40). 279

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Figure 5. [A] AFM force curves on the cartilage matrix were fit with the Hertz indentation model. The plot on the left uses the experiment-relevant slope CP (the cantilever approaches the point where forces first appear) and the Hertz prediction does not fit the data well. The plot on the right uses the Hertz-relevant CP (derived for giving the best fit to data) and it provides a better fit to the experimental data. [B] The Hertz CP and indentation modulus becomes constant with depth after an initial region where the fitting is affected by the collapsed layer. [C] The Hertz CP provides a height profile that is more reflective of the surface features than the Slope CP.

The specific shapes of the cells, PCM, and ECM in the elasticity profiles reflect the inhomogeneity of cartilage morphology. As the spherical probe indents deeper, the contact area increases bringing in contributions from both the neighboring and deeper features of the region. For instance, the trough-shaped elasticity profile of a cell (shaded region in Fig.6A) arises not because the cell becomes progressively stiffer towards the PCM, but because the contribution from the underlying/neighboring PCM and ECM regions increases as the cell’s periphery is indented (Fig. 7B). Consider a sample force curve from the cell region in Fig. 6A (Fig.7B). It contains serial contributions from the cell and the PCM/ECM region, with the latter being much stiffer (large slope) and its contribution increases towards the cell periphery. Fitting these curves with a single modulus produces the trough-shaped elasticity profile for the cell regions. The ECM regions appear as spikes in the elasticity profile because on either side of the spike the probe starts sampling contributions from neighboring cells/PCM at increasing depth. The latter are more compliant and lower the matrix elasticity. This is especially an issue in neonatal mouse cartilage, which is known to have high cellular density. Also, features that are below the surface and not clearly visible in the optical image can still be distinguished in the elasticity profiles. For instance, the marked region in Fig. 6B shows a region of constant height that has ‘troughs’ in the elasticity profiles due to cell or lacuna present below the surface. Finally, we observed that the indentation force curves of cells in the proliferative/hypertrophic region were significantly different from those in the articular/resting region (Fig. 7C). The former has a region of low force development with large compressive strains characteristically seen in buckling shells (41). The cells in the resting zone have stem-cell like character and are recruited to divide and form chondrocytes in the proliferative and hypertrophic zones (14).

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Figure 6. Sample plots of the elasticity and height profiles obtained by microindentation along the growth line in four growth zones of the neonatal mouse cartilage, shown along with corresponding optical images. The four growth zones are [A] Articular zone, [B] Resting zone, [C] Proliferative zone, and [D] Calcified zone.

3.4. Matrix Mechanics along the Growth Line Matrix-only indentation curves were selected using in-house software which displayed individual force curves against location on the optical image along with the corresponding elasticity and height profiles. The moduli of the matrix regions along the growth line are plotted in Fig. 8A. Elasticity profiles across matrix septa between cells exhibit bell-shape. This may be because toward either end of the profile, there is contribution from neighboring cells or empty lacunae to the force curve and these regions are much more compliant than the matrix. Another explanation may be that the matrix becomes softer as we approach a cell, entering the pericellular matrix region around the cell. Either way, the peaks of the bellshaped elasticity profiles are the best estimates of the true matrix elastic modulus and hence, the outer envelope of the elasticity scatter plot, as shown in Fig. 8A, is the best estimate of the overall elastic modulus map across the whole tissue. The profile of matrix elasticity along the growth line exhibits the following trend: The modulus increases from the articular surface towards the resting zone, and decreases in the proliferative zone toward the bone surface. There may be a short hypertrophic region where the moduli increase. Average values of the matrix obtained from 4 samples also show similar trends (Fig. 8B). Radhakrishnan et al. (23) reported that the matrix moduli increased from the articular surface to the resting zone in microindentation studies of adult rabbit growth plate, and the values of their moduli were in the range measured in our study. However, their values continued to increase beyond the resting zone to the bone surface, while they decreased in our study. One reason for the difference could be that their matrix stiffness is tracking the increasing calcium content between the resting zone and bone surface, whereas the calcium was depleted from our tissue slices and only the stiffness contribution from the soft material components of cartilage was probed. Differences could also arise because the model systems were different (adult rabbit vs. neonatal mouse) and because of the different extents of load-induced remodeling. There is no load-induced remodeing in neonatal cartilage and the latter is known to affect the structure of the proliferative zone (15). On the other hand, multiple researchers have reported the stiffness of the proliferative zone to be less than the resting zone in millimeter scale compression tests. Sergerie et al (22) reported that in newborn swine the proliferative zone was at least two times less stiff and more permeable than the reserve zone. 283

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Figure 7. [A] Representative force curves showing indentation into regions containing only cell, PCM, and ECM as indicated by the sketch to the right. [B] Sequential indentation along a line in a composite region of cell, PCM, and ECM with the force curves showing sharp changes in slope to reflect the elasticity of successive entities being indentated. [C] Cells in the reserve and proliferative region respond differently to indentation, with the latter exhibiting more shell-buckling character.

Figure 8. A: Changes in matrix indentation elasticity along the growth line shown in the cartilage slice B. C: Average matrix elastic modulus extracted from indentation data in different zones along the growth line. 285

When it comes to correlating elasticity maps with composition profiles one has to take into account that while chemical analysis gives the collagen and PG contents, elasticity analysis also reflects the organization of the collagen. For instance, we observe that cartilage elastic modulus increases from the articular surface towards the resting zone but decreases in the proliferative zone. In Mertz et al (33) , the collagen concentration also increases from the articular surface inward but stays relatively unchanged further into the deeper regions. The elasticity result would also reflect the changes in the collagen structure and organization between the resting and proliferative zones. Collagen fibers are thinner and oriented in all directions parallel to the articular surface while they are thicker and oriented along the bone axis in the hypertrophic zone (42). Therefore, the AFM indentations will probe different directions in an anisotropic tissue. It is possible that the elasticity of the proliferative zone could be reflecting the organization of matrix that is turned over to accommodate dividing and hypertrophic cells (31). 3.5. Osmotic Modulus Map of Mouse Cartilage AFM makes it possible to determine the local elastic modulus of cartilage which provides invaluable information on the mechanical properties of the tissue. The elastic modulus is directly related to the osmotic compression modulus Mos; the latter defines the load bearing ability of cartilage. Mos quantifies the volume resistance of the tissue to an applied compressive load that encompasses not only the elastic properties of the material but also its composition and interactions with its environment

where sw is the osmotic swelling pressure and φ is the polymer concentration of the sample. Mos can be estimated from the concentration dependence of Πsw. At equilibrium swelling (φ = φe), the shear modulus G balances the osmotic pressure, i.e., Π(φe) = G(φe) and Πsw(φe) = 0 (43). At φ > φe we have Πsw(φ) = Π(φ) G(φ). Experimental findings indicate that the concentration dependence of both Π and G follow a simple power law and for solutions of associating polymer G µ φ (44). Thus,

where m is the power law exponent of the osmotic pressure. Our measurements made on 1 day old cartilage samples yield m = 2.6. We developed a procedure for mapping the osmotic compression modulus of biological tissues such as cartilage by making tandem measurements of the elastic and osmotic properties combining AFM and osmotic swelling pressure observations made by a tissue micro-osmometer (TMO) described previously (45). In the TMO tissue swelling/deswelling is induced by equilibrating the samples with water vapor of known vapor pressure at constant temperature. The 286

mass change associated with the water uptake is measured by a quartz crystal microbalance. The apparatus allows us to detect small changes (< 0.1 µg) in the mass of the swollen tissue. The osmotic modulus maps quantify the effect of micro- and nano-scale inhomogeneities on the load bearing properties of the tissue.

Figure 9. Variation of the elastic and osmotic moduli as a function of the position in mouse cartilage sample. Figure 9 shows the variation of the osmotic compression modulus and the elastic modulus measured along a line at different positions. The elastic moduli E were directly obtained from the AFM force-indentation measurements. For each point the local polymer concentration in the gel was estimated from the local elastic modulus assuming that the macroscopic linear relationship remains valid on the microscopic level. We derived the shear modulus from the experimental values of E using the relationship G(φ) = E(φ)/3, i.e., assuming that the Poisson ratio was 0.5. The osmotic compression moduli were estimated using Eq. . Figure 9 illustrates that the osmotic modulus is more than an order of magnitude greater than the elastic modulus, and it exhibits significantly larger local variations reflecting the strong dependence of Mo on the polymer concentration. The elastic and osmotic property maps are particularly important to estimate the compressive behavior of biological tissues. These new observations shed light on the relationships between morphology (e.g., molecular packing) and the local elastic properties of the sample and that can serve as the baseline for further 287

studies of various tissues. For instance, it is known that a decrease in the shear modulus of articular cartilage results in reduced compressive resistance and hence compromised load-bearing capacity. In knee and hip, in which cartilage is exposed to large-amplitude repetitive loading during walking (or other physical activities), complete and rapid recovery of the tissue after unloading is an essential requirement for normal function. A relatively smooth map of Mos implies that resorption of water occurs consistently throughout the sample while large variations in Mos result nonuniform recovery.

Summary We chose to study mouse cartilage as mouse is the most commonly used animal model for many diseases, including various types of arthritis. Mapping the elasticity of mouse cartilage through tissue thickness presents several challenges. First, mouse cartilage has a very dense population of cells leaving small regions of exposed matrix to probe. Second, sectioning the tissue causes proteoglycan loss and creates a surface layer that is rough and much softer than the intact matrix. In addition, stress release also associated with sectioning causes anisotropic thickness changes to the tissue sections used to probe elasticity. We used mild fixation to prevent proteoglycan losses. To account for the softer but indeterminate surface layer we quantified the roughness, and based on that, we chose the optimal probe size and indentation depths to ensure that we were probing beyond the surface layer and into the intact matrix underneath. The issue of the indeterminate surface layer is more generally encountered, particularly with biological samples. To extract elastic moduli from the indentation data that account for both surface layer and matrix, we developed a novel force curve fitting method that introduces both coordinates of the contact point as independent fitting parameters. This defines an effective contact point for the intact matrix. It is demonstrated that as indentation increases the values of the elastic moduli converge to the true matrix moduli. The effect of the narrowness of the matrix septa between cells on the apparent elasticity and the possibility that the matrix becomes itself softer within the pericellular region require further investigation. In our measured elasticity profiles along tissue thickness we observe an apparent correlation with chemical composition near the articular surface. It is however known that both collagen fiber thickness and fiber orientation vary between different zones. More detailed studies of the elastic properties that account for this anisotropy will be needed to better correlate mechanics with composition.

Acknowledgments This research was supported by the Intramural Research Program of the NICHD, NIH. We are grateful to Howard University undergraduate student, Mr. Nolan English, for assistance with organizing and analyzing force curves from different samples. The authors also acknowldge Dr Edward Mertz (NICHD/NIH) for providing the mouse cartilage specimen and many useful discussions. 288

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Chapter 15

Gels for the Cleaning of Works of Art D. Chelazzi, E. Fratini, R. Giorgi, R. Mastrangelo, M. Rossi, and P. Baglioni* Department of Chemistry Ugo Schiff and CSGI, University of Florence, Via della Lastruccia 3, Sesto Fiorentino, 50019 Florence, Italy *E-mail: [email protected].

Works of art must be readable and well preserved in order to be accessible. Therefore, the removal of unwanted layers (dirt, soil, aged adhesives and varnishes) is fundamental in conservation practice, to maintain the readability of artworks and prevent their degradation. Because most artworks’ surfaces are sensitive to aqueous solutions or organic solvents, the cleaning fluids must be confined in retentive networks able to grant a controlled release and the non-invasive removal of the unwanted layers, without affecting the original components of the artifacts. This contribution reports on the most promising classes of polymer networks that have been specifically developed and applied for the cleaning of artworks, namely: chemical hydrogels based on poly(2-hydroxyethyl methacrylate) (pHEMA), chemical organogels based on Poly(methyl methacrylate) (PMMA), peelable hydrogels based on poly(vinyl alcohol) (PVA), and physical cryogels based on PVA. The physico-chemical properties and applicative aspects of these materials are discussed. Key characteristics include high viscoelasticity (to grant the feasible handling and removal of the gels from the treated surfaces) and retentiveness. Some representative conservation cases are shown, regarding the cleaning of metal objects and easel paintings. Overall, a large palette of innovative formulations has been provided to the conservation community, to improve on the limitations of traditional solvent thickeners.

© 2018 American Chemical Society

Introduction The surface of an artwork conveys the aesthetic values and the message of the artist. Any alteration of the surface directly affects the readability and enjoyability of the work, with potential impact on the social and economic aspects related to the accessibility and exhibition of the artwork. The surface of the work of art is continuously subjected to degradation induced by weathering (for exterior facades, murals, statutes, stone, etc.), light, temperature and relative humidity, pollution gases and volatile organic compounds (VOCs), dust and soil, microorganisms, and even materials applied in previous restoration interventions that may prove detrimental (1–4). Not surprisingly, the removal of unwanted materials (e.g. dust, soil, patinas, aged adhesives) from the surfaces of artworks is one of the most frequent operations in the restoration practice that requires great care and attention to avoid the removal or alter the original components of the work. Traditionally, conservators have used both wet and dry methods to clean works of art. Dry cleaning with conventional tools such as scalpels, swabs and brushes, is difficult to control, with the risk of unselective removal or physical damage to the artwork; recently, the potential of laser cleaning for easel paintings has been explored (5). Wet cleaning is commonly adopted as a standard procedure, and the main approach is to select solvents whose solubility parameters (e.g. as indicated in a Teas chart (6)) match those of the unwanted layers that need to be removed. This allows to swell (and mechanically remove) or directly solubilize the layers, which are then absorbed into cotton swabs, blotting paper, or other absorbents. However, the use of solvents involves several risks to the artwork and the operator. Once the solvents are applied onto the artwork’s surface they are difficult to control, and are able to penetrate through porous substrates, unselectively affecting original components along with unwanted materials. This can lead to swelling, leaching or solubilization of dyes, binders, and other components of the work of art. Moreover once the unwanted layers are solubilized, they can be transported within the pores of the artwork, making their effective removal difficult. Finally, the use of solvents involves health risks that must be taken into account. The ecotoxicological impact can be greatly reduced using aqueous solutions of surfactants, chelating agents, enzymes, acids or bases. By tuning the conductivity and ionic strength of the solutions, it is also possible to limit the extraction of watersoluble original components from painted layers (7). A significant improvement that emerged in the last decade is the use of oil-in-water (o/w) microemulsions, where limited amounts of solvents are stably dispersed as nano-sized droplets in a continuous water phase, using surfactants; these aqueous systems interact with aged adhesives and varnishes through different mechanisms mainly belonging to classic detergency, and in some cases dewetting the unwanted layers from the surface. o/w microemulsions have proven a valid alternative to solvent blends in the removal of aged adhesives, varnishes, soil, and other unwanted materials from the surface of artefacts (8, 9). The main drawback is due to the fact that the use of free (non confined) aqueous systems can be risky on highly water-sensitive surfaces; this is the case, for instance, of paper artworks featuring water-soluble inks or dyes, or some formulations of acrylic or oil paintings. 292

To overcome these limitations, solvents and aqueous systems can be confined in retentive networks, able to upload the fluids and release them at controlled rate. The gradual release of fluids favors the selective removal of unwanted layers, preserving the original surface. Besides, when solvents are confined, their evaporation rate is reduced, hence the toxicity of the whole cleaning system consistenly is reduced. Thickeners have been used for decades in the restoration practice to increase the viscosity of cleaning fluids, so as to limit their spreading and penetration. Several products have been derived from cosmetics, food science and pharmaceutics, e.g. cellulose derivatives (hydroxypropylcellulose, methyl 2-hydroxyethyl cellulose, hydroxypropyl methylcellulose) and polysaccharides (agar, gellan, xanthan gum). These polymers have been used to thicken aqeuous solutions of enzymes, chelating agents and surfactants, or blends of water and polar solvents (e.g. alcohols and glycols). While the thickened solutions are relatively easy to prepare and use, the main concern involves the possibility of leaving polymer residues on the treated surface (10). At the concentration values typically used for cleaning purposes, cellulose ethers solutions display the mechanical dynamic response of viscoelastic liquids: once applied on a surface, the thickened solutions are still able to flow, granting only limited control of the cleaning intervention; moreover, their removal from the treated surface is difficult, owing to the fact that the weak cohesive forces within the polymer solution are comparable to the adhesive forces between the polymer chains and the surface. Gellan and agar are often prepared as “rigid” sheets (11), which behave rheologically as strong gel networks, and as such can be removed from surfaces leaving only minimal or no polymer residues. However, in several cases artworks have surface roughness on the order of millimiters or centimeters, and rigid sheets can not grant homogeneous adhesion and removal of dirt. Polyacrylic acid (PAA) was introduced in the restoration practice by Richard Wolbers in the late 1980s (12). PAA chains unfold at alkaline pH, forming extended 3D networks that increase the viscosity of the solution. When alkaline surfactants are used to deprotonate PAA, the thickened solution acquires emulsifying and detergent properties. Typically, tertiary amine ethoxylates (Ethomeen®) are used to prepare these systems, named “solvent gels”, which have been widely adopted by conservators. One of their main advantages relies in their versatility: using Ethomeen® surfactants with different HLB (hydrophilic-lipophilic balance), it is possible to thicken a wide range of solvents, from low-polarity (aliphatic and aromatic hydrocarbons), to averageor high-polarity (alcohols, ketones, esters), and even enzyme solutions. Short application times are needed, typically few minutes. Similarly to cellulose ethers, the main drawback regards the presence of polymer residues and other non-volatile compounds left on the artwork’s surface. Because the cross-links between the PAA chains are not permanent, the thickened solutions display a prevalently viscous behavior, and once applied (e.g. with spatulas or swabs) they must be removed coupling mechanical action with the use of clearing solvents. However, it has been shown that residues of PAA and Ethomeen can be found on the surface of paintings even after clearance with solvents (13), and clearing solvents can induce changes to the surface. Moreover, some concerns have been 293

raised regarding the possible long-term synergistic effect of amine N-oxides (formed by the degradation of Ethomeen) on the degradation of terpenoid resins and oils used in paints (14). To improve on traditional thickeners, several systems have been developed in the last decades in the framework of colloids science and soft matter. The fundamental idea is to formulate polymer networks with tunable properties, so as to adapt the vast range of conservation issues found in the cleaning of artworks. The formulations must exhibit optimal mechanical behavior and retentiveness of the uploaded fluids. High viscoelasticity is fundamental to grant the feasible handling of the systems and their removal in a single step from the surface (e.g. by peeling) after the application, without rinsing. Both chemical gels (i.e. held by covalent crosslinks) and physical gels (held by secondary bonds) have been explored, monitoring the rheological properties, the micro- and mesoporosity, and the macroscopic behavior of the formulations (15, 16). By changing the nature of the polymer and adjusting the pore size distribution of the network, it is possible to obtain highly retentive gels that are usable even on sensitive layers. The desired viscoelasticity for practical applications can be obtained tuning the amount of crosslinks between the polymer chains. In the case of physical gels, strong networks can be obtained without using crosslinkers, for instance via freeze-thaw cycles that form highly ordered regions (crystallites) where the polymer chains are held by secondary bonds. A particularly interesting aspect regards the possibility of loading the gels with nanostructured cleaning fluids, i.e. o/w microeulsions. Recently, the structure of an o/w microemulsion, confined in a poly(vinyl alcohol) (PVA) gel, have been investigated; only minimal alteration of the structure of both the fluid and gel occurs, thus the functionality of the cleaning system is maintained (17). Besides hydrogels (loaded with aqueous systems or polar solvents), organogels (loaded with average- or low-polarity solvents) have been proposed as complementary tools for surfaces that can not tolerate any contact with water (18, 19). Overall, a palette of tools and solutions has been provided to conservators, who can select, together with formulators, the best candidate for each cleaning case study. In the following sections, an overview of the most promising classes of hydro- and organogels is presented, namely: chemical hydrogels based on poly(2-hydroxyethyl methacrylate) (pHEMA); chemical organogels based on Poly(methyl methacrylate) (PMMA); peelable hydrogels based on PVA; physical cryogels based on PVA. The physico-chemical properties of these systems will be discussed, and the main applicative aspects regarding their use for the cleaning of artworks will be highlighted. These formulations have been selected as they represent some of the most advanced tools currently available for the cleaning of works of art, and have been successfully used on artifacts belonging to the classic, modern, and contemporary Cultural Heritage, from inked manuscripts to stone, wall paintings, and easel paintings by artists such as Pablo Picasso and Jackson Pollock (20–23).

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Polyvinylalcohol-Based Formulations for Cleaning The great variety of artistic substrates to be cleaned, and the complex surface morphology that some of them present, may require cleaning tools with mechanical and rheological properties that vary depending on the case study. This means that in some cases highly viscous systems are preferred, while in others it is more advisable to work with strong gels with high elastic modulus. Polyvinylalcohol (PVA) with different hydrolysis degrees, even combined with other components, is a versatile macromolecule that allows obtaining gels with characteristics that fulfill most of the conservators’ requirements. Condensation of alcohol groups with borates originates a network of chains that provides high viscosity to the system (24, 25) The first formulation investigated for art conservation was based on an aqueous dispersion of highly hydrolyzed PVA. Depending on the average molecular weight of PVA, its concentration, the concentration of borate ions, the pH of the aqueous solution (26), and the temperature, the system can be very stiff or quite malleable (27). Rheological characterization provided a quantitative description of the obtained systems. The frequency sweep curves obtained for all the formulations investigated are typical of Highly Viscous Polymeric Dispersions (HVPD): at low frequency, the loss modulus G” is greater than the storage modulus G’ (i.e. the elastic character), but at high frequency, G’ exceeds G” (28). Successively, an aqueous dispersion of poly(vinyl alcohol-co-vinyl acetate) random copolymer (PVAc), cross-linked through the addition of borates, was developed. While the presence of the hydroxyl groups grants the cross-linking reactions, the vinyl acetate groups (about 27% w/w) allow the inclusion of relevant amounts of the organic solvents normally used by conservators for cleaning purposes (e.g. acetone, ethanol, propanol, ethyl acetate, etc.) (28). The high shear elastic modulus of PVAc-borate HVPDs accounts for their peeling from the cleaned surfaces. This allows minimizing the amount of residues left onto the paint surface, which is the biggest limitation of thickened solvents (i.e. solvent gels). Particularly relevant is the role of solvents in structuring and reinforcing the gel network. It was demonstrated that increasing the solvent concentration, the free water index (FWI, i.e. the mole fraction of water that behaves as if it were in the neat bulk) decreases linearly down to a value of 0.45 at 25 wt % 1-propanol (i.e. the highest concentration possible without syneresis). 1-propanol acts as a water-structure maker, with a consequent reinforcement of the gel network (e.g. the elasticity is enhanced, see figure 1), and the same behaviour was observed with methylethylketone, MEK (28). PVA- and PVAc-borate HVPDs loaded with solvents of medium polarity possess good adaptability to rough surfaces thanks to their viscous character, but at the same time, their elasticity allows a gentle peeling off of the gel network, without residues left on the cleaned area. These systems were successfully used for the cleaning of different artwork surfaces. Water/MEK blends loaded into PVAc-borate systems were used to remove aged protective varnish layers from wood paintings and contemporary oil on canvas paintings (29). In both cases, few minutes are required for an almost complete swelling of the undesired layer, 295

which is then fully removed with gentle mechanical action performed with a wet cotton swab. FTIR measurements performed on the cleaned areas, demonstrated that no residues of the cleaning systems could be detected on the surface after the application and removal of the HVPDs. Besides, laboratory tests performed on model films of shellac, showed that the PVAc-borate systems used during the cleaning tests exhibited fluorescence. This led to the conclusion that the shellac resin had partially migrated inside the HVPD during the cleaning (30).

Figure 1. Removal of hydrogels by peeling them off of a glass surface by means of a spatula. (Left): 3 wt % PVA/0.6 wt % borax/20 wt % 1-propanol; (middle) 2 wt % PVA/0.4 wt % borax/20 wt % 1-propanol; (right) Crossover parameters Gc (crossover modulus) (black circles) and τc (i.e. 1/ωc, where ωc is the crossover frequency) (black squares) as a function of 1-propanol (1- PrOH) content. The vertical bars are standard deviations of six measurements. Adapted with permission from ref. (28). Copyright 2009 American Chemical Society.

Recently, partially hydrolyzed poly(vinyl acetate) was combined with benzene-1,4-diboronic acid (BDBA), that forms covalent cross-links, to obtain a soft and peelable organogel, able to load a set of solvents largely used by conservators (e.g. dimethylsulfoxide, 2-ethoxyethanol, tetrahydrofuran). Some formulations were successfully used for the removal of aged varnish from a 16th century reliquary and from valuable oil paintings, without leaving any residue on the surface, and respecting the delicate paint layer (31). Aqueous dispersions of PVA exhibit peculiar film forming properties (32), besides excellent chemical stability, high biocompatibility, low toxicity and low costs. This makes PVA dispersions highly attractive as film forming systems, which can be loaded with chelating agents for the selective surface cleaning of copper-based artifacts. In particular, partially hydrolyzed semi-crystalline PVA shows high water solubility and the ability to form films with good mechanical properties, thanks to the presence of ordered (crystalline) and amorphous domains (33). The film forming PVA-based dispersion used in association with a complexing agent, such as EDTA that is effective in the removal of copper ions (34), yields a cleaning system with enhanced performances in terms of applicability and efficacy on corroded metal artifacts. This system is particularly relevant for bronze 296

artworks affected by the “bronze disease”, an irreversible process originated by the contact of chlorides with copper alloys, which brings to the formation of tenacious and undesired patinas (35). For conservation purposes, the system must fulfil the following requirements: i) its softness and adhesiveness should permit its application on both horizontal and non-horizontal surfaces; ii) the evaporation rate of the liquid phase should be slow enough (but not longer than ca. four hours for a single application) to allow the reaction of the chelating agent with the patina; iii) the formed film should be strong, elastic, and easy to remove in one piece, by means of a gentle peeling action; iv) polymer dispersions should be able to load an appreciable amount of ligand. During the evaporation process, the formation of two distinct regions occurs (36). A glassy region forms at the polymer-air interface, where the solvent evaporation proceeds faster, and the progressive immobilization of the chains hinders the formation of crystalline domains. The formation of this glassy barrier decreases the solvent evaporation rates, favouring the formation of crystalline domains in the underlying rubbery region, which is characterized by residual mobility of the entangled polymer chains throughout the whole drying process. The glassy-rubbery interface moves inward as the drying process proceeds until a glassy film, containing crystalline domains, is formed. At the interface between the rubbery region and the corrosion patina, the ligands solution is free to diffuse and interact with the corrosion products, and the formed complexes are confined within the film. This innovative system represents an enhancement with respect to the commonly used cleaning procedures since it permits to i) achieve complete patina removal thanks to the simultaneous chemical and mechanical action (provided by the gentle peeling of the film); ii) adjust the physical and mechanical properties of the viscous paste (texture, adhesiveness, transparency, etc.) to adapt to different substrates (non-horizontal, rough and irregular surfaces). Different plasticizers, mainly polyglycols, can be added to the formulation in order to improve specific properties, e.g. the softness of the final dry film that permits its easier peeling. Frequency sweep tests on the investigated systems show a prevalent viscous behavior with G’ < G” over almost the entire range of explored frequencies in a 0-300 minutes time range. A cross-over between G’ and G” is observed at high frequencies, typical of polymer dispersions with low cross-linking density. As the volatile fraction evaporates, the progressive increase of G’ values indicates an increase in entanglement density of the polymer chains due to the formation of inter- and intra-molecular hydrogen bonds. The frequency sweep curves of an already dried film are characterized by the absence of a crossover between G’ and G” curves: G’ is higher than G” over the whole range of investigated frequencies, indicating that after drying the system is characterized by a solid-like behavior. A significant difference can be observed between films obtained from dispersions containing or not EDTA. The storage modulus (G’) of a dry film obtained from an EDTA solution is almost double (7000 Pa) than that of a system without EDTA (4500 Pa), as a consequence of enhanced chain entanglement promoted by the presence of EDTA, which results in a stronger network. It is 297

worth noting that the magnitude of G’ accounts for the easy peeling of the final film in a single piece (as shown in figure 2 (c)). Preliminary cleaning tests were performed on artificially aged samples in order to observe the cleaning performances of the selected formulations. These mock-up samples were originally attacked with an acidic solution, and then submitted to natural aging (burial for several months) producing samples with a highly adherent and inhomogeneous patina. A preliminary characterization, performed by XRD, indicated the presence of copper oxychlorides (atacamite, clinoatamite) on the surface, and of an underlying cuprite layer. After a first cleaning test, performed with a dispersion loaded with 3% w/w EDTA (pH 10), a partial removal of the corrosion products was obtained. The EDS analysis revealed a reduction of 59 % w/w of the typical elements coming from the burial soil (Na, Si, P, Cl). An additional application of gel loaded with 4% w/w EDTA (pH 10) resulted in the complete observable removal of the surface corrosion products, and in a 92% w/w reduction of the extraneous elements (37).

Figure 2. (A) Weak gel of hydroxypropyl cellulose (Klucel) used as reference; (B) vial containing a 3% w/w EDTA (pH 10) loaded PVA70 formulation; (C) easy removal of the dry film by peeling; (D) film containing the removed corrosion patina. The first cleaning test on real artworks was performed on a bronze fountain (17th century) made by Pietro Tacca in Florence (37). Corrosion patinas were composed by copper carbonates (malachite CuCO3(OH)2), sulphates (antlerite Cu3(SO4)(OH)4, brochantite Cu4(SO4)(OH)6), nitrates and chlorides (atacamite 298

Cu2Cl(OH)3 and its polymorph clinoatacamite). The cleaning test was performed by applying a 3.5% w/w EDTA solution (pH 7) loaded in a PVA-based formulation. After a single application, both white calcium carbonate/sulphate and copper corrosion layers were removed. In fact, EDTA is an effective complexing agent also for Ca2+ ions, thus performing a double cleaning action. High control of the cleaning process was also ensured, since the complexing reaction cannot further occur after loss of the volatile fraction and the formation of the polymeric film. As previously mentioned, chemically cross-linked hydrogels possess a highly cohesive structure, which is able to prevent the release of gel residues on the surface of a painting. Nevertheless, a chemical network is not the only option to ensure the physical integrity of the final system. A cyclic freeze-thawing (FT) procedure has been applied to PVA solutions in order to obtain solid-like gels (38). The low temperature in the freezing step causes a phase separation (39). Water starts to freeze, and the ice crystals squeeze the PVA chains in a polymerrich phase: hydrogen bonding among the hydroxyl groups eventually leads to the formation of polymer crystallites, i.e. the tie-points in the newly formed physical gel (40, 41). The term “physical gel” is usually taken to mean a structure whose cross-links are both physical and transient. It behaves as a liquid on long time scales (42). Gels obtained through freeze-thawing (FT) are physical gels (because PVA chains interact through hydrogen bonds), but they mostly behave as solids, showing mechanical properties close to those of a chemical gel. In this context is thus more appropriate to further distinguish between ‘strong’ and ‘weak’ physical gels (43): -

strong gels, like cryogels, have a network that is permanent under certain conditions (44), even in the absence of chemical cross-links. weak gels fall under the general description of physical gels given above.

Due to their high biocompatibility, PVA hydrogels have been broadly investigated for medical applications, such as substitution of damaged articular cartilage (45), wound dressing (46), and controlled release of drugs (47, 48). In addition to high cohesion and low chemical reactivity, PVA cryogels show other salient characteristics that made them ideal for the cleaning of artworks: high porosity (41), high water content (49) and retention (17), and a pronounced adaptability to irregular surfaces. When a painting requires cleaning, a key aspect to select the cleaning system is the morphology of the painted surface. For instance, in modern art canvases, the relief of the brushstrokes often creates an uneven and fragile background. In this case, mechanical removal of soil is not advisable. PVA FT hydrogels, produced as thin films (figure 3-C), easily adapt this type of surface. The flexibility of the system is strongly related to its rheological characteristics, and can be tailored varying the polymer concentration, the duration of the freezing steps, and the number of FT cycles. All these aspects influence the degree of crystallinity of the resulting gel (50). 299

Recently (17), the physico-chemical properties of PVA cryogels prepared by one or three FT cycles (starting from polymer solutions at the same concentration) were investigated. Rheological measurements on the gels showed that G’ is higher than G” in the entire range of frequencies: the gels are solid-like. Moreover, the values of G’ and G” strongly increase with FT cycles (figure 3-A); the number of tie-points is higher in the FT3 gel, causing the structure to be more dense and elastic. An evidence that the FT3 hydrogel contains a higher concentration of polymer in its structure is also provided by measuring the gel content G(%) (51), i.e. the residual fraction of polymer after storage in water, and the crystallinity XC (52), see figure 3-B.

Figure 3. (A) Storage (G’, circles) and loss (G”, triangles) moduli measured for PVA FT1 (filled markers) and PVA FT3 (empty markers) gels; (B) Gel content (G(%)) and crystallinity (XC(%)) for PVA FT1(blue bars) and PVA FT3 (orange bars). Adapted from ref. (17). Copyright 2017 Royal Society of Chemistry.

Indirect consequences of these properties are the higher ability to swell and the larger volumetric capacity of the FT1 gel. In order to achieve effective cleaning, fluids should be able to freely diffuse inside the polymer matrix and reach the surface on which the gel is lying: high porosity and interconnected channels are required. The porosity of the cryogels is caused by the formation and growth of ice crystals during the freezing steps: they act as templates for the final spongy structure, while packing the polymer chains together (53). Therefore, the higher the number of FT cycles, the larger the pores, the thicker the polymer walls of the gels (figure 4-A,B). The transmittance of light also changes (figure 4-C). While water-loaded gels are suitable for the removal of dust, o/w microemulsions embedded in the network are needed to remove hydrophobic dirt from a surface, capturing and holding it inside the gel matrix (figure 5-A). 300

The diffusion in the gel of a labelled o/w microemulsion can be studied through Fluorescence Correlation Spectroscopy (FCS). The implemented model (54, 55) (figure 5-B) confirms that the diffusion of the microemulsion droplets is free in both FT1 and FT3 gels, albeit showing some boundaries in the FT1 sample: as a matter of fact, water-polymer phase separation is less distinct after only one FT cycle, and free polymer chains can occlude some gel channels, and then entrap few droplets.

Figure 4. (A-B) SEM images of PVA FT1 (A) and PVA FT3 (B) gels (bar is 1 micron); (C) Appearance of the two gels. Adapted from ref. (17). Copyright 2017 Royal Society of Chemistry.

Acrylate/Methacrylate-Based Chemical Gels Poly(methyl methacrylate) (PMMA) is a transparent and durable polymer that has been used in a wide range of fields and applications, spanning from technological elements to medical and aesthetic uses (56–59). Due to its hydrophobicity, PMMA based organogels can be obtained by free radical copolymerization of methyl methacrylate (MMA) and diacrylate monomers in several organic solvents. These organogels have been reported in the literature to study the diffusion of polymer chains in gels (60) and control the swelling of polymeric network through measurments of fast transient fluorescence (61), but only recently their use in the field of conservation of cultural heritage has been considered (18). Traditionally, unwanted hydrophobic layers were 301

often removed applying organic solvents directly onto the artifacts surface, even if this method caused some issues (10), as discussed in the previous sections. Therefore, the development of chemical gels, where the confined liquid phase is a low-polarity solvent (as complementary tools to hydrogels), expands the applicability of chemical networks for the cleaning of cultural heritage.

Figure 5. (A) Microemulsion droplets diffusing in the gel (1), interacting with a dirty model substrate and entrapping the dirt (2), and then carrying it into the gel (3); (B) Correlation curves for a microemulsion marked with a fluorescent amphiphilic dye: diffusion in FT1 gel (full marker), in FT3 gel (empty marker) and free diffusion (stars); solid lines show the fit. Adapted from ref. (17). Copyright 2017 Royal Society of Chemistry. PMMA organogels have been recently synthesized tuning the amount of cross-linker, the type of solvent (i.e. methyl ethyl ketone (MEK), cyclohexanone (cyclo), ethyl acetate (EA) and butyl acetate(BA)), and the monomer/solvent ratio (18, 19). A decrase of the cross-linker density usually leads to an increase in the mesh size, even if the gel porosity is mainly influenced by the equilibrium solvent content (Q), that has the highest value in the systems with MEK. The evaporation kinetics of free and confined solvents were evaluated comparing the loss of 302

weight of swollen PMMA gels to that of a petri dish containing the solvent. Due to its retention power, the evaporation rate is reduced in the polymeric network (Figure 6), allowing the control of the cleaning action and decreasing the impact of the solvents on operators. All the obtained organogels exhibit good optical transparency, useful to directly observe the treated surface during the cleaning action, and good mechanical stability. No gel residues are left on the treated surface, as confirmed by ATR-FTIR analysis.

Figure 6. Evaporation kinetics of free and confined solvents in PMMA gels. Reprinted with permission from ref. (18). Copyright 2015 Springer Nature.

A PMMA gel, synthesized with EA, was applied on a canvas painting (early 20th century) and, after 5 minutes, it swelled and softened the unwanted varnish layer, which was then mechanically removed. Part of the varnish was also solubilized, and migrated into the polymeric network (Figure 7) (18). PMMA-MEK organogels, with different amounts of cross-linker, were applied on a 19th century printed missal book to remove paraffin wax. Two successive applications of 15 minutes were performed in order to obtain a gradual and controlled removal. In fact, only after the second application, the swollen wax that did not adhere to the gel was easly removed with a cotton swab (19). Only the polymeric network with the highest cross-linker density has enough retentiveness to avoid uncontrolled diffusion of MEK across the paper surface. Therefore, these results confirmed that it is possible to tune the synthetic procedure to change the retentiveness of the PMMA organogel, in order to extend their use to several substrates with different porosity, hydrophilicity and surface roughness. 303

Figure 7. Application of a PMMA-EA organogel on an early 20th century oil canvas painting. Images before (A), during (B) and after (C) the application of the organogels. Spot after the mechanical removal of the swollen varnish (D) and PMMA-EA gel after the application (E). Reprinted with permission from ref. (18). Copyright 2015 Springer Nature.

Poly(2-hydroxyethyl methacrylate) (pHEMA) hydrogels were first prepared and described for biological use by Wichterle and Lim (62). Thanks to their high water content, soft and rubbery consistence, and low interfacial tension, these hydrogels have physical properties similar to those of living tissue. Therefore, they have been applied or proposed as biomaterials for synthetic prostheses (63), artificial skin (64) and corneal replacement (65), in addition to being used as contact lenses (66) and drug delivery (67) systems. pHEMA hydrogels are obtained by free radical copolymerization of 2-hydroxyethyl methacrylate (HEMA) and a cross-linker, usually a diacrylate monomer, in water solution. To ensure the production of optically transparent and homogeneous gels, the solvent content in the monomer mixture must not exceed 40-45 wt% (68, 69); in fact, larger amounts of water lead to phase separation during polymerization (70). When a salt, such as NaCl, is added during the synthesis, a heterogeneous hydrogel with a water content less than 40 wt% is obtained. The salt addition also influences the structure of the polymeric network, which is inverted from a pore interconnetted microstructure to an irregular macroporosity consisting of interconnected spheres. This effect is due to a decrease of pHEMA compatibility with the solvent that becomes more polar, leading to the so called salting out effect. 304

It is also possible to vary the water content and mechanical strength of the polymeric network using different types and amounts of cross-linkers during the hydrogel synthesis. Anyway, classical pHEMA hydrogels does not swell enough to get the required softness for many applications, especially in the field of conservation of cultural heritage. For this reason, a wide range of co-monomers can be incorporated into the pHEMA network, to improve its chemical, physical and mechanical properties. For example, introducing different amounts of N-vinyl-1-pyrrolidone (VP), it is possible to increase the equilibrium water content and change the porosity (Figure 8) and optical transparency, but these gels usually do not have good mechanical stability.

Figure 8. SEM micrographs of classical pHEMA (left) and pHEMA/VP hydrogels (right).

Semi-interpenetrating (semi-IPN) hydrogels, constituted by linear or branched polymers embedded into one or more polymeric network during the polymerization reaction, can overcome this problem, since the obtained hydrogel has features similar to the average of the single homopolymer properties. Domingues et al. (71) developed a new class of semi-IPN polymeric networks, pHEMA/PVP hydrogels, consisting of a pHEMA network, which provides mechanical strength to the hydrogel, and an interpenetrated polymer polyvinylpyrrolidone (PVP), which increases the hydrophilicity and porosity of the system. Hydrogels with various water contents and PVP/HEMA ratio were synthesized to evaluate how these parameters affect the gels’ structure, mechanical behaviour (i.e. softness, elasticity and resistance to tensile strength) and affinity to water. In particular, three different hydrogels were obtained with water contents of 50, 58, and 65 wt% and with HEMA/PVP ratios of 50/50, 40/60, and 30/70 respectively. It was found that the addition of higher amounts of PVP into the reaction mixture leads to an increase of the network hydrophilicity and equilibrium water content (EWC), causing an increment of the average micro and nano porosity. Moreover, also the free water index is affected by the PVP and water content. In fact, the free water index increases of about two times from the hydrogel with 50 wt% of water to that with 65 wt% of water, as a consequence of 305

a lower number of water molecules in contact with the pore walls due to larger pore dimensions. Rheological characterization showed that these systems are rigid (72), thus they can be applied and removed in one step without leaving residues on the treated surfaces, as confirmed by ATR-FTIR analysis (Figure 9) (71). Due to the tunable retentiveness, water-loaded pHEMA/PVP hydrogels can be used to clean water-sensitive artefacts. In particular, a pHEMA/PVP hydrogel with a water content of 58 wt% and a HEMA/PVP ratio of 30/70 was tested on a very delicate Thang-Ka (a Tibetan votive artefact made with a ‘tempera magra’ on canvas; the pigments are only poorly cohered and adhered to the surface) mock-up. The chosen hydrogel grants the homogeneous and confined cleaning of the grime layer without causing any colour leaching (Figure 10), as instead occurs using traditional agar-agar hydrogels (71).

Figure 9. ATR-FTIR spectra of: pHEMA/PVP hydrogels (slash-dotted line); canvases in contact with hydrogels (1) and (2); canvas as is (3). Adapted with permission from ref. (71). Copyright 2013 American Chemical Society.

Figure 10. Thang-Ka mock-up with different level of soil removal: not cleaned (1); after 20 minutes of pHEMA/PVP hydrogel application (2); after further 20 minutes of application (3). Adapted with permission from ref. (71). Copyright 2013 American Chemical Society. 306

Figure 11. Removal of aged varnish from an 18th-century canvas painting. (a) Photographs of the painting and of the poly(2–hydroxyethyl methacrylate)/poly(vinylpyrrolidone) hydrogel application. From left to right: the painting before cleaning (visible light); the painting before cleaning (ultraviolet light); the application of the hydrogel (visible light); the painting after cleaning (visible light); and the painting after cleaning (ultraviolet light). (b) Ultraviolet photographs of the painting showing the feasibility of using chemical gels over a large area. Ultraviolet light fluorescence highlights the efficacy of the cleaning process (left image, not cleaned; right image, cleaned). (c) Visible light photographs of the painting showing the feasibility of using chemical gels over a large area (left image, not cleaned; right image, cleaned). Reprinted with permission from ref. (73). Copyright 2015 Springer Nature.

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pHEMA/PVP hydrogels loaded with a water-ethanol solution (50%) were also successfully used for the removal of aged dammar varnish from oil paintings on canvas (see figure 11) (73). In order to remove hydrophobic layers from surfaces and limit the cleaning action at the interface, microemulsions can be loaded into pHEMA/PVP hydrogels. In particular, ethyl acetate/propylene carbonate-based o/w microemulsions (µEAPC) were confined into pHEMA/PVP polymeric networks and applied onto a canvas painting, to swell and partially solubilize artificially aged polymer adhesives. In this way, the swollen hydrophobic coating cloud be easily removed by gentle mechanical action (74) (see figure 12). Moreover, from confocal microscopy measurements, Mazzuca et al. showed that these hydrogels can be loaded with hydrolytic enzymes that can digest selectively aged pastes and glues, usually found in old paper artworks. The diffusional properties and the pore size of the gels allow the absorption of the product, detached from the paper during the cleaning process, into the polymeric network (72).

Figure 12. Optical microscopy images (x100 magnification) of canvas before (left) and after (right) the removal of aged adhesive using microemulsions confined in the pHEMA/PVP hydrogel with 65 wt% of water. Reprinted with permission from ref. (74). Copyright 2014 Springer Nature.

Conclusions A wide palette of formulations has been developed in the framework of colloids science and soft matter, specifically designed to allow the controlled removal of unwanted layers from the surface of artworks. The formulation of hydrogels and organogels enables to confine, and gradually release, a wide range of cleaning fluids, from aqueous solutions (of enzymes, chelators, acids/bases, surfactants) to oil-in-water microemulsions, and average- and low-polarity solvents. It is thus possible to remove surface dirt, hydrophilic or hydrophobic soil, overpaints, and aged coatings, adhesives and varnishes. Networks of polymers such as poly(2-hydroxyethyl methacrylate) (pHEMA), Poly(methyl methacrylate) (PMMA), and poly(vinyl alcohol) (PVA) have been formulated. By changing the type of polymer and the synthetic process, it is possible to tune the physico-chemical properties of gels, polymer viscous dispersions, and films. Highly viscoelastic materials can be easily handled, applied, and removed from 308

the surface of artworks without leaving observable polymer residues (e.g. by ATR-FTIR), as opposed to traditional thickeners (e.g. cellulose ethers or “solvent gels” of polyacrylic acid). Highly viscous polymer dispersions (HVPDs) of PVA can be loaded with water or polar solvents, applied on artworks (e.g. to remove yellowed varnishes), and removed from the surface in a single step. Films of PVA can be cast from polymer dispersions (for instance, loaded with chelators) directly on the surface of metallic artifacts; then, the films are peeled off the surface, selectively removing corrosion patinas. Organogels of PMMA, loaded with average-polarity solvents, allow the quick removal of adhesives or wax from solvent-sensitive inked manuscripts. Finally, highly retentive semi-IPN hydrogels based on pHEMA and PVP allow the controlled removal of surface dirt from highly water-sensitive surfaces, where the colors are poorly cohered and adhered. These systems have been validated on numerous case studies, regarding the cleaning of objects and masterpieces from the classic, modern, and contemporary art productions. Overall, a new generation of cleaning tools has been provided to the conservation community, to improve on traditional solvent thickeners.

Acknowledgments CSGI and the European Union (NANORESTART project, Horizon 2020 research and innovation programme under grant agreement No 646063) are gratefully acknowledged for financial support.

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Chapter 16

Polymeric Nanoparticles Explored for Drug-Delivery Applications Heba Asem and Eva Malmström* Department of Fibre and Polymer Technology, School of Chemical Science and Engineering, KTH Royal Institute of Technology, Teknikringen 56, SE-100 44, Stockholm, Sweden *E-mail: [email protected].

The main drawback of conventional chemotherapeutics is their non-specific distribution in the body which causes serious side effects to healthy cells. As a consequence, the drug concentration reaching the tumor is reduced, resulting in suboptimal therapeutic efficacy. The discovery that polymer-based nanomaterials can be used for controlled drug delivery systems offers well-defined reservoirs for a wide spectrum of pharmaceutical agents, with the ability to reduce the toxic response. The most widely explored polymeric nanocarriers, including biodegradable polymers, amphiphilic copolymers and polymers that form unimolecular micelles, are discussed in this brief chapter.

Introduction Personalized medicine is a rapidly growing and important research area which can lead to significantly more efficient and patient resilient treatment, giving societal benefits such as improved quality of life for patients and lower costs for care. Personalized medicine has stimulated the design of various delivery platforms for pharmaceuticals and chemotherapeutics, in particular to overcome the limitations with respect to toxicity encountered by the conventional delivery of drugs (1, 2). The integration of nanotechnology with medicine leads to the development of tailored nanomaterials facilitating a personalized and efficient therapy. In this respect, nanoparticles (NPs), typically with dimensions © 2018 American Chemical Society

below 200 nm, have gained increasing interest for the efficient delivery of active components (3). Such NPs can be based on inorganic materials or on soft matter, such as silica NPs and others or polymeric macromolecules (Figure 1). NPs have also been shown advantageous in solubilizing therapeutic cargos, substantially prolonging the circulation life times of drugs. Particle size and size distribution are the major factors affecting the circulation, extravasation through vasculature leakage, macrophages uptake and renal clearance of NPs upon intravenous administration (4). Biological barriers to deliver NPs to their destination prevent the delivery of drugs and hence decrease their therapeutic activity. These barriers include opsonization, renal clearance and mononuclear phagocyte system (MPS). Particles with a diameter greater than 200 nm are sequestered and accumulated in liver and spleen by MPS (4, 5). The renal filtration threshold of NPs is · 10 nm in diameter and the renal molecular weight cutoff size of polymers is · 48 kDa (6). NPs of intermediate sizes, 20-100 nm, thus have the optimal potential for in vivo applications, owing to their ability to circulate in the blood stream for long periods of time. These NPs are large enough to evade renal clearance and small enough to avoid rapid clearance from circulation. Due to the inherent size of NPs, they can be selectively accumulated in the tumor tissue through the enhanced permeation and retention (EPR) effect which is characterized by the presence of leaky vasculatures having an incomplete endothelial barrier, defective vascular architecture and an impaired lymphatic drainage system of the tumor (7). Polymers have attracted significant attention as therapeutic carriers due to their inherent physical, chemical, and biological properties and their highly beneficial size. Polymeric nanoparticles (PNPs) offer significant advantages over inorganic NPs with regard to design flexibility and biological fate. Inorganic NPs (gold, superparamagnetic iron oxide, silica NPs and quantum dots) are potential carriers for the cellular delivery of various drugs, but inorganic NPs have to be subjected to chemical and/or biological modification to meet the stringent requirements for cellular delivery, such as good biocompatibility (8). Moreover, it may be difficult to efficiently clear these NPs from the body due to lack of biodegradability, and they are therefore exposed to various intracellular degradative enzymes to improve their clearance from the body (9). PNPs offer great versatility in terms of composition and functionalization when platforms for effective therapeutic delivery are being designed (10). Biodegradable polymers which can be degraded chemically or enzymatically and excreted safely from the body through the renal system have emerged as promising materials for drug delivery systems (DDS) due to their biodegradability and biocompatibility (11). Most therapeutic drugs are released rapidly after intravenous administration and this may lead to an increased drug concentration in the blood, leading to toxic levels. Moreover, many drugs such as anticancer drugs, are hydrophobic in nature and can be subjected to physiological degradation. Controlled DDS can inhibit systemic drug toxicity with a relatively high drug concentration at the site of treatment. The drug(s) can be entrapped in the DDS via physisorption to form polymer-drug dispersions or via chemisorption to form polymer-drug conjugates (12). The advances in polymer-based drug carriers allow the spatiotemporal release of therapeutics in both pulsatile dose delivery products and implanted 316

reservoir systems. Sustained drug release from nanocarriers maintains the plasma drug concentration in the therapeutic window and minimizes the adverse effects of the drug (11).

Figure 1. Schematic representation of different nanocarrier systems for drug delivery.

Polymeric Nanocarriers for Drug Delivery PNPs represent a fascinating class of materials, and they are extensively utilized for biomedical applications owing to their small size, design flexibility based on functionalization, macromolecular synthesis methods and polymer diversity. PNP-based drug carriers have been developed to improve the diagnosis and treatment of a wide range of diseases including cardiovascular diseases, respiratory diseases, neurodegenerative diseases, viral infections and cancer. PNPs are defined as colloidal particles, 3-200 nm in size, designed for drug delivery applications (3). Due to their large surface area, a pharmaceutical agent of interest can be adsorbed onto the surface of the PNPs, or encapsulated or conjugated to the PNPs permitting a high loading capacity. PNPs can host a variety of active constituents including chemotherapeutics, contrast agents, and DNA as well as proteins for cancer and gene delivery. The main purpose of any DDS is to deliver the active agent (drug) to the intended pathological site in a selective manner and in a sufficient amount to increase efficacy and reduce cytotoxicity towards peripheral healthy tissues. Two strategies of drug targeting 317

can be applied to the site of action, active or passive targeting. Active targeting requires cell-specific ligands, attached covalently to the surface of engineered PNPs. Various target ligands can be attached to the drug carrier such as antibodies, peptides, folate, sugar moieties and other ligands (13). For the potential targeting of liver cell carcinoma, glucosamine was conjugated with paclitaxel (PTX)-loaded-poly (γ-glutamic-co-lactic) acid NPs (14). Folate-modified PNPs are widely investigated as agents to target tumors, because the folate receptor is highly overexpressed in various types of human tumor cells (15–17). In passive targeting, tumor tissue is characterized by impaired lymphatic drainage facilitating the penetration of PNPs through leaky blood vessels and accumulation in tumor tissue, a phenomenon known as the EPR effect (7, 18). The decoration of PNPs with poly(ethylene glycol) (PEG) allows stealth effect of NPs and improves NPs clearance from the circulation. PEGylation involves coating the surface of NPs with PEG so that ethylene glycol (EG) units interact with water molecules by hydrogen bonds to form a hydrating layer (19). This hydrating layer in turn reduces protein adsorption and subsequent clearance by MPS. PEG is approved by FDA for food, cosmetics and pharmaceutical purposes. It is a hydrophilic non-toxic biocompatible polymer soluble in a wide range of solvents and lacks immunigenity (20). PEG is also a thermo-responsive polymer with a lower critical solution temperature (LCST) above 100 °C (21, 22). Thermo-responsive polymers display a phase transition in aqueous solution, switching from a hydrophilic to a hydrophobic character upon heating, due to inter- and intramolecular hydrogen bonds between water molecules and polymer chains. The high LCST of linear PEG is not appropriate for drug delivery applications, for this reason many research groups have studied copolymerization of PEG with hydrophobic monomers to reduce its LCST and make it more suitable for drug delivery applications. Poly(ethylene oxide-stat-propylene oxide) block copolymer has been investigated as a thermo-responsive polymer (23). Although, poly(N-isopropyl acrylamide) (PNIPAM) is a popular thermo-responsive polymer with a LCST of · 32°C extensively used in drug delivery applications, including hyperthermia (24). However, it has been reported that PNIPAM exhibits cytotoxicity at a physiological temperature, which could be due to the presence of unreacted monomers (25). In addition, secondary amide groups distributed pendant to the back-bone of PNIPAM form undesired hydrogen bonds with proteins (26). During the last decades, poly (oligo(ethylene glycol)) methacrylate (POEGMA)s have been explored as an alternative to PNIPAM (27). This non-linear PEG analogue exhibits thermo-responsive properties in water or physiological media. It has a carbon-carbon backbone connected to EG segments up to 85 % of its weight, and it therefore, displays both water solubility and biocompatibility (27–29). The LCST of these polymers can be tuned in the range of 26-90 °C depending on the length of EG units in the side chain. Several research groups have studied the polymerization and copolymerization of oligo(ethylene glycol) methyl ether methacrylate (OEGMA) monomer using different polymerization methods including atom transfer radical polymerization (ATRP) and reversible addition-fragmentation chain transfer (RAFT). Lutz and his coworkers studied the random copolymerization of di (ethylene glycol) methyl ether methacrylate (DEGMA) and OEGMA via ATRP with tunable LCST (30, 318

31). A library of homopolymers and copolymers of OEGMA with methacrylic acid (MAA) was investigated using RAFT polymerization with adjusted LCST (32). We conclude that the precise design of PNP-based drug carriers, in terms of particle size and chemistry, will influence their biological safety, fate in the body and drug pharmacokinetics. The chemistry of PNPs and their hosted payloads have a great impact on their biodegradability, tissue biodistribution and cellular fate. Different classes of polymers are able to form PNPs-based drug delivery systems, including biodegradable polymers, amphiphilic copolymers, dendrimers and hyperbranched polymers. In the following part of the chapter we discuss biodegradable polymers and amphiphilic copolymers. In the next section, we shall consider hyperbranched polymers forming unimolecular micelles. Biodegradable Polymers Biodegradable polymers have emerged as promising candidates for therapeutic devices such as temporary prostheses, three-dimensional porous structures as scaffolds for tissue engineering and drug delivery systems. The principal features of a biodegradable polymer is that it degrades in vitro and in vivo either into products that are normal metabolites in the body or into products that can be eliminated from the body with or without further metabolic transformation (33). Collagen and gelatin are natural biodegradable polymers that have been studied most as drug delivery system due to their nontoxicity, biocompatibility and ease of extraction and purification. However, collagen has shown an immunogenic response which may limit its implementation as a drug carrier. Moreover, most natural polymers are water-soluble and must be cross-linked to produce a water-insoluble polymer network, a DDS-scaffold. In a gelatin-based drug delivery system, gelatin is cross-linked with glutaraldehyde. However, glutaraldehyde as a non-specific cross-linking agent interferes with protein drugs such as interferon (IFN-α) leading to inactivation of these drugs and loss of efficacy (12, 34). Synthetic biodegradable polymers offer remarkable advantages over natural polymers owing to their flexibility, having a wide spectrum of properties with good reproducibility. Fine control of the degradation rate of these polymers is possible by varying their structure (35). Synthetic biodegradable polymers include poly(lactic acid) (PLA), poly(glycolic acid) (PGA), poly(ε-caprolactone) (PCL), polyanhydride, polyphosphoesters and polyphosphazenes (35, 36). Among these, PLA, PGA, and their copolymer poly(D, L-lactide-co-glycolide) (PLGA) are the most well-defined and most frequently used polymers in drug delivery. The first FDA-approved drug delivery system, Lupron® Depot, based on a biodegradable polymer was released in 1989. Lupron® Depot consists of PLGA microspheres encapsulating leuprolide for the treatment of prostate cancer (37). The drug release rate from the biodegradable formulation is controlled by the biodegradation of PLGA, allowing a sustained drug release profile and thus minimizing toxic side effects and increase patient compliance. Khan et al. (38) synthesized PLGA NPs and encapsulated ormeloxifene for pancreatic carcinoma therapy. They showed that the prepared drug formulation, having a particle size 319

of 100 nm, displays significant anti-cancer activity toward pancreatic cancer cells with high accumulation in the cytosol and mitochondria. In another study, PLGA nanocarrier co-encapsulated two or more active agents, doxorubicin (DOX) and epidermal growth factor receptor (EGFR) siRNA in which the angiopep-2 (ANG) was conjugated for glioma therapy. They found that both DOX and siRNA were released in a controlled manner from PLGA NPs. The main role of ANG is to permeate the blood brain barrier that is known to restrict the passage of drugs to the brain (39). Theranostic is a wide medical concept in which both diagnosis and therapy are achieved using a single nanocarrier system. Schleich and his coworkers (40) developed nano-theranostic PLGA particles loaded with PTX and contrast agent to achieve simultaneous molecular imaging, drug delivery and real-time monitoring of the therapeutic response. A biodegradable amphiphilic linear-dendritic hybrid polymers based on PEG as the hydrophilic segments and a dendron branched PCL as the hydrophobic segments are synthesized. Theses polymers can form micelles with average size about 100 nm which were used to encapsulate DOX at loading efficiency up to 22 %. The cellular toxicity of these micelles were evaluated on two breast cancer cell lines and primary human macrophages. The pristine micelles showed no cell death below 35 µg/ml, while the Dox-loaded micelles displayed a significant decreases in the cell viability (41). Amphiphilic Copolymers Amphiphilic block copolymers can form polymeric micelles, leading to drug-loading systems with unique characteristics for drug delivery applications such as improved stability, enhanced drug solubility and bioavailability. Amphiphilic block copolymers can self-assemble above their critical micelle concentration (CMC) in aqueous solution forming core-shell micelle architectures. This created an integrated multifunctional system consisting of hydrophobic inner core to encapsulate water-insoluble drugs with a hydrophilic outer shell protecting the micelle and drug from the surrounding environment and providing colloidal stability. Stealth properties of polymeric micelles originate from the PEG forming corona giving a prolonged residence time in the blood circulation. The micelle-forming process starts when a number of amphiphilic polymer chains, amphiphiles or unimers, gather at the air/water interface. At a certain unimer concentration, the CMC, they associate in an entropy-driven process, by releasing water molecules to the bulk of the aqueous phase (42). The equilibrium between micelles and their individual amphiphiles is crucial for micellar stability. Upon dilution or other changes, thermodynamics may end to a disassembly of the micelles, resulting in a premature release of their cargo. A facile approach to increase the micellar stability in a highly diluted environment is to covalently connect the blocks that form either the core or the shell of micelles by crosslinking (43–45). Core cross-linking seems to be the more promising approach to preserve the loaded cargo in the core of the micelles. The core can be cross-linked by the addition of a difunctional reagent to a reactive core-forming block. Several cross-linkers are highly reactive to functional groups in the block copolymer such as diamine (46), bis-succinimidyl crosslinker (47) and bis-benzophenone photocross-linker (48). On the other 320

hand, the amphiphilic block copolymers produced by reversible-deactivation radical polymerization (RDRP) of monomers such as acrylates or methacrylates can self-assemble in aqueous solution and form micelles. These micelles can be stabilized and core cross-linked by chain extension in the presence of a difunctional monomer possibly containing acid-labile or -reducible disulfide functions for pH- or reduction-controlled drug release (49–51). In this context, micelles containing disulfide bonds in the core are exploited for intracellular drug delivery, since they are accessible to chemical cleavage under reduction conditions such as glutathione. Glutathione is found in cell cytosol and other organelles at a concentration of 0.5-10 mM, while its extracellular amount in plasma is 2-20 µM and that limits the dissociation of the disulfide bond (52, 53). Preservation of the micelles maintains the colloidal stability during blood circulation. When drug loaded-micelles penetrate a cell, they are subjected to intracellular disassembly and release the drug in a controlled fashion. The Lee and Lam research groups (54, 55) investigated the loading of anticancer drugs such as docetaxel and PTX into disulfide-cross-linked micelles; and showed that cross-linked micelles improve the therapeutic efficacy and enhance the tumor specificity in tumor-bearing mice compared to noncross-linked micelles. Wei et al. (56) developed reduction-sensitive reversibly core cross-linked micelles based on poly(ethylene glycol)-b-poly(N-2-hydroxypropyl methacrylamide)-lipoic acid (PEG-b-PHPMA-LA) conjugates. The PEG-b-PHPMA copolymer was obtained under control of RAFT, it was prone to conjugate with lipoic acid via esterification of the hydroxyl groups in the copolymer forming amphiphilic PEG-b-PHPMA-LA polymer. The micelles showed a high DOX loading efficiency of 90 %. However, the drug release profile at 37 °C showed that only 23 % of the DOX released from the cross-linked micelles in 12 hours while about 87 % of the DOX was released after treatment with 10 mM dithiothreitol (DTT) showing high anti-tumor activity in HeLa and HepG2 cells. In another study, a bioreducible moiety was introduced via click chemistry to produce cross-linked micelles in which azide-functionalized biodegradable polymeric micelles encapsulated methotrexate for breast cancer therapy. The micellar cores were cross-linked at their pendent azide groups with disulfide-containing bisalkyne. The drug-loaded-cross-linked micelles inhibited the metabolic activity of human breast cancer cells (MCF-7) more than drug-loaded-uncross-linked micelles or the free drug (57).

Unimolecular Micelles: Synthetic Aspects In the previous section conventional amphiphilic block copolymers forming-micelles, known as multimolecular micelles were discussed. There is always an equilibrium between the micellar form and their individual molecules, with a constant and rapid chain exchange, when they are present in concentrations above the CMC. If they are diluted to a concentration below the CMC, a change in solution conditions such as temperature, pH, ionic strength or shear forces results in the dissociation of micelles into free polymeric chains which may lead to undesired drug release and systemic toxicity (Figure 2). Unimolecular micelles have therefore attracted great interest owing to their unique properties where a 321

single molecular architecture exhibits micelle-like properties, and it is possible to stabilize the construct individually in extremely dilute conditions. Unimolecular micelles were first proposed by Newkome et al. (58) as an alternative way of designing stable polymeric micelles. Significant efforts have been devoted to design macromolecular architectures that mimic the spherical 3D structure typical for micelles, and are covalently linked to avoid any dynamic nature. Some parameters have been shown to be crucial to accomplish individual stabilization including balanced amphiphilicity, high molecular weight and an extensive number of hydrophilic, stabilizing arms. Two main strategies have been suggested to design unimolecular core-shell type micelles, which can be divided into the “arm-first” and the “core -first” approaches (59).

Figure 2. Different behaviors of unimolecular and multimolecular micelles upon dilution. (60). Adapted with permission from reference (60). Copyright © 2015 Elsevier Inc.

Arm-First In the “arm-first” approach, linear amphiphilic AB diblock copolymers are linked covalently to form the characteristic morphology of a micelle. This can be accomplished by taking advantage of the spontaneous self-assembly of amphiphilic and low molecular weight polymers to form conventional micelles, followed by post-crosslinking of the hydrophilic (A) or hydrophobic (B) domains to stabilize the assembly (43, 44, 61), as illustrated in Figure 3A. Another concept studied in the last decade is the formation of linear hydrophilic macroinitiators followed by a cross-linking during the polymerization of the hydrophobic domain in the presence of a small amount of bifunctional monomer (Figure 3B). In this way shape-directed monomer-to-particle synthesis has been shown to produce unimolecular micelles (62). Hawkett et al. (63) and Charleux et al. (64) utilized the polymerization-induced self-assembly (PISA) technique to 322

obtain NPs. In this technique, a hydrophilic macroinitiator is used to polymerize hydrophobic monomers in a surfactant-free emulsion polymerization typically conducted in water. Once the hydrophobic block is long enough, the diblock copolymer self-assembles into a well-defined NPs with a hydrophilic corona and a hydrophobic core. Davis et al. (65) demonstrated the use of PISA to construct NPs intended for drug delivery, where the hydrophobic core was subsequently cross-linked. Core-First In the “core-first” approach, the focus has been on structural hybrids based on dendritic segments and linear polymers (Figure 3C). Dendritic polymers, with their globular structure, their large number of functional groups in the periphery and their highly branched structure, are extremely suitable for subsequent chainextension by linear segments enabling steric stabilization as unimolecular micelles (66, 67). However, the tedious and costly synthesis of dendrimers as well as their limitation in size (typically ≤ 10 nm), has diverted attention to their less perfectly hyperbranched analogues (68, 69).

Figure 3. Schematic illustration of the different strategies to synthesize unimolecular micelles: A) self-assembly of amphiphilic linear block-co-polymers and subsequent crosslinking of core or shell (arm first), B) core crosslinking by using a small amount of bifunctional monomer (arm-first), C) chain-extension of dendritic polymers with linear segments to form dendritic-linear hybrids (core-first). 323

Amphiphilic Hyperbranched Polymers Hyperbranched polymers are highly branched macromolecules with 3D dendritic architectures, and these polymers have been used for the preparation of unimolecular micelles. They have attracted significant attention for the design of NPs for use in therapeutic delivery systems. Hyperbranched polymers are synthesized via the step-growth polymerization of ABx-type monomers (x ≥ 2) which was postulated by Flory (70) in 1952. Another approach to produce hyperbranched polymers developed by Fréchet et al. (71) is the radical polymerization of AB*-type monomers (A is a monomer vinyl group and B* is an initiator fragment), referred as self-condensing vinyl polymerization (SCVP). In both cases the polymer produced is characterized by a broad molecular weight distribution; i.e., high polydispersity (72, 73). The immense progress of RDRP now renders a unique structural control over the hyperbranched polymer structure possible, thereby narrowing down the molecular weight distribution.

Figure 4. Schematic illustration of the synthetic route to Hyperbranched Dendritic-Linear Polymers via SCV(C)P-ATRP and followed by ATRP polymerization techniques (74). Reprinted with permission from reference (74). Copyright © 2014 American Chemical Society. 324

The introduction of the SCVP technique also makes it possible to employ RDRP to synthesize hyperbranched polymers in a more controlled fashion (72). This gives great freedom of design, where the polymer composition and architecture can be readily tailored by a careful choice of starting materials. Previously, our group has, among others, developed the synthesis of high molecular weight amphiphilic polymers based on a hydrophobic hyperbranched core synthesized through a combination of ATRP and self-condensing vinyl homo- and copolymerization (SCV(C)P) (74) (Figure 4). This strategy makes it possible to create highly sophisticated hyperbranched dendritic-linear polymers (HBDLPs) via a straightforward two-step protocol, and this strategy makes it possible to finely-tune the inherent features of the unimolecular micelle such as; size, stealth, targeting, drug and selective delivery. In another study, an amphiphilic hyperbranched terpolymer was synthesized through SCVP of OEGMA and methyl methacrylate (MMA) monomers in the presence of a vinyl-functionalized chain transfer agent (C12-raft) under the control of RAFT polymerization. The hyperbranched polymer produced can encapsulate a hydrophobic molecule, epoxiconazol, which could make a complex with MMA segments forming unimolecular micelles in aqueous solution (75).

Figure 5. Schematic illustration of the synthetic route to unimolecular micelles with (a) backbone-cleavable disulfide bonds and (b) azide-functional cleavable pendant disulfide bonds (59). Reprinted with permission from reference (59). Copyright © 2015 American Chemical Society. 325

Smart Unimolecular Micelles Responsive, or smart, polymers have a great applicability in the field of controlled and self-regulated drug delivery for cancer therapy. Responsive polymers can undergo a rapid change in properties in response to endogenous stimuli, including redox potential, pH and enzymes, or to exogenous stimuli such as temperature, light and ultrasound (76). Unimolecular micelles based on these polymers can designed for delivery systems that closely resemble the physiological process as in cancer tissue and optimize drug release according to the physiological needs. Porsch et al. (59) showed how disulfide bonds can be conveniently introduced into HBDLPs using the SCVP technique that has previously been prepared by the same group (74). The disulfide bonds were attached to the backbone of HBDLPs to enable biodegradation or to the pendant groups to allow the triggered release of the cargo as shown in Figure 5. They showed successfully encapsulated chemotherapeutic DOX in the core of the micelles displaying a diffusion-controlled release profile in a reductive medium, including glutathione and dithiothreitol. In another study, pH-sensitive bonds were introduced to an amphiphilic hyperbranched polymer consisting of a hydrophobic hyperbranched polyacetal attached to hydrophilic PEG by hydrazine bonds. The micelles formed showed a high stability in pH 7.4 buffer solution but were quite fragile in a pH 5.0 buffer. The micelles loaded with DOX gave a faster drug release in pH 5.0 buffer than in a physiological pH solution (77).

Conclusions The rapid developments in nanotechnology and materials science are making it possible to improve the quality of human life. Polymeric nanoparticles are being used as versatile nanocarriers for a wide range of drugs to treat lethal diseases such as cancer. Essential characteristics of these polymeric drug carriers include size, design flexibility, functionality and biocompatibility, which are critical when designing macromolecules for use in drug delivery devices. Drug-nanocarriers based on polymeric platforms include biodegradable polymers, amphiphilic copolymers, and hyperbranched polymers that can form unimolecular micelles. Unimolecular micelles are promising for drug delivery systems due to their high stability. Their structures, properties and methods of preparation are also briefly discussed.

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Chapter 17

Using Polymer Science To Improve Concrete: Superabsorbent Polymer Hydrogels in Highly Alkaline Environments Kendra A. Erk* and Baishakhi Bose School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, United States *E-mail: [email protected].

When added to fresh concrete mixtures, superabsorbent polymer hydrogel particles behave as internal curing agents, capable of absorbing and subsequently releasing large amounts of water which reduces self-desiccation and volumetric shrinkage of cement and, in turn, results in hardened concrete with increased strength and durability. In this chapter, the interactions between polyelectrolyte hydrogel particles and alkaline cementitious mixtures are described with an emphasis on how swelling behavior and internal curing performance is controlled by the chemical composition and morphology of the hydrogel particles. The beneficial impacts of hydrogel addition on cement microstructure and mortar compressive strength are highlighted, including the preferential formation of specific inorganic phases within the cement that appear to be influenced by the organic chemistry of the hydrogel particles.

Introduction Concrete, the largest volume building material in use worldwide, is produced at levels twice that of steel, aluminum, and wood combined; and due to its versatility, accessibility, low price and high durability, it provides shelter for an estimated 70% of the world’s population (1, 2). Compared to other building materials, including steel, it possesses high compressive strength and excellent resistance to corrosive fluids, assuring its ubiquity in construction for long into the future. However, conventional concrete can be easily adulterated, leading to poor © 2018 American Chemical Society

quality mixtures subject to shrinkage and cracks as well as structures requiring frequent repair and replacement. Indeed, the amazing devastation following the 7.0-magnitude earthquake in Haiti in 2010 was directly linked to the poor quality concrete used for housing and other buildings (3). In addition, the frequent repair and replacement required for conventional concrete has a significant environmental impact as concrete production accounts for 5-8% of global CO2 emissions (4). To increase the overall performance of conventional concrete, a variety of chemical additives have been developed so that when incorporated into the mixture, the result is a high-performance concrete (HPC) that forms a denser microstructure upon curing, resulting in increased strength and durability. HPC has a very dense microstructure to ensure an optimum particle packing and a water-to-cement ratio so low that all the water is consumed during the hydration reaction (i.e., during cement curing) (5). The dense microstructure engenders a strong and durable structure (6) with reduced impact on the environment (7). The main technical challenge associated with HPC is the autogenous (volumetric) shrinkage that is encountered during the early stages of curing, eventually resulting in the formation of microcracks, increased porosity, and an overall reduction in strength (8). Shrinkage increases in magnitude as result of incomplete hydration of cement due to the scarcity of water to fuel curing, causing the mixture to self-desiccate (9, 10). Compressive stresses develop in the system driven by the negative capillary pressure within the aqueous fluid in the mixture (termed ‘pore fluid’), ultimately leading to collapse of the cement microstructure (9, 11). The lack of water inside the system can be offset by use of internal curing agents that effectively replenish the water reservoir from inside the mixture and aid in cement hydration. Among other methods, the use of superabsorbent polymers (SAP) is becoming increasingly popular for the internal curing of HPC. SAP hydrogel particles can absorb water and undergo voluminous expansion up to 1,000 times their original weight (12). Thus, SAP can provide a means of controlled release of an ample reservoir of water for internal curing of HPC (13, 14). Hence, the degree of autogenous shrinkage and microcracking in concrete is effectively reduced while ensuring the formation of a highly durable and strong concrete (9, 15–17). There are also additional benefits of using SAP particles as internal curing agents in concrete, some of which are active fields of research: concrete freeze/thaw resistance can be enhanced by control of size and shape of pore systems (18–27), thermal expansion can be mitigated (28) and cracks can be filled which facilitates crack healing (18, 29). The use of hydrogel particles also provides more control over the rheological properties (18, 30) of fresh concrete and a reduction in spalling due to fires (31). Use of SAP particles in HPC has its own set of challenges that needs to be carefully considered. The most important issue with hydrogel particles is that they are not chemically inert in cement mixtures although they are considered to be by many in the building materials community (32, 33). Multivalent cations, which are naturally occurring in the pore fluid of fresh concrete mixtures, have been shown to negatively impact the swelling characteristics of hydrogel particles, causing unexpected deswelling and subsequent collapse of the polymer networks (33, 34). Hence the stability of SAP particles is of significance and degradation needs to be 334

minimized for the particles to serve their internal curing purpose. Furthermore, the release of water at an ideal time is of upmost importance. A fast release of water before the final setting of the cement mixture would cause increased porosity in the mixture and corresponding reduction in strength while a slower release of water would not be able to effectively counteract self-desiccation and the resulting autogenous shrinkage. Also, nonuniform distribution of the SAP particles within the mixture and reduction of SAP particle size by coarse aggregates (rocks) during concrete mixing needs to be carefully monitored to ensure optimum benefits of using SAP in concrete.

Background Hydrogel Chemistry Hydrogel particles used as internal curing agents are composed of polyelectrolyte molecules (typically poly(acrylic acid-acrylamide) random copolymer molecules) that are covalently crosslinked to form a three-dimensional polymer network (35). As stated previously, hydrogel particles are not chemically inert within cementitious mixtures due to the presence of strongly alkaline pore fluids (pH > 12). In the case of hydrogel particles containing acrylic acid, the carboxylic acid (COOH) functional groups undergo deprotonation in alkaline conditions as the pKa of acrylic acid is approximately 4.5 (36), forming anionic COO- moieties in the polymer network and allowing significant amounts of water to be absorbed by virtue of ion-dipole interactions (33, 37–39). For these charged polymer networks, the primary mechanism of hydrogel particle swelling can be attributed to the creation of a chemical potential gradient between the particle and the surrounding fluid as the anionic network results in a higher concentration of free counterions within the hydrogel particle compared to the surrounding fluid in order to preserve electroneutrality within the system (40). This gradient in turn creates an osmotic pressure gradient which drives the diffusion of water into the hydrogel particle along with other ions in solution. The particle will continue to swell until the net osmotic pressure is reduced to zero. Cations present in the aqueous fluid (including sodium, calcium, and aluminum ions) will be electrostatically attracted to the COO- moieties and form ionic complexes that effectively act as crosslinks within the polymer network, the formation of which decreases the equilibrium absorption capacity of the hydrogel (37, 41) and can ultimately lead to collapse of the polymer network as we recently demonstrated (33). A schematic illustrating the various stages of hydrogel swelling is shown in Figure 1. In the concrete materials community, there is a growing body of research to accurately quantify the absorption and desorption behavior of hydrogel particles in cementitious pore fluids as certain hydrogel compositions (including some commercially available products) have been found to display strong sensitivity to the mono- and multivalent cations that are naturally present in pore fluids depending on mixture age (32, 33, 42–46). As the anionic nature of the hydrogel is increased (e.g., by greater concentration of acrylic acid in the network), ion-induced deswelling is enhanced due to the greater presence of anionic sites 335

in the polymer network which can complex with counterions in solution (see Figure 1c) (34). Additionally, when the pH is highly alkaline (pH > 12-13, as is typical for pore fluids), the amide groups in the acrylamide segments are partially hydrolyzed to form anionic COO- moieties as well, encouraging swelling even in majority-acrylamide copolymer particles (47).

Figure 1. Idealized schematic of a polyelectrolyte hydrogel network in (a) the dry state, (b) swollen with water, and (c) deswollen in the presence of counterions. AA and AM indicate acrylic acid and acrylamide segments.

Synthesis pathways for hydrogel particles can be broadly classified into solution polymerization (48) and suspension polymerization (49). Hydrogel particles made from solution polymerization have uneven, angular shapes while hydrogel particles made from suspension polymerization are typically spherical or ellipsoidal in shape. The major constituents of both the pathways are same, i.e., water, monomer (acrylic acid (AA) and acrylamide (AM)), and neutralization solution (NaOH); the composition of synthesized hydrogel particles may be controlled by varying the amounts of these constituents. Note that for the sake of brevity, here hydrogels will be referred to by the weight percent of their first component only and denoted with abbreviations of AA and AM. The solution polymerization procedure is hereby summarized, adapted from Zhu, et. al. (43) Water, monomer, and neutralization solutions are added to scintillation vials followed by the crosslinker solution N-N’methylenebisacrylamide (MBAM) and initiator solutions. The vials are placed in a temperature-controlled oil bath at 50-60°C until gelation is observed. The thermally controlled bath ensures that gelation occurs within 1 to 8 hours. The hydrogel particles are then soaked and washed with water to remove any unreacted monomer, cut into rough, cm-sized pieces and dried in an oven between 50-80°C for 8 hours. The pieces are then ground and sieved for further use. Grinding and sieving may be repeated as required to obtain the desired hydrogel particle size distribution (see Figure 2). 336

Figure 2. Size distribution of dry, sieved hydrogel particles: (a) spherical 17% AA, (b) spherical 83% AA, (c) angular 17% AA, and (d) angular 83% AA. Reproduced with permission from reference (34), Copyright 2018 Springer.

The inverse suspension polymerization procedure to create spherical hydrogel particles requires the formation of a dispersed aqueous phase within an organic continuous phase. The aqueous droplets are stabilized by a surfactant, and the droplet size is a function of the mixing speed (e.g., 400-1200 rpm) with greater speeds creating smaller droplets and, in turn, smaller hydrogel particles. The aqueous phase is prepared by mixing water, monomer, neutralization solution, crosslinker, and an initiator. The aqueous phase is then added to the organic phase (e.g., cyclohexane containing the surfactant) and stirred continuously as a catalyst is added to the mixture to initiate polymerization of the monomer within the dispersed droplets. The solution is heated at a specified temperature until the reaction is complete and the hydrogel particles are then filtered and rinsed. Details of this procedure can be obtained from Davis, et. al. (50) Figure 2 and 3 depict the particle size distribution and optical microscopy images, respectively, of hydrogel particles prepared by solution polymerization (angular in shape) and suspension polymerization (spherical in shape). 337

Figure 3. Optical microscopy images of dry (a) spherical and (b) angular 17% AA hydrogel particles. Reproduced with permission from reference (34), Copyright 2018 Springer.

Cement Chemistry Concrete is mainly comprised of cement, aggregates and water (51, 52). As a simple approximation, concrete is composed of two phases: hydrated cement paste and aggregates. Therefore, concrete inherits its properties from its two constituent phases and the interfaces between the phases. The interface is known as the interfacial transition zone and is usually the mechanically weakest area in concrete. The aggregates in concrete are mainly divided into two types: fine aggregates (sand) and coarse aggregates (rocks). Supplementary cementitious materials (e.g., silica fume, fly ash) may be used in HPC to impart specific properties to the hardened concrete (53). The hydration reactions that occur within a fresh concrete is due to the cement paste. Various different types of Portland cement are used in concrete mix design, depending on the type of structure to be constructed. Overall, the raw material for Portland cement contains four oxides: CaO, SiO2, Al2O3, and Fe3O3, which forms the clinker (53). Clinker together with gypsum (CaO.2H2O), forms Portland cement and their composition is adjusted to impart specific properties necessary in the concrete produced from it. The main composition of Portland cement with their chemical formulae (54) are shown below in Table 1.

Table 1. Chemical Composition of Portland Cement Cement Compound

Chemical Formula

Tricalcium silicate (C3S)

Ca3SiO5 or 3CaO·SiO2

Dicalcium silicate (C2S)

Ca2SiO4 or 2CaO·SiO2

Tricalcium aluminate (C3A)

Ca3Al2O6 or 3CaO ·Al2O3

Tetracalcium aluminoferrite (C4AF)

Ca4Al2Fe2O10 or 4CaO·Al2O3·Fe2O3

Gypsum

CaSO4·2H2O

338

The addition of water causes hydration of each of these compounds and this is referred to as ‘curing’ of concrete. The calcium silicates are mainly responsible for contribution of strength to hardened mixtures. Tricalcium silicate is responsible for early strength in concrete (first 7 days) (55) along with the setting of cement (i.e., the time taken for the transition of cement from a fluid paste to a rigid material) (54, 56). Dicalcium silicate, which reacts more slowly, imparts strength at later stages (2, 44, 48, 52, 57, 58). Tricalcium aluminate affects setting time of cement and contributes to the hardening of cement.. Significant heat is generated during hydration of C3A (2, 48) and hence a higher proportion of this constituent is avoided to prevent cracking in concrete (59) C4AF contributes to the color of the cement and acts as a flux during the production of cement (60). It does not have a significant effect in strength gain. Gypsum is added to cement to prevent ‘flash setting’, a phenomenon where a higher percentage of C3A in cement leads to immediate stiffening of cement (54). The hydration reactions relevant to strength development (58) are shown below (Table 2).

Table 2. Reactions Pertinent to Strength Development in Cement Paste Tricalcium silicate + Water → Calcium silicate hydrate + Calcium hydroxide 2 Ca3SiO5 + 7 H2O → 3 CaO·2SiO2·4H2O + 3 Ca(OH)2 + 173.6 kJ Dicalcium silicate + Water → Calcium silicate hydrate + Calcium hydroxide 2 Ca2SiO4 + 5 H2O → 3 CaO·2SiO2·4H2O + Ca(OH)2 + 58.6 kJ

The hydration reactions produce calcium silicates (commonly known as CSH) and calcium hydroxides (referred to as CH). The behavior of cement paste can be explained by the hydration mechanisms and associated chemistry involved with it. At the onset of hydration, there is a rapid liberation of CH into the pore fluid, which results in the development of shell-like formations of CSH on the cement grains (54, 61). This layer hinders further reactions which allows the cement paste to remain workable for a few hours. With time, this outer shell is disrupted due to osmotic pressures (54) and/or by further growth of CH (62). CH forms thin, plate-like crystals that are brittle in nature. The crystalline gelatinous mass (2), mainly comprised of CSH, contributes to adhesive properties (2, 57) and strength by a combination of cohesive bonds due to van der Waals’ forces and chemical bonds (54). In general, the hydration of Portland cement involves a progression of reactions between the solid cement components and an aqueous fluid. The fluid is initially water, and, as the reactions progress, the water is converted to a complex alkaline, sulfate-bearing solution soon after mixing (63). An interconnected internal pore structure results when the cement sets and is filled with the aqueous pore fluid. Only a small extent of hydration is complete before setting occurs and hence most cement hydration involves reactions with pore fluid (63). The aqueous pore fluids are highly alkaline in nature (pH greater than 12) (64) and are usually concentrated solutions of alkali hydroxides and a small fraction of other components (63). Analysis of pore solution by previous researchers have shown 339

that it consists primarily of ions such as sodium, potassium, and hydroxide, in addition to marginal amounts of multivalent calcium and sulfate ions (64).

Hydrogel-Cement Interactions When incorporated into cement, hydrogel particles are generally used in very small amounts (generally only 0.2% by weight of dry cement). The hydrogel and cement are mixed in their dry state, the required amount of water and superplasticizer are added, and the mixture is hand or vacuum mixed in the laboratory (or machine mixed in the field). Use of a vacuum mixer can yield more uniform mixing in addition to ensuring that any porosity would be due to capillary water and hydrogel particles and not due to non-uniformity in the manual-mixing process (34). The superplasticizer, generally a water reducing admixture (such as a polycarboxylate comb polymer (65, 66)), is added to ensure good workability of the cement paste as the paste for HPC has a very low water-to-cement (w/c) ratio. The addition of water in the mixture immediately causes the hydrogel particles to swell such that the hydrogel particles are most likely fully swollen by the time the cement mixture is placed (i.e., cast). Figure 4 is an illustration of the phenomena occurring in cement containing hydrogel particles from the time it is cast to the time when the cement has reasonably hardened. As the hydrogel particles are used to ensure proper hydration of the cement matrix, the interaction between the cement paste and hydrogel particles is of primal significance; the coarse aggregate (pieces of rocks) and fine aggregate (sand) have been omitted from the illustration for the sake of simplicity. Also, it is presumed that a similar process of hydration would occur in mortar and concrete samples.

Figure 4. Cross-section of cement mixture containing hydrogel particles and cement grains: (a) immediately after mixing and placement; (b) after a few minutes to hours (before final setting of cement); and (c) after a few days when a substantial amount of cement has reacted and the hydrogel particles have partially deswollen (dehydrated). Initially, the cement grains start to hydrate from the water available in the mixture causing hydration products to form an outer layer on the grains as aforementioned and illustrated in Figure 4b. This causes a retardation in 340

the process of hydration as the unhydrated core of the cement grains will have reduced access to water. As the cement curing proceeds, water is extracted from the hydrogel particles to fuel the hydration reactions, driven by osmotic pressure gradients in the system and facilitated by the formation of capillary networks in the cement matrix. Eventually the hydrogel particles deswell (as shown in Figure 4c) from a combination of two factors: the extraction of water by the cement paste and the intrusion of cations from the pore fluid into the polymer network. Even after a few days (or years, for some types of cement), hydration reactions are still incomplete, and there is always some unreacted cement grains in the cement paste (C2S takes a long time to undergo hydrolysis). It is possible that the cement grains in close vicinity to the hydrogel particles may undergo faster and greater amounts of hydration than those further away, especially if there is an inhomogeneity in the dispersion of the hydrogel particles throughout the cement paste. Over time, hydration products form on the outer surfaces of the voidspace that remains from the dehydrated hydrogel particles (described in detail later). Since the hydration reactions of C3S start immediately after water is added to the dry cement grains, it would take a few minutes to hours for the hydration products to form. Meanwhile, depending on the composition of the hydrogel particles, cement alkalinity, and the availability of water, it might take a few minutes to hours for the particles to reach maximum swelling capacity. The deswelling of the hydrogel particles creates voidspace (porosity) in the hardened cement paste (Figure 5), which can enhance the durability and freezethaw resistance of concrete (21). However, careful dosage of hydrogel particles has to be ensured so as to not significantly reduce the compressive strength of the concrete due to the increased porosity from hydrogel-related voidspace.

Figure 5. Scanning electron micrograph of a 24-hour cured mortar cross-section showing a void remaining from an angular hydrogel particle.

Hydrogel Swelling Behavior The gravimetric “tea-bag” method (46, 47, 67, 68) is a common method for evaluating the swelling capacity, Q, of a collection of hydrogel particles. The procedure is fairly simple and involves loading a known mass of dry particles into a prewetted, commercially available tea-bag and immersing the tea-bag into a 341

desired solution. At specified time intervals, the tea-bag is removed, excess water is allowed to drain, and the tea-bag is weighed to obtain the swelling capacity, given by the following equation:

where ms is the mass of the wet, swollen samples and md is the initial dry mass. Effect of Hydrogel Size, Morphology, and Crosslinking Density Figure 6 displays results obtained from swelling tests performed on two different size distributions (106–425 µm and 425–850 µm, respectively) of angular hydrogel particles containing 2 wt.% covalent crosslinking and immersed in pure water and a salt solution (calcium nitrate solution) (43). The results show that in both solutions, particle size distribution causes a significant change in swelling rate, as the smaller size distribution displays a faster swelling rate than the larger distribution considering that particles ideally start at Q = 0 (dry). Note that the values of Qeq at relatively long times (i.e., beyond 30 minutes) are independent of particle size.

Figure 6. Swelling behavior of 17% AA angular particles of two different sizes immersed in pure water and 0.025 M CaNO3 solutions. Reproduced with permission from reference (43), Copyright 2014 Springer. Hydrogel particle shape (e.g., spherical particles from suspension polymerization vs. angular particles from solution polymerization) was observed to have no prominent effect on the apparent swelling kinetics for collections of hydrogel particles measured using gravimetric tea-bag tests (34), although individual, isolated particles with greater surface area to volume ratios would be expected to swell more quickly. An increase in covalent crosslinking density within the polymer network limits the volumetric change that is possible during 342

swelling (67) and results in an overall decrease in measured absorption capacity and thus decreased values of Qeq (43).

Comparison of Hydrogel Swelling Behavior in Various Solutions A general trend can be observed when hydrogel swelling curves in different solutions are plotted (see Figure 7) (32). A higher percentage of acrylic acid (AA) in the polymer network generally increases the hydrogel’s maximum swelling capacity. However, due to the anionic nature of AA (described previously in this chapter), ionic complexes can form between the COO- moieties and the multivalent cations present in salt solutions, which collapses the network by expelling water that was initially bound to the polymer. By comparison, hydrogel particles containing a majority of acrylamide (AM) segments in their networks are largely unaffected by the presence of cations as AM has relatively few anionic sites at pH < 12. Hence the presence of cations and increasing cationic valency has a negative impact on maximum absorption capacity of hydrogel particles. Tap water, which contains a plethora of ions, also leads to reduced swelling compared to reverse osmosis (RO) water; note that in practice, most concrete mixtures are formulated using municipal tap water.

Figure 7. Swelling behavior of (a) 17% (b) 33% (c) 67% and (d) 83% AA angular hydrogel particles submerged in various types of solutions, including sodium (pH 6.7±0.2), calcium (pH 6.7±0.2), aluminum (3.8±0.2) salt solutions, RO water (pH 6.7±0.2), tap water (pH 7.3±0.2) and pore fluid (pH 12±0.2). Reproduced with permission from reference (32), Copyright 2016 Springer. 343

Further scrutiny of the swelling ratios observed in aluminum sulfate solutions indicates that swelling is suppressed as the concentration of trivalent Al3+ in solution is increased (see Figure 8) (33). Additionally, real-time observations indicate that the hydrogel particles develop a stiff outer shell with elastic modulus values proportional to the concentration of AA in the network, most likely due to localized collapse/densification of the outer regions of the polymer network due to Al3+ complexation (33). The presence of a mechanically stiff shell is evidence of different transport behavior of aluminum ions within a polymer network compared to sodium and calcium ions; and indeed, the ionic complexation of trivalent ions may be considerably stronger than that of divalent ions (33, 69).

Figure 8. Swelling behavior of four different compositions of angular hydrogel particles in (a) 0.005M and (b) 0.025M of aluminum sulfate solution. Reproduced from reference (33), Copyright 2017 MDPI.

Swelling characteristics, including maximum absorption values and the sorption kinetics, are important indications of the usefulness of the hydrogel particles as effective internal curing agents for concrete mixtures. These factors must be kept in mind when selecting the amount of water for concrete mixture design and when the concrete is intended for use in places of high salinity (e.g., coastal regions) or places with increased water hardness. It is important to note that the results from swelling tests in specific solutions are merely an indication of general trends (i.e., the relative sensitivity of a particular hydrogel composition to the presence of ions in solution) and cannot be used to accurately predict how a hydrogel will behave in a cementitious mixture. The pore fluids sometimes used in gravimetric tests (discussed in the next section) are an idealized condition of an infinite reservoirs of water and ions and is in stark contrast to the low water-to-cement ratio HPC mixtures where increased competition for water could result in reduced swelling kinetics and absorption capacities (32). 344

Hydrogel Swelling in Cementitious Pore Fluids There is a prominent difference in swelling behavior when hydrogel particles are immersed in cementitious pore fluid (see Figure 9) (32). Pore fluid naturally contains a complex mixture of mono- and multivalent ions – Na+, K+, Ca2+, Mg2+, Al3+, Si4+ among others (70) – all by-products of the ongoing hydration reaction between the Portland cement grains and water. For hydrogel particles containing a greater concentration of AM, the swelling capacity is fairly constant over time, while for particles containing a greater concentration of AA, a more parabolic swelling-deswelling behavior is observed (32). The alkaline pH of the pore fluid (12.5-13.8) (71, 72) causes the deprotonation of the COOH groups of the AA segments in the polymer network and initially leads to greater swelling. However, the exposed COO- also serves as sites for cations to bind, resulting in rapid deswelling, especially for particles containing the highest concentration of AA (i.e., 83% AA in Figure 9). This extreme sensitivity of some hydrogel compositions to the presence of cations has to be kept in mind while selecting the appropriate hydrogel compositions for internal curing of concrete as differences in cement compositions will generate pore fluids with different constituent ions and hence alkalinities.

Figure 9. Swelling behavior of different compositions of angular hydrogel particles immersed in pore fluid with pH = 12±0.2. Reproduced with permission from reference (32), Copyright 2016 Springer.

Impact of Hydrogel Particles on the Microstructure of Cement For any discussion of the use of hydrogel particles in cementitious mixtures to be complete, a close scrutiny and analysis of the hydrogel-cement microstructure is necessary. As described previously and illustrated in Figure 4, the water-swollen hydrogel particles deswell during the course of the hydration reaction, leaving 345

behind voids in the cement matrix (refer to Figure 5 and see Figure 10 and 11). Interestingly, microscopy of hydrogel-containing samples revealed the formation of specific inorganic phases within the voids including calcium hydroxide (CH) and calcium-silicate-hydrate (CSH), the latter being the ‘glue’ that binds the cement grains together and is thus primarily responsible for concrete’s exceptional compressive strength (33).

Figure 10. Scanning electron micrographs of cement paste containing (a) 17% and (b) 33% AA angular hydrogel particles. The blue areas indicate CH formation inside the remaining hydrogel voidspace; note that some of the remaining dehydrated hydrogel is visible in (a). Reproduced from reference (33), Copyright 2017 MDPI.

It was also observed that CH was more likely to develop in cement that was internally cured with AM-rich hydrogel particles. As previously mentioned, the amide groups present in AM are less sensitive to cation-induced deswelling of the polymer network; thus, these AM-rich hydrogel particles may retain water longer to facilitate a greater conversion of calcium silicates to CH and CSH (refer to Table 2). Figure 11 clearly illustrates the significant growth of CH crystals within the hydrogel voidspace for cement paste containing 100% AM (0% AA) hydrogel particles. Energy Dispersive Spectroscopy (EDS) performed on the features of interest displayed results which corresponded to composition of CH (within the range of uncertainties) and lacked any of the elements (Al, S, etc.) characteristic of ettringite formation (another product of hydration of cement). The dependence of CH formation on hydrogel particle composition is reported in Figure 12, indicating that the AM-rich hydrogel particles (17 and 33% AA) contained voids with the greatest amounts of hydrated product (33). These results demonstrate that hydrogel particles could potentially be engineered to refill voidspaces with inorganic phases, leading to further increases in compressive strength dependent entirely on the organic chemistry of the hydrogel particles (33, 34). 346

Figure 11. Scanning electron micrographs of cement paste containing 100% acrylamide spherical hydrogel particles, showing significant CH growth in the hydrogel voidspace (note that hydrogel particle is not visible).

Figure 12. Percentage of voids in 3-day cured paste samples filled with CH and any other hydrated products (CH + CSH) as a function of hydrogel composition. Reproduced from reference (33), Copyright 2017 MDPI.

Impact of Hydrogel Particles on the Mechanical Properties of Mortar Effect of Hydrogel Composition on Autogenous Shrinkage and Durability One of the primary reasons for using hydrogel particles as concrete internal curing agents is because the water released from the particles has been found to reduce autogenous shrinkage (9, 22, 42, 73). ASTM C1698 (74) is generally followed for the determination of autogenous shrinkage of mortar samples. Figure 13 shows results of autogenous shrinkage testing of mortar samples containing 347

a similar dosage (0.2% by weight of cement) but different compositions of hydrogel particles (32). The slopes of the control mortar samples remain negative throughout the test, indicating a perpetual process of self-desiccation and corresponding volumetric shrinkage, measured here as negative strain. All the samples containing hydrogel particles showed significant decrease in autogenous shrinkage compared to the controls. Thus, it is evident that hydrogel particles can effectively alleviate the shrinkage caused by self-desiccations (73, 75–79).

Figure 13. Effect of hydrogel particle compositions (17-83% AA) on the linear autogenous strain of mortar samples mixed at a w/c ratio of 0.32±0.03. Reproduced with permission from reference (32), Copyright 2016 Springer. Additionally, the incorporation of hydrogel particles to cementitious mixtures can have a positive effect in mitigating freeze-thaw effects in concrete (18–26) and thus increase the durability of pavements in cold-weather climates. Two common types of durability tests are water permeability (80) and rapid chloride permeability tests (81). Researchers have shown that the presence of hydrogel particles in concrete cause drastic decreases in water and chloride permeability when compared to hydrogel-free control samples under similar conditions (82). Hydrogel-modified concrete has also been shown to decrease the tensile creep of concrete (83). Creep is associated with the movement of water and development of microcracks over a long duration of time, and hence, any increase in creep resistance may be an additional benefit of using hydrogel-based internal curing agents in concrete. Effect of Particle Morphology on Compressive Strength The effect of hydrogel particles on the overall compressive strength of hardened cementitious composites (including mortar and concrete) is fraught with contradiction across literature. While some researchers report an increase in compressive strength following addition of hydrogel particles to the mixture, data reporting significant decreases in strength can also be found. Although addition of hydrogel particles for use as internal curing agents directly contributes to 348

increased strength of cementitious mixtures by creating a denser cement matrix and mitigating shrinkage and the subsequent development of stress cracks, it also increases the porosity within the microstructure and can increase relative humidity, both of which lead to decreased strength (9, 22, 84–86). It is also worth noting that in contrast to impact-resistant polymer composites, in which the addition of micron-sized rubber particles can increase the strength and toughness of the material (e.g., rubber-modified epoxies (87, 88)), here the dehydrated hydrogel particles do not have a strong interfacial bond with the surrounding cement matrix (refer to images in Figure 10). Thus, it is unlikely that any significant elastic energy is ever transferred between the cement matrix and the hydrogel particles. Figure 14 demonstrates the effect of hydrogel particle shape on the compressive strength of mortar (cement containing fine aggregate) (34). All mortar samples containing hydrogel particles displayed greater 28-day compressive strengths than the hydrogel-free control mixture, and there were no significant differences observed between mortar containing angular particles and mortar containing spherical particles. The mechanical performance of the internally cured mortar is even more impressive considering that the hydrogel particles will leave behind voids within the cement matrix, such that the density of these hydrogel-containing samples is expected to be less than the density of the hydrogel-free control samples. These results are promising as concrete mixture design is generally performed based on 28-day compressive strength values. It might be possible that for some hydrogel compositions, the development of compressive strength is delayed as the particles release water over different timescales. Also it is noteworthy that although the hydrogel particles are ultimately designed for use as internal curing agents in concrete, results from mortar and cement compression tests are typically used to infer the hydrogel particle’s effectiveness as an internal curing agent. This is reasonable since concrete contains coarse aggregates (rocks) which makes it less vulnerable to failure than either mortar or cement by restricting crack propagation.

Figure 14. Average compressive strength of mortar samples at various ages containing different hydrogel compositions and particle shapes but very similar size distribution (reported in Figure 2). Reproduced with permission from reference (34), Copyright 2018 Springer. 349

Conclusions and Implications High-performance concrete mixtures derive significant benefit from the inclusion of water-swollen hydrogel particles. These internally cured mixtures ultimately have increased compressive strength and service life due to the reduced volumetric shrinkage during curing that is afforded by the hydrogel particles as well as increased freeze-thaw resistance resulting from the residual voidspace. The internal curing performance of hydrogel particles is strongly dependent on the physical and chemical structure of the internal polymer network, especially the sensitivity of the polyelectrolyte molecules to the presence of multivalent cations which occur naturally in fresh cementitious mixtures. By determining these key structure-property-performance relationships through careful experimental study, the chemical composition of the polymer network can be successfully designed to create hydrogel particles that have a desired sorption behavior and can trigger the growth of specific inorganic phases within cement microstructure, leading to the development of next-generation high-performance concrete materials.

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Chapter 18

Heterogeneity in Cement Hydrates K. Ioannidou* Multiscale Materials Science for Energy and Environment, MIT-CNRS-AMU, Department of Civil and Environmental Engineering, MIT Energy Initiative, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States *E-mail: [email protected].

Cement hydrates named C-S-H are the main products of the reaction of cement with water. The C-S-H phase is the most important phase of cement paste as it glues all other phases together in a solid rock-like material. C-S-H gels form and densify via out-of-equilibrium precipitation and aggregation of nano-grains during cement hydration. In this chapter, the link between the making and densification of C-S-H gels and amorphous solids is discussed by coarse-grained models based on the evolution of interaction potentials and an out-of-equilibrium simulation approach for particle precipitation. In particular, we characterize and correlate mesoscale structural and mechanical heterogeneities resulting into residual local eigenstresses. This underlying microscopic picture explains recent macroscopic measurements of the volume change of hydrating cement in fully saturated conditions.

Introduction Calcium-Silicate-Hydrate (C–S–H) is the primary hydration product of Portland cement that precipitates, upon mixing it with water, as nano-scale colloids in the pore solution. The nano-colloids form a highly cohesive gel, a soft glue whose properties in the early stages of the hydration affect the strength that cement and concrete attain after setting, when the material eventually hardens. Hence, in spite of the fact that the use of cement for concrete infrastructures and buildings relies upon its properties as a hard solid, those properties are controlled © 2018 American Chemical Society

by its soft matter state, mainly the C–S–H gel precursor of the hardened paste in the early stages of the hydration. The investigations of the gel during its formation are very limited, most of the structural characterization being done on the hardened paste via neutron scattering, atomic force microscopy (AFM) or scanning electron microscopy (1–3). These studies have been mainly performed on tricalcium silicate, the main reactant in Portland cement, that it is also often used as a model system for cement hydration. They indicate amorphous mesoscale organization built upon structural units of typical size 5-15nm (4). The sub-nanoscale structure of C-S-H building blocks is complex, resembling that of Tobermorite minerals at low calcium over silica ratio (Ca/Si) and that of disordered glasses at high Ca/Si (5). Recent advances of atomistic modeling of C-S-H have revealed characteristic of the structure and mechanical properties of the nano-colloids (5, 6) and have provided a first description of the effective interaction potentials between such nano-colloids (7–9). The effective interactions between the C– S–H units depend strongly on the chemical environment that evolves in time, with the dissolution of the cement grains and the precipitation of various hydration products (10). In fact, the effective net attraction between the C-S-H particles progressively increases with the changing physico-chemical environment, mainly due to strong charge heterogeneities and ion correlations growing in the pore solution. Such effective interactions are favored by the presence of multivalent ions (Ca+2) and may feature a combination of short-range cohesion and longer-range electrostatic repulsion resulting in an attractive well and a repulsive shoulder. A series of controlled experiments with fixed calcium ionic concentration provided useful indications on how the effective nano-scale interactions may indeed evolve over time in conditions relevant to cement hydration (11). Atomic force microscopy measurements show that the main change in time consists in the progressive reduction of the repulsive shoulder with time, which most probably completely disappear by the end of setting (11). Building on this experimental information we have investigated how equilibrium properties and aggregation changes in colloidal suspensions in presence of effective interactions that correspond to different physico-chemical conditions of hydration (12). The emerging picture is that the evolving effective interactions provide a thermodynamic driving for the growth of C-S-H gel and densification towards amorphous solid porous structures that are crucial to cement strength (13). In the past, with the idea that the gel can be regarded as a random assembly of sticky units, the gel growth has been prevalently addressed in terms of an irreversible aggregation of colloidal nanoparticles, as in a diffusion-limited cluster aggregation (DLCA) process (14). Nevertheless, this scenario has little or no correspondence to the morphology revealed by the experiments on the hardened cement paste. It does not explain how high packing fractions required for the final strength are reached. Moreover, C–S–H is produced through an exothermic reaction and its growth kinetics, measured in terms of the time dependence of the heat flow, is strongly non-monotonic, being characterized by an acceleration and followed by a deceleration regime. This feature is difficult to reconcile with the monotonic growth kinetics expected in the case of DLCA. 358

A recent simulation approach for C–S–H gelation and densification based on colloidal particles precipitation was able to reconcile several experimental results of the early and late stages of cement hydration (12, 15). In particular, the non-monotonic growth kinetics and the densification of the structure locally up to volume fractions 75% was rationalized. Moreover, these studies provided a quantitative description of local densities, pore size distributions, effective surface areas, hardness and elastic moduli that characterize C-S-H porous solids in hardened cement paste. Here, we discuss the mesoscale modeling scheme with emphasis on the effective interactions and how features of local packing connect to out of equilibrium phenomena of reactive densification in cement hydration. This is related to the development and (recently measured) eigenstresses resulting to bulk volume changes (16). We demonstrate this at the level of local packing and mesoscale organization of matter by correlating locally dense and locally stressed regions.

Mesoscale Model for Reactive Solidification of Cement Despite the remarkable complexity of colloidal physical chemistry, the equilibrium phases of colloidal suspensions are usually well-described with coarse-grained models assuming short range interactions, reminiscent of simple liquids (17–19). However, in complex fluids the relaxation times are typically much longer than in simple fluids and often it is important to understand the interplay between kinetic and thermodynamic trends (20). For instance, a variety of arrested, out-of-equilibrium states like gels or glasses can occur upon changing the control parameters or environmental conditions (e.g., varying the solid volume fraction or the strength of the interactions or applying a rate-dependent mechanical perturbation). The structural complexity of the metastable states typically emerges from the combination of a local/medium range order, bearing a signature of the underlying thermodynamics, with the slow kinetics eventually leading to an amorphous self-organization of the material over larger length-scales. Several experiments have been reported where complex aggregation pathways and structural arrest have been observed, or where equilibrium phases and metastable states resulted from complex effective interactions: arrested spinodal decomposition (21, 22), fluid cluster phases, unusual microcrystalline gels, colloidal membranes (23–25) or string-like or tetrahedrally packed aggregates (26–28). For investigations of cement hydrates gels and amorphous solids, coarse-grained modeling was employed based on nano-grains/colloids precipitation interacting with evolving attracto-repulsive potentials (12). The potentials are composed of short range attraction with a longer-range repulsion resulting in an attractive well, a shoulder and a repulsive tail. To account for the creation of new particles in the precipitation simulation, the μVT statistical ensemble is assumed, where μ is the chemical potential, V the volume of the simulation box and T the temperature. The interaction potential of the particles is fixed for each simulation and the chemical potential determines the particle 359

equilibrium density. However, cement hydration occurs in short time. Therefore, non-equilibrium simulations of different kinetic rates were performed. The chemical potential was chosen such that it promotes densification of the system. In this type of μVT precipitation approach, the kinetic path is build up upon the progressive increase of particle density. A metastable state of density ρ1 is the precursor of state ρ2, ρ2> ρ1. This has a significant implication on the structural and mechanical heterogeneities of amorphous solids states of volume fraction 40% or larger, relevant for the hardened cement paste (see Discussion section). Gels and solids with the same potentials were also obtained via variation of traditional control parameters such as the solid volume fraction and temperature (13). In more details, during cement hydration C-S-H colloids precipitate in the pore solution because of the ongoing chemical reactions causing dissolution of anhydrous cement grains and precipitation of the C-S-H phase along with other minor various hydration products. In this scheme, newly precipitated C-S-H colloidal particles in the simulation box interact with existing one, stick together, and form aggregates that eventually create a stress-bearing gel. A free energy gain related to the chemical potential μ drives the precipitation of C-S-H particles. The effective inter-particle forces for cement hydrates have been obtained from sub-nanoscale simulations and AFM experiments (11, 29). The simulations consist of a grand canonical Monte Carlo (GCMC) scheme, where the chemical potential corresponds to the free energy gain of a new particle creation coupled to molecular dynamics (MD) allowing to follow both the densification and the dynamics of the aggregated structures. The formation and growth of the C-S-H mesoscale structures are determined by the interplay between free energy of the system (resulting from the chemical potential and the inter-particle potential) and the imposed out-of-equilibrium conditions (corresponding to the rate at which GCMC events take place with respect to the structural relaxation time of the aggregated structures). A relatively common feature of effective colloidal interactions is a competition between a short-range attraction with a longer-range repulsion resulting in an attractive well, a shoulder and a repulsive tail. The physical origin of attraction at small separations can be very different, e.g. van der Waals forces as in the DLVO theory (30), polymer-mediated depletion interactions (31), polarization effects in case of induced magnetic interactions (25), micro-ion correlation in case of multivalent electrolytes (32), bond formation in DNA-coated colloids (33) or even activity of self-propelled particles (34). The long range repulsion typically originates from colloids being charged (35, 36) or from other system-specific interactions like magnetic, steric etc. Often, such systems are inherently many-body (37), which adds further complexity to the problem. However, in some cases the macroscopic properties are well-described by pairwise additive effective interactions (38). In case of charged suspensions, this might be true under high salt conditions when the physical charges on the particle surfaces are efficiently screened. For highly charged particles, i.e. in charged stabilized suspensions, the repulsive part of the interaction potential dominates the behavior (the height of the shoulder is much larger than the thermal energy), while more complex behavior can be observed in weakly charged colloids where 360

both the attractive well and the repulsive shoulder are of the order of kBT (39–45). Such a scenario can arise in systems like heterogeneously charged surfaces and membranes (46) and in materials like clays (47) or C-S-H (10). The electric double layer theory of Gouy and Chapman (GC), based on the solution of the Poisson–Bolzmann (PB) equation, describes the formation of a diffuse electric double layer when a charged surface is in contact with an electrolyte solution. It allows to calculate the interaction between two colloids. Combination of the GC or PB theory with van der Waals interactions led some 70 years ago to the so-called DLVO theory which is still the reference frame for many colloidal chemistry applications and is extensively developed in textbooks (35). The interaction between two identical particles immersed in an electrolyte, as predicted by the DLVO theory, is composed of two independent and additive parts: the double layer interaction, always repulsive, and the van der Waals interaction, always attractive. It is now clear that this was not correct and that a system composed of two charged particles with like-charges may generate attractive configurations due to correlations in the local concentration of ions due to thermal fluctuations. This has been known for more than twenty years (47, 48) and the suggestion that this may contribute to the cohesion of set cement was made more than two decades ago (49). The attraction appears when the electrostatic coupling in the electrolyte is sufficiently large. The electrostatic coupling can be evaluated from the colloidal surface density of charge, the ionic charge and radius, the solvent dielectric constant (in an implicit solvent description) and the temperature (50). In aqueous media, this happens with divalent or multivalent ions at short separation, say in the nm range. The reason why the PB treatment and DLVO theory miss the possibility of attractive double layer interactions is due to the neglect of thermally-driven ionic concentration fluctuations. The PB equation is therefore an example of the so-called mean field approximation. Taking into account electrostatic interactions only, the overall shape of the force (or pressure) versus inter-colloid distance can therefore vary from a continuously decreasing function (as in the DLVO theory or at weak electrostatic coupling) to a single well curve. For large enough and charged enough ions in interaction with highly charge colloids, this pressure-distance curve exhibits a short-distance negative well continued with a positive shoulder that eventually dies out at large distance. Note that in this case, the van der Waals contribution will be a small correction. The systems of C-S-H gels and solid investigated composed of spherical particles with diameter σ interacting via effective potentials, which are a combination of a short-range generalized Lennard-Jones (LJ) attraction and a long-range Yukawa repulsion (35):

where r is the inter-particle distance, γ the exponent in the generalized LJ interaction and κ the inverse screening length. The interaction potentials are truncated and shifted to zero at 4σ. Prefactors ε and Α measure the relative strength of the attractive and repulsive interaction terms. The functions V(r,γ,κ,ε,A) of Equation 1 with all possible parameter values define a family of interaction potentials with an attractive minimum at r=rmin and a repulsive barrier at r=rmax. 361

A sub-family of potentials was considered with fixed γ=12 and κ-1=0.5σ and combinations of A and ε values such that the depth of the attraction well at rmin is fixed to V(rmin)=-1kBT and the height of the repulsive shoulder is between 0 < V (rmax) ≤ 0.5 kBT.

Simulations Parameters Specifically, we focus on three cases the high shoulder HS (A=4, ε=1.5), the low shoulder LS (A=12, ε=2.4) and no repulsive shoulder LJ (A=0, ε=1.5). The three interaction potentials are displayed in Figure 1. In all cases under consideration the attraction is short-ranged, i.e. the width of the attraction well is in the range between 0.1σ and 0.3σ.

Figure 1. The inter-particle potentials combine a short-range 12-24 Lennard-Jones attraction and a long-range Yukawa repulsion. The black dotted line corresponds to HS, the red dashed line to LS and the green solid line to 12-24 LJ. The attraction to repulsion ratio ε/Α depends upon the concentration of calcium cations. 362

Regarding the simulation approach, GCMC accounts for the interplay between the chemistry -in specific the free energy gain from the production of one new C-S-H particle, and the interactions between the particles. Each GCMC cycle consists of Np particle insertion or deletion attempts succeeded by M=100MD steps in NVT conditions. R=Np/(M·L3·δt) where L is the length of the simulation box and δt=0.0025(mσ2/ε)1/2, is the rate of hydrate production. Simulations with higher values of R bring the system further out of equilibrium (12). Time was measured by MD unit time (mσ2/ε)1/2, the temperature was T=0.15 and the chemical potential μ=−1 all in reduced units. The chemical potential is chosen to promote densification. The simulations have been performed in two system sizes, one of box size 585.54nm with up to 610,000 particles (large) and of 390.36nm with up to 180,000 particles (medium). The diameters of the particles were ranging between 4-10nm.

Discussion The early formation of open gel C-S-H structures is reached due to interactions of HS-type that provide two body attraction but also favor the formation of elongated clusters due to the strength (height) of the repulsive shoulder (12, 41, 42, 45). Such HS interactions during cement hydration occur at low Ca+2 ions concentration when large capillary pores are filled with water during the partial dissolution of cement grains (tricalcium silicate). As already mentioned, the physical reason for attracto-repulsive interactions during cement hydration is ion-correlation forces between highly charged C-S-H nano-colloids meditated through divalent ions in the pore solution. The attraction to repulsion strength is controlled from the concentration of Ca+2 ions (11). Moreover, the HS potential facilitates the precipitation of C-S-H particles at lower supersaturation. For temperatures relevant for the formation of solid aggregates (T~0.15kBT), the energy gain to form clusters at low volume fractions is larger with the HS potential than with the LS one. The chemical potentials μ for HS and LS potentials were computed in Reference (13). This is also supported from recent experimental findings in controlled in situ hydration of tricalcium silicate, where clusters of nano-particles of C-S-H are observed in the vicinity of but not yet stuck to the reacting cement grain (51). Overall, type HS potentials at the early stages of hydration are beneficial as C-S-H nano-colloids can precipitate more easily and form elongated clusters that eventually impinge into an arrested gel and contribute to the initial gelation of cement hydrates. An extensive study of this potential can be found in References (12, 13). If HS interaction between C-S-H particles was present throughout hydration, cement would not densify to form the compact solid material we know. From precipitation (12) and equilibrium (13) simulations it is shown that in order to attain higher volume fractions the repulsive shoulder shall reduce and disappear. Simulation data such as densification curves, coordination number and free energies support the fact that the continuous densification of the material is intimately related to the underlying equilibrium-phase behavior of the evolving effective interactions between the hydrates (12, 13). 363

Figure 2 shows the distributions of nearest neighbors for amorphous solid structures of volume fraction η=0.37 resulted from precipitation simulations using the hybrid GCMC and MD scheme for HS and LS potentials. The LS potential enhances the number of nearest neighbors allowing for denser local packing compared to HS. The inset shows the average number of nearest neighbors for HS and LS for configurations resulted from equilibrium MD simulations. The nearest neighbors of particles interacting with LS potential are around 10 irrespectively of the volume fraction whereas the one with HS transition from 6 neighbors to 10 as the η increases. The mesoscale structures of particles interacting with HS are elongated clusters that form gels at lower η than LS. This is related to the fact that local particles pack in Bernal spirals (6 neighbors) (13). HS provides the initial gelation and LS favors local densification.

Figure 2. Distributions of nearest neighbors for samples of volume fraction η=0.37 produced from precipitation simulations with potentials HS (circles) and LS (triangles). The inset shows the average number of nearest neighbors for HS and LS from MD simulations. The data plotted here are from Reference (12).

Densification of the initial gel structure occurs due to the reduction of the repulsive shoulder (from HS to LS and to LJ). As more hydrates are produced the pore volume reduces and, in many cases, leads to localization of calcium ions among C-S-H hydrates that are at close distances. The initial open, thin-branched structure obtained with the HS potential, densifies resulting to fewer and thicker strands with larger pores in-between similar to coarsening. A proof of concept of this coarsening process when switching interaction from HS to LS can be found in Reference (13). 364

An important point to note is that HS interactions switch to LS and eventually LJ due to confinement. The system under investigation takes place into a capillary pore of hundreds of nm up to few μm. If densification continued with HS, the pressure would have increased as HS favors expansive open structures (building up of positive pressure). The fact that the precipitation of hydrates is confined, eventually causes the confinement of calcium ions that localize in-between C-SH particles and modify the effective interaction from HS to LS and eventually to LJ. This signals the transition from attracto-repulsive ion correlation forces to electrostatic interactions (the ions being localized in or at the surface of solid C-SH particles) with strongly attractive wells that can be modelled with a LJ potential, ultimately providing the strength of the hardened cement paste. Recent measurements of bulk volume changes in saturated cement pastes at constant pressure and temperature conditions showed the development of non-monotonic colloidal eigenstresses suggesting a competition of different attracto-repulsive mechanisms occurring in different large capillary pores for different ionic concentrations (16). Hydrating cement initially expands and after hundreds of hours begins to shrink (16). This behavior is a macroscopic average of capillary pores filled with newly formed cement hydrates interacting with HS type potentials, (hence expanding) and of capillary pores with denser solid aggregates of C-S-H interacting with LJ type potentials, hence shrinking. As hydration time proceeds the balance shifts towards the shrinking mechanism due to the tighter confinement of the ions. Such volume changes in hydrating cement play a critical role in many engineering applications that require precise calculation of stress and pressure developments. The mechanical properties of hardened cement paste strongly depend on the evolution of effective interactions and the eventual transition to strongly attractive forces between C-S-H particles. The moduli and hardness measured by nano-indentation experiments are in quantitative agreement with simulated ones by the precipitation scheme (15). Experiments show a distribution of moduli and hardness values indicating that cement is a very inhomogeneous rock-like material (52). The reason for this is that cement forms in very short time (~1 month) compared to geological times taken for minerals or sedimentary rocks. On one hand this fast setting of cement allows for high-rise building. On the other hand, structural and mechanical heterogeneities are inevitable as the C-S-H amorphous solids do not have time to reach equilibrium. This is especially important for concrete buildings and infrastructure’s durability and aging. Figure 3 shows such structural heterogeneities developed during the out-of-equilibrium process of particle precipitation interacting with LJ potential. Hardened cement paste exhibits a broad heterogeneity of local volume fractions ηlocal (15, 53). After thresholding the configuration for increasing local volume fractions, an underlying percolating network of highly packed (>64% RCP) particles is revealed. The percolating network of particles locally packed at higher volume fraction than the random close packing (RCP) covers only ~20% of the simulation box volume. In nano-indentation measurements, these are the regions that are responsible for the remarkable hardness and moduli of cement (15). Here, we move further to understand also the role of particles with local volume fraction below 60%. 365

Figure 3. Snapshots of a configuration of hardened cement paste of volume fraction η=0.52 of polydisperse sized particles. They depict the different local volume fractions ηlocal. a) All local volume fractions are included. Particles with ηlocal ≥0.4, ηlocal≥0.5, ηlocal≥0.64 and ηlocal≥0.66 are shown in b, c, d and e respectively. The color code for all snapshots is shown in f.

Figure 4 shows the correlations between local volume fractions and local pressure Plocal in a configuration of hardened cement paste where the total eigenstress (at the level of the simulation box) has been relaxed (~10kPa) (53). In the population of particles with local volume fractions larger than 60% a tail towards positive local pressure is observed, hence overall particles are under compression. Thresholding the configurations by local volume fraction around 0.6, two types of networks reveal in Figure 5b. On one hand, the one of Figure 5b that contains the particles with ηlocal≥0.6 is very compact and its average pressure is positive. On the other hand, the one of Figure 5a containing particles with ηlocal