Magnetic Nanoparticles in Biosensing and Medicine 1107031095, 9781107031098

Table of contents :
Cover
Front Matter
Magnetic Nanoparticles in
Biosensing and Medicine
Copyright
Contents
Contributors
Preface
Abbreviations
1 Magnetism, Magnetic Materials,
and Nanoparticles
2 Preparation of Magnetic
Nanoparticles for Applications
in Biomedicine
3 Magnetic Nanoparticle
Functionalization
4 Manipulation
5 Modeling the In- Flow Capture
of Magnetic Nanoparticles
6 Sensing Magnetic Nanoparticles
7 Magnetic Nanoparticles for
Magnetic Resonance Imaging
Contrast Agents
8 Magnetotactic Bacteria and
Magnetosomes
Appendix: Units of Magnetic Properties
Index

Citation preview

i

Magnetic Nanoparticles in Biosensing and Medicine Drawing together topics from a wide range of disciplines, this text provides a comprehensive insight into the fundamentals of magnetic biosensors and the applications of magnetic nanoparticles in medicine. Internationally renowned researchers showcase topics ranging from the basic physical principles of magnetism to the detection and manipulation, synthesis protocols, and natural occurrence of magnetic nanoparticles. Up-​to-​date examples of their clinical use and research applications in the biomedical fields of sensing by diverse magnetic detection methods, in imaging by MRI, and in therapeutic strategies, such as hyperthermia, are also discussed, providing a thorough introduction to this rapidly developing field. Each chapter features questions, with answers available on the online resources page, key equations and definitions, and numerous illustrations to help readers grasp key concepts. Mathematical tools, together with key literature references, provide a strong underpinning for the material, making it ideal for graduate students, lecturers, medical researchers, and industrial scientific strategists. Nicholas J. Darton is the Technical Lead (Formulation) at Arecor Limited, where he is responsible for internal and external collaborative biopharmaceutical formulation development programs. Adrian Ionescu is a Research Associate at the University of Cambridge. He specializes in magnetic surfaces and nanoparticles, and has been awarded three Knowledge Transfer Fellowships. He currently works on quantum computing devices based on spin qubits. Justin Llandro is an Assistant Professor at Tohoku University, where he currently works assembled biomimetic 3D nanostructures and ultra-​ small magnetic tunnel on self-​ junctions for spintronics applications.

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Magnetic Nanoparticles in Biosensing and Medicine Edited by N I C H OLAS J .   D ARTON Arecor Limited

A D R IAN IO N ESCU University of Cambridge

J U S T IN LLAND RO Tohoku University

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University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 314–​321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi –​110025, India 79 Anson Road, #06-​04/​06, Singapore 079906 Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107031098 DOI: 10.1017/9781139381222 © Nicholas J. Darton, Adrian Ionescu, and Justin Llandro 2019 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2019 Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall A catalogue record for this publication is available from the British Library. ISBN 978-​1-​107-​03109-​8 Hardback Additional resources for this publication at www.cambridge.org/darton. Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-​party internet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

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Contents

List of Contributors Preface List of Abbreviations 1

Magnetism, Magnetic Materials, and Nanoparticles

page ix xi xiii 1

Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

2

1.1 Introduction 1.2 Fundamental Concepts 1.3 Magnetization Processes 1.4 Magnetic Measurements 1.5 Structural Analysis Sample Problems

1 2 16 30 45 46

Preparation of Magnetic Nanoparticles for Applications in Biomedicine

52

Pedro Tartaj, Sabino Veintemillas-​Verdaguer, Teresita Gonzalez-​Carreño, and Carlos J. Serna

3

2.1 Introduction 2.2 Fundamentals of Solution Routes and Some Interesting Examples 2.3 Nanocomposites from Solution Routes 2.4 Gas and Solid Routes 2.5 Conclusions and Perspectives Sample Problems

52 53 58 61 63 63

Magnetic Nanoparticle Functionalization

68

Justin J. Palfreyman

3.1 Gold-​Coated Particles 3.2 Coupling to Epoxides 3.3 Quantification Sample Problems

68 79 85 88

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Contents

4 Manipulation 4.1 A Survey of Tweezers for the Manipulation of Micro/​Nanoentities

91 91

Donglei Fan and Chia-​Ling Chien

4.2 Magnetic Drug Delivery

112

Thomas Schneider and Urs O. Häfeli

5

Sample Problems

134

Modeling the In-​Flow Capture of Magnetic Nanoparticles

151

Bart Hallmark, Nicholas J. Darton, and Daniel Pearce

6

5.1 Introduction 5.2 Physical Mechanisms Underlying Nanoparticle Capture 5.3 Concluding Comments Sample Problems

151 151 168 168

Sensing Magnetic Nanoparticles

172

6.1 Hall Effect Biosensors

172

Adarsh Sandhu and Paul Southern

6.2 Spin Valve and Tunnel Magnetoresistance Sensors

181

Susana Cardoso de Freitas, Simon Knudde, Filipe A. Cardoso, and Paulo P. Freitas

6.3 Magnetoimpedance Biosensors

206

Galina V. Kurlyandskaya

7

Sample Problems

221

Magnetic Nanoparticles for Magnetic Resonance Imaging Contrast Agents

228

Nohyun Lee and Taeghwan Hyeon

8

7.1 Introduction 7.2 Basic MRI Principles and Properties of MNPs 7.3 Control of MR Relaxivity of MNPs 7.4 Toxicity of MNPs 7.5 Conclusion Sample Problems

228 230 236 245 246 246

Magnetotactic Bacteria and Magnetosomes

251

Dennis A. Bazylinski and Denis Trubitsyn

8.1 Introduction and History 251 8.2 Magnetotactic Bacteria: Diversity, Phylogeny, and Physiology 252 8.3 The Bacterial Magnetosome: Composition, Size, Arrangement, and Morphology 255 8.4 Function of Magnetosomes: Magneto-​Aerotaxis 257 8.5 Genomics of Magnetotactic Bacteria 260

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Contents

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8.6 Biomineralization of Magnetosomes 8.7 Mass Culture of Magnetotactic Bacteria and Purification of Magnetosomes 8.8 Applications of Magnetotactic Bacteria and Magnetosomes 8.9 Concluding Remarks and Future Directions of Research Sample Problems

262

Appendix Index

285 287

265 267 270 271

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Contributors

Dennis A. Bazylinski, University of Nevada Filipe A. Cardoso, INESC-​Microsistemas e Nanotecnologias Susana Cardoso de Freitas, INESC-Microsistemas e Nanotecnologias and Instituto Superior Técnico-Universidade de Lisboa Chia-​Ling Chien, John Hopkins University Nicholas J. Darton, Arecor Limited Donglei Fan, University of Texas at Austin Paulo P.  Freitas, INESC-​ Microsistemas e Nanotecnologias and Instituto Superior Técnico-​Universidade de Lisboa Teresita González-​Carreño, Instituto de Ciencia de Materiales de Madrid Urs O. Häfeli, University of British Columbia Bart Hallmark, University of Cambridge Taeghwan Hyeon, Seoul National University Adrian Ionescu, University of Cambridge Simon Knudde, INESC-​Microsistemas e Nanotecnologias Galina V. Kurlyandskaya, University of the Basque Country and Ural Federal University Nohyun Lee, Kookmin University Justin Llandro, Tohoku University Justin J. Palfreyman, Seven Kings School Daniel Pearce, ConocoPhillips (UK) Ltd. Adarsh Sandhu, University of Electro-​Communications, Tokyo Thomas Schneider, University of Washington Carlos J. Serna, Instituto de Ciencia de Materiales de Madrid Paul Southern, University College London Pedro Tartaj, Instituto de Ciencia de Materiales de Madrid Denis Trubitsyn, Longwood University Sabino Veintemillas-​Verdaguer, Instituto de Ciencia de Materiales de Madrid Kurt R. A. Ziebeck, University of Cambridge

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Preface

The last decade has seen dramatic growth in research on applications of magnetic nanoparticles. New avenues of investigation have been developed, such as magnetic actuation and the use of magnetic particles for MRI drug delivery. Furthermore, magnetic nanoparticle-​based point-​of-​care diagnostic systems for the detection of substances ranging from cardiac infarction markers to narcotics have been released to market. International conferences on magnetism and solid-​state physics, such as the IEEE International Magnetics Conference (Intermag) and Conference on Magnetism and Magnetic Materials (MMM), have increasingly included sessions solely dedicated to research on magnetic nanoparticles and their applications in life sciences. Concurrently, international conferences in life sciences are also hosting sessions to discuss this research. As a result of the proliferation of interest in magnetic nanoparticles in so many areas, there is a need for a handbook to be compiled to act as an interdisciplinary lexicon. The goal of this monograph is to provide a first point of reference for the design, synthesis, and application of magnetic nanoparticles in biosensing and medicine, not only for newcomers to this field, but also established scientists looking for potentially new applications of their research. The eight chapters in this book aim to cover the diverse range of disciplines that together define biomedical applications of magnetic nanoparticles. In Chapter  1, the theory of magnetism, and the properties of magnetic materials and nanoparticles is presented (Ionescu, Llandro, and Ziebeck). This chapter provides an introduction to the origin of magnetism in transition metals and the fundamental magnetic properties exhibited by magnetic nanoparticles that define their behavior in applied magnetic fields. In Chapter 2, the synthesis of magnetic nanoparticles is described (Tartaj, Veintemillas-​ Verdaguer, Gonzalez-​Carreño, and Serna). In this chapter, a detailed practical guide is given on the best synthesis strategies for making magnetic nanoparticles. The relative advantages and disadvantages of each synthesis strategy are examined to enable the correct selection for the desired application. In Chapter  3 on magnetic nanoparticle functionalization (Palfreyman), a comprehensive guide to coating and functionalizing magnetic nanoparticles for biomedical applications is provided. Issues that are addressed in this chapter include the advantages and disadvantages of different chemical functionalization strategies, and

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Preface

detailed approaches to quantify the extent of surface coating and loading of ligands on nanoparticles. In Chapter  4 on manipulating magnetic nanoparticles (Fan, Chien, Schneider, and Hafeli), the application of nanoparticles in targeted medicine is reviewed. These applications include the control of magnetic nanoparticles for the targeted delivery of therapeutics to sites of disease and magnetic hyperthermia. Different approaches to nanoparticle manipulation are presented to provide an approach for future precision control of nanoparticles in medical applications. Chapter 5 is on modeling the capture of magnetic nanoparticles from flow (Hallmark, Darton, and Pearce). In this chapter, a method of developing a robust model for predicting magnetic nanoparticle behavior in applied magnetic fields in the body is presented. This model offers a method for optimizing magnetic targeting of nanoparticle-​linked therapeutics, and highlights the key physical properties of magnetic nanoparticles and their environment that affect targeting. In Chapter  6, sensing of magnetic nanoparticles by diverse magnetic sensors is described (Sandhu, Southern, S.  Cardoso, Knudde, F.  A. Cardoso, Freitas, and Kurlyandskaya). This chapter details the underlying physical principles that affect the detection and imaging of magnetic nanoparticles in a number of biomedical sensing applications. It provides insights into how magnetic nanoparticle sensing systems may be developed to provide the most sensitive diagnostic approaches available for potentially revolutionary advances in medical science. In Chapter 7, the design of nanoparticles for contrast agents in MRI (Lee and Hyeon) is investigated. In this chapter the optimal properties of magnetic nanoparticles for application in the medical imaging area of MRI are described. Different magnetic nanoparticle compositions and coatings are compared to provide a clear guide on material selection for obtaining the best contrast agents. In Chapter 8, magnetotactic bacteria are reviewed (Bazylinski and Trubitsyn). In this chapter, the occurrence of magnetic nanoparticles in nature and how these biological systems are able to produce endogenous magnetic nanoparticles are investigated. The harnessing of these systems is discussed to provide a scalable and low-​cost approach to yield biomagnetic nanoparticles with tailored magnetic properties for biomedical applications. We believe that the collaboration and exchange of ideas driving the interdisciplinary field of magnetic nanoparticle research that we have outlined in this book will help to provide the next generation of diagnostics and treatment strategies for improved medical care in the future.

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Abbreviations

a Real-​space lattice parameter a0 Bohr radius AFM Atomic force microscopy AF Antiferromagnetic AMR Anisotropic magnetoresistance AP Antiparallel α Demagnetization factor (-) α Magnet-​to-​vessel distance αH Modified Hooge parameter B Magnetic flux (T) |B| Absolute magnetic flux (T) βdi Integral width Bhf Magnetic hyperfine field BJ Brillouin function C Curie constant CDF Cation diffusion facilitator CLIO Cross-​linked iron oxide nanoparticle CMOS Complementary metal oxide semiconductor Carbon nanotube CNT CT Computed tomography ChT Chemotherapy Current in plane CIP Cyclo olefin copolymer COC CPP Current perpendicular to plane χ Susceptibility Effective magnetic susceptibility χeff χ Landau Landau susceptibility χ Larmor Larmor diamagnetic susceptibility χv Volume susceptibility (-​) χVV Susceptibility arising from Van Vleck paramagnetism χop Pauli susceptibility D Hydrodynamic drag (N) d Diameter

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Abbreviations

Da Dalton, measure of molecular mass (1 Da = 1.6605 × 10−27 kg) DEP Dielectrophoretic force DIC Diisopropylcarbodiimide DMF Dimethylformamide DMSA Dimercaptosuccinic acid DNA Deoxyribonucleic acid DOPA 3,4,-​dihydroxyl-​L-​phenylalanine DOTA 1,4,7,10-​tetraazacyclododecane-​1,4,7,10-​tetraacetic  acid DUV Deep ultraviolet DSPE 1,2-​distearoyl-​sn-​glycero-​3-​phosphoethanolamine DTPA Diethylene triamine pentaacetic acid dts Double-​triangular shaped (anisotropic crystals) DV Volume-​weighted domain size E Electric field e 1.6021765×10 −19 C, the unit charge for the carrier i.e. an electron EB Energy barrier EDC 1-​ethyl-​3-​(3-​dimethylaminopropyl) carbodiimide hydrochloride Edip Dipole-​dipole  energy EEW Electric explosion of wire EF Fermi energy EGF Epidermal growth factor emu Electromagnetic unit En Energy of the nth electron shell EPR Enhanced permeation and retention ESION Extremely small iron oxide nanoparticles < 4 nm in size Estrain Magnetostriction energy ε Adhesion energy (m2  kg/​s2) εm Permittivity of the medium ε0 Permittivity of free space η Viscosity (Pa s) ηK Kerr ellipticity F Force Fab Fragment antigen-​binding (region) FC Field cooled Fc Fragment crystallizable (region) FDA Food and Drug Administration Fgrad Gradient force Fh Shear force (N) FION Ferrimagnetic iron oxide nanoparticle Fm Magnetic force (N) FM Ferromagnetic Fmoc Fluorenylmethyloxycarbonyl Fr Resultant force acting on an immobilized nanoparticle (N)

xv

Abbreviations

Fscat Fur Fv FWHM φ φm ΦK ϕK G Gf

xv

Scattering force Ferric uptake regulator Volumetric body force term in the Navier–​Stokes equations (N/​m3) Full width at half the maximum intensity Volume fraction of nanoparticles in suspension (-​) Nanoparticle packing fraction (-​) Kerr effect Kerr rotation Modulus of rigidity Thermodynamic potential (free energy)

G Pair distribution function GC Graphitic carbon g Gravitational acceleration vector (m/​s2) gJ Landé g-​factor GMI Giant magnetoimpedance GMR Giant magnetoresistance gs Electron spin g-​factor (approximately 2.002319) γ Phenomenological Hooge’s parameter that quantifies the magnitude of noise for a certain device γ Electron gyromagnetic ratio:  the ratio between the magnetic dipole moment and angular momentum of the free electron H Magnetic field (A/​m) |H| Absolute magnetic field (A/​m)  H Hamiltonian of the system h Planck’s constant Hac Alternating drive field Hb Nanoparticle fringe field Coercive field Hc Hdc Time invariant dc magnetic field Hexch Exchange coupling field Hext External field Hf Magnetostatic coupling HGMS High-​gradient magnetic separation HGT Horizontal gene transfer Hint Internal field HJ Sense current field Hk Anisotropy field Hkeff Effective anisotropy field ℏ𝓁 Orbital angular momentum HN Néel coupling HOBt Hydroxybenzotriazole HPG Hyperbranched polyglycerol ℏs Electron’s intrinsic angular momentum or spin

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Abbreviations

0 H sw Switching field at 0 K IDT Interdigital transducers InSb Indium antimonide ITO Indium tin oxide J ijex Exchange constant between two spins si and sj KL Kendal fitting parameter K Clausius–​Mossotti  factor K1 Cubic anisotropy constant kB Boltzmann constant (= 1.3806 × 10–​23 m2 kg/​(s K)) k Crystal wavevector kP Power law fluid consistency index (Pa s(n+1)) Ku Uniaxial anisotropy κ Magnetic softness (-) L Capillary length (m) LDH Lactate dehydrogenase LLG Landau–​Lifshitz–​Gilbert equation LOR Lift-​off  resist LSP Localized surface plasmon λs Saturation magnetostriction M Magnetization m Magnetic dipole vector (A m2) m Number of Bohr magnetons per particle MAI Magnetosome island MAR Motional averaging regime MBE Molecular beam epitaxy MDC Magnetic drug carrier me Mass of an electron Microelectromechanical systems MEMS MeOx Metal oxide Malignant fibrous histiocytoma MFH Magnetic force microscopy MFM Class II major histocompatibility complex MHC II MI Magnetoimpedance Multicellular magnetotactic prokaryotes MMP MOKE Magneto-​optical Kerr effect Metal-​organic framework MOF MR Magnetoresistive Magnetic resonance imaging MRI MWCNT Multiwall carbon nanotube Magnetic nanoparticles MNP MR Remanence: remanent magnetization after saturation in the absence of any applied field MRAM Magnetic random-​access memory

xvi

Abbreviations

MRS Magnetic relaxation switch MSC Mesenchymal stem cells MSN Mesoporous silica nanoparticle Msat Maximum moment Ms Saturation magnetization (A/m) MTJ Magnetic tunnel junction MTT 3-​(4,5-​dimethylthiazol-​2-​yl)-​2,5-​diphenyltetrazolium bromide MZFC Zero-​field cooled magnetization μ Magnetic permeability μ0 Vacuum permeability (T m/​A) μB Bohr magneton µ eff Effective paramagnetic moment µ k Mean of the Gaussian distribution μr Relative permeability n Power law index (-​) NdFeB Neodymium iron boron NEMS Nanoelectromechanical systems NHS N-​hydroxysuccinimide NLM National Library of Medicine NM Non-​magnetic N A Avogadro’s constant 6.02 × 1023 mol −1 N ↑1 Spin up electron density of state nb Index of the medium N c Number of carriers in current I nh Number of vacancies in the valence band NMR Nuclear magnetic resonance NP Nanoparticles NSF Nephrogenic systemic fibrosis OAI Oxic-​anoxic interface OATZ Oxic-​anoxic transition zone OGMS Open-​gradient magnetic separation Ω Angular velocity ω0 Attempt frequency P Spin polarization of the FM electrodes p Pressure (Pa) p Crystal momentum ΔP Pressure drop (Pa) PCC Pyridinium chlorochromate PCR Polymerase chain reaction PDMS Polydimethylsiloxane PEEM Photoemission electron microscopy PET Positron emission tomography PEG Polyethylene glycol PEI Polyethylenimine

xvii

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xviii

Abbreviations

PL-​PEG Phospholipid-​poly(ethylene glycol) PMA Perpendicular magnetic anisotropy PMMA Poly(methyl methacrylate) PNBP P-​nitrobenzyl pyridine PS Polystyrene PSA Polysialic acids PTX Paclitaxel PVC Planctomycetes-​Verrucomicrobia-​Chlamydiae ψ Wavefunction Q Fluid volumetric flow rate (m3/​s) q Charge R Capillary radius (m) R Resistance r Radial coordinate (m) ra Nanoparticle aggregate radius (m) rp Nanoparticle radius (m) Re Reynolds number Re(K) Real part of the Clausius–​Mossotti factor K RES Reticuloendothelial system RF Radio-​frequency RHT Regional hyperthermia RKKY Ruderman–​Kittel–​Kasuya–​Yosida RNA Ribonucleic acid RT Radiotherapy ρ Density (kg/​m3) S Magnetic viscosity SAM Self-​assembled monolayers SAR Specific absorption rate SAW Standing acoustic wave SCID Severe combined immunodeficiency SDR Static dephasing regime SELEX Systematic evolution of ligands by exponential enrichment SEM Scanning electron microscope SERS Surface-​enhanced Raman scattering SIBA Self-​induced back-​action SM Isobaric-​isothermal magnetic entropy SNR Signal-​to-​noise SPECT Single photon emission computed tomography SPION Superparamagnetic iron oxide nanoparticle SPB Superparamagnetic beads SPP Surface plasmon polariton Sr Atomic spin

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Abbreviations

ST Soft tissue SQUID Superconducting quantum interference device SV Spin valve σ Standard deviation of the Gaussian distribution T Temperature (K) T Torque t Time (s) TB Blocking temperature TC Transition temperature TE Echo time TEM Transmission electron microscopy th Thickness of immobilized MNP bed (m) Tir Irreversibility temperature TN Néel temperature TMR Tunnel magnetoresistance TRM Thermoremanent magnetization TSHR Thyroid-​stimulating hormone receptor TT Thermotherapy Ttr Transition temperatures Expectation value of the dipole operator τ Relaxation time τmag Magnetic relaxation time τN “Néel” relaxation time θc Capture angle (degrees) θc,crit Critical capture angle (degrees) Θf Free layer Θp Pinned layer USPIO Ultrasmall superparamagnetic iron oxide nanoparticles UV Ultraviolet V Voltage v Velocity  (m/​s) Vc Crystal field potential υf Average flow VH Hall voltage Vp Particle volume (m3) VSM Vibrating sample magnetometer W Electronic band width WSIO Water-​soluble iron oxide WSION Water-​soluble iron oxide nanoparticle x x-​component ξ Coherence length XANES X-​ray absorption near edge structure

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x

xx

Abbreviations

XMCD y Z Zi z ZFC ζ

X-​ray magnetic circular dichroism y-​component Total impedance of a ferromagnetic conductor Total number of electrons in the atom or ion z-​component Zero field cooled Effective electric potential

Brackets indicate the SI unit of the parameter or if (-) the parameter is dimensionless.

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Magnetism, Magnetic Materials, and Nanoparticles Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

1.1 Introduction Significant changes in the physical properties of materials occur as any of a sample’s dimensions are reduced from the bulk (>50 μm) to the nanometer scale. An underlying reason for this change is the increased influence of the surface, for example, the relative contribution of the surface energy to the electrochemical potential. The electrochemical potential for electrons (also termed the Fermi level) in a solid is a thermodynamic measure (containing the electrostatic contribution) of the energy required to add or remove an electron from the valence band to the vacuum level. It has been reported that the changes begin when the surface to volume ratio of atoms in the particle approaches 0.5 [1]. If the size of the particle approaches the de Broglie wavelength of the electron (the ratio of the Planck constant, h, to the electron’s momentum, p), then quantum size effects can occur. The deviation from bulk behavior and, in particular, the magnetic characteristics, depend not only on the particle size but also on features such as the surface morphology, particle shape, dimensionality, and interactions, among others. For example, the shape of ferro/​ferrimagnetic particles influences the preferred direction of their magnetization (magnetic anisotropy) and is therefore crucial for the development of magnetic recording. More recently, magnetic nanoparticles have been used in a range of medical applications, such as drug delivery and MRI contrast imaging, as discussed in Chapter  4, Section 4.2 and Chapter 7, respectively. Their occurrence in natural phenomena, such as sediments and biological organisms, as described in Chapter  8, further enhances their importance. Several comprehensive reviews about synthesis, functionalization, and magnetic properties of nanoparticles are available [1–​9]. In most cases, the nanoparticles contain transition metals, and the following discussion will be restricted to this group of materials, although nanoparticles containing rare-​earth elements also exhibit a rich variety of magnetic phenomena [10, 11].

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

1.2

Fundamental Concepts

1.2.1

Quantum Mechanical Concepts The origins of magnetism arise from quantum mechanical effects. Therefore, a brief introduction to concepts and notation of quantum mechanics is required. Based on the realization in the early twentieth century that particles can behave like waves and vice versa, the theory of wave mechanics was proposed. Combined with the concept of quantization, from the observation that the emission spectra of atoms were composed of spectral lines of discrete energies, a quantum mechanical description of the atom was formulated. To quantify the discrete energy levels of electrons orbiting around a positively charged nucleus, Erwin Schrödinger proposed a description of the electrons in the atomic orbitals as standing waves, represented by a state or wavefunction ψ. The time-​ independent Schrödinger equation states that ψ = E ψ , H n



(1.1)

 is the Hamiltonian of the system including the kinetic and potential energy where H contributions and En is the energy of the nth electron shell. In this description, the Hamiltonian is conceived as an operator, which acts on the wavefunction ψ; for the Schrödinger Hamiltonian, stationary states (such as electrons in stable atomic orbitals) are the “eigenstates” of the system. This means that if a wavefunction ψ is an eigenstate,  on ψ is simply the same wavefunction ψ multiplied by the result of the operation of H a proportionality constant, which is En. The concept can be extended to time-​dependent problems or to slight modifications of the potential energy contribution, which are seen as small perturbations to the stationary case above. For describing quantum states, one can use the bra ( ψ ) − ket ( ψ ) notation as introduced by Paul Dirac. For example, the bra, ψ = ∫ψ * ( r , t ) d r , could represent the V

integral over the volume V of the complex-​conjugated wavefunction ψ * ( r , t ), which is dependent on the position r in three-​dimensional (3D) space and time t. Conversely, the ket ϕ = ∫ϕ ( r , t ) d r, will be the volume integral over the wavefunction ϕ ( r,t ). The V

overlap expression ψ | ϕ will give the probability amplitude of the state φ to collapse into ψ. Measurable quantities or observables in a quantum mechanical system are represented  , and the probabilistic result of a measurement of the observby operators such as H able is known as the expectation value of the corresponding operator. The expect , when the system is in the state ψ, is defined as  ψ | H  |ψ . ation value of H Strictly speaking, solving the time-​ independent Schrödinger equation yields accurate and discrete energy levels solely for a two-​body system, such as an electron orbiting a proton (the hydrogen model). For three or more body problems,

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Magnetism, Magnetic Materials, and Nanoparticles

3

approximations have to be introduced into the potential energy term, reflecting the interaction on each particle by the mean field created by all the other particles (the crystal field). A very widely used approximation is the Hartree–​Fock method, which provides the wavefunction and energies for many body quantum systems.

1.2.2





Atomic Magnetic Moments The magnetic properties of materials can be classified in accordance with their response to an applied magnetic field. This response will usually change as a function of additional external influences, such as pressure or temperature, and except for very low temperatures (< 4 K) it arises from the electronic degrees of freedom (the distribution of electrons into the available energy levels of the atom or the band structure of the solid). In the simplest case, this response may originate from a single isolated atom giving rise to paramagnetism. More complex behavior will arise from atoms coupling in a solid, which can exhibit cooperative phenomena, such as ferromagnetism [12]. A classical picture of the origin of the magnetic moment can be obtained from Ampère’s law, which states that an electric charge in circular motion will generate a magnetic field. In the case of each electron orbiting an atom, there are two contributions to the total magnetic moment. One contribution comes from the motion of the electron around the atomic nucleus, the orbital angular momentum, ℏl, and the other from the electron’s intrinsic angular momentum or spin, ℏs. The orbital moment is μ=

e l = µ B l, 2 me

(1.2)

where e is the elementary charge, me is the mass of the electron, ħ is the reduced Planck constant, where h = 2πħ, and we introduce the Bohr magneton μB, defined as

µB =

e = 9.27 × 10 −24 J/T. 2 me

(1.3)

Equivalently, the Bohr magneton has a value of 5.79 × 10–​5 eV/​T. For comparison, a magnetic moment of 1 μB in a field of 5 Tesla has an equivalent temperature T = E/​kB ~ 3.4 K (where E is the energy of the system and kB is the Boltzmann constant) and so the statistical mechanics of magnetic systems is dominated by thermal energies. The spin moment is μ s = gs µ B s,



(1.4)

where gs is the electron spin g-​factor (approximately 2.002319 [13]). In a similar fashion to the spin-​only situation above, we can define the Landé g-​factor gJ for the total angular momentum J: gJ =



J ( J + 1) − S ( S + 1) + L ( L + 1)

≈1 +

+ gs

2 J ( J + 1) J ( J + 1) + S ( S + 1) − L ( L + 1) 2 J ( J + 1)

.

J ( J + 1) + S ( S + 1) − L ( L + 1) 2 J ( J + 1)

(1.5)

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

The first term in Eq. (1.5) represents the orbital contribution and the second term arises from the electron spin. If the total orbital angular momentum L = 0, the Landé g-​factor is 2, and if the total spin angular momentum S = 0, gJ is 1. Hence the total atomic moment is μtotal = μorbital + μspin = μB(𝓁 + 2s). For multi-​electron atoms, moment formation occurs through filling the energy levels of the atom in a manner consistent with the Pauli exclusion principle.

The Pauli exclusion principle states that the total quantum mechanical wavefunction of two identical fermions (particles with non-​integer spin, such as electrons) must be antisymmetric upon exchange of the two fermions. This implies that not all of the four quantum numbers can be the same for two electrons in an atom.

The four quantum numbers are as follows: 1. the principal quantum number n (an integer representing the energy level or electron shell, alternatively labeled with upper case letters K, L, M, N, O, etc.); 2. the orbital (or azimuthal) quantum number 𝓁 (representing the subshell, with values ranging from 0 to n –​1, conventionally labeled with lower case letters s, p, d, f, g, etc.); 3. the magnetic quantum number m𝓁 (representing a specific orbital within the subshell, and thus the projection of the total orbital angular momentum L along the z-​axis, with values ranging from –​𝓁 to +𝓁); and 4. the spin quantum number s (representing the projection of the total spin angular momentum S along the z-​axis, with values ranging from  –​s to +s). For example, the 3d electrons reside in the “d” (𝓁 = 2) subshell of the third (n = 3, or “M”) shell.

For electrons orbiting an atom, the Pauli exclusion principle requires that two electrons occupying the same atomic orbital must have antiparallel spins. Except for heavy atoms, the total orbital and spin angular momenta are related by Russell–​Saunders coupling [12], governed by ℏL = ℏΣl and ℏS = ℏΣs. The resultant L and S then combine to give the total angular momentum J = L + S as in Figure 1.1. The z-​components of J, mJ, may take any value from |L-​ S| to |L + S|, each (2J + 1)-​fold degenerate, thus producing a multiplet in which the separation of the levels is determined by the spin-​orbit coupling λL ⋅ S , where λ is the spin-​orbit coupling constant. The values of S, L, and J for the lowest energy state are given by Hund’s rules, which are applied in the following sequence:

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Magnetism, Magnetic Materials, and Nanoparticles

5

Figure 1.1  The relationship between angular momenta S, L and J and the magnetic moment μ as

well as their projections Jz and μz along the z-​axis.

1. S takes the maximum value permitted by the Pauli exclusion principle. Each subshell is given one “spin-​up” electron before pairing it with a “spin-​down” electron, starting from the lowest energy subshell (smallest m𝓁 value). 2. L takes the maximum value consistent with this value of S. 3. For a half filled shell J = |L -​ S| and for a shell more than half full J = |L + S|. Hund’s rules for electrons in d-​orbitals (for which 𝓁=2 and m𝓁 can take the values –2, –1, 0, 1, and 2) in doubly ionized Mn2+, Fe2+, Co2+, Ni2+, and Cu2+ (i.e. 3d5, 3d6, 3d7, 3d8, and 3d9) lead to the following angular momentum and magnetic moments shown in Table 1.1. It can be seen that the experimental effective Bohr magneton numbers (pexp) are closer to the spin-​only values (pS). However, the situation becomes more complex when the atoms come together to form a solid. Since the 3d electrons are the outermost (valence) electrons, they can participate in the bonding. In ionic solids these electrons are perturbed by the inhomogeneous electric field Ec produced by neighboring ions (termed the crystal field or sometimes the ligand field), which breaks the coupling between L and S so that the states are no longer specified by J. Under the influence of the crystal field, the

6

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Table 1.1  Electronic configurations and effective Bohr magneton numbers pJ (total) and pS (spin-​only) for some doubly ionized elements. S

L

J

gJ

pJ = gJ J ( J + 1)

pS = gS S ( S + 1)

pexp

Mn2+

5/​2

0

5/​2

2

5.92

5.92

5.9

Fe2+

2

2

4

1.50

6.7

4.9

5.4

Co

3/​2

3

9/​2

1.33

6.63

3.87

4.8

Ni2+

1

3

4

1.25

5.59

2.83

3.2

Cu

1/​2

2

5/​2

1.20

3.55

1.73

1.9

2+

2+

(2L + 1) degenerate orbital states in the free atom will be split. If this degeneracy is entirely lifted, then in a non-​centrosymmetric field, the orbital angular momenta are no longer constant and may average to zero. This is conventionally called quenching of the orbital angular momentum (L  =  0). However, in reality, the differences from the spin-​only formula for the magnetic moment still arise from omitting the orbital angular momentum and spin-​orbit coupling; hence, we can only really speak of partial quenching (L ≈ 0). A more detailed description is given in [14, 15]. If the neighboring ions are treated as point charges, which assumes no overlap or hybridization of their electron orbitals, then the crystal field (or ligand field) potential Vc satisfies Laplace’s equation, ∇2Vc = −∇Ec = 0. Since the electric field Ec = −∇Vc , this implies that the gradient of the crystal field Ec is constant. Hence, the solutions are the Legendre polynomials, and the potential Vc (r , θ, ϕ ) = ∑∑ Alml r l Yl ml (θ, ϕ ) can be l

ml

expanded in spherical harmonics Yl ml (θ, ϕ ). The energy-​level scheme and the occupation are governed by the symmetry of the crystal field, and the relative scales of the energies are given in Table 1.2. Note that the Coulomb interaction between the electrons and the atomic nucleus yields energy level spacings of the order of eVs, much larger than available thermal energies, which allows the total magnetic moment to be thermally stable. For an octahedral field, the five m𝓁 states are split into two groups: a doubly degenerate eg multiplet and a triply degenerate t2g multiplet, which are separated by the crystal field energy Δ, with the latter multiplet being lower in energy, as shown in Figure 1.2. Their occupation depends on the relative importance of the energy Δ and spin-​orbit energy λ(L·S). If Δ >> λ(L·S), Hund’s rules do not apply, and for Fe2+, the six d-​electrons pair up and occupy the t2g states producing S = 0. This represents the low-​spin or strong-​ field configuration. For Δ 0, or negative, J ijex < 0, giving rise to parallel (ferromagnetic, FM) or antiparallel (antiferromagnetic, AF) alignment of the spins. Ferrimagnetism occurs if two

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

ferromagnetic sublattices of unequal moments are coupled antiferromagnetically. An estimate of the strength of the interactions is given by the transition temperatures, known as the Curie temperature TC for ferromagnets, which for Fe, Co, and Ni are 1043, 1395, and 633 K, respectively, and the Néel temperature TN for antiferromagnets, which for Cr and NiO are 311 and 513 K, respectively. Again, these values are considerably higher than those predicted on the basis of pure dipole-​dipole interactions, for which the Hamiltonian has the form

(



)(

)

   dip = µ 0 μ i ⋅ μ j − 3 μ i ⋅ rij μ j ⋅ rij , H  3  4 π  rij rij5 

(1.20)

where rij is the separation between magnetic moments μi and μj located at positions ri and rj. By using Eq. (1.17), this interaction yields transition temperatures of the order of only 1 K. We can estimate the relation between Jex and TC through the gain in potential energy of the magnetic moment μj in the magnetic field Hi produced by the moment μi as



1  E = − μ j ⋅ H i = − 2  gs2 μ 2B λ  si ⋅ s j 2  ⇒ J ex =

3kB Tc , 2 nS (S + 1)

(1.21)

(1.22)

where now n represents solely the number of the nearest neighbors, each connected with the central atom j by Jex (for all other atoms Jex =0). The shortcoming of this model lies in its assumption that the interacting electrons are strongly localized to the atoms, so it does not accurately describe ferromagnetism in materials such as Fe, Co, and Ni, where the magnetic moment-​carrying electrons are delocalized in the conduction band. Predictions of the Curie temperature TC and Jex given by Eq. (1.22) above are either of the wrong sign or too small. For those cases, a better model was proposed by Edmund Stoner that takes into consideration the band structures of the materials. Here the bands are spontaneously split into two subbands depending on their spin-​orientation. The energy dispersion relation is now spin-​dependent and can be expressed as

E↑ ( k ) = E0 ( k ) − I

n↑ − n↓ , n↑ + n↓

(1.23)



E↓ ( k ) = E0 ( k ) + I

n↑ − n↓ , n↑ + n↓

(1.24)

where E0(k) is the unperturbed band, n↑ and n↓ are the number of spin-​up and spin-​ down electrons, and I the Stoner parameter. The parameter is defined as I  =  Δ / ​μ, where Δ is the difference in energy between the spin-​up and spin-​down bands, and

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Magnetism, Magnetic Materials, and Nanoparticles

15

μ the magnetic moment in units of μB per atom. The condition for ferromagnetism, n − n↓ ≠ 0, is then given by the Stoner criterion: that is, the spin polarization P = ↑ n↑ + n↓ I ρ ( EF ) > 1, (1.25)



ρ ( EF ) is the density of states per atom per spin orientation at EF. Usually, 2N s and p electrons are delocalized, 4f electrons are localized, and 5f and 3d/​4d electrons are somewhere in between. In materials with contributions to the magnetic interaction from both delocalized and localized electrons (e.g. Gd), the Ruderman–​Kittel–​Kasuya–​ Yosida (RKKY) model is the currently accepted mechanism. In this model, which accounts for an indirect exchange mechanism, the localized moment (e.g. of the Gd 4f electrons), polarizes the electrons in the 6s/​5d hybridized conduction band, which then couple to more distant moments. Assuming that gJ = 2, the exchange is given by [17] where ρ ( EF ) =

J RKKY ( R ) = −



9π J 02 ( 2 kF R )� cos ( 2 kF R ) − sin ( 2kF R ) , 8 EF ( 2 k F R )4

(1.26)

where R is the distance between localized (l) and itinerant electron (i), kF is the wavevector at the Fermi energy, and J0 is the exchange integral between localized and itinerant electron wavefunctions at zero momentum transfer, that is, q = kl –​ ki = 0. From  Eq. (1.26), we see that the exchange oscillates between AF and FM coupling, and the amplitude decreases rapidly with increasing distance (see Chapter  6, Section 6.2.1.2). Indirect exchange interaction can also give rise to helical magnetic order, such as in the rare-​earth element Eu, while in insulating compounds, such as NiO and MnO, it usually gives rise to antiferromagnetism. Depending upon the crystal structure, both cation-​cation and cation-​anion-​cation interactions can occur. For superexchange interaction, the wavefunctions of the outermost electrons on the cation admix with those on the anion, thus enabling two cations to couple indirectly. For example, in NiO, superexchange arising from hybridization between 3d Ni2+ and 2p O2–​ states leads to AF order. An extension of the model, double exchange, was proposed to account for transport properties in compounds such as the ferrimagnet Fe3O4 (magnetite) in which the cations have two different valencies, that is, Fe3+ and Fe2+. In contrast to superexchange, where the electrons remain in their respective ions, in double exchange they can move between the two cations through the intermediate anion, giving rise to metallic conductivity.

Magnons We can also use the mean field approach as introduced in Sections 1.2.1 and 1.2.4.3 (Susceptibility of Local Moments) to describe the temperature dependence of the saturation magnetization Ms of a ferromagnet below TC. However, this time we need to use the

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

whole expression for the Brillouin function BJ(x) as given in Eq. (1.14), remembering that the magnetization is given by M  =  NgJμBJBJ(x). For J  =  S =1/​2 and gJ  =  2, we  µ B  µ λM  have M s = N µ B tan h  B  = N µ B tan h  B , if we assume the magnetic field B  kBT   kBT  to be solely the internal field Hint, which can be solved numerically for 0 ≤ T ≤ Tc. As the temperature increases, the magnetization smoothly decreases and vanishes completely at TC, reminiscent of a second-​order phase transition from a ferromagnetic to a paramagnetic state. The decrease of the saturation magnetization with increasing temperature is driven by the thermal excitations (spin waves). In the simplest model, one can picture a one-​ dimensional chain in which all the spins are ferromagnetically aligned, except for one spin that has been flipped. As the spin is quantized (up or down), so is the excitation, which is termed a magnon. The exchange energy as described by the Heisenberg model in Eq. (1.19) to completely reverse a single spin amounts to 8JexS2, which is relatively high. The energy of the excitation can be considerably reduced by spatially distributing the magnon through a continuous gradual rotation of the magnetic moments of many neighboring spins in the chain. This gives the magnon a continuous wavelike character. In localized antiferromagnets or ferromagnets, which can be approximated by the Heisenberg model, magnons propagate through the Brillouin zone with a dispersion relation (the dependence of the angular frequency ω on the crystal momentum k) given by ω ( k ) = 4 J ex S (1 − cos ka ) ≈ ( 2 J ex Sa 2 ) k 2



(1.27)

for a ferromagnet, where a is the lattice constant and D  =  (2JexSa2) is the spin wave stiffness constant, and ω ( k ) = 4 S J ex sin ka ≈ 4 SJ ex ak



(1.28)

for an antiferromagnet. In both cases, the approximation assumes ka « 1, that is, the wavelength is large compared to a. In the Heisenberg model, the transition from the ferromagnetic to paramagnetic phase is driven by transverse fluctuations of the moment, with its magnitude remaining fixed. This is in contrast to the Stoner model in which the paramagnetic phase is driven by amplitude fluctuations, with the moment decreasing as the temperature increases until it vanishes at TC.

1.3

Magnetization Processes

1.3.1

Magnetic Anisotropies In single crystalline ferromagnets, the magnetization depends on the magnitude and direction, with respect to the crystallographic axes, of the externally applied magnetic field. This gives rise to easy and hard directions of magnetization (the anisotropy being greater the lower the crystal symmetry). The origin of this magneto-​crystalline anisotropy is the spin-​orbit interaction. For cubic crystals, for example, body-​centered cubic (bcc) Fe, and face-​centered cubic (fcc) Ni, the anisotropy energy density, EK, is usually

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Magnetism, Magnetic Materials, and Nanoparticles

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Table 1.6  Magneto-​crystalline anisotropy constants. K1 × 104Jm–​3

K2 × 104Jm–​3

Fe (4.2K)

4.8

± 0.5

Ni (4.2K)

−0.50

−0.20

Co (300K)

45.0

15.0

expressed in terms of the directional cosines αi, which are the cosines of the angles between the magnetization M and the three crystallographic axes x, y, z, namely

EK = K o + K1 ( α12 α 22 + α 22 α 32 + α 32 α12 ) + K 2 ( α12 α 22 α 32 ) + higher orrder terms.

(1.29)

The magneto-​crystalline anisotropy constants Ki can be obtained from magnetization measurements using single crystals by making use of the work done in the magnetizaMs

tion process

∫ H ⋅ d M , which represents the area between M = M

s

and the magnetiza-

0

tion curve for the crystallographic direction of interest. If the third term is zero, then the easy axes are for K1 > 0 (as for Fe) and for K1 < 0 (as for Ni). For uniaxial systems, for example, hexagonal closed packed (hcp) Co, the expression in polar coordinates becomes

EK = K o + K1 sin2 θ + K 2 sin 4 θ + higher order terms,

(1.30)

where θ is the angle between the magnetization and the hexagonal axis. If K1 = K2 = 0, the magnetization is isotropic. For K1 > 0 and K2 > –​K1, the easy axis of magnetization is the hexagonal axis and for K1 > 0 and K2 < –​K1, it is fixed in the basal plane. In all cases, K0 is chosen to make EK zero along the easy axis. Some measured values of the magneto-​crystalline anisotropy constants for Fe, Co, and Ni are given in Table 1.6. The values decrease with increasing temperature, vanishing at TC. The variation is predicted [24] to be



K1 (T )

 M (T )  =  , K1 ( 0 )  M ( 0 )  δ

(1.31)

where δ = 3 or 10 for uniaxial and cubic ferromagnets, respectively. Nanoparticles or films in the ultrathin limit of a few nms are usually assumed to have a uniaxial crystalline anisotropy given by

E B = K uV sin 2 θ. (1.32) This has minima at θ = 0 and π that are separated by an energy barrier EB of height KuV, as shown in Figure  1.4. However, other types of anisotropy may dominate. Classically, the magnetization must overcome this energy barrier to reverse, although the possibility of quantum mechanical tunneling has also been considered [25]. When a ferromagnet or ferrimagnet is placed in a magnetic field, magnetic poles of opposite

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

EB

H

EB 0

π/2

π

θ

0

π/2

π

θ

Figure 1.4  A representation of the energy of a uniaxial magnetic nanoparticle as a function of the

direction of the magnetization. The height of the barrier EB characterizing the thermally induced magnetization reversal is given by KV, where K is the magnetic anisotropy constant and V the particle volume. Changes in the energy landscape in the (a) absence and (b) presence of an applied external magnetic field are indicated schematically.

signs are induced at the ends of the specimen and a demagnetizing field is established that opposes the direction of the externally applied field. The demagnetizing field is responsible for the magnetostatic energy, which depends on the direction of the magnetization and the shape of the specimen, which is why it is also termed the shape anisotropy. For a prolate spheroid with the semi-​major axis c and the semi-​minor axes a = b, the magnetostatic energy is given by

1 Eshape = µ o M s2V ( N a − N c ) sin2 θ, 2

(1.33)

where Na and Nc are demagnetization factors in the a and c directions, and θ is the angle between the magnetization and the c axis. For spheres, Na = Nc and Eshape = 0, but for non-​spherical particles, Eshape can be significantly larger than the magneto-​crystalline anisotropy. In addition, magneto-​elastic anisotropy occurs when strains in the specimen give rise to a non-​uniform structure. The strains may arise during fabrication via defects or dislocations, epitaxial growth on a substrate with a different lattice constant, or can be purposely externally applied, for example, with a pressure cell. The magnetization process gives rise to magnetostriction with an associated energy, which for an isotropic system is given by

3 Estrain = − λ s σ cos 2 θ, 2

(1.34)

in which λs is the saturation magnetostriction, σ is the stress, and θ the angle between the magnetization and the strain. Exchange (bias) anisotropy occurs when a sample containing an interface between a ferromagnet and an antiferromagnet is cooled below the antiferromagnet’s Néel

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Magnetism, Magnetic Materials, and Nanoparticles

M

M

19

M MS

MR HC

HK

H

Figure 1.5  The magnetization M as a function of field H for a (a) superparamagnet, (b) soft

ferromagnet, and (c) hard ferromagnet. Hc, HK, MR, and Ms are the coercive field, the anisotropy field, the remanence and the saturation magnetization, respectively.

temperature TN, where the TC of the ferromagnet is significantly higher than TN. This was originally observed in ferromagnetic Co particles covered by a shell of AF CoO [26]. When the cooling takes place in a magnetic field, an exchange bias occurs, in which the magnetization versus applied field curve (M-​H loop or hysteresis loop) is displaced along the field axis in the direction that opposes the applied field. An increased coercivity (or coercive field, the applied field required to reduce the total magnetization to zero) is also observed after cooling, which disappears together with the exchange bias as TN is approached.

1.3.2

Magnetic Domains The magnetization process of a ferromagnet is shown in Figure  1.5. In the virgin state and in the absence of an applied field, the macroscopic magnetization is generally significantly less than maximum saturation owing to the presence of domains. Within each domain, the magnetization is saturated, but its direction in neighboring domains is different. The domain structure [27] can be imaged using Bitter patterns, optically using Faraday or Kerr rotation, XMCD photoemission electron microscopy (PEEM) [28, 29] or, more recently, magnetic force microscopy (MFM) [30, 31]. Similarly, upon cooling below the Néel temperature, AF domains emerge. AF domains have been extensively studied using neutron diffraction [32], X-​ray and neutron diffraction topography [33], and X-​ray magnetic linear dichroism (XMLD) PEEM [34]. From neutron scattering, it is known that upon entering an ordered magnetic phase, additional diffraction peaks emerge that are not present in the paramagnetic phase, such as the (½,½,½) peak of NiO presented in Figure  1.6. The reason for this is that the magnetic lattice has a lower symmetry than the crystal lattice (which can represent the pure paramagnetic phase), adding a new degree of freedom to the system to lower its total magnetostatic energy by breaking up the magnetic phase into domains. In terms of

20

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

Figure 1.6  The nuclear (2 2 0) peak at 550 K and the AF magnetic (½½½) peak at 5 K with

Gaussian fits convoluted with the instrument resolution function used to determine the particle and magnetic sizes.

symmetry groups, if the order of the paramagnetic group is p and that of the magnetic group is m, then the number of different domains will be p/​m. Magnetic domains can be classified into the following groups depending on the symmetry lost upon magnetic ordering: 1 . configuration domains –​translational symmetry; 2. 180° domains –​time inversion symmetry; 3. orientation domains –​rotational symmetry; and 4. chirality domains –​ centrosymmetry. Configuration domains occur whenever the propagation vector τ in reciprocal space describing the magnetic structure is not transformed into itself or itself plus a reciprocal lattice vector by all the symmetry operators of the paramagnetic group. The presence of 180° domains in a crystal implies that τ = 0 and the directions of the magnetic moments in one domain are reversed with respect to corresponding moments in the other and hence, the perpendicular magnetization is reversed. Orientation domains occur when the magnetic space group is not congruent with the group describing the configurational symmetry, that is, the magnetic configuration from one domain into another cannot be transformed through rotation. If the paramagnetic space group is centro-​symmetric, for example, bcc, but the magnetic structure is not, then chirality domains can occur [35].

1.3.2.1

Domain Walls The transition region between neighboring domains is known as a domain wall, over which the magnetization continuously changes from its value in one domain to that in the other. Similar to the spin wave argument (Section 1.2.4.3 (Magnons)), the entire rotation of the magnetization between domains takes place gradually over many atomic planes, as the exchange energy is lower when the change is distributed over many spins. For a Bloch wall, the magnetization rotates out of the plane defined by the magnetizations of

21

Magnetism, Magnetic Materials, and Nanoparticles

21

Figure 1.7  Schematic depicting (a) a Néel and (b) a Bloch domain wall within the box.

the two domains (Figure 1.7) and is thus most common in ferromagnetic bulk samples or thick films. The width δdw of the wall separating neighboring 180° (π) domains is governed by contributions from both the exchange interaction Jex and the magnetic anisotropy K, which prevents the domain wall from extending over the whole sample, and is given by [11]:



 A δ dw = π    K

1

2

 NJ ex S 2  = π  Ka 

1

2

,

(1.35)

where a is the length of the side of the unit cell and A is the exchange stiffness constant given by

A=

NJ ex S 2 , a

(1.36)

where N is the number of atoms per unit cell. For bcc Fe, Jex = 2.16 × 10–​21 J, S = 1, a = 2.9 × 10–​10 m and N = 2, so that A = 1.49 × 10–​11 Jm–​1. Measured values of A for Co, Ni, and Fe as determined by spin-​wave resonance [17] are shown in Table 1.7. Typically, δdw is of the order 30 nm in Fe at room temperature (around 100 unit cells). The energy stored in the domain wall is given by

Edw = 2 π ( AK )

1

2

 NJ ex S 2 K  = 2π    a

1

2

.

(1.37)

Under the application of a magnetic field, the volumes of domains whose directions are closest to that of the field reversibly increase. Owing to crystal imperfections, this growth becomes irreversible at higher fields with the magnetization finally rotating into the field direction. The overall process gives rise to hysteresis, as shown in Figure 1.5. The ratio of the remanence MR (the remanent magnetization after saturation in the

2

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

Table 1.7  Measured exchange stiffness constants [17]. A × 10–​11 Jm–​1 Fe (295K)

2.5

Ni (295K)

0.75

Co (295K)

1.3

Co (4K)

1.43

absence of any applied field) over the saturation magnetization Ms is often used to indicate the ‘squareness’ of the hysteresis when assessing materials and optimizing their hysteresis for particular technical applications. For example, permanent magnets require a high coercive field Hc and remanence MR, whereas transformers need a narrow hysteresis to reduce energy loss  ∫ MdH (the area enclosed by the hysteresis loop) as afforded by the high relative permeability μr in soft ferromagnets. Note that the relation between B and H in vacuum is thus modified to B = μrμ0H in a medium. As the magnetic configuration is governed by exchange on the short scale and dipolar energy at a larger scale, the competition between these energies results in a characteristic distance below which exchange dominates and above which magnetostatic interactions dominate. This very important distance is the length scale over which the perturbation due to the switching of a single spin decays in a soft magnetic material, and is termed the ferromagnetic exchange length [36]:

Lex =

A , µ o M s2

(1.38)

which represents the ratio between the square roots of the exchange energy and the magnetostatic energy, and is typically 3  nm in Fe-​and Co-​based alloys. Whether a material is considered magnetically ‘hard’ or ‘soft’ is defined by a dimensionless parameter κ, the ratio of Lex and δdw:

κ=

K π Lex = . δ dw µ o M s2

(1.39)

For hard magnetic materials, κ approaches unity, whereas it tends to zero for soft ferromagnets.

1.3.2.2

Magnetization Reversal Magnetization Reversal in Thin Films and Particles As the dimensions of the specimen are reduced, the energy required to form a domain wall becomes greater than the reduction in magnetostatic energy as indicated by Lex. As a result, for thin films whose thickness approaches that of the domain wall width, a different type of wall, a Néel wall [37], is established in which the magnetization rotates within the plane defined by the magnetizations of the two domains (Figure 1.7). Eventually, with further reduction in dimensions, a particle will form that consists of a

23

Magnetism, Magnetic Materials, and Nanoparticles

23

Table 1.8  Critical diameter dc and domain wall energy for Fe, Co, Ni, γ-​Fe2O3, and Fe3O4 [1, 38]. dc [nm]

Edw [mJ/​m2]

Fe

14

3

Co

70

8

Ni

55

1

166 128

Coercivity Hc (A/cm)

γ-​Fe2O3 Fe3O4

d –1 d6

Grain Size d Figure 1.8 Log10-​log10 plot of the coercivity Hc versus grain size d for several soft magnetic systems. ■ permalloy, □ 50NiFe alloys, ○ FeSi6.5 alloys, ● nanocrystalline materials, + amorphous alloys. Adapted from [41].

single domain. For a particle with uniaxial anisotropy Ku, the critical radius rc for this to occur is [11]:

rc =

9π AK u 9 Edw = 9πκ Lex = . 2 2µ o M s µ o M s2

(1.40)

Values for the critical diameter dc and domain wall energy Edw of various ferro-​and ferri-​magnetic materials are given in Table 1.8. Depending on the material, the critical radius lies in the range 2.5–​500 nm. The effect of particle size on the coercivity has been investigated by a number of groups, as shown in Figure 1.8 [39–​42] and the schematic variation of Hc as d varies [41] is shown in Figure 1.9. The increase in Hc as the particle size decreases was predicted in the Stoner–​Wohlfarth model to arise from the coherent rotation of the magnetization, when domain wall formation is energetically impossible due to the small size of the particle [43]. However, the observed values of Hc are generally smaller than those predicted by the model. This may be accounted for if it is assumed that degrees of freedom other than simple rotation are involved, such as fans and swirls. Pure coherent rotation is only

24

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

Single-domain

Multi-domain

blocked

Hc superparamagnetic

dc

d

Figure 1.9  The qualitative dependence of the coercivity Hc on the particle diameter d, indicating

blocked and superparamagnetic regions below the critical diameter dc.

possible in homogeneous magnetic particles with zero surface anisotropy. For multi-​ domain particles, the rotation can be associated with domain boundary movement. However, this mechanism becomes less important as the particle size decreases and a single-​domain is formed. Thus, Hc increases as d becomes smaller down to dc. For single-​domain particles the role of thermal fluctuations becomes important and so Hc decreases for d less than dc.

Magnetization Dynamics The decay rate of the remanent magnetization MR is an important parameter. For example, it indicates the stability of data stored in magnetic recording. In a simple experiment a sample of non-​interacting particles is cooled in a magnetic field which is then abruptly switched off at a particular temperature T. The thermoremanent (TRM) magnetization M(T) is then measured as a function of time with the approach to equilibrium given by:  t  M ( t ) = M R exp  −  ,  τN 



(1.41)

with τ N , the “Néel” relaxation time, being given by the Néel–​Brown equation [44, 45]:

 E   KV  τ N = τ 0 exp  B  = τ 0 exp  a  ,  kBT   kBT 

(1.42)

where the anisotropy energy density K = HcMs / ​2 and EB = KVa represent the energy barrier height for magnetization reversal, which depend on the activation volume Va. For a single domain particle, Va is the entire volume of the particle; for a domain wall, Va is the volume swept by a single jump between two pinning centers. Often the quantity τ 0 is given as a constant, usually taken to lie between 10–​9 and 10–​11s, but its value, as Néel has shown, depends very strongly on the ratio between V and T [44]:

τ0 =

me 1 eH c 3G λ s + DM s2

πGkBT , 2V

(1.43)

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Magnetism, Magnetic Materials, and Nanoparticles

25

where me is the mass of an electron, e is the electron charge, G is the modulus of rigidity, λs is the saturation magnetostriction constant averaged over three crystallographic axes, and D is a numerical coefficient that considers the shape of the particles (for a sphere, 4π/​5). The process is characterized by thermal activation over energy barriers, and for real systems, the barrier heights and widths vary because of the particle size distribution. For a rectangular barrier distribution (all particles capable of activation are identical, with the same activation energies) a logarithmic dependence of the relaxation of M with t is observed [46]: M ( t ) = M R − Sm ln ( t ) , (1.44)



where Sm is the magnetic viscosity: Sm =



kB TM s f ( H , T ), Va K

(1.45)

and where f(H,T) is a function determined by the precise nature of the magnetization process. Experimentally, Sm can be determined as the slope of the plot of M(t) versus log10(t). In general, f(H,T) has maxima at the coercive field Hc and at the Curie temperature Tc (the Hopkinson effect). An alternative method of investigating the validity of the Néel–​Brown equation (Eq. (1.42)) is to measure the mean switching field (or coercive field) Hsw at different temperatures and magnetic field sweep rates (ν  =  dH/​dt). The variation of Hsw is predicted to be [47]:

H sw



1    kB T  cT   κ   ln  κ −1   , = H 1−    E B  υh      0 sw

(1.46)

0 where H sw is the switching field at 0 K, EB is the energy barrier as given in  H  k H0 Eq. (1.42), c = B sw , and the reduced field h =  1 − 0  . When plotted as Hsw versus τ 0 κ EB H sw   1

  cT   κ  Tln  υhκ −1   , the data has been found to scale for 65 nm diameter Ni nanowires with the exponent κ = 1.5 [48], indicating a reversal via the motion of a rigid domain wall [47]; for an ideal single domain particle κ = 2. The equilibrium magnetic properties in small particles and thin films are generally modeled by solving the Landau–​Lifshitz–​Gilbert (LLG) equation (Eq. (1.47)) under different boundary conditions. A wide range of software packages, for example, OOMMF [49] or mumax3 [50], are available which have enabled parameters, such as the coercive field, switching times, interlayer coupling strength, domain wall characteristics, and vortex motion to be studied. The LLG is a dynamical model to describe the precessional motion of the magnetization with time in the response to an effective field Heff containing applied, demagnetizing field, and quantum mechanical corrections, such as anisotropy.

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

ZFC

M (a.u.)

FC

Tmax

Tir

T (K) Figure 1.10  Schematic of the temperature dependence of the magnetization M for zero field cooled (ZFC) and field cooled (FC) measurements for a system of nanoparticles.

The first term describes the precession and the second, a dissipative (or damping) term, which describes the relaxation of the magnetization M(t) as it aligns with Heff:



d M (t ) dt

=

γ αG γ  M ( t ) × H eff  − M ( t ) ×  M ( t ) × H eff  , (1.47) 2  (1 + α G ) (1 + α G2 ) M s

gs µ B is the electron gyromagnetic ratio, the ratio between the magnetic  dipole moment and angular momentum of the free electron, and αG is the Gilbert damping parameter, which depends on the material. where γ =

1.3.3

Magnetization of Nanoparticles A schematic representation of the magnetization as a function of temperature for nanoparticles is shown in Figure 1.10. The precise variation depends on the nature of the particles, such as shape, size distribution, interactions, magneto-​crystalline anisotropy constant, and details of the measurement, for example, thermal history or method of measurement. It is usual to measure the magnetization in a low field while warming from helium temperatures (4.2 K), the sample previously having been cooled either in zero field (zero field cooled (ZFC)) or in a small field (field cooled (FC)). At high temperatures, the two magnetizations coincide, but at low temperatures, a bifurcation occurs at the irreversibility temperature Tir when the MZFC curve falls below that of MFC. A  maximum occurs in MZFC at a temperature Tmax, which for a sample containing a range of particle sizes is related to the average blocking temperature . The blocking temperature TB of a single domain particle is the temperature at which the magnetic relaxation time τmag increases to the same order as the duration of the experiment τexp (measurement time) [51]:

27

Magnetism, Magnetic Materials, and Nanoparticles



TB =

K uV . kB ln τ exp / τ mag

(

)

27

(1.48)

Below TB the moments in the ZFC sample are assumed to be frozen in random directions (blocked). Then Tir is taken to be TB for the largest particles. At low temperatures the coercivity decreases with increasing temperature up to TB where it becomes zero. For large particles the temperature dependence of the coercive field Hc is given by [36, 51]:

 T  H c (T ) = H c ( 0 )  1 − , TB  

(1.49)

where Hc(0) is the coercive field at 0 K. A similar power law is predicted for the field dependence of the blocking temperature: δ



 H TB ( H ) = TB (0) 1 −  , H c  

(1.50)

where δ = 2 in low fields and 2/​3 in high fields, and Hc = 2K/​Ms. The analysis of the magnetization is usually carried out using the Langevin equation (Eq. (1.13)), which is applicable for particles in thermal equilibrium and for which all directions of the magnetization are energetically equivalent. Hence, the magnetic anisotropy is considered negligible. For this case, the Langevin function can be rewritten as [52]:



    nµ B µ 0 H 1 M ( H ) = N p nµ B  coth − , nµ B µ 0 H  k BT   k BT 

(1.51)

where M is the mass magnetization, H is the applied field, Np is the number of particles per gram, n is the number of Bohr magnetons per particle, and hence, Ms = NpnμB. Therefore, fitting this equation estimates the average magnetic moment per particle and the number of nanoparticles in the sample. Based on this analysis, the reduced magnetization (M/​Ms) at different temperatures should fall on a common curve when plotted as a function of H/​T. This relation is often taken as evidence for superparamagnetism. Superparamagnetism appears in ferromagnetic or ferrimagnetic nanoparticles when the magnetization is thermally excited and randomly flips its direction. The time between two flips is called the Néel relaxation time τN (Eq. (1.42)). If the measurement time is longer than τN, the particles’ magnetization seems to be zero, on average, in the absence of an applied field. The magnetization with applied field mimics that of a paramagnet; however, a superparamagnet saturates at much lower fields. In this picture, a nanoparticle’s magnetization acts as a macroscopic moment or macrospin.

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The magnetic moment, μ  =  mμB, obtained from this analysis is associated with a large cluster of atoms and so can reach ~104 μB. The large moments produce dipole µ µ2 interactions with a dipole-​dipole energy Edip = o 3 , where d is the distance between 4 πd Edip neighboring dipoles, giving potential transition temperatures Ttr ≈ ~ 30 K or even kB higher for concentrated systems [53]. Depending on the nature of the media in which the particles are suspended, or the proximity of particles, exchange coupling may also occur. Furthermore, the large moments and low transition temperatures mean that μμ0H is of the order of kBT at room temperature, and so the magnetization can approach saturation in normal laboratory fields, in contrast to a paramagnet. For very small clusters of atoms, the influence of particle size, number of atoms and coordination number on the magnitude of the Fe, Co, and Ni moments has been investigated in a Stern–​Gerlach type experiment [54]. The results are presented in Figure  1.11. The magnetic moments of the three elements depend on the number of atoms per cluster N. For small N, the observed moments approach the atomic values, whereas for high N, the bulk values are observed. For very small Fe clusters containing 12 atoms, a magnetic moment per atom of 5.4±0.4 μB has been reported, reducing to ~3 μB for a 13 atom cluster [55]. It has been noted that the per-​atom moments of such small Fe clusters are substantially higher than the spin-​only value of 3 μB, indicating that orbital angular momentum is not completely quenched in these cases. As the particle size becomes smaller, the band width is reduced and the 3d electrons spend more time at a particular atom and adopt a more localized character. Electronic structure calculations show that both the atomic structure and nearest neighbor interactions are of paramount importance in such systems. Although the surface anisotropy becomes increasingly important as the particle size decreases, for a qualitative description of the magnetization, only a uniaxial component will be considered as described in Eq. (1.32). On cooling below TB in the absence of an applied field, the zero-​field cooled magnetization MZFC of nanoparticles with uniaxial anisotropy Ku will be fixed along the easy axis of magnetization (θ = 0 or π). Hence, the macroscopic magnetization is zero, assuming all magnetic moments of the particles are blocked in random directions. If a magnetic field H is applied at angle φ to the easy axis, then for (θ–​ϕ) < π/​2, the moments will rotate to a minimum energy given by:

E (θ ) = K uV sin 2 θ + M s HV cos (θ − ϕ )

(1.52)

to produce a small magnetization M. However, the moments for which (θ–​ϕ)>π/​2 need to overcome the potential barrier KuV in order to reach the equilibrium direction. The system is then in a metastable state, with an essentially temperature independent magM 2µ H netization M ≈ s 0 , which was derived initially by Stoner and Wohlfarth [56]. If 3K u the applied field H is lower than the switching field Hsw, that is, Hc, the minima in E(θ) occur at different levels separated by barriers with varying heights that are proportional to TB, as shown in Figure 1.4(b). Hence, when H is larger than Hsw, it enables the

29

Magnetism, Magnetic Materials, and Nanoparticles

29

Figure 1.11  The average magnetic moment per atom in μB for Ni and Co clusters at 78 K

and Fe clusters at 120 K as a function of the number of atoms N in the cluster as the bulk value is approached. Adapted from [54].

magnetization to rotate irreversibly. The particle anisotropy can be determined by measuring Hsw as a function of ϕ, which mathematically represents an astroid [57]: H sw =

HK

, 3 2 2   23  sin ϕ + cos 3 ϕ

(1.53)

where HK = 2Ku/​Ms is the anisotropy field (see Figure 1.5), the field at which the gradient of the hysteresis loop changes (for fields applied along the magnetic easy axis, HK = Hc).

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

On warming above TB, a stable superparamagnetic state is attained with a magnetizaM 2 µ HV tion M (T ) ≈ s 0 , as approximated by a series expansion of the Langevin function 3k B T (Eq. (1.51)) and setting mμB = MsV. The same formula applies to the field cooled measurement above TB; however, below TB, the magnetization does not change over the period of measurement, and so it is essentially constant. A detailed description on fitting ZFC/​FC nanoparticle magnetization curves assuming a log-​normal size distribution was given by Hansen and Mørup [58]. The thermal fluctuations of non-​interacting nanoparticle moments with uniaxial anisotropy were first described by Néel and later extended by Brown, the relaxation time being given by an Arrhenius law (Eq. (1.42)). For small particles, KuV can be comparable to thermal energies, enabling the magnetization to fluctuate between the two minima with opposite magnetization directions. This phenomenon is known as superparamagnetic relaxation and is a limiting factor for the use of nanoparticles in magnetic recording. The results obtained for the relaxation depend sensitively on the experimental technique used. If the measurement time τexp of the experimental technique is long compared to the relaxation time τmag characterizing the magnetic fluctuations, then a time average is obtained (as in paramagnetic measurements). If τexp is short compared to τmag, then an instantaneous measurement is obtained. At low temperatures KuV >> kBT, thermal equilibrium occurs only after a long time. The relaxation also depends on the particle size, which gives rise to different anisotropy and hence, barrier heights. If KuV 0 and M–​ 0, and if a < 0, it is the negative solution. For a magnetically ordered system in the absence of a field B, a(T) can be written as a(T) = aʹ(T –​ Tc), where aʹ is a constant. To determine the susceptibility (χ ~ ∂M/​∂B), the spontaneous magnetization, M00, and the Curie temperature, TC, the case for B ≠ 0 must be considered. In this case, from Eq. (1.64):

B 1 B a = 2 a + 4bM 2 ⇔ M 2 = − . M 4b M 2b

(1.65)

Hence, plotting M2 versus B/​M (Arrott plots shown in Figure  1.15) yields linear isotherms [59], the slopes of which do not change as a consequence of the assumption that b is temperature independent and the only coefficient changing with temperature is a. As one determines the intersection with either the x or the y-​axis the lines are shifted parallel to one another as a function of temperature. The isotherm going through the origin defines the Curie temperature and the intercept on the M2 axis (y-​axis) enables the spontaneous magnetization in the ordered state to be determined. The intercept on the B/​M axis provides the reciprocal of the susceptibility in the paramagnetic state. For 1 1 = , which is consistent with the molecular field theory and T > TC, χ = 2 a 2 a ′ (T − TC ) represents the Curie–​Weiss law (Eq. (1.17)).

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

M2

T < TC T = TC T > TC

B/M Figure 1.15  Schematic Arrott plots for an isotropic ferromagnet above and below the Curie temperature.

For an antiferromagnet, the transition occurs at the Néel temperature TN and there are no anomalies at TN in the Arrott plots. Instead of crossing the origin below the AF phase transition, the Arrott plots shift back in the opposite direction as compared to the case of the ferromagnet. An external magnetic field produces an additional shift in the AF phase transition, which has a quadratic dependence on the magnitude of the field, that is, ΔTN is proportional to B2. It should be noted that the Landau theory on which this analysis is based is essentially a mean field description of the magnetic phase transition. Thus, magnetic fluctuations are neglected, even though close to the critical point of the phase transition they have large amplitudes and long lifetimes, and therefore cannot strictly be treated as small perturbations.

1.4.3

Critical Phenomena As the transition at TC is approached, the principal interest is the behavior of the thermodynamic properties that are assumed to have a simple power law dependence on the T − TC reduced temperature ε = and are characterized by a set of critical exponents TC [66]. A high degree of precision in the determination of both the order parameter and the temperature is required, and therefore the establishment of TC is not straightforward. Furthermore, any comparison between measurements should be confined to results obtained within the same temperature interval Δε.

1.4.3.1

Thermal Dependence of the Order Parameter In the limit of a small applied field, the spontaneous magnetization MHT goes continuously to zero as TC is approached. The thermal variation is given by [61]:



M HT = lim M ( H , T ) ∝ εβ , Hi → 0

(1.66)

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Magnetism, Magnetic Materials, and Nanoparticles

37

where the critical exponent β is observed to be < 1, typically taking values from 0.32 to 0.39 depending on the type of phase transition. We have introduced here the internal field Hi, given by [59]: Hi = H − N demag M ( H , T ) ,



(1.67)

in which Ndemag is the demagnetization factor and H the applied field.

1.4.3.2

Thermal Dependence of the Initial Susceptibility As the temperature decreases toward TC, the initial susceptibility diverges in a manner given by:  ∂M  χi =  ∝ ε−γ ,  ∂Hi  Hi → 0



(1.68)

where the critical exponent γ  typically takes values from 1.3 to 1.4.

1.4.3.3

The Field Dependence of the Order Parameter along the Critical Isotherm At the critical isotherm, TC, the spontaneous magnetization is not a smooth function of the magnetic field but follows: 1

M ( H , Tc ) ∝ Hi δ ,



(1.69)

where the critical exponent δ typically takes values from 4.3 to 4.7. Reliable values of δ can only be obtained close to the critical point where ε is small, that is, if ε < 10 −2. According to Widom [62], the exponents β, γ, and δ should satisfy the relation γ = β (δ–1).

1.4.3.4

The Specific Heat A singularity is observed in the specific heat at TC in zero field, which can also be described by a power law:



C ε − α C ∝  ↑ − α’  −C↓ ε

T > TC . T < TC

(1.70)

The constants C↑ and C↓ are observed to be different, whereas the exponents α and αʹ are found to be the same within the experimental error. Typical values of α and αʹ lie between 0.11 and 0.19.

1.4.3.5

The Thermal Variation of the Spin Density Fluctuations close to TC In order to describe neutron scattering, in 1954 van Hove [63, 64] introduced the concept of the pair distribution function G between the atomic spin S0 at lattice position zero, considered at time zero, and the atomic spin Sr, at lattice position r, considered at time t:



G T ( r , t ) = S0 ( 0 ) . Sr ( t ) T ,

(1.71)

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

where T denotes the average over the thermal distribution. This pair distribution  q, ω ) used to calculate the partial was included into the response (scattering) function S( differential cross section for neutron scattering: kf  d2 σ S (q, ω ), = Nr02 dΩdE f ki



(1.72)

where q = ki –​ kf is the neutron wave vector change between initial to final state momenta, N is the number of unit cells in the sample, and r0 = −5.4 fm = γn(e2/​mec2) is the value of the neutron magnetic moment (γn = −1.913) multiplied by the classical electron radius, e2/​mec2 = 2.82 fm. Van Hove [63] had already shown that due to large thermal fluctuations of the spin density as the temperature decreases toward TC the neutron response function for magnetic scattering becomes: S ( q, ω ) =



∞

1 ∫ e−iωt S α ( −q, 0) ⋅ S β (q, t ) 2 π N  −∞

T

dt ,

(1.73)

where α and β are Cartesian coordinates x, y, and z. In the static or quasi-​static limit, assuming a localized model and neglecting the mag2 netic Bragg scattering contribution ~ S α T , which is close to zero at TC (paramagnetic scattering), the Fourier transform of the pair distribution function is given by: ∞



Γ ( q ) = ∫S ( q, ω ) dω = 0

1 2π N

∞

∫e

−∞

− iqr

( S (r ) −

S ) ⋅ ( S (0) − S

)

T

dV ,

(1.74)

where the average spin density is zero unless T TC, the function f   is assumed to have the form  ξ constant A is only weakly dependent on ε.

 R

−   R f   = Ae  ξ  , where the  ξ

39

Magnetism, Magnetic Materials, and Nanoparticles

39

As mentioned before, most magnetic transitions are second order, characterized by a continuous variation across the transition of the order parameter (the magnetization M0T for ferromagnets and the staggered magnetization for ferrimagnets and antiferromagnets). This implies that the system is in a unique critical phase at the transition and long-​range fluctuations cannot be neglected; Ginzburg showed this caused the general Landau mean-​field theory of phase transitions to give incorrect predictions in the region near the transition. Work on the problem by researchers such as Widom [62], and Wilson and Kadanoff [65] on homogeneity, scaling laws, and renormalization gave rise to renormalization-​group theory. This showed that continuous phase transitions all fall into one of a small number of classes with the same critical behavior, governed not by microscopic details of the system but its fundamental symmetries, such as the number of degrees of freedom n (of the spins for a magnetic system) and the number of spatial dimensions d. A very important consequence is that all transitions in the same universality class should have the same critical exponents; for example, studying the superfluid phase transition in He4 (where the order parameter is the wavefunction describing the fraction of He atoms in the superfluid state, the amplitude and phase of which give two degrees of freedom) can provide useful information about the critical behavior of an planar ferromagnet or a superconductor, as all three systems are in the same universality class (where n = 2 and d = 3). Another consequence of the theory is that there must be relations between the critical exponents: any three critical exponents can be related by an inequality. Some of these inequalities are summarized below [66]:



α + 2β + γ = 2; 2 − α = β ( δ + 1) ; γ = ν ( 2 − η) ; 2 − α = d ν.

(1.76)

In order to obtain actual predictions of the critical exponents, renormalization-​group theory was applied to models consisting of discrete spins arranged in a regular lattice, which interact with the external field and their nearest neighbors only. The features of the most important models are briefly introduced below and their critical exponents are collected in Table 1.9. 2D Ising (n = 1, d = 2): The spins sit on the sites of a two-​dimensional (2D) lattice (e.g. square and honeycomb) and are constrained to have only values si = ±1 pointing along a particular direction (e.g. up or down along the z-​axis). The 2D Ising model is the only one on this list which has an exact solution. 2D XY (n = 2, d = 2): The spins are still confined to a single plane as for the 2D Ising model but can now point along any direction within that plane. 3D Ising (n = 1, d = 3): The spins now sit on the sites of a regular 3D lattice (e.g. simple cubic); they still interact with their nearest neighbors only and still take only values si = ±1 along one axis. 3D XY (n = 2, d = 3): The planes of 2D XY spins are stacked on top of each other; although the spins can only rotate in their own plane or layer, they can interact with the spins in the next adjacent layer.

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Table 1.9  Critical exponents of phase transitions calculated for various magnetic models and compared to measured values from real substances [66]–​[68]. Values are exact for the mean-​field theory and 2D Ising models. Degrees of freedom

Exponents

β

δ

T < Tc

at T = Tc

½

3

η

α = α’

γ = γ’

ν = ν’

α ’, γ ’, ν’ (T < Tc); α, γ , ν (T > Tc)

Models Mean-​field

0

0

1

½

n = 1

2D Ising

⅛

15

¼

0

1¾

1

n = 1

3D Ising

0.3265

4.789

0.0364

0.110

1.2372

0.6301

n = 2

3D XY

0.34861

4.7801

0.03812

–​0.01513

1.31782

0.67171

n = 3

Heisenberg (S = ½)

0.36893

4.7833

0.03755

0

1.39609

0.71125

0.623

Measured n = 1

Xe, Ar

0.341

–​

0.0426

0.11

1.145

n = 2

4

0.347

–​

-​

–​0.0127

1.320

0.6676

n = 3

Ni

0.395

4.35

-​

–​0.11

1.345

–​

He, Gd2IFe2

Heisenberg (n = 3, d = 3): The spins can point in any direction in space and spin-​spin interactions must therefore also be considered in three dimensions. This model is appropriate for isotropic ferromagnets. It is worth noting that it is only possible to obtain the exact values of the critical exponents of the 2D Ising model in zero magnetic field. An exact solution in non-​zero field for the behavior of the 2D Ising model or any of the 3D models are still open research questions; the critical exponents are therefore calculated numerically and are constantly being refined [67].

1.4.4

AC Susceptibility The time-​varying (dynamic) magnetization processes can be investigated using AC susceptibility measurements, where AC driving fields with frequencies ω between 10–​2–​105 s–​1 are superimposed on a DC background. If the magnetization M is subject to an alternating magnetic field H = H 0 eiωt , it is generally delayed by the phase angle δ( ω,T ) = δ because of energy losses in the reversal process and is hence expressed as M = M 0 ei ( ωt − δ ) . ∂M The complex susceptibility χ ( ω,T ) = can then be written as [11]: ∂H



χ ( ω, T ) =

M 0 − iδ M 0 e = (cos δ − i sin δ ) = χ ′ ( ω, T ) − iχ ′′ ( ω, T ) , (1.77) H0 H0

where χʹ and χʺ are the in-​phase (real) and out-​of-​phase (imaginary) susceptibility components, χʺ being proportional to the energy absorbed. For nanoparticles above the blocking temperature TB, introduced in Section 1.3.3, χʺ is small and χʹ(ω,T) generally follows the Curie law χ ′ ∝ T −1, as expected for paramagnetic behavior. Assuming

41

Magnetism, Magnetic Materials, and Nanoparticles

41

a single particle size from the slope of 1/​χʹ versus T, the blocking temperature can be obtained and the particle volume can be estimated [69]. While the variation of χʹ is similar to that of χZFC, χʺ peaks at TB. However, the peak position and hence the measured value of TB depend on the drive frequency (i.e. inverse measurement time) following Eq. (1.48). Comparison of the observed frequency dependence of TB to the predictions given by the Néel–​Brown equation (Eq. (1.42)) enables the presence of interparticle interactions, such as clustering due to dipole-​dipole interaction to be identified. The presence of interparticle interactions gives rise to a stronger frequency dependence of the susceptibility [6, 70]. For non-​interacting particles, both χʹ and χʺ are shifted to higher temperatures with increasing frequency. For interacting particles, the shift is more significant, as is the effect on the shape and height of the χʺ line shapes.

1.4.5

Mössbauer Spectroscopy Mӧssbauer spectroscopy [71]–​[74], which has a characteristic time scale τm ~ ns, has been used to investigate a number of systems using the isotope 57Fe. Nuclei of this isotope emit gamma rays as they relax from their 3/​2 excited state to the 1/​2 ground state. By moving the 57Fe source back and forth with a linear drive, the energy of the emitted gamma rays can be scanned via the Doppler effect to a very high degree of precision so as to enable recoilless (energy conservation) absorption by an Fe-​containing sample. A typical range of velocities for a 57Fe source is ±11 mm/​s (1 mm/​s = 48.075 neV) with a resolution down to ~1 neV. If the transmission spectrum versus source velocity is measured, a characteristic series of dips is observed. Below TB, the relaxation time of the magnetization is long compared to τm and the spectrum is comprised of six lines due to the Zeeman splitting of the nuclear energy levels produced by the magnetic (hyperfine) field generated by the electrons. In a paramagnetic state this reduces to a single dip. By varying the sample temperature and measuring the area beneath the sextet of lines, TB is estimated as the temperature at which the measured area beneath the sextet of lines is the same as the area beneath the superparamagnetic “central” dip. The form of the time averaged magnetization M (T ) can be understood by realizing that the spins in a single domain nanoparticle act collectively as a macrospin, that is, they have a uniform precession angle. Therefore, it acts as a classical magnetic moment and the magnetization component along the quantization axis, M s cos θ , can be calculated by Maxwell–​Boltzmann statistical treatment and by using Eq. (1.32) [72]:



M (T ) = M s

∫

π/2

e

− E (θ ) kB T

−π/2

∫

π/2

e

−π/2

cos θ sin θdθ

− E (θ) kB T

sin θdθ

k T  ≈ Ms 1 − B  .  2 KV 

(1.78)

For particles with uniaxial anisotropy, the magnetic hyperfine field Bhf is proportional to the average magnetization and is given by:

k T  Bhf = Bo  1 − B  ,  2 KV 

(1.79)

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Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

where Bo is the saturation hyperfine field, that is, the magnetic field acting on the nucleus in the absence of superparamagnetic relaxation. If a large field is applied above TB and below TC, the superparamagnetic relaxation is inhibited and the spectrum again comprises six lines. The average magnetic hyperfine splitting of the Mӧssbauer spec µ(T ) B  > 2 of the Langevin trum is then proportional to the high-​field approximation   kBT  function (Eqs. (1.13) and (1.51)) [74]:  k T  Bhf = Bo  1 − B  − B,  µ(T ) B 



(1.80)

where μ(T) = mμB = M(T)V is the magnetic moment of the particle, V is the particle volume, M(T) is the magnetization, and B is the applied field. A plot of Bhf + B versus B–​1 yields a linear dependence, the gradient of which gives the moment, or if this is already established, the particle volume V = μ(T)/​Ms.

1.4.6

Neutron Scattering Neutron diffraction and XMCD can be used to determine the magnitude, direction, and anisotropy of atomic magnetic moments. Within the Born approximation, the differential cross section for elastic neutron scattering from the magnetic potential is given by [75]:



))

( (

∂σ 2  e iq . r dr 3 ki , S = r02 k f , S ′ S n ⋅ ∫ eq × M ( r ) × eq ∂Ω 

2

,

(1.81)

 n is the spin-​operator for the neutron, e is the where r0 was introduced in Eq. (1.72), S q  unit vector along q, and M ( r ) is the operator of the spatially dependent total magnetization, in which the neutron spin states S and Sʹ may change. The magnetic structure  ( q) = − 1 M  ( q) is related to M  ( q), the Fourier transform of M  ( r ). factor operator Q 2µ B  ( q), also called the magnetic form factor, is a vector, each component may be Since M complex:

 (q ) = M M ∫  ( r ) eiq⋅r dr 3 .

(1.82) 2

2  , where the magThe scattering cross section is proportional to S ′ S n ⋅ Q ⊥ (q ) S   ( q) = e × Q  ( q) × e . A consequence of this relanetic interaction vector operator is Q q q ⊥ tion is that neutrons only see the components of the magnetization perpendicular to the scattering vector. If the initial direction of the neutron spin is taken to be parallel to e z , the direction of a magnetic field applied to the sample, then the cross section for scattering 2 2 without change of the spin direction (non-​spin-​flip) is given by e z ⋅ Q⊥ ( q ) = Q⊥ , z ( q ) 2 and with a change of direction (spin-​flip) by e z × Q⊥ ( q ) . The precise determination of

(

)

43

Magnetism, Magnetic Materials, and Nanoparticles

43

the magnetization distribution in ferromagnetic materials makes use of the interference between the nuclear and magnetic scattering in which the sample is magnetized parallel to the spin direction of the incident polarized neutron beam. Assuming here that both the nuclear structure factor N ( q ) = ∑ bd eiq⋅r e −Wd (where bd is the average nuclear d

scattering length at atomic position d and Wd the Debye–​Waller factor), and the magnetic structure factor Q(q) are real, the non-​spin-​flip scattering cross section is proportional to N ( q ) ± 2 N ( q ) Q⊥ , z ( q ) + Q⊥ , z ( q ) . The plus or minus sign refers to the 2

2

neutron spin direction being parallel or anti parallel, respectively, to Q⊥ , z ( q ) and the quantity measured is the ratio of the two cross sections, namely the ‘polarization ratio’ Q⊥, z ( q ) 1 + 2γ + γ 2 R= , where γ = . This enables a precise determination of Q⊥ , z ( q ), 1 − 2γ + γ 2 N (q ) which can then be compared directly with electronic structure calculations. Neutron scattering with an intrinsic time scale of 10–​14–​10–​7 s is particularly appropriate for studying the wavevector k and frequency ω of magnetic fluctuations [76]. Below TB the magnetic response is not significantly affected by superparamagnetism, but relaxation and collective processes may occur. Relaxation processes are characterized by a quasi-​elastic response centered on zero energy transfer (ω = 0), whereas collective excitations have a finite energy transfer [77]. For isotropic bulk ferromagnets, the long wavelength (k → 0)  limit of the spin wave dispersion is ħω  =  Dk2, as shown in Eq. (1.27). This defines a magnon wavelength given by:

λ = 2π

D , ω

(1.83)

which for iron at 5 K corresponds to ~7 nm. Owing to the finite size of the particle, the collective excitation spectrum is quantized and therefore discrete. This may be demonstrated by considering the modes within a cuboid of side d. The spin wave energies are given by: 2



 nπ  En = Dkn2 = D   ,  d

with

n = 1, 2, 3,...

(1.84)

Thus, a spin wave gap Δ is produced given by: 2



 π Δ = D  ,  d

(1.85)

which for 5 nm iron particles is about 11 meV. The presence of this gap significantly influences the thermodynamics of the particles. Hence, the low temperature thermal variation of the saturation magnetization is no longer given by the Bloch T3/​2 spin wave formula (Eq. (1.57)). On the basis of experimental results, a power law variation has been proposed:

M (T ) = M s [1 − BT β ], (1.86)

4

44

Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

where β depends on the particle size, varying between 2 down to 1.5 for bulk samples. On the basis of neutron scattering measurements, both quasi-​elastic and inelastic features have been reported, the details of which are dependent on the system studied. Through the fluctuation dissipation theorem [78], the imaginary part of the generalized susceptibility χ(q, ω) = χʹ(q, ω) + iχʺ(q, ω) is related to the response function for mag1 1 netic scattering S ( q, ω ) = χ ′′(q ,ω ). Hence, the frequency ω and wavevector ω π  − kB T  1 − e   dependence q of the response can be determined by neutron scattering. The uniform susceptibility (static q = 0 value) is often defined as per unit mass (χρ) or per mole (χmol) and can be either positive or negative.

1.4.7

X-​ray Magnetic Circular Dichroism (XMCD) The XMCD technique is element specific while also allowing the spin and orbital contributions to the magnetic moment to be separated. In this process, a core electron in the examined material is excited to an empty valence state and the energy required is specific to the atomic species. In addition, due to the spin-​orbit interaction, the X-​ray absorption of a ferromagnet depends also on the relative orientation of the magnetization with respect to the direction of the incident photon spin. Since the transitions are governed by the Δ𝓁 = ±1 selection rule, d band transition metals are usually studied using the L2,3 absorption edges (2p → 3d) [79, 80]. The spin and orbital moments are related to the absorption spectra σ+ and σ–​ obtained with right-​ handed and left-​handed circularly polarized X-​rays by [81, 82]: mL = LZ ⋅ µ B = 2 nh





∫ ∫

7 3   mS = 2  SZ + TZ  ⋅ µ B = nh   2 2

L3 + L2

L3 + L2

∫

L3

σ + − σ − dE

σ + + σ 0 + σ − dE

⋅ µB ,

σ + − σ − dE − 2∫ σ + − σ − dE L2

∫

σ + σ + σ − dE +

L3 + L2

0

(1.87)

⋅ µ B , (1.88)

where is the expectation value of the dipole operator, nh is the number of vacancies in the valence band (holes), σ0 = ½(σ ++σ –​) and the integral over the adsorption edges L2 and L3, and ∫ dE is the sum of the areas under the absorption curves at the L2 and L3 L3 + L2

energies. The number of holes, which can significantly differ from bulk for thin films or particles, can be determined by measuring the white line intensity by X-​ray absorption spectroscopy. This involves taking an extra spectrum with linearly polarized X-​rays in addition to the absorption spectra σ+ and σ–​ required for XMCD.

45

Magnetism, Magnetic Materials, and Nanoparticles

1.5

45

Structural Analysis Analysis of the microstructure is usually investigated using diffraction techniques, but real space imaging is also often employed. As a result of the X-​ray adsorption in XMCD, secondary electrons are emitted, which can be analyzed by PEEM [83] to provide resolutions of up to ~10  nm. Transmission electron microscopy (TEM) provides information on the size and morphology of particles and the structure of thin films. If high resolution TEM is used, then atomic planes within samples can be imaged and possible imperfections, such as dislocations, identified. TEM has also been used to determine the size distribution of nanoparticles, which severely affects the magnetic properties and is a limiting factor in the interpretation of results. The volume distribution is generally found to follow a logarithmic-​normal distribution of the form:



f (V ) =

 (ln (V ) − µ )2  exp  −  , 2σ 2 σ 2π   1

(1.89)

where σ is the standard deviation, σ2 is the variance and μ is the mean of the variable’s natural logarithm. These are correlated to the mean, m, and variance, v, of the real sample values by:



  m µ = ln  v   1 + 2 m

  v    , σ 2 = ln  1 + 2  .   m  

(1.90)

When diffraction techniques are employed, X-​rays [84] and neutrons [85] provide complementary measurements; in general, X-​rays provide a better spatial resolution than neutrons. The broadening of diffraction peaks can arise from the domain size or microscopic strain. The broadening is usually characterized by the full width at half the maximum intensity (FWHM) of the Bragg peaks. The integral width, βsi (in radians), of a Bragg peak with index i at a scattering angle, 2θi, due to a small domain size is estimated by the Scherrer formula [86]:

β si =

Kλ , DV cos θi

(1.91)

where DV is the volume-​weighted domain size, λ is the wavelength of the incoming beam and K is a dimensionless shape factor with a value of about 0.9, which, however, varies with the actual shape of the crystallites. The integral width, βdi, due to microstrain can be approximated as [87]:

β di = 4 tan θi ,

(1.92)

46

46

Adrian Ionescu, Justin Llandro, and Kurt R. A. Ziebeck

where ε is the microstrain. Assuming a Cauchy-​shaped profile (Lorentz distribution) for both the size and strain components, the corresponding integral widths are linearly additive:

βtot = β si + β di ⇔ βtot cos θi =



Kλ + 4 sinθi . DV

(1.93)

Thus, a plot (Williamson–​Hall) [88] of βtot cos θi versus sin θi for as many θi as possible Kλ should be linear, with the intercept giving and the gradient yielding 4ε. DV An alternative method involves the convolution of the instrumental resolution D(θ) with a function (often a modified Voigt profile) representing the intrinsic line shape h(θ) to give the observed line shape I(θ), I (θ ) = h(θ) ⊗ D(θ). If the intrinsic and instrumental line shapes can both be represented by Gaussian functions, then the observed width βobs is given by: 1

2 2 βobs = (βintr + βinst )2 ,



(1.94)

where βintr and βinst are the intrinsic and instrumental integral widths. The instrumental resolution can be established using a standard sample. Profile refinement programs, such as Fullprof [85], enable the full diffraction pattern to be analyzed, and possible anisotropic particle shapes and strains to be identified. Neutron diffraction also enables the possible magnetic structure of the particles to be established. If the particles are ferromagnetic, the magnetic scattering occurs at the nuclear positions. Heating above the Curie temperature will render the Bragg peaks entirely nuclear in origin, but this may change the nuclear structure. Alternatively, it may be possible to align the moments along the scattering vector to extinguish the magnetic Bragg component (Section 1.4.6). For some specific problems, the use of polarized neutrons may be required to uniquely extract the nuclear and magnetic contributions. However, if the particles have an AF structure, then, in general, the magnetic peaks occur at different Bragg positions. This distinction enables the nuclear and magnetic particle sizes to be established at the same temperature in the antiferromagnet NiO [89]. The spherical 6.5 nm particles have been found to have a 5.1 nm AF core with an outer shell of significantly reduced magnetization.

Sample Problems Question 1 (a) Using Table 1.1, Eq. (1.5), and Hund’s rules, calculate S, L, J, pJ, and pS for a Ti2+ ion (e.g. in a metallo-​organic complex) and comment on how pJ and pS compare to the experimental value. (b) In similar fashion, calculate S, L, J, pJ, and pS for a V2+ (or Mn4+) ion. (c) In similar fashion, calculate S, L, J, pJ, and pS for a Mn3+ (or Cr2+) ion.

47

Magnetism, Magnetic Materials, and Nanoparticles

47

Question 2 (a) By using Eq. (1.9), the expression for the mean square ionic radius 1 r2 = 0 ∑ri2 0 , and the substitution r 2 = a02, calculate the value of the Z i Larmor (molar) diamagnetic susceptibility for graphite (Z = 6) and compare it to the experimental value given in Table 1.4. Remember that the values in Table 1.4 are in CGS units, so the magnetic units conversion table in the Appendix should be used to convert from SI units. (b) Repeat the exercise in (a)  for Cu (Z  =  29). Comment on the quality of the agreement. (c) Repeat the exercise in (b)  using instead the expression for the radius of the free electron sphere rs given in Eq. (1.10) and the substitution rs2 = 0

∑r

i

2

0 ,

i

assuming a valence of 1 for Cu. Suggest a reason for the difference in the quality of the agreement between the newly calculated and experimental values. References [1]‌ S. P. Gubin, Y. A. Koksharov, G. B. Khomutov, and G. Y. Yurkov, Magnetic nanoparticles: Preparation, structure and properties. Russ. Chem. Rev., 74:6 (2005), 489–​520. [2]‌ X. Batlle and A. Labarta, Finite-​size effects in fine particles: Magnetic and transport properties. J. Phys. D: Appl. Phys., 35:6 (2002), R15–​42. [3]‌ R. Skomski, Nanomagnetics. J. Phys. Cond. Matter., 15:20 (2003), R841–​96. [4]‌ J. Bansmann, S. H. Baker, C. Binns, et al., Magnetic and structural properties of isolated and assembled clusters. Surf. Sci. Rep., 56:6–​7 (2005), 189–​275. [5]‌ D. L.  L. Mills and J. A.  C. Bland, Nanomagnetism:  Ultrathin Films, Multilayers and Nanostructures, 1st edn (Amsterdam: Elsevier, 2006). [6]‌ S. Mørup and M. F. Hansen, Superparamagnetic particles. In H. Kronmüller and S. S. Parkin, eds., Handbook of Magnetism and Advanced Magnetic Materials, Vol. 4 of Novel Materials. (Chichester: J. Wiley & Sons Ltd., 2007), pp. 2159–​76. [7]‌ B. Aktas and F.  Mikailov, eds., Advances in Nanoscale Magnetism, 1st edn (Berlin, Heidelberg: Springer, 2007). [8]‌ A. P. Guimaraes, Principles of Nanomagnetism, 1st edn (Berlin, Heidelberg:  Springer, 2009). [9]‌ T. Shinjo, ed., Nanomagnetics and Spintronics, 1st edn (Oxford: Elsevier, 2009). [10] R. Bozorth, Ferromagnetism, 3rd edn (New York, NY: Wiley-​IEEE Press, 1993). [11] S. Chikazumi, Physics of Ferromagnetism, 2nd edn, (Oxford:  Oxford University Press, 2009). [12] J. S. Smart, Effective Field Theories of Magnetism, (Philadelphia, PA:  W.B. Saunders Co., 1966). [13] B. Odom, D. Hanneke, B. d’Urso, and G. Gabrielse, New measurement of the electron magnetic moment using a one-​electron quantum cyclotron. Phys. Rev. Lett., 97:3 (2006), 030801. [14] B. N. Figgis and J. Lewis, The magnetochemistry of complex compounds. In J. Lewis and R. G. Wilkins, eds., Modern Coordination Chemistry (New York, NY: Wiley, 1960).

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Preparation of Magnetic Nanoparticles for Applications in Biomedicine Pedro Tartaj, Sabino Veintemillas-​Verdaguer, Teresita Gonzalez-​Carreño, and Carlos J. Serna

2.1 Introduction The last ten years have seen both qualitative and quantitative advances in the synthesis of magnetic nanoparticles (MNPs) for their use in biomedical applications. This field is particularly well developed because simple synthesis routes for the preparation of MNPs have been around for a long time (mainly driven by fundamental studies and applications such as data recording). There are therefore many synthesis protocols that have been used in biomedical applications with differing degrees of success. Independently of the synthetic route used to produce MNPs, all of them must take into consideration a series of restrictions. The main restriction arises from the unique environment that bio-​applications impose, in which different applications may need different types of MNPs. The other important restriction arises from the strong dependence of the nanoparticle’s magnetic properties on size, crystallinity, surface effects, collective interactions, and shape, with the nanoparticle shape effect being the least developed dependence as most of the studies deal with spherical or quasispherical nanoparticles. Toxicity is a general restriction in biomedical applications and it is the main reason for the preference of iron oxides over other materials for MNP synthesis. However, the use of coatings can also allow otherwise toxic materials to be used in bio-​applications. An example is FeCo nanocrystalline alloys coated with graphitic shells that show combined capabilities for monitoring (magnetic resonance imaging [MRI]) and therapeutic (photothermal ablation) applications [1]. Throughout this chapter, most of the examples are thus primarily focused on iron oxides, though significant examples of successful synthesis routes for the preparation of other materials are also given. Among iron oxides, magnetite/​maghemite (Fe3O4, γ-​Fe2O3) are the ones that possess the highest magnetic moment and therefore are the most adequate for biomedical applications [2]. In these structures, the iron and oxygen atoms arrange in a cubic inverse spinel structure, with O2–​ anions forming a cubic close-​packed array and the Fe cations occupying interstitial tetrahedral and octahedral sites [3]. Maghemite differs from magnetite in that most, if not all, of the iron is in the trivalent state. Cation vacancies compensate for the oxidation of Fe (II) cations. This difference turns out to be of importance when dealing with magnetite and maghemite materials. There is a certain consensus that the

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Fe (II) present in magnetite could catalyze the oxidation of hydrogen peroxide (Fenton reaction) causing a degree of toxicity associated with the generation of reactive oxygen species (ROS). Therefore, maghemite should be preferred over magnetite for bio-​ applications. However, coatings are very important as they could be relatively effective in the inhibition of the Fe (II) catalytic effect. For bio-​applications (specially in in vivo applications, which can be considered the ultimate goal in biomedicine), the size, or more specifically, the hydrodynamic size (size in aqueous suspension) is one of the most relevant parameters. Restrictions on hydrodynamic size are strongly dependent on the particular anatomical features of the targeted nanoparticle delivery site we are interested in. While most endothelial barriers are permeable to nanoparticle/​aggregate sizes below about 150 nm, there are examples of much more restrictive barriers. The blood-​brain barrier is only permeable to very small and neutrally charged lipid soluble molecules (less than about 500 Da in molecular weight) [4, 5]. The high surface area to volume ratio is another limiting factor for the synthesis of MNPs. In ionic compounds the orientation of each moment at the surface can be altered as a result of competing exchange interactions in an incomplete coordination shell for surface ions [6]. This can lead to a disordered spin configuration near the surface and a reduced average net moment relative to the bulk material [7–​11]. Collective interactions (mainly of dipolar origin) are also important when designing a possible route for the preparation of MNP aggregates or nanocomposites. Aggregation is, for example, a feature now used to increase the capabilities of MNPs as contrast agents for MRI [12–​15]. The synthesis routes in a free medium can be grouped in three general categories according to the physical state of the precursors:  gas, solution, or solid (Figure  2.1). However, no matter which of these three approaches we use to produce MNPs, there is a general consensus in the scientific community that good control of the microstructure, in regards to the MNP size and shape, is beneficial for biomedical applications. As both size and shape control are much easier to achieve using solution routes, this approach is by far the most commonly used. Most of this chapter, thus, is devoted to describing the fundamentals of two of the most important solution routes considering the nature of the solvent in which reactions occur (aqueous or organic), the description of “barriers” used to avoid uncontrolled growth, and the preparation of magnetic nanocomposites (MNPs dispersed in either organic or inorganic matrices). Combining MNPs with a suitable matrix is essential to provide MNPs with extra capabilities in order to improve functionality and to overcome the technical hurdles associated with MNP synthesis for biological applications. These methods are grouped under the heading “synthesis in a confined medium” in Figure  2.1. Finally, we also briefly describe some interesting examples of gas and solid synthesis routes.

2.2

Fundamentals of Solution Routes and Some Interesting Examples Since the seminal paper of Lamer and Dinegar on the preparation of monodisperse sulfur hydrosols that established a general mechanism for the formation of monodisperse

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Figure 2.1  Schematic representation of the synthesis methods employed for the preparation of

the MNPs.

particles [16], most of the solution routes have pursued a common mechanism. This mechanism involves nucleation in a single event followed by further growth via the addition of monomers to the nuclei formed. In some cases, aggregation of primary nuclei play a significant role [17].

2.2.1

Aqueous Co-​Precipitation Routes Aqueous co-​precipitation is the traditional route and can still be considered as the most straightforward route to obtain MNPs. In this approach, Fe (II) and Fe (III) precursors are dissolved in adequate proportions and mixed with some basic reagent to precipitate the spinel form. For example, the Massart method, widely used for the production of stable aqueous MNP suspensions, uses the co-​precipitation route. In this method degassed solutions of Fe (II) and Fe (III) chlorides are added to an ammonia solution, washed several times, and then stabilized in suspension by using tetramethylammonium hydroxide (basic solution) or perchloric acid (acidic solution) [18]. Variations of this methodology involve, for example, the precipitation of the spinels in the presence of hydrophilic capping agents and/​or in confined spaces provided by very different

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Figure 2.2  TEM micrographs of iron oxide MNPs prepared from co-​precipitation (a) and

oxidative precipitation (b).

matrices, as described later. The aqueous medium in which the reactions occur and the low reaction temperatures required still make co-​precipitation-​based methods the most competitive for the preparation of MNPs. For the preparation of MNPs there is no doubt that aqueous co-​precipitation routes are losing ground to techniques in development that use hot organic solvents instead of water (see the next section). However, if particles above ~15–​20 nm are required, aqueous co-​precipitation techniques produce good MNPs in terms of their magnetic capabilities. Typically, MNPs with sizes above 15–​20 nm use Fe (II) precursors (usually FeSO4) [19], with a mild oxidant, and numerous variations of this methodology are available. For example, the partial replacement of water by ethanol allows rigorous control of the size and shape of spinels above 20–​30 nm, with the possibility of simultaneous doping with inorganic shells [20, 21]. In Figure 2.2, we present typical transmission electron microscopy (TEM) micrographs of 8 nm iron oxide MNPs prepared by the Massart method and 20 nm nanoparticles synthesized using oxidative precipitation of FeSO4. Co-​precipitation routes are also adequate for the production of rod-​like nanoparticles. To synthesize rod-​shaped nanoparticles, a solid intermediate that grows in a preferred orientation (say iron oxyhydroxides such as goethite or akaganeite) is heated in a reducing atmosphere after appropriate protection of the particles with an inorganic coating to avoid sintering [22, 23].

2.2.2

Hot Organic Solvents Since the introduction of hot organic solvents (typically in the boiling temperature range from 120 to 350 °C) [24], most of the interest in the synthesis of MNPs has been shifted to this methodology as it produces nanomaterials with high crystallinity and monodispersity. See Figure 2.1(B) for a standard experimental arrangement. As a typical solution route, the formation of MNPs are also understood in terms of the nucleation and growth mechanism. Thus, these methods involve fast nucleation followed by rapid growth, associated with the addition of monomers at concentrations well below the critical nucleation concentration. The presence of coordinating ligands in these

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Figure 2.3  TEM micrographs of iron oxide MNPs prepared by an organic decomposition method. The figure displays a correlation between the solvent stability and particle size. Basically, organic solvents with higher boiling points allow the synthesis of MNPs to take place at higher temperatures, and within the framework of nucleation theory larger particles are formed.

methods results in the formation of monodisperse nanosized particles with passivated surfaces. The MNP particle size obtained is controlled by the boiling temperature of the solvent used. In Figure 2.3, a set of TEM images of iron oxide nanoparticles prepared at different temperatures is presented. For historical reasons (found in seminal papers on the preparation of FePt alloys and the large-​scale synthesis of monodisperse MNPs via oleate decomposition [25, 26]), the methodology for the preparation of MNPs generally involves the mixing of components at room temperature and a controlled increase in temperature up to a point at which the rapid formation of MNPs occurs [27]. In essence, the method is similar to the alternative hot injection methods typically used for quantum dot preparation (though this method involves the injection of precursors at a high temperature). There are also successful examples of the production of monodisperse MNPs by hot injection routes [28]. In the approach used to prepare MNPs from hot organic solvents, the final product consists of hydrophobic particles that need to be further transferred to aqueous media before use in biomedical applications. For example, well-​ crystallized iron oxide MNPs of different sizes can be prepared using Fe(acac)3 as an iron precursor, lauric acid and lauryl amine as capping agents, and benzyl ether as the hot organic solvent [29]. These nanocrystals are transferred to aqueous media by using dimercaptosuccinic acid in a ligand exchange reaction with surface-​coordinated lauric acid using toluene and dimethyl sulfoxide as solvents. As previously highlighted, high crystallinity and low polydispersity are the main reasons to use hot organic solvents instead of aqueous solvents in the production of MNPs for biomedical applications. However, compared to aqueous solvents, hot organic solvents are preferred for the production of uniform magnetic metallic alloy MNPs, such as FePt (aqueous environments are oxidizing). For example, FePt-​Au nanocrystals, used as dual agents for biomedical applications, are prepared by using Fe(CO)5 and Pt(acac)2 as FePt precursors, oleic acid and oleylamine as surfactants, and benzyl ether as the solvent [30]. The heterodimers of FePt-​Au are

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obtained by dispersing the FePt nanocrystals in a solution of 1,2-​dichlorobenzene containing AuCl(PPh3) and hexadecylamine while bubbling with a 4% H2/​Ar gas mixture. Interestingly, the transfer into an aqueous medium is achieved by ligand exchange with lipoic acid polyethylene glycol with terminal hydroxy and amino functional groups.

2.2.3

Growth Under Confinement One of the main strategies to control the size and shape of MNPs is to limit the growth of the nuclei by performing the reaction in a confined space. Capping agents, for example, can be considered as a kind of dynamic confined space defined by the nuclei itself (by, e.g. selective adsorption on different crystallographic facets of the nuclei that leads to shape control). However, in general terms, a confined space is something that is already pre-​formed (say a matrix) and works as a physical barrier to avoid uncontrolled growth. The ultimate goal of the physical barrier (matrix) is not only to provide size and shape control but also to provide the MNPs with extra capabilities. As some of the examples that are given in the next section (nanocomposites from solution routes) fall within this category, here, the discussion is focused on a couple of successful MNP synthesis strategies that only control size and shape. Organized surfactant assemblies represent one of the most successful approaches to control size and shape in the synthesis of different particulate systems, among them MNPs. Many of them also provide MNPs with extra capabilities (a cell membrane is basically a lipid bilayer). An example of organized surfactant assemblies that are only intended for the production of MNPs with good size control are reverse microemulsions. Microemulsions are a thermodynamically stable dispersion of two immiscible liquids stabilized by surfactant molecules (Figure 2.1(E)). In reverse microemulsions, the continuous phase is the organic component (water nanodroplets are dispersed in the organic phase). Therefore, these assemblies are only intended to be used for the preparation of MNPs as these microemulsions, by definition, cannot be formed in a water-​rich environment. The surfactant-​stabilized microcavities of reverse microemulsions (typically in the range of 10 nm) provide confinement that limits particle nucleation, growth, and agglomeration. One of the advantages of the use of reverse microemulsions for the preparation of MNPs is that by changing the nature and/​or amount of the surfactant (e.g. ionic or non-​ionic), co-​surfactant (presence or absence), oil phase, water content, and reacting conditions it is possible to produce a variety of materials and microstructures [31, 32]. Anodic Al2O3 templates consist of uniform cylindrical pores that are aligned perpendicular to the surface of substrates and, as the name suggests, are formed by anodization of aluminium. The cylindrical pore structure makes these templates adequate for the preparation of elongated nanoparticles (nanowires). There are many examples in the literature that report the preparation of different materials in the form of pure nanowires after removing the alumina template by basic treatment. These unique templates can be used for the direct synthesis via electrodeposition of metallic Fe nanowires that shows low cytotoxicity in HeLa Cells (see Figure  2.1(F)) [33]. A  variation of this methodology uses nanoporous polycarbonate membranes instead of anodic alumina to produce

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Fe metallic nanowires that, due to their high magnetic moment, can be used for cell manipulation [34].

2.3

Nanocomposites from Solution Routes Encapsulation, coating, and entrapment are different strategies that can be applied to the synthesis of MNPs in the biomedical field to improve size and shape control (growth under confinement), enhance functionality, and improve the biodistribution, overcoming barriers associated with biological media. For example, for in vivo applications the injection of incompletely modified MNPs into the bloodstream rapidly generates an immunoresponse from the reticuloendothelial system by the adsorption of proteins (opsonization) that accelerates their clearance [35, 36]. Hydrophilic coatings are thus essential for increasing blood circulation times. The ultimate goal is to functionalize MNPs with the desired properties in a single step. For example polymer brushes can be used; these are thin polymer coatings in which at least one end of the polymer chain is tethered to a solid substrate [37]. Examples of polymer brushes that have been grafted to MNPs through strategies based on surface-​initiated polymerization are numerous (for more examples, please refer to Chapter 3).

2.3.1

Organic Matrices Organic matrices provide MNPs with unique chemical functionality and capabilities to avoid rapid detection by the immune system. There is, thus, substantial interest in developing magnetic nanocomposites made of MNPs and an organic component.

2.3.1.1

Polymer Matrices Natural and synthetic polymers, such as polysaccharides, polyesters, and poly(ethylenimines) (PEIs), are routinely used in combination with MNPs for applications in the biomedical field [38, 39]. Aside from grafting, which is closely related to functionalization, the main strategy to prepare polymer-​MNP nanocomposites is co-​precipitation in the presence of polymers. Co-​precipitation in the presence of dextran, for example, is used in the preparation of the commercial contrast agent Endorem® for use in MRI [40]. Variations of this methodology exist in which the refluxing times, which are normally used to prepare stable nanocomposites, are shortened. An example that fits into this category is the development of dual agents for MRI and positron emission tomography based on dextran-​64Cu-​doped MNPs [41]. Long refluxing times (typically no less than 2 h) during radioisotope incorporation weaken the radioactivity. Rapid microwave-​based synthesis (5 min.) overcomes this long-​standing problem [41].

2.3.1.2

Liposomes and Micelles Liposomes are a class of vesicle composed of uni-​lamellar or multi-​lamellar lipid bilayers. These colloids were first proposed as delivery vehicles during the earlier 1970s [42]. Since then, they have been established as excellent drug delivery carriers due to

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their unique capabilities, which include the possibility of delivering hydrophilic and lipophilic compounds [43, 44]. Magnetoliposomes are liposomes containing MNPs. There are standard methodologies to prepare magneto-​liposomes, such as dialysis of single unilamellar vesicles in the presence of MNPs [45] and extrusion of a mixture of MNPs with phospholipids [46]. As we are dealing with relatively established technology, advances in this field have mainly been made in developing magneto-​liposomes with compositions that minimize their detection by the reticuloendothelial system. For example, polymeric magnetoliposomes composed of amphiphilic polymer octadecyl-​ quaternized modified poly (γ-​glutamic acid) can easily be grafted with polyethylene glycol or peptides to create a multifunctional platform for targeted drug delivery [47]. Micelles, and more specifically, polymeric micelles made from the self-​assembly of amphiphilic polymers that contain hydrophilic and hydrophobic components, provide unique multifunctional platforms in the biomedical field [48]. The hydrophobic core allows the transport of hydrophobic compounds, while the hydrophilic shell allows stability in biological media and the size (below about 100 nm) allows access to multiple physiological sites. Besides their use in drug delivery, micelles are unique compartments to sustain and stabilize aggregates of MNPs. It has been widely reported that MNP aggregation leads to higher contrast capabilities when applied in MRI. Encapsulation of MNPs in micelles is thus a convenient route to obtain better contrast agents [12]. The methodology involves two procedures: the preparation of hydrophobic MNPs by using hot organic solvents as well as preparation of micelles by the self-​assembly of diblock copolymers. Loading the micelles with MNPs is carried out by a solvent-​evaporation procedure.

2.3.1.3

Nanogels and Solid Lipid Nanoparticles Hydrogels can be considered as one of the most promising materials for use in MNP synthesis for biomedical applications. They consist of hydrophilic polymeric networks that can contain large quantities of water or physiological fluids. The significance of hydrogels in biomedical applications is due to their high biocompatibility and the high therapeutic agent loading/​releasing characteristics [49, 50]. Among hydrogels, nanogels, which can be thought of as particulate hydrogels with sizes below the micrometer range, are especially promising materials. Their size allows uptake by cells and intracellular delivery [49]. For example, aqueous polymeric nanogels can be prepared by batch copolymerization of N-​ vinylcaprolactam, acetoacetoxyethyl methacrylate (AAEM), and vinylimidazole in an aqueous medium in the presence of a crosslinking agent and a water-​soluble azo initiator. The porosity of these nanogels allows them to be used as a template for the in-​situ formation of MNPs via the basic hydrolysis of FeCl2 and FeCl3 salts (Figure 2.1(G)) [51]. Solid lipid nanoparticles represent an alternative platform for drug delivery. They are made of lipids that remain solid at body temperature, with melting temperatures of 45–​55 °C. One of the advantages of these carriers is that the constituent lipids are mostly physiological lipids, such as fatty acids, mono-​, di, or triglycerides [52, 53]. The unique characteristics of MNPs that facilitate their magnetic targeting and enable their localized heating through the application of an alternating magnetic field make

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MNPs/​solid lipid composites an important emerging field of research. The preparation of these composites is facile and involves, for example, the preparation of MNPs and further incorporation in a solid lipid matrix [54].

2.3.1.4

Metal-​Organic Frameworks (MOFs) Metal-​organic frameworks (MOFs) are porous compounds in which metal ions or clusters are coordinated with organic molecules. The high surface area of these compounds makes them attractive for use in catalysis as well as many other applications, such as gas storage, purification, and separation. Non-​toxic porous iron (III)-​based MOFs have also been shown to have dual capabilities in drug delivery and medical imaging [55]. Their synthesis procedure is relatively easy as it involves solvothermal or microwave methods and easy-​to-​manipulate reactive agents.

2.3.2

Inorganic Matrices Inorganic matrices, although not as easy to chemically modify as their organic counterparts, have superior chemical and mechanical stability. There is therefore a lot of interest in developing purely inorganic nanocomposites. Silica is the preferred inorganic matrix as many standard protocols exist for functionalization. However, with the development of the first carbon nanotubes (CNT) and, more recently, graphene-​like materials, there is a growing interest in applying the knowledge obtained in the functionalization of carbon-​like materials to the preparation of carbon-​MNPs nanocomposites. Additionally, less popular matrices, such as TiO2, that have high affinity for phospho-​containing molecules are also gaining some ground. Controlled hydrolysis of silicon alkoxides (included amino-​ functionalized silicon alkoxides) by ammonium hydroxide using the Stöber method is the preferred way to coat MNPs with silica. Two variants of this methodology are normally used:  (1) the traditional Stöber method that involves the use of alcohols (ethanol, n-​propanol) as solvents or (2) microemulsions formed by inverse micelles typically in the system cyclohexane/​nonylphenyl ethers/​water [56]. Silica, for example, can be used to provide additional functionalities to CNTs decorated with MNPs [57]. The combination of the silica coating with the unique capabilities of CNTs makes these magnetic nanocomposites adequate as dual agents for biomedical applications. Briefly, CNTs that have been treated with concentrated nitric acid are suspended in a solution containing FeCl3. Temperature controlled hydrolysis followed by silica coating using the Stöber method and thermal treatment in a reducing atmosphere produces the composites. Methods to prepare magnetic nanocomposites composed of MNPs dispersed or encapsulated in porous matrices, or hollow capsules, are mainly based on two strategies. The first strategy involves impregnation of a porous matrix with a soluble salt or decoration of a porous matrix with MNPs (for the case of impregnation, further heating is needed). The porous matrix is usually obtained through co-​operative surfactant templating (silica matrices) and nanocasting (carbon matrices). The second strategy, which is intended for developing porous coatings, centers on the basic hydrolysis of tetraethoxysilane in

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the presence of porogens. Hollow capsules with porous walls containing MNPs can be made by combining these two strategies. An example of an advance made in the preparation of porous magnetic nanocomposites is in the production of porous MNP coatings other than porous silica, such as porous TiO2 coatings [58]. TiO2 has been shown to be very effective at trapping phosphoproteins and/​or phosphopeptides, the mass spectrometry analysis of which is essential in the field of proteomics. The combination of a magnetic component and a TiO2 mesoporous matrix can therefore confer the benefits of both materials (rapid separation and selectivity) to applications in proteomics. To achieve this, MNPs are coated with a TiO2 non-​porous layer by selective hydrolysis of titanium alkoxide onto the MNPs surface. The resulting composites are hydrothermally treated in basic media to develop porosity in the shell [58]. Significant advances have also been seen in the development of magnetic nanocomposites made of MNPs composed of materials different to iron oxides. MRI contrast agents based on superparamagnetic iron oxide nanoparticles are now routinely used for imaging/​monitoring a wide variety of in vivo processes. However, they belong to the T2 group that provide “negative” contrast to images. Iron oxides thus fail to give sufficient contrast capabilities when a hemorrhage or blood clot is present, for example [59]. There is, therefore, substantial interest in developing T1 (“positive”) contrast agents based mainly on manganese oxide nanoparticles. The increased number of MNP atoms per MNP particle and their contact with water is the reason why nanosized objects are preferred over chelates. Hollow manganese oxides with a large surface area offer a unique characteristic by enabling the loading of therapeutic agents while giving unique T1 capabilities [59, 60]. Hollow manganese oxides can be prepared by thermal decomposition of an oleate complex to produce monodisperse MNO nanoparticles, which are then transferred to water, with a phthalate buffer (pH = 4.6) added to partially carve out the MNO core [60]. A variation of this method produces mesoporous silica-​ coated hollow manganese oxide particles by basic hydrolysis of tetraethoxysilane in the presence of cetyltrimethylammonium bromide [59].

2.4

Gas and Solid Routes Gas-​phase synthesis can be considered the most adequate method for the production of a wide variety of nanoscale particles in terms of its efficiency and scalability, as well as particle size control for particles around 5  nm or less [61]. This synthesis approach involves the formation of a supersaturated vapor of condensable gaseous species via chemical reactions that create new species, or via physical processes (such as cooling) that reduce the vapor pressure of condensable species [62]. A supersaturated vapor consists of atoms or molecules of a given species present at a partial pressure higher than the vapor pressure of that species. At sufficiently high supersaturation, new particles form by homogeneous nucleation. Of the different gas phase routes available, the laser pyrolysis of carbonyl precursors has been shown to be the best for the production of MNPs for biomedical applications. This method involves heating a flowing mixture of gases with a continuous wave carbon

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Figure 2.4  TEM micrograph of Fe-​C MNPs produced by laser pyrolysis of iron pentacarbonyl in

the gas phase. The core shell microstructure formed by the iron core and the iron oxide shell can be easily appreciated.

dioxide laser, which initiates and sustains the decomposition reaction. Once a certain threshold of energy density is surpassed, metal atoms are produced that rapidly coalesce, forming nanoparticles that could undergo additional reactions with other components of the gas to give the final product (Figure  2.1(C)). This method was used, for example, to synthesize Fe-​C MNPs with good characteristics for application in MRI [63]. Figure 2.4 shows a TEM micrograph of Fe-​C MNPs. Interest in gas phase techniques, however, is shifting to the formation of homogeneous coatings on preformed MNPs. For example, the graphitized carbon coated FeCo nanocrystalline alloys, described in Section 2.1 as an alternative to iron oxides, were prepared by infiltration of iron and cobalt salts in a silica template, and then reduction followed by methane chemical vapor deposition for carbon deposition. Finally, the silica was etched with hydrogen fluoride [1]. Solid synthesis routes, although providing the highest yield, fall into one of the three synthesis (solid, gas, and solution) categories, mentioned previously, that is used less frequently in the production of MNPs for biomedical applications. The reason for this is that as the MNP size requirement falls below 20–​30  nm, these methods lack the rigorous size control that the other two (solution and gas) routes have, with the additional risk of product contamination. Among solid routes, mechanochemical synthesis is the most promising method to achieve the desired size control. Mechanochemical synthesis involves the mechanical activation of solid-​state displacement reactions in a ball mill. Thus, mechanical energy is used to induce chemical reactions. For example, mechanochemical synthesis of Fe3O4 via milling of mixtures of iron hydroxides can produce, with careful control, relatively monodisperse particles of around 15–​20 nm  [64].

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Figure 2.5  Comparison among the different synthesis methods with respect to the productivity,

degree of microstructural control, and range of particle sizes attainable.

2.5

Conclusions and Perspectives As a summary, Figure 2.5 gives a comparison of the yield (“productivity”), particle size, and degree of microstructural control achieved with the different MNP synthesis strategies. The last ten years have seen an exponential growth in both the quantity and quality of the synthetic routes used in the production of MNPs for biomedical applications. Some of these routes, although very successful, are still not ready for widespread application as they involve relatively cumbersome methodologies and therefore often lack inter-​lab reproducibility. There is no doubt that, within the next ten years, efforts must be focused on the refinement of these routes or the development of new routes capable of widespread entry into the biotechnology market beyond their application as contrast agents for imaging the liver by MRI. Finally, although there is no current requirement for economical synthesis routes in bio-​applications (MNPs are by far the cheapest components with regards to the reactants required for their synthesis), it might be desirable in the future, after the widespread entry of MNPs to the market, to consider more economical routes for MNP production.

Sample Problems Question 1 Are state-​of-​the-​art synthesis routes ready to jump into mainstream commercial use?

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[18] R. Massart, Preparation of aqueous magnetic liquids in alkaline and acidic media. IEEE T. Magn., 17:2 (1981), 1247–​8. [19] T. Sugimoto and E. Matijevic, Formation of uniform spherical magnetite particles by crystallization from ferrous hydroxide gels. J. Colloid. Interface. Sci., 74:1 (1980), 227–​43. [20] M. A. Verges, R. Costo, A. G. Roca, et al., Uniform and water stable magnetite nanoparticles with diameters around the monodomain-​multidomain limit. J. Phys. D. Appl. Phys., 41:13 (2007), 134003. [21] M. Andres-​Verges, M.  P. Morales, S. Veintemillas-​Verdaguer, F.  J. Palomares, and C.  J. Serna, Core/​shell magnetite/​bismuth oxide nanocrystals with tunable size, colloidal, and magnetic properties. Chem. Mater., 24:2 (2012), 319–​24. [22] Y. Piao, J. Kim, H. Bin-​Na, et al., Wrap-​bake-​peel process for nanostructural transformation from beta-​FeOOH nanorods to biocompatible iron oxide nanocapsules. Nat. Mater., 7:3 (2008), 242–​7. [23] A. F. Rebolledo, O. Bomatí-​Miguel, J. F. Marco, and P. Tartaj, A facile synthetic route for the preparation of superparamagnetic iron oxide nanorods and nanorices with tunable surface functionality. Adv Mater., 20:9 (2008), 1760–​5. [24] J. A. Hollingsworth and V. I. Klimov, Soft chemical synthesis and manipulation of semiconductor nanocrystals. In V. I. Klimov, ed., Nanocrystal Quantum Dots, 2nd edn (Boca Raton, FL: Taylor and Francis, 2010), pp. 1–​62. [25] S. H. Sun, C. B. Murray, D. Weller, L. Folks, and A. Moser, Monodisperse FePt nanoparticles and ferromagnetic FePt nanocrystal superlattices. Science, 287:5460 (2000), 1989–​92. [26] J. Park, K. An, Y. Huang, et al., Ultra-​large-​scale syntheses of monodisperse nanocrystals. Nat. Mater., 3:12 (2004), 891–​5. [27] T. Hyeon, Chemical synthesis of magnetic nanoparticles. Chem. Commun., 8 (2003), 927–​34. [28] J. E. Rockenberger, C. Scher, and A. P. Alivisatos, A new nonhydrolytic single-​precursor approach to surfactant-​capped nanocrystals of transition metal oxides. J. Am. Chem. Soc., 121:49 (1999), 11595–​6. [29] Y. W. Jun, Y. M. Huh, J. S. Choi, et al., Nanoscale size effect of magnetic nanocrystals and their utilization for cancer diagnosis via magnetic resonance imaging. J. Am. Chem. Soc., 127:16 (2005), 5732–​3. [30] J-​S. Choi, Y-​W. Jun, S-​I. Yeon, H.  C. Kim, J-​S. Shin, and J. Cheon, Biocompatible heterostructured nanoparticles for multimodal biological detection. J. Am. Chem. Soc., 128:50 (2006), 15982–​3. Dominguez, K. Pemartin, and M. Boutonnet, Preparation of inorganic [31] M. Sanchez-​ in-​ water microemulsions:  A soft versatile approach. Curr. Opin. nanoparticles in oil-​ Colloid Interface Sci., 17:5 (2012), 297–​305. [32] J. Wang, Z. H. Shah, S. Zhang, and R. Lu, Silica-​based nanocomposites via reverse micro­ emulsions: Classifications, preparations, and applications. Nanoscale, 6:9 (2014), 4418–​37. [33] M-​M. Song, W-​J. Song, H. Bi, et al., Cytotoxicity and cellular uptake of iron nanowires. Biomaterials, 31:7 (2010), 1509–​17. [34] S. Song, G. Bohuslav, A. Capitano, et al., Experimental characterization of electrochemical synthesized Fe nanowires for biomedical applications. J. Appl. Phys., 111 (2012), 056103. [35] Z.  R. Stephen, F.  M. Kievit, and M. Zhang, Magnetite nanoparticles for medical MR imaging. Mater. Today, 14:7–​8 (2011),  330–​8. [36] M. Mahmoudi, S. Sheibani, A. S. Milani, et al., Crucial role of the protein corona for the specific targeting of nanoparticles. Nanomedicine (Lond.), 10:2 (2015), 215–​26.

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Magnetic Nanoparticle Functionalization Justin J. Palfreyman

3.1

Gold-​Coated Particles Gold is a useful element when it comes to the bio-​functionalization of materials as it provides a natural stepping stone from the hard device fabrication process to the soft surface chemistry. It is commonly used as a capping material due to its inertness and resistance to oxidation. There are a number of growth techniques compatible with gold deposition (e.g. sputtering, thermal evaporation, and electrochemical deposition) meaning it is usually possible to add the gold coating in situ with most devices. It is of no surprise therefore that the field of gold functionalization is now well established; alkane-​ thiols are by far the most studied molecules used to grow self-​ assembled monolayers (SAMs) [1]. While most of the early research has been conducted on gold planes, often the (111) plane, the key principles can easily be transferred to gold-​coated nanoparticles. In fact, as we shall see in Section 3.1.5, moving to nanoparticles opens up a whole new dimension of possibilities. In this section, we shall not concern ourselves with the fabrication of the gold surface explicitly, but it is important to recognize the diversity of substrates available; of particular interest may be core/​shell nanoparticles. For example, these might consist of a magnetic core with a gold shell; such structures are written as Fe3O4@Au [2] (Figure 3.1). With the advent of DNA synthesizers  –​instruments capable of building custom strands of DNA, base by base  –​the starting point for many biosensors is to use oligonucleotides1 with a chemical modification on the 5’ end (Figure 3.2). Commercial suppliers, such as Sigma-​Aldrich, offer (for a small fee) modifications, such as a six-​carbon chain terminated with a thiol, amine, or biotin functionality. Although a thiol terminated oligo can be attached directly to a gold-​coated particle (as shown in Figure 3.1), this may not lead to the best yield/​sensitivity. If the oligos are too tightly packed, they will sterically hinder the hybridization process or may quench fluorescence, which is commonly used as an indicator for positive binding events. In the following sections, let us assume that we have chosen amine-​terminated oligos as our probes, and we will explore how to optimize the surface chemistry for the efficient binding of a probe and target capture. Oligonucleotide (or simply oligo) describes a short nucleic acid polymer typically with 50 or fewer bases.

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Figure 3.1  (a) A schematic of a core-​shell nanoparticle functionalized with custom-​made

oligonucleotide probes with a thiolated end. (b) A top-​view of a densely packed SAM on a (111) gold surface; the sulfur occupies the well between three gold atoms.

Figure 3.2  The structure of DNA. (Left) The two pairs of bases, G-​C and A-​T, showing the

hydrogen bonds formed during hybridization. (Right) The phosphate-​sugar backbone that holds the bases together. The two reactive ends (OH and PO3 groups) are labeled 3’ and 5’ because of the carbon atom to which they are attached.

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Figure 3.3  Building a monomer for self-​assembly on gold. The monomer has three

components: tail, chain, and head. Some of the more exotic components are shown in the bottom panel, including a photosensitive chain (COO-​Coumarin-​7-​O), which breaks when illuminated with 350 nm UV light, exposing a carboxylic acid head group.

3.1.1

SAM Monomers The choice of monomer used to grow the SAM can be tailored somewhat depending on the application, and can be considered as the construct of three building blocks: the tail group, chain, and head group. Some of the most common options are shown in Figure  3.3, which also includes an example of the more exotic options that are now available commercially.

3.1.1.1

Tail Groups The tail group is the anchor that connects the SAM to the gold surface, and is usually a thiol group.2 There exists a strong affinity between sulfur and gold,3 which holds them together with a bond strength in between that of ionic and covalent interactions. This means that high temperatures can melt the SAM and displacement reactions can occur if competing thiol groups are present. Although not currently widely available Carboxylic acids are another important class of tail group. These can be used to form SAMs on metal oxides, such as Al2O3 [4] or Ni [5]. 3 Sulfur also binds strongly with many other noble metals, such as platinum and silver [4]. 2

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commercially, research groups have developed rather novel monomers in-​house. For example, Frederix et al. [3] made three-​legged monomers, which are much harder to displace. These monomers are particularly useful when thiol (or disulfide) groups will be present in subsequent reaction steps, as the risk of displacement would be significant otherwise.

3.1.1.2 Chain The alkane chain usually contains 6–​13 carbon atoms for most applications, although longer (polymer brushes) and shorter (primer) chains can be used. The composition of the chain is usually chosen to match the solvent: either organic or aqueous. Oxygen-​ containing chains are more polar and disperse better in polar (e.g. ethanolic or aqueous) solutions. The solubility of hydrocarbons in polar solvents decreases with increasing length, and solvents like hexane or acetonitrile may be required or mixed with a preferred solvent. Longer chains may even be a mixture of a hydrocarbon (usually toward the tail) and polyethylene glycol (PEG) (usually toward the head). Such a construction is similar to lipids (or soaps), which have a polar and non-​polar end. Recently, photocleavable chains have emerged commercially and provide an alternative way to produce patterned SAMs. This idea will be discussed further in Section 3.1.4.

3.1.1.3

Head Groups The head group is the business end of the SAM: it is the functional group that will be exposed for further reactions. Almost all major reactive groups are available commercially (except those that react directly with thiols, such as epoxides and aldehydes), but we will focus on the most common. Hydroxyls: These groups are often used to provide a hydrophilic surface/​coating and can be used to reduce non-​specific binding (bio-​fouling) [6]. These are especially useful in mixed SAMs (see Section 3.1.2) since they are relatively inert. That said, if one insists on linking to a hydroxyl, it can be done. The difficulty arises from the fact that the hydroxyl moiety is a poor leaving group.4 To form a reactive intermediate, we can either protonate the hydroxyl or add a molecule such as p-​toluenesulfonyl chloride (Figure 3.4). An SN2 reaction5 is now possible. Given this complexity, it is often easier to convert the hydroxyl to a more familiar/​ reactive group. It is relatively easy to oxidize the group to an aldehyde or carboxylic acid. For instance: 1. Potassium permanganate (KMnO4) and potassium dichromate (K2Cr2O7) will oxidize an alcohol (hydroxyl) all the way through to a carboxylic acid (Figure 3.5). 2. Pyridinium chlorochromate (PCC) will only oxidize a primary or secondary alcohol to an aldehyde or ketone, respectively. However, the high toxicity of PCC means that aldehydes are often made using stronger oxidizing agents and distillation used to collect the aldehyde before it is oxidized further. As a rule of thumb, the happier a group is to exist freely (in a particular solvent), the easier it is to displace. An SN2 reaction is a nucleophilic substitution in which the rate determining step involves two reagents.

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Figure 3.4  Hydroxyl groups can be converted into better leaving groups with acid to protonate

them to water, or with a base and p-​toluenesulfonyl chloride. Used, with permission, from [9].

Figure 3.5  Oxidation of a primary alcohol by potassium permanganate, first to an aldehyde/​

hydrate and then to a carboxylic acid. As the permanganate is reduced, it changes color from purple to green and may precipitate as MnO2. Used, with permission, from [9].

Carboxylic acids: Amide bonds, also known as peptide bonds, are a preferred conjugation route and are among the most important conjugation to life6 as we know it. Amino acids are the fundamental building blocks of the peptides (proteins) built inside cells; it is DNA that determines the order of these amino acids (Figure 3.6). Chemically, an amide bond is formed in a condensation reaction (water is removed) between a carboxylic acid and primary amine. In cells, enzymes are used to promote the reaction, but in the test tube the chemist must use auxiliary chemicals.7 There are standard protocols to carry out this reaction in both aqueous and organic solvents. A family of reagents, called carbodiimides, have a R1-​N=C=N-​R2 signature that couples to the carboxylic acid, forming a (very) reactive intermediate. Since this intermediate will react with even weak nucleophiles (such as water), we usually add a catalyst to form a more stable reactive intermediate, such as an N-​hydroxysuccinimide (NHS) group (Figure 3.7). Amines: Nucleophiles like primary amines are reactive with several other functional groups, such as epoxides, aldehydes, NHS esters, and activated carboxylic acids. To avoid repetition, these reactions shall be discussed under each individual subsection rather than here. It is useful to note, however, that basic conditions can deprotonate the amine (NH2 –​ [H+] → NH–​) and increase the rate of nucleophilic attack.

Hydrogen bonding and phosphodiester linkages are crucial for DNA (see Figure 3.2). This is also the case with nucleotide chains: while biologically the chain grows from the 5’ to 3’ direction, the chemist will build the chain in the 3’ to 5’ direction using a complex cycle. This process has been automated in machines called synthesizers, so it is now possible to buy relatively short “designer” oligonucleotide sequences from companies such as Sigma Genosys.

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Figure 3.6  Amino acids, so called because of their common amine and carboxylic acid groups,

use enzymes to form amide/​peptide bonds. There are 20 amino acids, all with the same backbone. The differences are the groups attached to the amine carbon atom. Alanine, the second simplest amino acid, has a methyl group in this position.

NHS esters: These groups are the pre-​activated form of carboxylic acids and will react readily with nucleophiles like primary amines. Since these groups are labile and prone to hydrolysis, they must be used quickly and carefully: they are not recommended for long-​term storage. An example of the displacement reaction with a primary amine and water can be seen in Figure 3.17 in Section 3.2.2. Biotin: We now begin to cross over from chemical binding to biological recognition. This is “key and lock” territory: biotin (also known as vitamin H or B7) is the key and the locks that it fits are the proteins streptavidin and/​or avidin; the latter is found in egg white. This system is often used since the carboxylic tail on biotin means it is easy to attach, a process known as biotinylation, and it binds very tightly (dissociation constant of the order of 4 × 10–​14 M). Streptavidin is less water soluble than avidin, but is preferred due to reduced non-​specific binding. Both proteins have four available keyholes for biotin, so can be used to amplify (triple) the labeling of assays, as suggested in Figure 3.8.

3.1.2

Mixed SAMs It is often important to optimize the spacing between reactive groups, considering the rather large size of the proteins/​oligonucleotides, etc. to be attached. If these larger molecules are packed too densely, the resulting surface will not be porous enough for molecules to traverse and find their binding sites, as illustrated in Figure 3.9. For this reason, it is often preferred to only have a minor incorporation (2–​10%) of the actual binding monomer in the SAM. The other monomer, which we will refer to as the filler SAM, also plays an important role. It should have a shorter chain that can easily access and fill the available surface sites, which pushes the binding SAM upright (Figure 3.10). Its head group should not interfere with the reaction, but can also be advantageous, for instance, in discouraging bio-​fouling. Unfortunately, such an approach is a bit of a black art, and to simply assume that a 25:1 ratio of filler to binding SAM in solution will produce such a ratio on the substrate

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Figure 3.7  Reaction mechanism of DIC-​mediated peptide bond formation, with the HOBt

catalyst: The double-​bonded oxygen of the carboxylic acid group (1) attacks the central carbon of the carbodiimide (carbodiimides all have the N=C=N signature) (2). This forms a short-​lived amine-​reactive complex (3). The HOBt catalyst (4) converts this intermediate into a much longer lived complex (5), releasing urea (6) as a (DMF soluble) by-​product. Reaction with an amine group (7) forms the amide bond (8) recycling the HOBt catalyst. Reproduced, with permission, from [9].

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Probe ss-DNA

Biotinylated target DNA

Streptavidin

Biotinylated Fe3O4@Au nanoparticles

GMR sensor Figure 3.8  Biotin and streptavidin being used in a sandwich-​style assay to increase the reporter

signal.

Figure 3.9  SAM problems: Even with one type of monomer, there are many possible interactions

that can prevent the formation of an ideal flatmonomer.

is naïve. The stability of the monomers in the solvent plays a crucial role; with different length chains and different head groups, solubilities can be vastly different. It is now quite common to use a two-​step approach, where the binding monomer is first allowed some time to attach before incubation with the filler monomer completes the SAM [7,8]. For example, a two-​step protocol that has been shown8 to give a 3:1 ratio of spacer to binding SAM is as follows: 1. Incubation with the longer (binding) monomer: 50 μM 11-​mercaptoundecanoic acid in ethanol for 2 hours at 40 oC. 2. Incubation with the shorter (filler) monomer: 50 μM 6-​mercaptohexanol in ethanol for 3 hours at 40 oC. Using in-​flow measurements with an electrochemical quartz crystal microbalance, as reported in [9].

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Figure 3.10  Mixed SAM: Even a perfect SAM may not be ideal for binding, steric hindrance and close-​packing can result in less chemically active surfaces. Mixed SAMs offer tighter control on these conditions and can include additional (e.g. hydrophobic) surface properties.

3.1.3

Fluorescence Quenching/​Enhancement Another property that makes gold a natural choice for a surface coating is its interaction with fluorophores, as it is able to both inhibit and enhance fluorescence through resonant energy transfer, depending on the separation and curvature [10]. A typical assay that makes use of this property might consist of a strand of DNA that is bound to the gold nanoparticle at one end, with a fluorophore attached to the other end. The sequence is chosen so that its target-​specific section is flanked by two self-​complementary sections. In the absence of the target sequence, these flanking sections hybridize, forming a hairpin structure (Figure 3.11). This results in the fluorophore being held close to the gold surface, which quenches its fluorescence. When the target strand hybridizes, this breaks the hairpin and produces a linear structure, which will now fluoresce.

3.1.4

Chemical Suppliers Pre-​mixed solutions are available from NanoThinksTM, (e.g. 5 mM undecanoic acid in ethanol). Besides the main chemical suppliers (Sigma-​Aldrich, Fisher, Alfa Aesar, etc.), there are a number of companies that specialize in SAM materials, such as Ambion, Sensopath (www.sensopath.com), and Prochimia (www.prochimia.com)  –​some will even make custom molecules (if they can find a way to do this).

3.1.5

Aside: Classical Photolithography Photolithography is used to transfer a pattern from a mask, with feature sizes as small as a micron, to a photoresist. The photoresist is then used as a mask or a mould to deposit

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Figure 3.11  (Left) Hairpin structured DNA keeps the fluorophore close to the gold surface, which quenches its fluorescence. (Right) Upon hybridization of the DNA, the fluorophore is separated from the gold surface and fluorescence is no longer inhibited.

further structures, such as metallic strip lines for circuitry or multilayer structures for sensors. This is a very widely used and well-​developed technique, so there are a plethora of different photoresists available with different properties; here we will describe only the basics, schematically illustrated in Figure 3.12. A photoresist is a mixture consisting of a monomer, photocatalyst, and solvent. It can be spun-​coat to a range of thicknesses (the higher the rpm, the thinner the resulting film) from a few nanometers (e.g. LOR and PMMA) to several microns (e.g. SU8, AZ-​series). Once spun, the job of the solvent is done and it is removed by a quick bake on a hot plate (e.g. 60 s @ 110oC). The spun photoresist is brought into close contact with a pre-​fabricated mask, and then irradiated with UV (280–​400 nm) or DUV (100–​280 nm) light for a set time.9 The setup costs for photolithography are very high, and will require a clean-​room environment with yellow light (to exclude background UV). The cost of a mask can vary considerably, depending on the requirements. Small features are patterned by e-​beam lithography into a chrome layer, either on glass or quartz. Glass is less expensive, but due to its absorption properties, is not suitable for use with DUV active photoresists. The light activates a chemical (e.g. a photo acid) in the photoresist, which then catalyses polymerization in the case of a positive photoresist, thus making the exposed regions more difficult to dissolve. The opposite effect is produced with negative photoresists, where photoactivation causes degradation of the monomer, making it easier to dissolve in solvents such as acetone.

This can be anywhere from a few seconds to several minutes, depending on the particular photoresist and thickness chosen.

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Figure 3.12  Photolithography: Patterning a template for electrochemical deposition. A metallic layer is often pre-​deposited (for release or conduction) onto a silicon or glass wafer; the photoresist is spun-​coated on top (often with a thin adhesion layer) and soft-​baked on a hot plate; UV light and a mask are used to expose selected areas, which causes a chemical reaction to weaken (or strengthen) those areas; and a chemical etch selectively removes the weaker areas. Used, with permission, from [11].

Following exposure, the sample may be baked again to complete the polymerization and remove any remaining solvent. The sample is then immersed in a solvent to remove the softer areas  –​this is known as development. Once developed, the metal layers are deposited somehow (e.g. evaporation, sputtering, molecular beam epitaxy (MBE), and electrochemical deposition), and finally, the remaining photoresist is treated with another chemical, such as acetone, to remove it –​this is called lift-​off.

3.1.6

Alternative Directions Among the more exotic monomers are photocleavable chains, which can be thought of as a type of protecting group (see Section 3.2.2). Their primary purpose, however, is not to be deprotected en masse, but selectively in a pre-​determined pattern. They provide an alternative to the standard photolithography route outlined above, where instead of patterning sections of gold, the SAM is grown on a gold-​coated slide/​wafer and the desired areas are exposed to light to reveal an active group.

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Figure 3.13  SU8, an epoxy resin, can be reacted with primary amines (upper panel) or hydrolysed with acid catalyst (lower panel) [14]. Used, with permission, from [11] and [15].

This is a simplification of the protocol, removing the need for all the photoresists and chemical steps (development and lift-​off), but currently, the cost of the monomer is prohibitive for large-​scale devices. One may also consider the downside of having “wells” as opposed to “hills,” as accessibility can be reduced, especially around the rim. However, since the feature size is linked to photolithography, this is a minor consideration.

3.2

Coupling to Epoxides Epoxides are another useful functional group to consider, especially since they are native in polymer coatings, such as epoxy resins. For instance, the SU8 series of photoresists (positive and UV sensitive) are biocompatible and often used to make microstructures for biochemical coupling (e.g. [11–​13]). Epoxides react well with primary nucleophiles, such as –​NH2 groups, through a ring-​ opening mechanism –​shown in Figure 3.13. It is also possible to convert epoxide groups to hydroxyl groups by hydrolysis (reaction with water), although this reaction requires a little help. Either an acid or a base can be used to catalyse the hydrolysis of epoxides [14, 15], although it is a fairly standard procedure to use a capping reagent, such as ethanolamine (Figure 3.14). Provided the increased chain length and possible side reactions with any other electrophilic groups are not undesirable, the reaction with ethanolamine will produce the same result through an easier reaction. If given a choice of coupling a primary amine to a carboxylic acid or an epoxide, the epoxide is by far the easier route. Due to the extra strain from the three-​membered ring structure, the epoxide is much more susceptible to nucleophilic attack. The reaction

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Figure 3.14  Ethanolamine can be used to cap epoxide groups, leaving hydroxyls. Although ethanolamine has two nucleophilic groups, the primary amine is much more reactive.

Figure 3.15  Conversion of an alcohol to an epoxide using epichlorohydrin. Used, with permission, from [11].

is best carried out in a basic solution (e.g. pH 9), as this will deprotonate the primary amine (Figure 3.15). However, this is a balancing act, since increasing the pH further (e.g. pH 11) will promote hydroxyl groups (including water) to also react strongly [16].

3.2.1

Organic or Aqueous? The complication of hydrolysis can be mitigated completely by switching to an organic solvent, such as DMF. Indeed, most reactions produce much higher yields when carried out in an organic solvent. Figure 3.16 illustrates carbodiimide chemistry in both aqueous and organic solvents as an example. The decision of which solvent to use for a particular conjugation is not always straightforward and may depend on where it fits into the overall scheme. For example, if a proceeding or subsequent reaction requires a particular solvent, then the benefits of an increased reaction yield may be offset by the additional wash steps required to switch between solvents. Efficient washing can require numerous steps, depending on the miscibility of the two solvents, and it is often recommended to first wash into an 1:1 mixture of solvents A and B, then an 1:3 mixture followed by a 1:6 mixture, before washing into 100% solvent B. This is a painful and monotonous process, which will require a centrifuge and mixer (e.g. Whirlimixer™) to resuspend.

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Figure 3.16  Carbodiimide chemistry in aqueous (left) and organic (right) solvents. EDC and sulfo-​NHS are the ionic (salt) analogs of DIC and NHS, respectively.

If each wash step is 95% efficient (i.e. you lose 5% of the sample in the pipettor tips or changing Eppendorf tubes, etc.), then with 14 wash steps, you will lose more than half of your precious material. Another factor to consider is the solubility of the reagents in a particular solvent and this could determine the practicality of the chosen solvent. Long alkane chains (such as those used in SAMs) are not very soluble in aqueous solvents unless they have polar end groups. It is usually possible to find a polar analog to a particular reagent to allow just this choice.

3.2.2 Linkers There is an aspect of conjugation chemistry that is similar to joining cables or electrical piping. We are all familiar with the “male” and “female” terminology, and that if we want to connect two “male” terminated cables, we must use a “male-​to-​male” adapter –​ a component with two “female” ends. This terminology is not used in chemistry because we have more than two possible end groups and there is no hard and fast way to categorize a particular group. That said, if we limit ourselves to a subset of the functional groups, we can build up a rough guide. To not stray too far off subject, we shall call our two sexes “nucleophile” and “electrophile.” (See Table 3.1). Suppose we wanted to connect two electrophiles, e.g. an epoxide and carboxylic acid. A molecule that would serve this purpose would need to have two nucleophilic groups, such as primary amines. A  molecule of this type is known as a homo-​bifunctional linker, and a family of these featuring primary amines is shown in Figure 3.17. Although each linker molecule has the same functional groups, the differing chain lengths and compositions confer different reactivities and solubilities in polar and non-​ polar solvents. As we will see in Section 3.2.3, the chain length and type can also have an important role to play when optimizing sensitivity.

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Table 3.1  Functional groups categorized by their ability to act as an electrophile or nucleophile. The groups become weaker as you go down the table. Electrophile (electron acceptor)

Nucleophile (electron donor)

NHS ester

Primary amine: R-​NH2

Epoxide

Thiol: R-​SH

Aldehyde: R-​CHO

Alcohol: R-​OH

Carboxylic acid: R-​COOH

Water: H2O

Figure 3.17  (top panel) Reaction scheme for coupling a primary amine to a carboxylic acid group via carbodiimide activation. Commercially available homo-​bifunctional cross-​linkers: (i) 2,2’-​ (ethylenedioxy)bis(ethylamine), (ii) Jeffamine ED800, (iii) 1,3-​diaminopropane, (iv) N-​Fmoc-​ cadaverine hydrobromide, and (v) 4,7,10-​trioxa-​1,13-​tridecanediamine 2,2’-​(ethylenedioxy) bis(ethylamine). Image reproduced from [9] with permission.

There is an obvious caveat when using homo-​bifunctional molecules, since unwanted side reactions are possible and particularly likely. Let us say that one end of the linker has attached to the nucleophile on a support as desired. Assuming the support has more than one surface nucleophile, what is to stop the free end from also reacting with the support and forming a closed loop? This is called cyclization, and the answer is usually

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Figure 3.18  The Fmoc protecting group is cleaved by a reaction with piperidine in DMF.

nothing. So what can be done? It turns out there are a number of strategies that can be employed: here we will consider three: 1. The numbers game: Here we use a large excess of the linker molecule, often 10–​100 times equivalence.10 The hope is to outcompete the bound molecules and react with neighboring nucleophiles before the bound linker gets a chance to do this. This method works reasonably well and is economical, if the linking molecule is cheap. It is worthwhile noting that shorter molecules are more likely to cyclize, since they are confined to spend their time nearer to the surface (and the other nucleophiles). 2. Protecting groups (or blockers):  This is where one of the ends of the linker is disguised, this may be because the intended end is actually in the middle of the molecule. For example, Figure 3.18 shows an electrophile-​to-​electrophile linker: only one of the –​NH2 groups is exposed; the other is protected and unavailable for the first reaction. The protecting group (e.g. Fmoc) can be cleaved, in this case with a mild basic treatment (although acid and photo-​absorption (Section 3.1.6) are also common strategies), to expose the second NH2 group, ready for the next reaction. Also see Sample Problems, Question 2. 3. Succinic anhydride:  This is a special case, and is a nucleophile-​to-​nucleophile linker in disguise. The amazing thing about this molecule is that its five-​membered ring structure provides just enough internal strain that it is susceptible to nucleophilic attack, but once the ring is opened, the exposed end becomes an unreactive carboxylic acid. Unreactive, that is, until activated by a carbodiimide (Section 3.1.1.3).

Equivalence is defined as one molecule per binding site.

10

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Figure 3.19  (Left) The homo-​bifunctional linker molecule bis(sulfosuccinimidyl)suberate has two electrophilic sulfo-​NHS groups, which are prone to attack from even weak nucleophiles, such as water. (Right) Succinic anhydride will react once with a strong nucleophile (primary amine), but a second reaction requires the terminal carboxylic acid group to be activated first.

3.2.3 Spacers A spacer molecule should11 be defined as a molecule that simply adds to the length of the carbon chain, while maintaining the same functionality. Such a molecule must have two complementary ends, so one of the reactive groups must be protected. For instance, a PEG spacer might be added purely to increase the solubility in polar solvents. An electrophile-​to-​electrophile spacer may be used to increase the separation from the surface –​for example, to prevent gold from quenching fluorescence. We can always add succinic anhydride, if we want to recover a carboxylic acid, but note that this adds another four atoms to the chain, as seen in Figure 3.19.

3.2.4

Aldehydes/​Tosyl Some other common functional groups that may be available commercially are tosyl and aldehyde groups. Although aldehydes are not a common head group found on

The term is used more loosely to describe a molecule whose primary purpose is to add a chain extension and need not maintain the original functionality.

11

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Figure 3.20  Amine bond formation between an aldehyde and primary amine via imine formation.

commercial SAM monomers because of their high reactivity with thiols,12 they do provide another way to conjugate nucleophiles, such as amines. It is useful to compare the reaction in Figure 3.20 with that using a carboxylic acid, since it is relatively easy to convert one to the other through oxidation (see Figure 3.5) or reduction. The main benefit in using an aldehyde is that the reaction proceeds without the need for auxiliary chemicals (e.g. a carbodiimide). Although, to drive the equilibrium to the right, a dehydrating agent (silica, 3Å molecular sieves) and weak acid, such as sodium cyanoborohydride,13 should be added to convert the Schiff base (imine) formed to a more stable amine linkage [18].

3.3 Quantification Working with nanoparticles requires an element of faith: you know they are there, or at least they were there at the start of the process. Several steps down the line, it may be more difficult to believe that your precious sample has not all been washed away. Occasional centrifugation reassures us that there is a dark speck at the bottom of the Eppendorf tube, and we happily persevere. Now, let us go one step smaller: we now want to carry out a reaction on the surface of the nanoparticles. This may be a new reaction for which we have not established a good protocol, such as the best temperature, time, or concentration to use. It would be easy to optimize these conditions, if we could see the reaction happening, but we are not even sure the nanoparticles are still there, let alone reacting. Feedback is key, but not always available at every step along the way. Sometimes we can see (even without a microscope) that a reaction has occurred: there may be a

The cyclic molecule 2-​hydroxypentamethylene sulfide can be used to form an aldehyde terminated SAM [17]. It equilibrates between its ring and chain forms; the latter is able to grow the SAM. 13 Too much acid will protonate the amine to an ammonium ion, i.e. NH3+, and stop the reaction. The reaction is quickest when half the amine is protonated, pKa = 10. 12

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Figure 3.21  Kaiser test reaction scheme: a primary amine couples to a ninhydrin molecule in a condensation reaction. The N = C bond is cleaved by hydrolysis, and then a second ninhydrin molecule reacts with the intermediate, forming a purple colored complex.

noticeable color change or the nanoparticles become easier to resuspend in a particular solvent (e.g. after PEGylation in ethanol).14 Sometimes you simply cannot tell if a reaction has been successful, but there may be a way to (destructively) test it. Although the test may be destructive, it may also be quantitative, which can be a lot more useful in determining optimum conditions than witnessing a simple color change. A couple of such tests are described below:

3.3.1

Kaiser Test (for Primary Amines) The ninhydrin (or Kaiser) test [19], is a simple colorimetric test for primary amines. The reagents can be bought in a prepared kit.15 The reaction scheme is shown in Figure 3.21, where essentially, two colorless ninhydrin molecules are coupled if a primary amine is present to start the reaction. A colorful (purple to pinkish) complex16 is the result, and although the primary amine is destroyed (converted to an aldehyde) in the process, this

Incidentally, if you have a solution of DNA in water that you want to check is still there, try adding a few drops of ethanol and the DNA will precipitate out –​this is particularly striking if the DNA is also labeled with a fluorophore. 15 Product code 60017 from Sigma-​Aldrich. 16 A colorful molecule can often be recognized from its chemical diagram. The key identifier is a large system of unconjugated pi-​bonds. The more “spread out” the electronic state, the lower its energy state. If the energy gap Eg = hc/​λ between this ground state and an excited energy state corresponds to a visible wavelength of light (λ = 400–​700 nm), the molecule will appear colored. 14

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means that by measuring the concentration of the purple complex, we can determine the number of primary amines in the initial sample.

3.3.2 Spectrophotometry It can be relatively inexpensive to quantify results, and bench-​ top UV-​ visible spectrophotometers can be bought for less than $4,000 (e.g. Jenway 6305 from ColePalmer). Following the Kaiser test, the supernatant should be collected in a volumetric flask17 as any unwashed nanoparticles can interfere with the measurement. The absorption at 570 nm should be compared with a calibration control sample, and Beer’s Law can be used to calculate the concentration: A(λ ) = ε(λ ) ⋅ l ⋅ c,



where the absorbance at a particular wavelength, A(λ), is dependent on the path length, l (cm); concentration, c (M); and molar extinction coefficient, ε(λ) (M–​1.cm–​1). For Ruhemann’s purple, ε(570 nm) = 1570 M–​1.cm–​1 [20]. It is sometimes possible to use spectrophotometry to measure a reaction in situ, although the option to mix and heat the solution at the same time is lost. Such a reaction might be a deprotection step, where the concentration of Fmoc can be measured, since it absorbs strongly at 301 nm (ε = 7800 M–​1.cm–​1).18

3.3.3

Fehling’s Test (for Aldehydes) Fehling’s test is a quantitative color test for the presence of aldehydes, and standard reagents can be bought, for example, from Sigma-​Aldrich:  Fehling’s I  36018 and Fehling’s II 36019. The protocol is to mix equal volumes of the two solutions with the sample and boil for a minute. If aldehydes are present, they cause the reduction of copper (II) ions to copper (I) ions, which then form copper (I) oxide –​a red precipitate.

3.3.4

Tests for Alcohols There are a number of simple color tests to show the presence of alcohols, some of these should be familiar from secondary school chemistry, others are a little more involved. As mentioned in Section 3.1.1.3, potassium permanganate will readily oxidize alcohols, and as it does it will change color. Initially a deep purple, manganese (VII), is reduced to a greenish manganese (V) and eventually a black/​brown manganese dioxide will precipitate, leaving a colorless solution. This is a fantastic test, if hydroxyl groups are the only

Ideally, use a 5 ml flask with five washing cycles. Each cycle consists of: (1) collecting the nanoparticles, which is either done by centrifugation or using a magnet if they are magnetic nanoparticles; (2) removing 1 ml of supernatant using a (micro)pipette; (3) adding 1 ml of fresh solvent; (4) resuspending the nanoparticles through vortex mixing or otherwise. 18 DMF and other organic solvents may dissolve plastic cuvettes, for these solvents one should use non-​ disposable quartz cuvettes. 17

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Figure 3.22  Hydroxyl groups are first converted into tosylates, and then p-​nitrobenzyl pyridine displacement occurs via an SN2 mechanism, which is then converted to a strongly colored salt by treatment with a base. Used, with permission, from [11].

choice, since this oxidizing agent is not selective and will also oxidize aldehydes and hydrates, and even convert alkenes to alkynes –​the latter forms the basis of Baeyer’s test. Another test developed by Kuisle et al. [21] works by first adding p-​toluenesulfonyl chloride to the hydroxyl group (see Figure 3.22) and then performing a SN2 reaction with p-​nitrobenzyl pyridine (PNBP). When treated with a base, a strongly colored pink salt is produced.

Sample Problems Question 1: Loading Level You have bought some commercial polystyrene beads, which have terminal amine groups on their surface. The specification on these beads is as follows:  density 1.05 g.cm–​3, concentration 5% w/​v, size 0.8 μm diameter. You extract a monodisperse sample of 100 μl and perform the Kaiser test, collecting a final volume of supernatant of 5 ml. The calibrated absorbance reading at 570 nm is 0.250 –​calculate the loading level (number of free amines per nanoparticle). What is the surface density of active sites, and how does this compare to an idealized SAM? Question 2: Gold/​SU8 Microcarrier A microcarrier has been designed that has an SU8 side and gold side; this is to allow two different probes (a reference and target) to be attached. Devise a pathway to allow the directed coupling of different oligonucleotide probes to either side; the probes have an NH2 modification on their 3’ end.

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References [1]‌ J. C. Love, L. A. Estroff, J. K. Kriebel, R. G. Nuzzo, and G. M. Whitesides, Self-​assembled monolayers of thiolates on metals as a form of nanotechnology. Chem. Rev., 105:4 (2005), 1103–​69. [2]‌ X. Zhao, Y. Cai, T. Wang, Y. Shi, and G. Jiang, Preparation of alkanethiolate-​functionalised core/​shell Fe3O4@Au nanoparticles and its interaction with several typical target molecules. Anal. Chem., 80 (2008), 9091–​6. [3]‌ F. Frederix, K. Bonroy, W. Laureyn, et al., Enhanced performance of an affinity biosensor interface based on mixed self-​assembled monolayers of thiols on gold. Langmuir, 19:10 (2003), 4531–​7. [4]‌ K. Bandyopadhyay, V. Patil, K. Vijayamohanan, and M. Sastry, Adsorption of silver colloidal particles through covalent linkage to self-​assembled monolayers. Langmuir, 13:20 (1997), 5244–​8. [5]‌ A. K. Salem, P. C. Searson, and K. W. Leong, Multifunctional nanorods for gene delivery. Nat. Mater., 2:10 (2003), 668–​71. [6]‌ M. Kyo, K. Usui-​Aoki, and H. Koga, Label-​free detection of proteins in crude cell lysate with antibody arrays by a surface plasmon resonance imaging technique. Anal. Chem., 77 (2005), 7715–​21. [7]‌ C-​Y. Lee, L. J. Gamble, D. W. Grainger, and D. G. Castner, Mixed DNA/​oligo(ethylene glycol) functionalized gold surfaces improve DNA hybridization in complex media. Biointerphases, 1:2 (2006), 82–​92. [8]‌ K. F. Kastl, C. R. Lowe, and C. E. Norman, Encoded and multiplexed surface plasmon resonance sensor platform. Anal. Chem., 80:20 (2008), 7862–​9. [9]‌ J. Palfreyman, D.  M. Love, A.  Philpott, et al., Hetero-​coated magnetic microcarriers for point-​of-​care diagnostics. IEEE Tran. Magn., 49:1 (2013), 285–​95. [10] P. C. Ray, A. Fortner, and G. K. Darbha, Gold nanoparticle based FRET assay for the detection of DNA cleavage. J Phys. Chem. B, 110:42 (2006), 20745–​8. [11] J. J. Palfreyman, Fabrication and functionalisation of multibit magnetic tags. Unpublished Ph.D. thesis, University of Cambridge (2009). [12] G. Cavalli, S.  Banu, R.  T. Ranasinghe, et  al., Multistep synthesis of SU8:  Combining microfabrication and solid-​phase chemistry on a single material. J. Comb. Chem., 9:3 (2007), 462–​72. [13] R. Marie, S. Schmid, A. Johansson, et al., Immobilisation of DNA to polymerised SU-​8 photoresist. Biosens. Bioelectron., 21:7 (2006), 1327–​32. [14] M. Joshi, R. Pinto, V. R. Rao, and S. Mukherji, Silanization and antibody immobilization on SU-​8. Appl. Surf. Sci., 253:6 (2007), 3127–​32. [15] J. Llandro, J.  J. Palfreyman, A.  Ionescu, and C.  H. W.  Barnes, Magnetic biosensor technologies for medical applications: A review. Med. Biol. Eng. Comput., 48:10 (2010), 977–​98. [16] G. T. Hermanson, Bioconjugate Techniques, 1st edn (New  York: Academic Press, 1996). [17] R. C. Horton, T. M. Herne, and D. C. Myles, Aldehyde-​ terminated self-​ assembled monolayers on gold:  Immobilization of amines onto gold surfaces. J. Am. Chem. Soc., 119:52 (1997), 12980–​1. [18] D. Peelan and L. M. Smith, Immobilization of amine-​ modified oligonucleotides on aldehyde-​ terminated alkanethiol monolayers on gold. Langmuir, 21:1 (2005), 266–​71.

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[19] E. Kaiser, R. L. Colescott, C. D. Bossinger, and P. I. Cook, Color test for detection of free terminal amino groups in the solid-​phase synthesis of peptides. Anal. Biochem., 34:2 (1970),  595–​8. [20] V. K. Sarin, S. B. H. Kent, J. P. Tam, and R. B. Merrifield. Quantitative monitoring of solid-​ phase peptide synthesis by the ninhydrin reaction. Anal. Biochem., 117:1 (1981), 147–​57. [21] O. Kuisle, M. Lolo, E. Quinoa, and R. Riguera. Monitoring the solid-​phase synthesis of depsides and depsipeptides. A color test for hydroxyl groups linked to a resin. Tetrahedron, 55:51 (1999), 14807–​12.

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4 Manipulation

4.1

A Survey of Tweezers for the Manipulation of Micro/​Nanoentities Donglei Fan and Chia-​Ling Chien In recent years, a myriad of research advances have revealed that nanoscale materials exhibit unique electric, magnetic, mechanical, optical, and other properties due to reduced dimensions, large surface areas, and quantum confinement effects. These properties are usually different from and often superior to their counterparts in bulk materials. A broad spectrum of prototype devices with nanomaterials as active components has been demonstrated in nanoelectronics, nanoelectromechanical systems (NEMS), and biomedical applications. However, manipulating and assembling nanoentities into essential functional devices has proven to be very challenging. Recently, a number of manipulating tools in the context of “tweezers” have been advanced that begin to address this. Some of the manipulating methods involve only stationary tweezers, which can hold a nanoentity in a fixed location, whereas others use dynamic tweezers to hold and move the nanoentity.

4.1.1

Optical Tweezers The first experimental demonstration of optical tweezers was reported in 1986 by Steven Chu et al., who received the Nobel prize in physics for this research in 1997 [1]. When a laser beam goes through a high numerical-​aperture objective, it creates a diffraction limited focusing spot. A nearby dielectric sphere, attached with helical DNA molecules, can be electrically polarized by the optical field and subsequently attracted toward the highest region of the optical field gradient to the focusing spot in the narrowest region of the laser beam profile, as shown in Figure 4.1(a). The value of the gradient force Fgrad for a spherical Rayleigh particle is given by [1]



Fgrad = −

nb3r 3  m 2 − 1  2   ∇E , 2  m2 − 2 

(4.1)

where nb is the index of the medium, r is the radius of the trapped particle, m is ratio of the index of the particles and the medium, and E is the electric field of the optical beam. The force can stably trap and move the dielectric sphere with the focal spot. For small displacements (~150 nm) of the trapped object from its equilibrium position, the force is roughly linear to the displacement from the focal point, and the optical trap can be well

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Figure 4.1  (a) A diagram showing a dielectric sphere trapped by the focused laser. Using the

sphere as a probe, single-​molecule biophysics, such as the RNA polymerization mechanism, can be studied, where the RNA is attached on the sphere as it is transcribing on the one-​end fixed DNA template[2]. (b) The gradient and scattering forces received by the dielectric sphere. (Stanford University, Steven M. Block)

approximated as a linear spring [2]. The spring constant depends on the magnitude of the optical gradient, the polarization of the dielectric sphere, and the power of the laser. In addition to the optical-​field gradient-​induced force, the dielectric sphere also receives an optical scattering force along the direction of the laser beam, with an intensity of I0 [1], which pushes the dielectric sphere in the direction of the laser beam and away from the focusing spot, as shown in Figure 4.1(b). Here the scattering force Fscat is given by

Fscat =

I 0 128π 5r 6 c 3λ

 m2 − 1  2  2  ∇E . m − 2

(4.2)

In practice, high numerical aperture objectives (NA > 1.2) as well as nanospheres with optimized diffraction index m and radius r are used to increase the ratio of the gradient force and the scattering force to be more than one. Lasers operating in the infrared region (800–​1000 nm) are used for trapping in order to minimize optically induced damage to biological species [3]. Various micro/​nanoparticles with feature sizes from 20 nm to a few μm can be manipulated. These objects include living biological cells [3], organelles in a living cell [4], lipid vesicles [5], and silica spheres. The application of optical tweezers is not limited only to spheres; recently optical tweezers have successfully been

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Figure 4.2  Integration of SnO2 and GaN nanowires into (a) cross and (b) lattice arrays with

optical tweezers [6].

used to transport inorganic nanowires for integration with functional devices [6, 7], as shown in Figure 4.2. It is worth mentioning that, in addition to trapping particles, optical tweezers that are equipped with circularly polarized laser beams carrying spin angular momentum can also rotate particles with birefringent properties, such as quartz nanorods [8]. Since its first realization, the optical tweezer technique has profoundly impacted single-​molecule biophysics research [2]. It has been exploited to study specific biochemical interactions between the trapped entity and a fixed particle. Both the force and the displacement can be readily measured to understand the interactions, such as that between a kinesin-​coated bead and a microtubule[9, 10], a virus-​coated sphere and erythrocytes[11], and single fibrinogen-​integrin pairs[12]. Optical tweezers have also been applied as a force and displacement transducer to probe the chemical-​ mechanical characteristics of biological events. Significant progress has been made in the understanding of the translocation and force in RNA transcription with optical tweezers, as shown in Figure 4.1(a). The detailed mechanism of translocation, stalling, pausing, and backtracking during transcription have been observed and measured [13–​16]. Moreover, the optically induced rotation of nanoparticles results in a new dimension of single-​molecule manipulation for biophysics research. In addition, torsional strains can be applied to stimulate biochemical responses [8]. Many more advances and applications of optical tweezers in biophysics research have been reviewed [17–​23], which will not be further elaborated in this survey.

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The key advantages of optical tweezers are the feasibility to conduct high precision execution and detection in both distance and force. A resolution of 1 nm in dislocation and a force of 1–​100 pN can be readily executed and detected to investigate single-​ molecule events. However, the optical tweezer technique is greatly limited by the high cost and complexity of the instrumentation. Only one, or at most a few, nano-​objects can be manipulated at a time. The heating effect from the laser and lack of specificity in the manipulation of dielectric particles can be unfavorable for single-​molecule research. Since optical tweezers only hold an object with an optical beam, the manipulation of a nanoentity becomes rather cumbersome, requiring the movement of the optical beam. Most unfortunately, optical tweezers can only manipulate dielectric materials and not metallic nanoparticles; nevertheless, there is a prominent role of the latter in nano optoelectronic devices.

4.1.2

Magnetic Tweezers The principle of magnetic tweezers is straightforward. A  magnetic field can readily align, transport, and rotate magnetic or paramagnetic micro/​nanoparticles, including spheres and nanowires [24–​30]. The magnetic nanoparticles (MNPs) are aligned with the magnetic field and transported in the direction of the magnetic field gradient. The magnetic force Fm for transporting nanoparticles is given by [31]



Fm =

   Vp χeff B ⋅ ∇ B

(

µ0

)

,

(4.3)

where Vp, χeff, and μ0 are the volume of the nanoparticles, magnetic susceptibility of the nanoparticles, and permittivity of the vacuum, respectively. Usually, multiple sets of small electromagnets instead of permanent magnets are employed to apply a specific magnetic field. The nanoparticles can be readily transported in any direction along arbitrary trajectories and can, for example, be used to trace out letters (Figure 4.3(b)) and rotate with controlled chiralities (Figure 4.3(a)) [24, 32, 33]. The forces applied by magnetic tweezers range from 10–​3 pN to 100 pN, with resolution to a few nanometers [2]. Unique applications of magnetic tweezers have been demonstrated in single-​molecule biological research, including studying topology [34], topoisomerases [35], mechanics of biomolecules under torsional stress [36], and enzyme functionality in DNA supercoiling [37, 38]. The flexibility and precision in rotating nanoprobes make magnetic tweezers more advantageous than optical tweezers. However, in this review, we will focus on the application of magnetic tweezers in nanorobotics, that is, transporting colloidal cargo with magnetic nanoentities manipulated by magnetic tweezers. By applying a rotating magnetic field, a magnetic nanowire can be readily rotated. This can be achieved by placing a physical boundary, such as a substrate or a wall, close to the rotating nanowire, as shown in Figure  4.4(a); also, an asymmetrical condition

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Figure 4.3  (a) Transport of a single paramagnetic nanosphere along the trajectory of a word.

(b) Rotation of an aggregate of magnetic beads [33].

can be introduced that changes the low Reynolds number governed reciprocal motion of nanowires into a non-​reciprocal motion and thus results in the propulsion of the nanowires [39, 40]. As shown in Figure  4.4(a), when the nanowire is rotating close to the substrate, the viscous force on the tip of the nanowire close to the wall is much higher than the other tip due to the boundary dragging effect in the vicinity of the wall [39]. Therefore, the velocity of the end of the wire close to the wall is always slower than that far from the wall. The rotation center shifts, resulting in a net lateral transport along the substrate (Figure 4.4(b)). By orienting the rotating plane of the nanowire, it can be transported along an arbitrary trajectory, as shown in Figure 4.4(c). With this technique, the rotary motion of nanowires can be transformed into linear motion and be used to transport a microbead to a desired location, as highlighted in the circles in Figure 4.5(a–​f). As discussed above, in low Reynolds number flow conditions, it is important to introduce asymmetrical boundary conditions to the rotating nanoentities to convert rotary motion into translational motion. In another example, a three-​segment nanowire

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a

(τm ,ω)

Vb

Va

b

(τm ,ω)

Figure 4.4  (a) Rotating nanowires close to a boundary can introduce asymmetry in the rotation

speeds of the two ends of the nanowires. (b) The nanowires can be transported (c) along arbitrary trajectories [39].

motor is designed with a flexible segment (porous Ag) connecting a magnetic (Ni) and a non-​magnetic segment (Au), as shown in Figure 4.6(a) [41]. Under a rotating magnetic field, the magnetic Ni segment can be readily rotated. Due to the flexibility of the porous Ag segment, the rotation of Ni induces a passive rotation of the Au segment, which has a time delay with the Ni segment. This assembly propels the nanomotor forward or backward depending on the relative length of the Au segments, as shown in Figure 4.6(b)–​(e).

4.1.3

Electric Tweezers The electric tweezers technique is based on the simultaneous application of uniform DC and AC electric fields on charged nanowires [42, 43]. In a uniform DC electric field E, a nanowire carrying a charge q experiences an electrophoretic force and reaches a constant terminal velocity v, as given by v = –​ε0εmζE/​η, where ζ is the effective electric potential, εm and η are the permittivity and viscosity of the liquid, respectively, and ε0 is the permittivity of free space. Both the sign and magnitude of the electric potential ζ can be altered by the charge q on the nanowires via chemical functionalization. Under a uniform AC field, as shown by



FDEP = ( p ⋅ ∇) E = Vparticle ε m Re( K ) ( E ⋅ ∇E ) =

1 Vparticle ε m Re( K )∇E 2 , 2

(4.4)

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Figure 4.5  (a)–​(f) Rotating nanowires can transport a microbead from one location to the

other [39].

Figure 4.6  (a) Three segment Au/​porous Ag/​Ni nanomotors. Depending on the length ratio of the

Ni and Au segments in the nanomotors, the rotation of Ni segments with magnetic tweezers can transport the nanomotor in the direction of (b) (c) the Au end or (d) (e) the reverse [41].

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Figure 4.7  (a) Nanowires can be transported by combined AC and DC E fields. (b) The

velocity increases with DC voltages. (c) The nanowires can be manipulated along arbitrary trajectories, such as zigzags, as in the overlapped images. (d) The precision is at least 150 nm, as demonstrated by joining two nanowires tip to tip [42].

where p = Vparticleεm Re(K)E is the effective induced dipole moment of the particle in the E field, Vparticle is the volume of the particle, and Re(K) is the real part of the Clausius–​ Mossotti factor K, there is no net dielectrophoretic force (DEP) to cause any motion of the nanowires, but there is a torque of p × E that aligns the nanowires. In short, the electric tweezers use a uniform AC field to align the nanowires and a uniform DC field to transport nanowires to achieve complete control of the manipulation. Therefore, nanowires can be independently transported in the direction of the DC E field and aligned in the direction of the AC E field. By applying the combined AC and DC E fields sequentially in two orthogonal directions, as shown in Figure  4.7(a), the nanowires with surface charges can be transported along arbitrary trajectories, such as zigzags (Figure 4.7(c)). Here, the AC and DC E fields were aligned in the same direction. Thus, the nanowires were transported along their long axis. The transport velocity increased with DC voltages (Figure 4.7(b)). Two nanowires carrying opposite charges (300 nm in diameter) with initial separation of 185 μm were connected tip to tip by the electric tweezers (Figure  4.7(d)), which indicates that the precision was at least 150 nm. Next, we will discuss a more complicated type of manipulation:  the rotation of nanowires. It is known that a DEP can align nanowires in the direction of the E field [44–​46]. If a rotating E field is generated at the center of a set of quadruple electrodes, nanowires will follow the rotating E field. We have demonstrated this idea by using such an electrode configuration with a gap of about 300 μm and applying a rotating electric field via four AC voltages with sequential 90° phase shifts (Figure 4.8(a)) [47]. The rotating field can drive the freely suspended nanowires, which do not have anchoring points, to rotate as shown by the snapshots taken at 30 fps (Figure 4.8(b)). These Au nanowires were 50 nm in diameter and 5 μm in length, and the applied AC

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Figure 4.8  (a) Schematics of the rotation of nanowires by AC voltages with 90° phase shift

applied on the four parts of a quadrupole electrode [47]. (b) Sequential images at 1/​30 s interval of free rotating Au nanowires (50 nm in diameter, 10 μm in length) at 5 V, 20 kHz. (c) Clockwise and counterclockwise rotation of nanowires. (d) Metallic, semiconductor, and magnetic nanowires, as well as MWCNTs were rotated, all with rotation speeds proportional to V2. (e) The rotation speed of Au reached 26,000 rpm, which is equivalent to that of a jet engine.

potential was 5 V at 20 kHz. There are three significant features of this method of producing a good nanomotor. First, the rotation angle varies linearly with time as the angular velocity Ω is precisely controlled by the AC field (Figures 4.8(c) and (d)). Second, the direction of the rotation can be repeatedly reversed by simply reversing the AC phase shift in Figure  4.8(c). Third, the actuation is instantaneous, that is, nanowires reach the terminal angular velocity instantly with no apparent acceleration or deceleration, and the rotation is instantly stopped when the voltages are removed (Figure  4.8(c)). Nanowires made of all types of materials, including metals, semiconductors, and multiwall carbon nanotubes (MWCNTs), can be rotated. At a fixed frequency, the rotation speed increases with V2 (Figure  4.8(d)). The V2 dependence is advantageous for achieving extremely high angular speed. Au nanowires with a large aspect ratio of about 16 have been rotated by an AC E field at 20 V, 100 kHz and reached a rotation speed of 26,000 rpm, similar to those encountered in a jet engine. This current high rotation speed record for nanoentities is likely to be surpassed (Figure 4.8(e)). Here, we will discuss three applications of electric tweezers, leveraging their high precision, efficiency, and versatility, in biology, microelectromechanical system (MEMS) devices and electronics. With electric tweezers, nanowires functionalized with drugs can be transported following a prescribed path and delivered onto a single cell in the midst of many other living and unaffected cells [48], as shown in Figures  4.9(a) and (b). Multiple nanowires can also be transported to a single cell sequentially to control the dosage of one drug, or the effect of multiple drugs, as shown in Figure 4.9(c)–​(e). Nanowires can also be assembled into MEMS devices, such as nano-​oscillators [45] and nanomotors [47]. As shown in Figure  4.10(a), we designed a nanomotor with a bent nanowire as the rotor, chemical bonding between the kink of the nanowire and the substrate as the bearing, and quadruple microelectrodes as the stator. The nanowire motor in suspension can be driven into rotation by AC electric fields and propels a dust particle on the substrate in a circle in Figure  4.10(b)–​(d). The overlapped image in Figure 4.10(e) shows the trajectory of the dust particle.

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Figure 4.9  (a) (b) The nanowires can be precisely transported onto a selected cell following

any prescribed trajectory using electric tweezers [43, 48]. (c)–​(e) Multiple nanowires can be delivered to a single cell one by one [48].

Moreover, AC electric field-​induced rotation of nanowires is a result of the interaction between the nanowire materials and the external electric fields (E). As a result, the mechanical rotation reflects the intrinsic electronic property of the nanowires, specifically the imaginary part of the Clausius–​Mossotti factor (Im(K)) as given by [49] Im( K ) = −



1 η l 2 ΩC 2 εmr 2 E 2 ,

(4.5)

where Ω is the rotation speed of the nanowires, η is the viscous coefficient, l and r are the length and radius of nanowires, respectively, εm is the dielectric constant of the suspension medium, and C is a constant. From Eq. (4.5) Im(K) can be readily determined from the rotation of nanowires/​nanotubes, as shown in Figure  4.11(a) (rotation as a function of frequency) and (b) (Im(K) as a function of frequency). We note that Im(K) changes from negative to positive with AC frequency, as shown in Figure 4.12. This can be understood from the equation of Im(K), given as [47] Im( K ) =

ε p σm − εm σ p . 2 1 2  ω ( ε m + L ε m − L ε m ) + 2 ( σ m + L σ p − L σ m )  ω  

(4.6)

Because the denominator is always positive, the numerator (εp/​σm –​ εm/​σp) dictates the sign of Im(K). Since ε/​σ is the charge relaxation time τ, Im(K) ∝ (τp – ​τm). When the charge relaxation time in the nanotubes is shorter than that of the suspension medium

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Figure 4.10  (a) Schematic diagram of nanomotors (b)–​(d) snap shots of rotating nanomotors driving a dust particle. (e) The dust particle goes through a rotary trajectory [47].

Figure 4.11  (a) Rotation speed as a function of AC frequency for MWCNT with length of 3.5 μm (squares), 5.6 μm (triangles), 7.2 μm (pentagons), and 9.5 μm (circles). The rotation switch orientations in the range of 10 kHz–​1 MHz. (b) Im(K) of MWCNT can be determined from the rotation of nanotubes with Eq. (4.5) [49].

Figure 4.12 Im(K) changes sign with frequency due to the change of sign of net values of (τp – τm) [49].

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Figure 4.13  (a) Rotation of various nanoentities show distinct (b) Im(K) spectra, which can be used to determine metallicities of materials[49].

(τp < τm), Im(K) is negative, corresponding to the observed nanotube rotation orientation at low AC frequencies. When the charge relaxation time in the nanotubes is longer than that of the suspension medium (τp > τm), Im(K) is positive, corresponding to the switched rotation orientation at high AC frequencies. When τp = τm, at 544 kHz, Im(K) = 0, the MWCNT does not rotate. In this manner, the Im(K) of various nanoentities can be determined from rotation (Figures 4.13(a) and (b)). It is found that metallic nanowires always rotate in one direction from 5 kHz to 1 MHz. However, semiconductor nanowires/​nanotubes such as ZnO, carbon nanotubes, Si, and Ga2O3, rotate in the same direction with Au at low frequencies but reverse to the opposite direction at high frequencies. Insulated nanowires, such as SiO2, always rotate in the opposite direction to Au from 5 kHz to 1 MHz. Previously, the measurement of electronic properties of a nanomaterial required making electrical contacts to it, a process that is arduous and destructive. Here, with electric tweezers, by simply rotating the nanomaterials, we can determine the metallicity from their mechanical rotation in a non-​contact and non-​destructive manner. Very recently, electric tweezers were applied to the assembly of nanosensors [50]. As shown in Figure 4.14(a)–​(f), arrays of nanocapsules consist of Ag/​Ni/​Ag nanowires as cores, silica coating as separation layers, and Ag nanodots on outside layers for surface-​ enhanced Raman scattering (SERS) detection. The nanocapsules were manipulated by electric tweezers and assembled into ordered arrays on patterned nanomagnets due to magnetic attraction between the Ni segments in the nanocapsules and the patterned nanomagnets (Figure  4.15(a)–​(f)). Various chemicals can be detected on the assembled nanocapsules by ultrasensitive and location detecting SERS biosensing (Figure 4.15(g)). In parallel with the electric tweezers discussed above, Edwards et al. developed another version of electric tweezers based on only the DEP [51, 52]. It is known that nanowires are aligned in the direction of the electric field and transported along the direction of the electric field gradient [53]. Assisted by five patterned

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Figure 4.14  Color enhanced scanning electron microscope (SEM) images of tri-​layer nano-​ capsules at (a) low magnification and (b) high magnification. (c) The contrast enhanced image of (b). (d–​e) transmission electron microscopy (TEM) images of a typical nano-​capsule show a fairly uniform distribution of Ag nanoparticles. (f) Arrays of junctions of the Ag nanoparticles < 2 nm [50].

microelectrodes, the electric field and electric field gradient can be controlled independently, which leads toward instant control of the position and orientation of an interesting nanowire captured from a real-​time charge-​coupled device camera. As a result, nanowires can be transported with arbitrary alignment and trajectories. The demonstrated precision of the manipulation is several micrometers and a speed of approximately a few μm/​s by estimation. Au nanowires have been also rotated synchronous with the frequency of the applied electric field, different from the aforementioned approach [54].

4.1.4

Optoelectronic Tweezers Optoelectronic tweezers were recently invented by Professor M. C. Wu at University of California, Berkeley [55]. As shown in Figure  4.16(a), an AC electric field is applied to an indium tin oxide (ITO) glass covered with a photosensitive layer made of amorphous Si and nitride. Then a light pattern is projected onto the photosensitive layer using a digital mirror display, which makes the light illuminated area of the ITO glass conductive. As a result, the DEP due to the AC electric field can be patterned by light illumination. With this technique, a large number of biological cells can be arranged into ordered arrays (Figure 4.16(b)), living cells can be separated from dead cells [56], semiconductor nanowires can be separated from metallic nanowires [56], and living cells can be propelled along a designed path using dynamic optical patterns projected on the substrate (Figure 4.16(c)).

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Figure 4.15  Nanocapsules can be precisely transported and assembled on the nanomagnets with electric tweezers. (a) A 3 × 3 array of nanomagnets fabricated using E-​beam lithography. With combined AC and DC E fields applied in both x and y directions, nanocapsules were transported along prescribed trajectories. such as “stairs” with (b) parallel and (c) transverse orientations. (d) (e) Overlapped snapshots show the assembling process of a nanocapsule, where the nanomagnets were highlighted. The nanocapsules can be maneuvered and positioned at designated positions, showing the high flexibility and precision of the assembling process. (f) An assembled 3 × 3 nanocapsules array. The bright nanomagnets are in the center of the nanocapsules, indicating that the attachment is due to the magnetic attraction between the Ni segments at the center of the nanocapsules and the magnetic layers in the patterned magnets. All the images were taken by reflective optical imaging. (g) From assembled nanocapsules, we have detected various chemicals, including R6G, methylene blue, and BPE [50].

4.1.5

Catalytic Tweezers Catalytic tweezers or nanomotors are based on the catalytic conversion of chemical energy to mechanical energy as a result of the decomposition of hydrogen peroxide fuel to water and oxygen, 2H2O2 → 2H2O + O2 on the surface of automotive nanostructures. Catalytic tweezers require neither complicated external power supplies nor chemical reservoirs to generate the motion of particles because they are self-​propelled in a fuel solution; effectively they have “fuel on board” [57]. Diverse applications of catalytic tweezers in microfluidic systems are also attractive. Despite their simple setup and versatility, the performance, efficiency, and dexterity of catalytic tweezers need to be improved. In addition, the H2O2 fuel solution is toxic, thus hinders its use in biological systems and lab-​on-​a-​chip applications. Furthermore, there are constraints on material selection to build these movable particles. Catalytic tweezers are composed of two segments. One is a catalytic metal segment, such as Pt [58–​65] or Ni [66], where the chemical decomposition occurs and the other is a segment chemically inert toward H2O2, such as Au [58, 63] or silica [65, 66], which results in an asymmetric chemical reaction. While it is apparent that the decomposition generates propulsion, how chemical energy converts to mechanical energy is less

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(b)

ITO Glass Projected Image AC

Glass Substrate Nitride

(c)

Light Emitting Diode

Undoped a-Si:H n+ a-Si:H ITO

DMD Microdisplay

All particles in upper path

Figure 4.16  (a) Schematic setup of optoelectronic tweezers. (b) Manipulation of living biological cells into large ordered arrays. (c) Transport of cells along designed path with the moving of an optical path projecting machine [55].

obvious. Different mechanisms have been proposed to account for the movement by catalytic tweezers. Differential pressure or bubble propulsion and diffusiophoresis have been suggested as mechanisms to explain the motion of a nanoparticle moving away from its catalytic end, that is, Pt [67]. A  particle can be propelled either by oxygen bubbles generated on the surface of a Pt segment or by oxygen diffusion from the surface of a Pt segment to another region due to the oxygen concentration gradient. In both cases, a catalytic nanomotor moves away from the Pt end. On the other hand, an interfacial tension gradient model and self-​electrophoresis are suitable mechanisms to explain the motion toward its catalytic end [57–​59], as illustrated in Figure  4.17. A catalytic nanomotor can be pulled by an interfacial tension gradient due to oxygen generated near the Pt end or driven by an electrophoretic effect initiated from the flux of charges, electrons through a metallic particle, and H+ ions on the outside. For metallic nanorods such as Au/​Pt [59], both the interfacial tension model and self-​electrophoresis are presumed to be responsible for the motion, while Pt/​silica spheres [65, 66] can be understood with the interfacial tension gradient model only because charges hardly flow through insulating particles.

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Figure 4.17  Energy conversion mechanisms of catalytic nanomotors based on (a) interfacial tension gradient and (b) self-​electrophoresis [57].

Further research on different materials has revealed that the performance of catalytic tweezers could be improved. Au/​Pt-​CNT nanorods [60] moved more than seven times faster and Ag75Au25/​Pt nanorods, indicating average speeds of 113.6 μm/​s, which is 11 times faster than Au/​Pt nanorods in 15 wt % H2O2 solution [62]. Au/​Pt-​CNT nanorods reached even higher speeds on the addition of hydrazine into the H2O2 solution. This effect was due to additives, such as CNT into Pt, Ag into Au, and hydrazine into H2O2 solution, enhancing catalytic decomposition even further. In most of the aforementioned cases, the entities move in random directions, whereas directional control is essential for the practical application of this technique. Different researchers have demonstrated the directionally controlled motion of catalytic nanomotors using external magnetic field and magnetic segments embedded in nanomotors. Pt/​Ni/​Au/​Ni/​Au [68] and Au/​Ni/​Au/​Pt-​CNT [69] nanorods were aligned along external magnetic field, which confined their motion in one dimension parallel or perpendicular to the magnetic field. Kline et al. [68] fabricated a striped structure of Pt/​Ni/​Au/​Ni/​Au whose Ni segments had single domains by controlling the thickness to less than 150 nm (Figure 4.18(a)). In the study, nanorods were aligned perpendicular to the external magnetic field by magnetic torque between the magnetic moment of Ni segments formed radially and the external field. Catalytic nanomotors could only move toward a Pt end so that they moved only in the direction perpendicular to external magnetic field. Burdick et al. [60] reported steering Au/​Ni/​Au/​Pt-​CNT nanorods within a microfluidic channel using magnetic field, as presented in Figure 4.18(b). In the study, in addition to directional control, [Co/​Pt]5-​capped silica spheres could be stopped by

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Figure 4.18  (a) SEM image of a Pt/​Ni/​Au/​Ni/​Au nanowire for directional control of catalytic nanomotors [68]. (b) Controlled motion of an Au/​Ni/​Au/​Pt-​CNT nanomotor within a microfabricated channel network [69]. (c) Stop-​and-​go motion control of [Co/​Pt]5-​silica microsphere using external magnetic field [65].

changing the orientation of the external magnetic field to the substrate [65]. Baraban et  al. prepared silica microbeads capped with a magnetic multilayer having perpendicular magnetic anisotropy (PMA), [Co/​Pt]5, and maneuvered them using an external magnetic field [65]. Figure  4.18(c) displays the speed change of a microbead during stop-​and-​go movement with the out-​of-​plane magnetic field. The insets are top-​view images indicating a dark part with a metal cap and a bright part of exposed silica. In the study, when the microbead stopped, the whole particle turned dark, which means catalytic propulsion pushed the bead toward the substrate. Catalytic tweezers are powerful techniques applicable in diverse micro/​nanofluidic systems. Using directional control of functionalized catalytic tweezers, Sundararajan et  al. [59, 70] and Burdick et  al. [69] demonstrated transport and drop off of cargo. In the studies, cargo, such as a polystyrene (PS) bead, was picked up by electrostatic, biotin-​streptavidin, or magnetic binding and delivered to a desired location by catalytic tweezers guided by a magnetic field. Figure  4.19 shows cargo delivered by catalytic nanomotors, including pick-​up, transport, and release. Kagan et al. [63] demonstrated drug delivery. In the study, drug-​ loaded poly-​ d,l-​lactic-​co-​ glycolic acid (PLGA) particles and liposomes were picked up, delivered, and released. Catalytic nanomotors were controlled magnetically and magnetic attraction also worked to pick up particles. Baraban et al. [65] developed a particle sorting technique in microfluidic channels based

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Figure 4.19  Sequential images of a single Au/​Ni/​Au/​Pt-​CNT nanomotor transporting a magnetic PS bead. Lines indicate the route traveled by the nanomotor without and with cargo, respectively [69].

on catalytic tweezers. Catchmark et al. [71] fabricated self-​rotating gears using Au/​Pt heterostructures. In addition to particle manipulation and actuation, the application of catalytic tweezers as sensors has also been reported. Kagan et al. [62] and Wu et al. [72] described motion-​based chemical and DNA detection, respectively.

4.1.6

Acoustic Tweezers Acoustic tweezers are relatively noninvasive to biological objects and applicable to most microparticles regardless of their optical, electrical, or magnetic properties [73]. This technique is biocompatible, requiring low power density, and can be readily fabricated using conventional photolithography techniques. Furthermore, particles can be manipulated rapidly at high speed (up to 1,600 μm/​s), which facilitates high-​ throughput assays in microfluidic devices and systems. In consequence, much attention has been focused on acoustic tweezers, including their application in the development of various microfluidic devices, such as a particle sorter [74] and a microfluidic mixer [75]. Acoustic tweezers are also suitable for manipulating and trapping cells and organs that are hard to manipulate noninvasively by other techniques. However, acoustic tweezers lack precision, so it is challenging to use them to manipulate nanoparticles. The structure of standing acoustic wave (SAW)-​based acoustic tweezers are illustrated in Figure  4.20(a) [73]. Two orthogonal pairs of interdigital transducers (IDTs) are deposited and patterned on piezoelectric substrates, such as LiNbO3. The distances between the fingers of IDTs are not uniform, which enables IDTs to generate a wide range of resonant frequencies. A microchannel is established by a polydimethylsiloxane (PDMS) wall placed between IDTs. Figure 4.20(b) shows how acoustic tweezers transport a particle. The SAW results in a differential pressure field in the fluid, which creates

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Figure 4.20  (a) Schematic diagram of acoustic tweezers with IDTs and a PDMS microchannel. (b) A standing SAW trapping and transporting a particle (a gray dot) as frequency shifts from f1 to f2. (c) Simulated pressure field in fluid induced by SAW. (d–​g) C. elegans transported by acoustic tweezers [73].

acoustic radiation forces. This acoustic radiation force pushes particles to pressure nodes or antinodes, indicated in Figure 4.20(c). As a result, a particle is trapped in pressure nodes or antinodes and, simply by modulating the input signal frequency, particles can be transported to new nodes or antinodes. Since there are two orthogonal pairs of IDTs, particles can be manipulated anywhere on the substrate. Two-​dimensional particle and cell delivery has been demonstrated using acoustic tweezers, and even multicellular organisms like C. elegans have been manipulated by this technique (Figure 4.20(d–​g)) [73]. Transporting a smaller particle, for example, a 10-​μm fluorescent PS bead, is presented in Figure 4.21(a). In addition to the delivery of a particle, cell, and organism, SAW-​based microfluidic particle sorters have also been reported [74]. As illustrated in Figure  4.21(b), particles flowing through the stream can be selectively sorted to either side of the channels by turning the IDTs on and off. It is also possible to confine and focus particles using acoustic tweezers (Figure 4.21(c)) [76].

4.1.7

Plasmon Nano-​Optical Tweezers Conventional optical tweezers are a versatile tool for manipulating micrometer-​sized objects, whereas trapping of smaller sizes remains challenging. In trapping smaller particles several challenges are encountered: (1) the trapping forces decrease rapidly,

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Figure 4.21  (a) Transporting a 10-​μm fluorescent PS bead using acoustic tweezers [73]. (b) SAW-​ based particle sorter [74]. (c) Particle focusing by acoustic tweezers [76].

resulting in a shallower trap; and (2) damping of the trapped specimen decreases due to the reduction of the viscous drag. Both of these effects alter the confinement of the object within the trap and allow inadvertent escape of the object from the trap. It is desirable to overcome the diffraction-​limited focus of a laser to achieve smaller-​scale confinement of light. Recent advances of plasmon nano-​ optics, which exploits the surface plasmon resonances supported by metallic nanostructures, is particularly efficient in controlling light down to the nanometer scale. There are two distinct types of surface plasmon known to exist, depending on the geometry of the metal: surface plasmon polariton (SPP) at a flat metallic film and localized surface plasmon (LSP) at metallic nanostructures (Figure 4.22) [77].

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Figure 4.22  Illustration of SPP and LSP [77].

Based on SPP and LSP, plasmonic microtrapping, nanotrapping with plasmonic antennas, and self-​induced back-​action (SIBA) trapping have been developed.

4.1.8

Plasmonic Micro-​Trapping Because SPPs in a flat metallic film lead to a homogeneous optical force field, trapping at a predefined location of the surface requires patterning the metal to introduce a lateral confinement of the trapping well. In the most popular coupling method, the so-​ called Kretschmann–​Raether configuration, a thin metal layer under total reflection is illuminated through a glass prism. The enhancement factor can be as high as 40. As shown in Figure 4.23(a), optical traps are created due to the confined light on the surface of gold pads. Such optical traps can trap micro-​objects, like PS beads (Figure 4.23(b)) [78, 79].

4.1.9

Nano-​Trapping With Plasmonic Antennas Trapping of sub-​micrometer objects can be achieved by nanostructures supporting LSPs. Of particular interest are plasmonic dimers/​antennas, in which strong field intensity is concentrated in the nanometer gaps. This leads to orders of magnitude smaller particle trapping than can be achieved with plasmonic micro-​trapping. Trapping of a sub-​micron PS bead, tens of nanometers Au nanoparticles, and single quantum dots have all been reported by this approach. Figure 4.24 is an example, showing dimers are able to simultaneously trap and sense 10 nm Au particles [80].

4.1.10

Self-​Induced Back-​Action Trapping Since metallic nano-​apertures rely on the high sensitivity of the aperture transmission to its dielectric environment, the concept SIBA trapping is introduced. The presence of an object within the aperture, where the mode is confined, modifies the effective refractive

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Figure 4.23  Plasmonic micro-​trapping. (a) Electric-​field and trapping potential distribution of gold nanopads, when excited with light. (b) Experimental results of PS beads being trapped to gold pads. Gold pad/​bead size: 4.8 μm [78].

index, hence red-​shifting the transmission spectrum. Using a red-​detuned laser so that the local field enhancement in the aperture gets stronger when the object is trapped, leads to automatic positive back-​action. The first demonstration of SIBA has recently been performed using a nano-​aperture in a metallic film, as shown in Figure 4.25. SIBA effects have lately allowed efficient trapping of 20 nm PS spheres. Recently, a double-​ circular aperture has been used to trap 10 nm-​sized protein [81]. In summary, we surveyed various state-​of-​the-​art nanomanipulation techniques based on distinct force fields, including optical, magnetic, electric, acoustic, and chemical forces. We reviewed the basic principles, manipulation precision, nature, and size of manipulated particles, and various applications to help readers quickly grasp the fast developing field of nanomanipulation.

4.2

Magnetic Drug Delivery Thomas Schneider and Urs O. Häfeli Conventional therapies for the treatment of diseases are based on the administration of therapeutic compounds that reach the target site. These compounds are either directly administered to the target site through a hypodermic needle, or are injected into

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Figure 4.24  As small as 10 nm Au particles can be trapped and detected. (a, b) The electric field is greatly enhanced in the junction of (c) two nanobars for trapping of an Au nanoparticle. (d) The presence of the Au nanoparticle can be detected from the dark field spectrum shift [80].

Figure 4.25  Illustration of SIBA trapping [78].

the bloodstream and transported to the target site by the vascular system. Direct target site administration, for example, the injection of drugs into a tumor, has the advantage that high local drug concentrations can be achieved. However, this method is limited to larger and easily detectable disease tissues and thus excludes, for example, spreading (metastatic) cancer and lesions smaller than a centimeter. By contrast, the administration of therapeutic compounds into the bloodstream addresses the challenge of multiple

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Figure 4.26  Principle of (a) passive and (b) active drug targeting. Passive drug targeting is facilitated by the EPR effect, while active drug targeting relies on molecular forces (i.e. specific binding interaction between surface markers and receptors, or phagocytosis) and/​or physical forces (i.e. accumulation of MNPs by an external magnetic field).

target sites and takes advantage of the vascular system for drug delivery. Unfortunately, this method of drug delivery exposes the whole body to the drug in order to maintain sufficiently high drug levels at the disease site. For some drugs, side effects in non-​ diseased regions of the body will limit the dose that can be given. To achieve higher target tissue doses without undue normal tissue toxicity, two guided approaches of delivering a therapeutic compound to the disease site have been developed: passive and active drug targeting. Passive drug targeting (Figure 4.26 (a)) [82] takes advantage of the enhanced permeation and retention (EPR) effect which occurs when the permeability of the vascular tissue is affected by disease. For example, the inflammation of tissue or the growth of tumors has an effect on nearby blood vessels by increasing the permeability of the endothelial lining (the innermost cell layer of the blood vessel) to macromolecular agents. Rapid uptake of the therapeutic compound in the affected site in combination with the badly developed lymph system in a newly grown tumor leads to high drug uptake and concentration. In contrast to passive drug targeting, active drug targeting employs specific binding to or concentrating of the therapeutic compound at the target site (Figure 4.26(b)) [83]. Specific binding is often accomplished through antibody–​antigen interactions between a therapeutic antibody-​ complex and specific antigen or receptor moieties in the diseased tissue. Both drug targeting methods can be accomplished with nanoparticles, nanometer-​sized particles that contain the therapeutic agent and can be used for targeting both by passive and active means. Actively targeting nanoparticles are functionalized with targeting molecules (e.g. ligands, antibodies), are designed to be stable under physiological conditions, and effectively become vectors for drug delivery [83]. Physical forces can further enhance active targeting, with the best example being the use of MNPs. Drug targeting and retention at the target site are possible by using an

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external magnetic field [84]. This method is called magnetic drug targeting [85] and is an elegant way to address the major challenges of conventional therapies by retaining and concentrating the compounds at a desired site. In this chapter, we will take a closer look at the background of magnetic nanocarriers and the challenges for magnetic drug targeting as a powerful active drug targeting method.

4.2.1

MNPs as the Base Unit for Magnetic Drug Targeting The term nanoparticle covers a broad variety of compounds sized less than 1 μm that range from molecule clusters in the form of hollow shells filled with liquid, such as vesicles and micelles, to solid aggregates of polymers, metals, and metal oxides. Metals that exhibit superparamagnetic and ferromagnetic properties are iron, cobalt, nickel, and their alloys. These materials are used in their oxidized states to avoid toxicities from charged metal ions. Nanoparticles made from these materials are termed MNPs. Placed near a magnet, MNPs are magnetized and attracted toward the area with high magnetic fields and field gradients. The reason for this behavior lies in the composition of the material. At the microscopic level, the magnetic metals are divided into tiny regions or magnetic domains that are of the order of tens of nm and are separated from each other by domain walls. In each domain, the magnetic dipoles (or spins) are aligned and the direction of magnetization is the same, while between domains, the direction of magnetization is not the same and appears to be random. When bulk iron is not magnetized, the different magnetic domains (and different directions of magnetization) help the bulk material to minimize its internal energy. When the material is placed into a magnetic field, the domains align with the external field and thereby render the bulk iron magnetic. Once the bulk iron is removed from the magnet, the magnetic dipoles in the domains realign to their original states. However, some domains retain their magnetized state and the bulk material remains magnetic. The realignment process is time dependent and is represented by a magnetic hysteresis. For bulk iron, the hysteresis follows a loop as the realignment of the domains lags behind the removal of the external magnetic field. For biomedical applications, however, the magnetic material and especially MNPs require a material to exhibit superparamagnetic behavior which shows no hysteresis. This means that the spin alignment of the domains follows the direction of an external magnetic field without delay and the material has no residual magnetism after removal of the field. This behavior is beneficial for biomedical applications as it helps to prevent the agglomeration of particles. The creation of homogeneous MNPs that are smaller than a single domain (and thus exhibit superparamagnetic behavior) and are stable for long periods of time is challenging. Typical high-​yield syntheses of MNPs [86] include wet chemical methods from iron salt solutions through co-​precipitation or through thermal decomposition in organometallic solvent solutions (see Chapter 1). Other methods, such as micelle synthesis and hydrothermal synthesis, have been shown in recent years to be versatile alternative methods [87]. Among the various MNP synthesis methods, co-​precipitation is the easiest and fastest method. MNPs can be created by co-​precipitation within a few minutes to a few hours and under ambient reaction conditions starting from basic Fe2+/​Fe3+ salt solutions.

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The type of starting material (i.e. iron chlorides, sulfates, or nitrates), the ionic iron ratio, as well as the ionic strength of the media and the reaction temperature directly impact particle size and shape. MNPs made by co-​precipitation typically have polydisperse size distributions and are reported to have saturation magnetizations of 30–​50 emu g–​1 [86]. The MNPs created by this method are not stable and oxidize easily. Thermal decomposition requires organometallic compounds dissolved in high boiling solvents under inert conditions and elevated temperatures [88, 89]. MNP synthesis by this method is more complex and can require several hours to days to complete. The MNPs made by thermal decomposition can be highly monodisperse with core particle sizes ranging from as small as 2 nm to 50 nm [90, 91] and easily oxidize once they are removed from the inert reaction conditions. Similar to co-​precipitation, the reaction conditions in thermal decomposition (temperature and time), as well as the starting ratio of the organometallic compounds, surfactants, and solvents directly impact the size and morphology of the particles. Compared to co-​precipitation, much higher saturation magnetization of the MNPs can be achieved by thermal decomposition, with values as high as 83 emu g–​1 reported for 16 nm Fe3O4 particles [89]. Newer methods for MNP synthesis, such as the micelle microemulsion technique, are as challenging as thermal decomposition and produce fairly polydisperse particles. The particle size in this method is controlled mainly by the molar ratio of water and surfactant of the water-​in-​oil suspension and allows a large dynamic range in particle sizes. By contrast, hydrothermal synthesis is based on liquid–​solid solutions and the particle synthesis is the result of a phase transfer at high temperatures and high pressures over prolonged times (hours to days) [87]. MNPs created by hydrothermal synthesis are reported to be very narrow in size distribution and to have diameters as small as 9.1 nm [87], but larger (up to 800 nm) ferrite MFe2O4 microspheres have been reported as well [92]. The saturation magnetization of MNPs created by this method ranges from 53.3 to 97.4 emu g–​1 for Fe3O4 [93]. Laser pyrolysis is another alternative method that gives rise to high mass throughput in the creation of ultrasmall MNPs with narrow size distributions (2.5 ± 0.5 nm [93]). The saturation magnetization of these MNPs is relatively low, up to 60 emu g–​1 [94], and appears to decrease with increasing particle size. Independent of the method used for MNP synthesis, additional steps are required to prevent particle aggregation. These steps include the addition of stabilizers, the coating of the MNPs with organic shells, or gentle oxidation of the particles to create a protective shell around the MNPs. The type of core material and coating can directly affect the final application of the MNPs. The coating of MNPs is crucial for surface functionalization to targeting moieties (i.e. functional group) and drugs, as discussed below. Coated MNPs can also be incorporated with therapeutic compounds in larger polymer nanoparticles or microspheres to form magnetic drug carriers (MDCs) useful for active magnetic drug targeting.

4.2.2

Biocompatibility of MNP for Use in Vivo When MNPs are used to deliver therapeutic drugs directly or as part of larger carrier particles, it is essential to determine their bioavailability, biodegradability,

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biocompatibility, and biodistribution, as well as that of their components (drug, targeting moieties, and matrix or coating materials). The bioavailability of a drug is defined as the ratio between the injected drug and the amount of drug that reaches the systemic circulation. For drugs encapsulated into or carried by particles, this definition can be extended to the relative amount of unchanged drug that reaches the target site. Release of the drug is complex and includes diffusion, (enzymatic) release, and degradation of matrix materials. The bioavailability of drugs is therefore often directly dependent on the biodegradability of the polymers used to form the MDCs [95]. The biocompatibility or toxicity of MDCs often depends on their degradation products and other released molecules that include solvents or materials used during MDC/​particle synthesis, and accumulate over time in susceptible tissues. Of particular interest is the composition of the MNPs that commonly include cobalt, nickel, and iron. The metals are typically used in their oxidized states as charged metal ions may cause unwanted toxicities. Iron oxides remain the core material of choice in MNPs for biomedical applications, although other transition metals have been proposed and used [96]. The choice of iron as an MNP material is due to its natural presence in the human body at about 4 g, its natural biodegradation in the human body within two to six weeks and its subsequent recycling by the body and use in the synthesis of new red blood cells [97]. Independent of the magnetic material, the toxicity of MNPs or MDCs and their components needs to be assessed first in vitro with the help of cell viability (e.g. 3-​(4,5-​dimethylthiazol-​2-​yl)-​2,5-​diphenyltetrazolium bromide (MTT) assay) and other toxicity (e.g. lactate dehydrogenase (LDH) assay) tests before their biocompatibility is confirmed in vivo. For more details on how to perform these toxicity tests, see, for example, Hafeli et al. [98] and Reddy et al. [99]. Biocompatible MDCs and MNPs are then further evaluated in biodistribution studies to assess their in vivo fate. The distribution of particles that do not degrade can be assessed post mortem by measuring the composition of the different organs and tissues. To more dynamically and less invasively measure the particles’ in vivo distribution, they can be investigated by susceptibility measurements of magnetic materials in tissue [100]. Other methods measure indirectly the particle’s influence on T1 and T2 relaxation times with the help of magnetic resonance imaging (MRI; T1 and T2 relaxation times are measures of the spin of molecules inside the body after excitation by the magnetic field). Another method employs radiolabeling of the particles before injection and subsequently assessing the quantitative distribution of the radioactive isotope (e.g. 123I, 111In, 99mTc, 124I, 68Ga) with the help of single photon emission computed tomography (SPECT) or positron emission tomography (PET) (Figure 4.27). The latter methods are very elegant, but indirect, as they rely on the stability of the connection between the particle and radiotracer. A crucial factor for biocompatibility and biodistribution of the MNPs and/​or MDCs is not only their magnetic core material, but also their surface coating. Following synthesis, MNPs are generally coated with polymers (e.g. polysaccharides, such as dextran), which help to reduce particle agglomeration and provide functional groups for further surface functionalization (see Chapter 2). Investigations into the in vivo effects of the surface coatings in native or functionalized form are best done early during proof

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Figure 4.27  Single-​photon emission and MRI with hybrid nanoprobes. The SPECT/​CT image (a) shows the preferential uptake of 111In-​mAbMB into A431K5 tumors (mesothelin-​positive) compared with A431 (mesothelin-​negative) tumors in severe combined immunodeficiency (SCID) mice. (b–​d) shows the T2-​weighted axial magnetic resonance images at preinjection and 24, 48, and 72 h postinjection time points for A431K5 xenograft tumors of SCID mice, injected intravenously with 15 mg/​kg bodyweight iron equivalent of 111In-​mAbMB-​superparamagnetic iron oxide nanoparticles (hybrid nanoprobes). The inset in (d) represents the autoradiographic image of a 20 μm tumor section obtained from the corresponding tumor. CT: computed tomography; SPECT: single-​photon emission computed tomography. (a) Reprinted from [101], Copyright (2011), with permission from Elsevier; (b-​d) Reprinted from [102], Copyright (2012), with permission from Elsevier.

of concept experiments. While cell toxicity experiments (see above) are easy to perform, it is difficult to judge how representative they are for the successive in vivo studies and human clinical trials. A recent Ph.D. thesis, for example, has shown that the proteins present in vivo seem to adhere to MNPs very rapidly, resulting in altered biodistribution and cytotoxicity profiles [103]. In fact, the sometimes observed toxic effects in vitro are in general less pronounced or completely missing in vivo. Knowledge in this area is still very limited, and results from large European studies into the effects of MNPs on the human body are still a few years away (e.g. the NanoTOES project in the European Union Seventh Framework Programme).

4.2.3

Functionalization of MNPs for In Vivo Drug Targeting Magnetic particles distribute in the body mainly to the liver and spleen. Extending their blood circulation time is often attempted with polymer coatings (e.g. poly(ethylene

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Figure 4.28  (a) Conceptual sketch of a functionalized MDC particle. The core matrix is functionalized with different ligands. (b) Sketch of an MNP with a schematic representation showing the coating of the metal oxide (MeOx) core. (c) TEM images of self-​organized Fe50Pt50 nanoparticles that show localized honeycomb-​like and hexagonal close-​packed structures (shown schematically in (i) and (ii), respectively). (c) Reprinted from [113], Copyright (2004), with permission from Elsevier.

glycol)). However, an even more exciting method to increase their concentration in the target tissue is to functionalize their surface with antibodies (size 10  nm, 150 kDa), aptamers (size 1 nm, 10–​15 kDa), peptides, and other small molecules (Figure 4.28). Magnetic micro and nanoparticles functionalized with antibodies are also known as immunomagnetic colloids and have been successfully commercialized for more than two decades. Life Technologies (Dynabeads®), Miltenyi Biotech, Stemcell Technologies, and BD Bioscience are among the many commercial providers of specialized immuno-​ conjugated magnetic particle products that are used in research and pre-​ clinical applications. The advantages of using these commercial products include the wealth of established protocols for bioconjugation and protocols for the detection, separation, and enrichment of immunomagnetically labeled tissues [104, 105]. Among the disadvantages of conjugating antibodies to MNPs is the low binding efficiency of antibodies due to their large size when compared to the MNPs and the target moiety. Difficulties in conjugating antibodies with MNPs and reducing non-​specific binding can be overcome by the use of newer Fc binding peptides [106], which target the fragment crystallizable (Fc) region at the tail region of the antibody, or other antibody fragments. Other strategies include the binding of antibodies covalently through reactive amine groups in the antibody’s fragment antigen-​binding (Fab) domain [107] or by immobilizing the protein [108–​110]. Some research studies have indicated the feasibility of a covalent bond after unspecific interactions facilitate rotation of the antibody at the particle’s surface before the binding occurs [111]. MNPs have also been used as molecular probes for

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bimodal MRI/​SPECT imaging by combining antibody functionalization and conjugation to radioisotopes [102, 112]. A potentially more tailored approach to antibody conjugation is the use of RNA aptamers to target specific small moieties. Aptamers are small molecules that consist of single stranded nucleic acids. Aptamers can be readily synthesized in a test tube and the composition of aptamers is the result of the systematic evolution of ligands by exponential enrichment (SELEX) [114, 115]. The advantage of using aptamers or peptides is that they are similar to endogenous particles (e.g. lipoprotein particles created inside the body) and are cleared quickly from the body. In addition, aptamers penetrate deep into tumor tissue and are more pH, heat, and solvent stable when compared to antibodies [116]. The smaller size of aptamer-​conjugated particles results in longer blood circulation half-​life and elimination rates, and an overall improved biodistribution. The aptamers used in practice today are mostly synthetically designed and bound to nanoparticles through conventional binding strategies (e.g. PEGylation or streptavidin-​ biotin and Au-​thiolated bonds). In recent years, aptamer conjugates have been used for the imaging and drug targeting of prostate cancer cells [117, 118], for targeting small cell lung cancer [119], in combination with MNPs as contrast enhancement [120], cancer cell pattern recognition [121], and as mediators for sensitive cancer recognition and cancer therapy [122]. A summary of the current state of aptamer-​based probes for different imaging technologies (CT, MRI, and PET) can be found in [123]. A different approach for tailoring the synthesis and the functionalization of MNPs is to adopt mechanisms and vehicles that already exist in nature (see Chapter  8). Biomineralization of metal oxides in lipid vesicles was shown by Mann et  al. in the 1980s [124] as a feasible route for the controllable creation of monodisperse iron nanoparticles. This strategy was later applied to in vitro synthesis of magnetoferritin [125]. A more recent approach is to utilize the transfection mechanism of the adenovirus, an active and deliberate introduction of molecules into cells, and combine it with MNPs to create virus-​MNP hybrids that enable drug and gene delivery [126, 127] that can be monitored by MRI. Such gentle synthesis and functionalization methods (i.e. near room temperature and near physiological pH) have also been shown through the immobilization of proteins on MNPs at low temperatures [128, 129] or the immobilization of fluorophores at the particle surface during synthesis [130]. All these methods that have been developed over the past three decades present a powerful tool box for MNP-​ based targeting and detection. However, further enhancements are needed to provide the necessary long-​term stability of the functionalized surfaces of MNPs in physiological conditions and show the applicability in extensive in vivo studies.

4.2.4

Magnetic Drug Targeting So far, we have discussed the challenges in the synthesis of MNPs and different strategies of surface modification to use the MNPs directly as immunomagnetic colloids for targeting, imaging, and separation methods, or as part of a drug carrier complex incorporated with therapeutic compounds in a matrix material to form MDCs. For both MNPs and MDCs, it is challenging to provide directed external magnetic fields that are

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strong enough to lead to successful magnetic targeting. While powerful directed magnetic fields are used in conventional MRI scanners for medical diagnosis, they are not optimized for magnetic drug targeting, are expensive, and require specially trained personnel to run and maintain the equipment. In the following section, we try to describe the physics, potential, and limitations of magnetically delivering MNPs and MDCs to a target site in vivo.

4.2.4.1

Magnetic Drug Targeting Forces The motion MNPs exert when they are subjected to a magnetic field is known as magnetophoresis and is analogous to the electric field-​induced motion termed electrophoresis [131]. The motion of a particle is therefore dependent on the particle’s mass (m) and the magnetic field intensity (B). The magnetic field-​induced motion can then be defined as [132]



 B2   v = mSm = m∇  0  ,  2µ 0 

(4.7)

where the magnetic force field strength (Sm) is equal to the energy density gradient (∇B02/​2μ0, where μ0 is the magnetic permeability of free space). Equation (4.7) assumes that all forces acting on a particle are balanced when subjected to a magnetic field as well as a low Reynolds number flow (Re < 0.1). In addition to the magnetic force acting on a particle, these forces include buoyancy, gravity, and drag force. It has to be noted that the definition of motion induced by a magnetic field assumes unhindered, low viscous flow. Considering Eq. (4.7) and its associated assumptions, it can be seen that there are several limits on the directed motion of a magnetic nanoparticle. The overall mass of a single MNP is small. The MNP mass is directly proportional to the magnetic energy density gradient. This means that in order to achieve a high particle momentum or velocity, a large magnetic energy density gradient is required. However, the magnetic field strength diminishes with increasing distance from the magnet (an inverse squared relationship). As a result, the magnetic force is greatest at the pole of the magnet and rapidly diminishes within a few millimetres from its surface. The interaction of the magnetic field with particles in vivo is therefore limited by the thickness of the tissue separating the target site from an external magnet. Additional forces can further reduce the effect that an external magnet has on MNPs. For example, additional resistance to the particle’s motion is introduced by viscoelastic forces (shear or drag forces) when the particle interacts directly with tissue (i.e. coming into contact with blood cells, rolling along the vascular walls, or passing through them), or when the MNPs interact or bind non-​specifically to molecular moieties of non-​target tissue. Ways to overcome the limitation in hindered motion of MNPs in vivo is to use MNPs with high saturation magnetization and/​or use very powerful external magnets to generate strong magnetic fields at the target site. The use of internal magnets is also possible [133, 134] and has been tested with magnetizable stents [135, 136]. In magnetic targeting, the magnetic field-​induced particle motion discussed above is primarily used for the deflection and capture of MNPs and MDCs transported by the

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vascular system. In order to estimate the particle size that is required to allow capture in vivo, one has to make several assumptions about the environment of the target site, the magnet to be used, and the MNP material. Furlani et al. [137] presented a numerical model to help estimate the forces required to magnetically capture Fe3O4 nanoparticles in a microvessel with a radius (Rv) of 75 μm. This model is based on earlier work by the group of Professor F. J. Friedlaender at Purdue University, a pioneer in the field of high-​ gradient magnetic separation (HGMS) who provided the theoretical framework for the capture of sub-​micron magnetic particles [138, 139]. The model system by Furlani et al. uses a round NdFeB rare-​earth magnet (d = 40 mm, thickness = 35 mm) placed next to the microvessel and assumes a particle mixture with sizes ranging from 150–​600 nm suspended in blood and flowing through the microvessel and past the magnet. The group calculated the particle trajectories for an average flow velocity (υ f ) of 15 mm/​s and for various magnet-​to-​vessel distances (ranging from 5–​25 mm). Additional assumptions were made for Fe3O4 nanoparticles such that the density of the particles was assumed to be 5,000 kg/​m3, with a saturation magnetization of the particle (Msp) of 4.78 × 105 A/​m, and the susceptibility of blood to be that of free space (χblood = χo). The results of the study show that the size of the smallest particle that can be captured increases with increasing magnet-​to-​vessel distance. For example, at a magnet-​to-​vessel distance of 5 mm, all particles that are larger than 150 nm in radius were captured (Figure 4.29(a)). When the magnet-​to-​vessel distance increased to 15 mm and 25 mm, only particles with radius of at least 350 nm and 550 nm could be captured, respectively. The group then presented an equation to estimate the minimum particle radius required for capture in such vessels when the particle trajectory starts at the axis of the microvessel (x0 = 0):

R p,capture =

(1 + α )2 Ms

32 ηυ f Rυ

µ 0 3π

,

(4.8)

where α is defined by the magnet-​to-​vessel distance with a dependence on the magnet size (d = (1+α)Rmag) and η is the viscosity of the fluid. Based on this study, a minimum particle size (Rp) for a given magnet-​to-​vessel distance was calculated and is presented graphically in Figure 4.29(b). The study by Furlani et al. highlights the importance of both the particle size and the size of the magnet used for particle capture. Interestingly, the ability to capture MNPs is not dependent on the distance between magnet and capture site, but the size of the magnet and the starting position of the MNP trajectory. Here, the starting position of the particles is assumed to be well outside the magnetic field, which sets practical limits for the size of the magnet in relation to the size of the (human) body. It could be argued that the size of the smallest MNP to be captured near a tumor, for example, can be well below the lowest Rp,capture shown in Figure 4.29(b). However, as noted by Furlani et al., this has practical limits as the size of the required magnet would be larger than the patient body. The MNPs injection site would be within the magnetic field and thus violate the assumptions for the theoretical capture estimation [137]. The capture model discussed above only addresses the motion and deflection of MNPs in liquid. The magnetic force acting on such relatively free flowing Fe3O4 particles with

r/Rv

(a)

Rp = 350 nm Rp = 300 nm Rp = 250 nm Rp = 200 nm Rp = 150 nm

Blood Flow

0.5

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Captured Particles

Bias Magnet

1.5

Free Particle

(b) Minimum capture radius (µm) 0.0 0.25

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2.0

0.50

0.75

1.00

x0 = 0

x 0 = Rv

1.25 α

1.50

1.75

2.00

2.25 2.50

Figure 4.29  Analytical model of the magnetic capture of Fe3O4 nanoparticles in a microvessel. The model takes into account the dominant magnetic and fluidic forces governing particle motion. (a) Example of particle capturing trajectories for narrow magnet-​to-​vessel distance (α = 0.25). (b) Trend of smallest particle size that can be captured with respect to magnet-​to-​vessel distance when the particle trajectory starts at the vessel wall (x0 = 0) or at the center of the vessel (x0 = Rv). Reprinted (figure) with permission from [137] Copyright (2006) by the American Physical Society.

Inner Wall of Microvessel

z/Rmag

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Axis of Microvessel

–4.0 –3.5 –3.0 –2.5 –2.0 –1.5 –1.0 –0.5

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a radius of 250 nm is reported to be on the order of 10–​2 pN [137]. The forces required to push MNPs through the endothelial lining of an artery and into affected tissue must likely be significantly higher. As stated earlier, in order to increase the magnetic force on the particle, we can either improve the MNP properties or increase the strength of the magnetic fields. While both strategies should be explored, the size of the vascular system near a target size often limits the size and amount of magnetic material that can be employed. As a result, significant advances will have to be made on delivering strong and localized magnetic fields, taking into account the increased availability of powerful low-​cost rare-​earth magnets [140]. The magnetic field of traditional horseshoe magnets attracts magnetic material toward the magnets’ pole pieces. This can be visualized nicely by placing fine iron powder on a piece of paper and holding a magnet close to the opposite side of the paper. The iron powder particles align with the magnetic field lines and concentrate near the pole pieces of the magnet. In addition, the magnetic field is not uniform across the surface of the magnet, and one can readily see that the field is strongest at the edges of the magnet. The attraction of magnetic material by conventional magnets can be used, for example, by implanting the magnet directly at the target site in the form of a magnetic band-​aid, or by use of magnetic stents [141, 142] or ferromagnetic microwires [133, 143] implanted into the vascular system of a tumor. However, in order to direct MNPs and control their motion in vivo, more sophisticated magnetic circuits will need to be used. Strong magnetic fields can be generated in the gap between the pole pieces of a dipole magnet. Such magnets have been used for analytical methods, such as sorting and characterizing magnetic microparticles and immunomagnetically labeled cells [144–​148]. The main limitation of dipole magnets is the size of the polar gap, which typically is in the order of millimeters. In vivo applications with such dipole magnets are thus limited to thin tissues. To overcome the need of pole gaps, one could use Halbach arrays, which force the magnetic field lines to one side of the magnetic array [149–​152]. Halbach arrays consist of several magnets placed next to each other, but are aligned such that the magnetization direction of each magnet changes throughout the array [153]. This maximizes the magnetic field onto one side of the array. However, the field still decreases rapidly with increasing distance from the Halbach array surface, limiting its application to thin tissues. Modified Halbach arrays have also been used to take advantage of the repulsive forces on one side of the pole [154]. Directed magnetic fields have been applied for fundamental studies on the molecular level through the use of magnetic tweezers (see Chapter 5). The working distances in these applications is limited and different methods are needed that will allow the penetration of tissue, such as skin, and enable the interaction with MNPs and MDCs further away from the magnet (i.e. millimetres to centimeters) than what is possible with conventional directed magnetic fields. One commercial method that takes advantage of the Halbach principle is the Niobe® Stereotaxis System [155]. The Niobe® system is used to navigate catheters and guidewires in three-​dimensional space through the use of large and powerful permanent magnets. It received Food and Drug Administration (FDA) approval in 2003 and is used clinically for cardiovascular and gastrointestinal

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applications [155, 156]. It has to be noted that the catheters with a magnet on their tip and guided with the Niobe® system are large compared to MNPs and MDCs discussed in this chapter. Further advances in the research of directed magnetic fields are needed to apply them to whole body therapies in humans. As stated in Eq. (4.7), the magnetophoretic mobility of a particle depends on its mass and the gradient of the magnetic field. High magnetic field gradients have long been explored for separation sciences, and limitations to the capture of iron oxide particles in HGMS with thin wires have been postulated by Friedlaender et al. in the 1980s. For example, when a force magnitude of 0.1 pN is assumed at a thin wire exhibiting a magnetic field, the critical particle size for capture is based on magnetic interactions and is  kT  approximately 40 nm  Dc, p ≡ [138]. The attraction and accumulation of smaller F   particles is governed by a different mechanism, involving static and dynamic interactions [138]. The attraction and capture of small MNPs in an artery is based on open-​gradient magnetic separation principles (OGMS), where the magnitude of the magnetic gradient is limited by the magnet size as shown by Furlani et al. [137]. As a result, one can conclude that the MNP size that can be attracted in an artery by a strong external magnet has to be in the order of hundreds of nm. The typically prepared single superparamagnetic nanoparticles sized between 10 nm and 20 nm can thus not be manipulated significantly or stopped in vivo, and are therefore not useful for magnetic targeting. Many types of MNPs, however, are used in the form of clusters and might be adequate.

4.2.4.2

Progress in Magnetic Drug Targeting and Magnetic Hyperthermia The unique properties of MNPs and MDCs are the foundation of numerous medical applications that have been developed over the past 50 years. These applications can be loosely categorized into applications that take advantage of the magnetic properties of MNPs and MDCs for drug targeting and delivery, but also those applications that take advantage of the controllable heating properties of MNPs. Here we focus on summarizing the recent advances in these applications. Applications that rely on the heating properties of MNPs include magnetic hyperthermia therapy and thermoablation. The heat development in MNPs is based on their hysteresis when placed in an alternating external magnetic field. Multidomain particles exhibit a lag in the hysteresis as a result of a changing external magnetic field. This lag is associated with an energy conversion to heat as a result of the interaction between the magnetic moments in multidomain particles at the atomic level. The heat development in MNPs can be multiplied with the help of rapidly changing external magnetic fields (for a more detailed description see [157, 158]). The most common clinical application is the local tumor treatment at elevated temperatures (up to 48°C) while healthy tissue is spared. A combination of hyperthermia therapy with chemo-​and other therapies is clinically advantageous and is often done. Thermoablation is an alteration of magnetic hyperthermia treatment, producing higher temperatures (up to 58°C), and is often used preclinically in proof-​of-​concept studies. Magnetic hyperthermia recently advanced into reimbursable clinical therapies with the regulatory approval of NanoTherm® [159]. This MNP-​based therapy for glioblastoma

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Figure 4.30  (a) (b) The first prototype malignant fibrous histiocytoma (MFH) therapy system evolved later to the NanoActivatorTM (MagForce.de) and is now approved together with NanoTherm® for clinical treatment of glioblastoma. (c) Example of the treatment of recurrent glioblastoma with MagForce particles to improve survival after first recurrence when combined with radiotherapy. (a) (b) Reprinted from [160], Copyright (2004), with permission from Elsevier. (c) Reprinted from [168], Copyright (2011), Springer Science+Business Media.

was developed by the German company MagForce AG (Figure 4.30). The regulatory approval of this therapy is the culmination of more than a decade of research and clinical studies by a team around Dr. Andreas Jordan at the Charité in Berlin, Germany. A summary of the clinical studies leading to the regulatory approval is given in Table  4.1 and the research into the field of hyperthermia is summarized in several well-​written research articles [160–​168] and recent reviews [158]. A detailed summary of advances in hyperthermia therapies until 2006 was covered by Hafeli [85]. The applications that rely on the magnetic properties of MNPs and MDCs include magnetic drug targeting, magnetic radionuclide delivery, magnetically induced drug release, magnetic induced therapy, and magnetofection. Many of these applications were discussed and summarized in a previous book chapter that focused on the advances with micro and nanoparticles until 2006 [85].

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Table 4.1  Summary of published clinical trials with magnetic fluids for thermotherapy. Target site

# of Type of therapy Magnetic fluid patients

Brain$)

14

RT & TT

*)112 mgFe/​mL 3.8–​13.5

0.1–​0.7 mL/​cm3

[164]

Brain$)

66

RT & TT

*)112 mgFe/​mL 2.0–​15.0

#)

0.5–​11.6 mL

[168]

Prostate

1

RT & TT

* 120 mgFe/​mL 2.5–​5.0

0.2 mL/​cm

Prostate

10

RT & TT

*)112 mgFe/​mL 2.5–​5.0

#)

ST Sarcoma 19

B [kA/​m] Administered volume

)

3

4.0–​14.0 mL

Ref.

[161] [162, 163, 165]

ChT & RHT

All studies were conducted at 100 kHz; $)glioblastoma multiforme; *)iron oxide MNPs (core 15 nm), water dispersion; #)per tumor; B = magnetic field; ChT = chemotherapy; RHT = regional hyperthermia; RT = radiotherapy; ST = soft tissue; TT = thermotherapy.

We will now summarize the advances that were made in these applications since then, with a particular focus on MNPs and MDCs. Magnetic drug targeting is an intermediate method between passive and active drug targeting, where the drugs are encapsulated in or part of the matrix material that forms the MDC. The MDCs are typically delivered to the target site (e.g. a tumor) through the bloodstream, enriched with the help of EPR, and retained by the magnetic field applied to the target area by an extracorporeal or implanted magnet. Drug targeting with MNPs dates back more than 40 years to early in vivo studies conducted with ferromagnetic fine particles by Nakamura et  al. [169]. Similar studies were subsequently expanded by Widder and Senyei to include chemotherapeutic agents, such as doxorubicin, to investigate magnetic drug targeting in terms of localized drug load and treatment efficiency in small mammals [170]. Since then, a variety of drugs have been shown to be viable candidates for magnetic drug targeting, particularly with MNPs. In 2006, we presented a comprehensive list of the different drugs used for magnetic drug targeting based on micro and nanoparticles [85]. A  PubMed search of the National Library of Medicine (NLM) reveals 1,562 entries since 2006 for the search term “magnetic drug targeting.” Of those, 316 studies fall under the search terms “magnetic drug targeting,” “nanoparticle,” “polymer,” and “drug.” A  detailed look at these studies shows, however, that only 88 studies published in the scientific literature truly represent MNPs smaller than 1,000 nm and are used to at least some extent for magnetic drug targeting. Figure  4.31 shows a graphical representation of the PubMed search, while details of the studies are summarized in Table  4.2. It has to be noted that not all journals are represented in the NLM and the actual number of studies conducted and published during that time exceeds the studies shown here. The anthracycline anticancer agent doxorubicin remains among the most prominent model drugs (Figure 4.31(a)) [171, 172], but others such as paclitaxel (PTX) encapsulated into MNPs [173] or conjugated to the MNP surface [173] and methotrexate–​MNP conjugates have been shown (Figure 4.32(b)) [174]. Recently, highly potent drugs, such as camptothecin, have found renewed interest for drug targeting with MNPs [175]. The focus today with this type of MNP application lies in improving enrichment efficiencies

128

Thomas Schneider and Urs O. Häfeli

(a)

20

40

15 Studies

Studies [% of total]

50

30

10 5

20

0 2006 2008 2010 2012 2014 2016 Year

10

Doxorubicin Paclitaxel Carboplatin Docetaxel Mitoxantrone Camptothecin Curcurmin Methotrexate Rapamycin Verapamil 5-FU Beta-glucosidase BCNU Chlorin E6 Ciprofloxacin Cisplatin Clodronate Cyclooxygenase-2 Dexamethasone-acetate Eosin Y Epidermal growth factor (EGF) Heparin HPPH Insulin Ibuprofen Linoleic acid Nerve growth factor Rhodamine 123 (silencing) RNA Serratiopeptidase Small interfering RNA Tamoxifen tPA

0

(b)

60 50 Studies [% of total]

128

40 30 20 10 0

Analytical In vitro

In vivo

In vitro & In vivo

Figure 4.31  Graphical representation of the types and numbers of studies reported in the literature on the topic of magnetic drug targeting. The majority of studies between 2006 and 2014 were conducted in China and the USA (inset in (a)) and nearly half of all studies tested the MDCs in vitro (b). Data based on Pubmed NLM search.

and reducing the side effects through the initial high losses and excretion of the particles through the liver [176]. Nearly half of the studies conducted in the USA and China were in vivo studies, mostly conducted in mice and rats. Most studies worldwide, however, only report in vitro results (Figure 4.32(b)). Combined with polymers, MNPs can form substrates for magnetically induced drug release [177–​179]. With the help of microfabrication techniques, implantable drug loaded carriers were prepared that contained flexible magnetic membranes sealed to a small reservoir containing the antiproliferative drug docetaxel. The magnetic membranes had small, 100 μm2 apertures and were actuated by a battery-​powered electromagnet to controllably release nanograms of the drug over periods of weeks [180, 181].

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129

Table 4.2  Summary of magnetic drug targeting studies between 2006 and 2014 based on PubMed NLM search. Drug

Material, particle size

Study

Country

Ref.

β-​glucosidase

DMNPs (Chemicell), 102.7–​267.3 nm

In vitro, in vivo (mice)

China/​USA

[196]

5-​FU

Fe3O4/​polymer, shell 140–​160 nm

In vitro

Spain

[197]

Fe/​cellulose, 400–​60 nm

Analytical, no bio

Spain

[198]

BCNU

Fe3O4, single domain

In vitro, in vivo (rats)

Taiwan

[199]

Camptothecin

Fe3O4, chitosan capsule 174–​488 nm

In vitro

China

[200]

FeOx, polymersomes 120–​150 nm

In vitro

Germany

[175]

Fe3O4, polymer micelles 50 nm

In vitro

China

[201]

Carboplatin

FeOx, core 25 nm,

In vitro, in vivo

China

[202]

Chlorin E6

FeOx hydrogels 40–​100 nm

In vitro

Iran

[203]

Ciprofloxacin

Fe3O4/​polymer, 9.5 nm

In vitro

India

[204]

Cisplatin

SPION 22–​56 nm

In vitro

Germany

[205]

Curcumin

Fe3O4 & γ-​Fe2O3, shell 99.9–​131.9 nm

In vitro

India

[206]

Cyclooxygenase-​2

Magnevist, Feridex, lipoplexes 162–​304 nm

In vitro, in vivo (mice)

USA

[207]

Dexamethasone-a​ cetate

Fe3O4 482.8 ± 158 nm

In vivo (guinea pigs)

USA

[208]

Docetaxel

SPIONs/​polymer 147 nm

In vitro

China

[209]

SPIONs/​polymer 187.4 ± 32.7 nm

In vitro, in vivo (mice)

China

[210]

NP complex 70.5–​144.7 nm

In vitro

Singapore

[211]

Doxorubicin

Fe3O4/​polymer, 23–​25 nm

In vitro

China

[212]

SPIONs, micelles, 8 nm

In vitro

USA

[213]

Doxorubicin

Fe3O4, core 5 nm

Analytical, no bio

USA

[214]

Fe3O4/​polymer shell, 411–​998 nm

Analytical, no bio

China

[215]

γ-​Fe2O3, 14–​43 nm

In vitro, in vivo (rats)

Singapore

[216]

Fe3O4, micelles, 10–​14 nm

In vitro

Singapore

[217]

FluidMag, 150–​361 nm

In vitro

India

[218]

FeOx, 10 nm; polymer shell 100 nm

In vitro

USA

[219]

FeOx, 8 nm core; oleic acid-​PEG 184 nm

In vitro

USA

[220]

FeOx, polymer vesicles 146–​152

In vitro

USA

[221]

(continued)

130

Table 4.2 (cont.) Drug

Doxorubicin

Doxorubicin, verapamil

Material, particle size

Study

Country

Ref.

SPIONs 10 nm, coated 18 nm, PEG 28 nm

In vitro

USA

[222]

Fe3O4/​polymer shell, core 9–​13 nm

In vivo (mice)

China

[223]

Fe3O4/​Au, 50 nm

In vitro, in vivo (mice, rats)

China

[224]

Hollow Fe3O4, 16 nm

In vitro

USA

[225]

Fe3O4, hydrogels 221 nm

In vitro

China

[226]

Fe3O4, 6 nm, micelles 84.6 ± 6.2 nm

In vitro

China

[227]

Fe3O4, 10 nm, nanocarriers 60 nm

In vitro, in vivo (mice)

USA

[228]

Fe3O4, 20 nm, polymer 25–​75 nm

In vitro

Iran

[229]

Fe3O4, coated particles 76.5 ± 3.1 nm

In vitro, in vivo (mice)

France

[230]

SPIONs, PEGylated 62.3–​68.0 nm

In vitro

France

[231]

SPION/​polymer 236–​265 nm

In vitro, in vivo (rabbits)

China

[232]

SPION, 9.6 nm,

In vitro

France

[233]

Fe3O4, hollow clusters 120 nm

In vitro

China

[234]

Magnetic polymer shell 419.2–​485.1 nm

In vitro

China

[235]

SPION polymersomes, 110 nm

In vitro

Taiwan

[236]

MNPs 9 nm, micelles 51–​79 nm

Analytical, no bio

USA

[237]

Fe3O4, 10 nm, shell 100–​400 nm

Analytical, no bio

Iran

[238]

FeOx 20–​25 nm

In vitro

India

[239]

SPION micelles 68 nm

In vitro

China

[240]

Fe3O4, 15 nm, hydrogels

Analytical, no bio

Iran

[241]

Liposomes 124–​130 nm, Magnevist

In vitro, in vivo (rats)

S. Korea

[242]

Fe3O4, 97–​186 nm

Analytical, no bio

Iran

[243]

FeOx, 55 nm

In vitro

Italy

[244]

FeOx, 138–​200 nm

In vitro, in vivo (mice)

China

[245]

FeOx 6–​8 nm, CS MNPs 80–​100 nm

In vitro

Turkey

[246]

FeOx 12 nm, PLGA 130–​140 nm

In vitro, in vivo (mice)

China

[247]

13

Table 4.2 (cont.) Drug

Material, particle size

Study

Country

Ref.

Curcumin, doxorubicin

Core shell 233.9–​398.7 nm

In vitro, in vivo (mice)

USA

[248]

Epidermal growth factor (EGF)

SPIONS 33.7–​47.6 nm

In vitro, in vivo (rats)

Russia

[249]

Epidoxorubicin

Fe3O4/​PEG, vesicles 60 nm

In vitro

China

[250]

Heparin

FeOx composite, 120 nm

In vitro, in vivo (mice)

S. Korea

[251]

FeOx, 143.8 nm

In vitro, in vivo (mice)

USA

[252]

HPPH

Fe3O4, micelles, 34.8 ± 7.2 nm

In vitro (tumor cells)

USA

[253]

Insulin

Fe3O4, hydrogels, 160–​350 nm

In vitro

China

[254]

Ibuprofen & Eosin Y

Fe3O4,shell 25–​45 nm

In vitro, in vivo (rats)

China

[255]

Linoleic acid

SPIONs, 12 nm, shell 67–​13 nm

In vitro, in vivo (mice)

S. Korea

[256]

Methotrexate

Fe3O4,27.8–​32.6 nm

In vitro

Singapore

[174]

Methotrexate, clodronate

Fe3O4, 4–​10 nm, polymer shell 160–​290 nm

In vitro, in vivo (mice)

USA

[257]

Mitoxantrone

FeOx, 100 nm clusters

In vivo (rabbits)

Germany

[176]

Nanomag-​CLD, 250 nm

In vivo (rats)

Germany

[258]

Fe3O4, PEG complex 35 nm

In vitro

Iran

[259]

Nerve growth factor

fluidMAG-​OS 4113-​1, 100 nm

In vitro

Italy

[260]

Paclitaxel

Fe3O4,263–​7 nm

In vitro, in vivo (rats)

USA

[173]

MNP, 49.5–​50.3 nm

In vitro, in vivo (mice, rats)

China

[261]

Fe3O4, 9.3–​13.7 nm, mesoporous particles 140–​233 nm

In vitro

China

[262]

Fe3O4, folate nanoparticles, 173–​179 nm

In vitro, in vivo (mice)

Taiwan

[263]

Fe3O4,9 nm

In vitro

Belgium

[264]

Fe3O4 13 nm, PLGA 101–​141 nm

In vitro, in vivo (mice)

China

[265]

Fe3O4 with PTBA, 249 nm

In vitro, in vivo (mice)

China

[266]

Paclitaxel, rapamycin, carboplatin

Fe3O4/​polymer, 240–​310 nm

In vitro, in vivo

India

[267]

Rapamycin

Magnetic polymer nanoparticles, 120 nm

Analytical, no bio

Brasil

[268]

Rhodamine 123

γ-​Fe2O3, less than 10 nm

In vivo (rats)

USA

[269]

(Silencing) siRNA

LipoMag (40–​146 nm), PolyMag (217–​1107 nm)

In vivo (mice)

Japan

[270]

(continued)

132

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Thomas Schneider and Urs O. Häfeli

Table 4.2 (cont.) Drug

Material, particle size

Study

Country

Ref.

Serratiopeptidase

Fe3O4, 16.9 nm

In vitro, in vivo (rats)

India

[271]

Small interfering siRNA

Fe3O4,6 nm, PEG complex 79.8 ± 2.3 nm

In vitro, in vivo (mice)

China

[272]

Tamoxifen

Fe3O4, PEG complex 50 nm

In vitro

Iran

[273]

tPA

Fe3O4,10–​30 nm

In vitro, in vivo (pigs)

Sweden

[274]

HPPH = 2-​[1-​hexyloxyethyl]-​2-​devinyl pyropheophorbide-​a; BCNU = 1,3-​bis(2-​chloroethyl)-​1-​ nitrosourea; PTBA = poly(tert-​butyl acrylate).

Magnetic induced therapy has also a high potential for therapies that require guidance, enrichment, and retention of vectors such as stem cells for tissue repair. A promising approach is the use of magnetically labeled cells to increase uptake in specific organs. This new approach is being shown successfully in vivo for eye targeting and therapy of damaged retinas [182–​185]. Magnetofection (see [85]) is another method where MNPs and magnetic fields improve on established techniques. The rate and extent of gene transfection in the cells of targeted tissues is increased when MNPs are labeled or tagged with DNA and introduced to the target site. Strong magnets are then used to drive the magnetic particle/​DNA complexes close to the surface of cells. In an ideal in vitro experiment, this can be envisioned by a tissue culture in a petri dish. The particle/​DNA complexes are introduced in the culture media and a strong magnet is placed below the petri dish to increase the speed at which the particles interact with the cell membranes of the cultured tissue [186, 187]. In a further development, the cells and MNPs with DNA are placed in an oscillating magnetic field, which has been shown to increase transfection efficacy and speed even further [188]. MNPs in combination with methods relying on the interaction with or the measurement of local magnetic fields (e.g. MRI) can be used to track magnetically labeled cells or transfected cells [189–​191]. The most common application of MNPs for diagnosis and treatment remains with MRI systems. The commercially available MNPs used in clinical practice, however, are in steady decline. GastroMARKTM (AMAG Pharmaceuticals), an iron oxide nanoparticle with a silicone coating, received approval as an orally administered MRI contrast agent in 1996 and has been in use since then in Europe and North America. The contrast agent Feridex I.V.® (AMAG Pharmaceuticals), a solution of dextran coated iron oxide MNPs with a 5 nm core diameter was used for liver and spleen imaging, but marketing was discontinued in 2008. Similarly, other MNP-​based agents such as Sinerem (also known as Combidex) marketed by Gueberet S.A. (AMAG Pharmaceuticals is a partner) were withdrawn from marketing before receiving full approval due to concerns from limited clinical trials. Finally, Resovist (Fujifilm RI Pharma Co.), a superparamagnetic iron oxide nanoparticle (SPION)-​based liver imaging agent, was withdrawn from the market in 2009 due mainly to the competition with the gadolinium-​based liver imaging agent

13

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133

Figure 4.32  Examples of MNPs used for therapeutic applications. (a, b) Magnetic drug targeting and (c, d) magnetofection. (a) MNPs with pH sensitive drug release [171]. (b) MNP-​g-​HPG-​ MTX2 nanoparticles dispersed in water [174]. (c) Commercially available fluid MAG-​Tween-​60 MNPs (Chemicell GmbH, Berlin, Germany) [189]. (d) Atomic force microscopy (AFM) of a single copolymer-​protected gene vector complex imaged in ultrapure water [191]. (a) Reprinted from [171]. Copyright © [2011] John Wiley and Sons. (b) Reprinted from [174]. Copyright (2013), with permission from Elsevier. (c) Reprinted from [189]. Copyright © [2010] John Wiley and Sons. (d) Reprinted (adapted) with permission from [191]. Copyright (2010) American Chemical Society.

Primovist (Bayer Schering Pharma AG). The steady demise in available MNP-​based diagnostic agents is a major challenge to the field of magnetic particle research and development for clinical applications [192]. Despite the recent decrease in available first generation MNP-​based contrast agents over the past decade, one can also see it as a temporary market adjustment and the beginning of next generation imaging agents. Scientific advances in the synthesis of MNPs and non-​traditional applications of MRI techniques led to the development of new imaging techniques that can provide more information. LodeSpin Labs LLC, a spin-​off at the

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University of Washington, develops tuned multifunctional MNPs that provide the next generation of contrast agents and tracers for magnetic particle imaging and MRI. New ventures like this provide a glimpse into the future of MNPs, particularly in the field of quantitative biomedical imaging. Improvements in the image quality of MRI-​based therapies will depend on the commercial success of novel MNPs that show superior material properties and can be used as theranostic agents (i.e. a particle that acts both as diagnostic and therapeutic agent). For a more detailed summary of the future of MNP-​based imaging, the interested reader is referred to recent reviews on the topic [193–​195].

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[257] R. R. Ragheb, D.  Kim, A.  Bandyopadhyay, et  al., Induced clustered nanoconfinement of superparamagnetic iron oxide in biodegradable nanoparticles enhances transverse relaxivity for targeted theranostics. Magn. Reson. Med., 70:6 (2013), 1748–​60. [258] M. G. Krukemeyer, V. Krenn, M. Jakobs, and W. Wagner, Magnetic drug targeting in a rhabdomyosarcoma rat model using magnetite-​dextran composite nanoparticle-​bound mitoxantrone and 0.6 tesla extracorporeal magnets  –​sarcoma treatment in progress. J. Drug Target., 20:2 (2012), 185–​93. [259] M. Heidari Majd et al., Specific targeting of cancer cells by multifunctional mitoxantrone-​ conjugated magnetic nanoparticles. J. Drug Target., 21:4 (2013), 328–​40. [260] G. Ciofani, G. G. Genchi, P. Guardia, B. Mazzolai, V. Mattoli, and A. Bandiera, Recombinant human elastin-​like magnetic microparticles for drug delivery and targeting. Macromol. Biosci., 14:5 (2014), 632–​42. [261] X. Jiang, X. Sha, H. Xin, et al., Self-​aggregated pegylated poly (trimethylene carbonate) nanoparticles decorated with c(RGDyK) peptide for targeted paclitaxel delivery to integrin-​rich tumors. Biomaterials, 32:35 (2011), 9457–​69. [262] B. Luo, S. Xu, A. Luo, et al., Mesoporous biocompatible and acid-​degradable magnetic colloidal nanocrystal clusters with sustainable stability and high hydrophobic drug loading capacity. ACS Nano, 5:2 (2011), 1428–​35. [263] Y. C. Chen, W. F. Lee, H. H. Tsai, and W. Y. Hsieh, Paclitaxel and iron oxide loaded multifunctional nanoparticles for chemotherapy, fluorescence properties, and magnetic resonance imaging. J. Biomed. Mater. Res. A, 100:5 (2012), 1279–​92. [264] M. Filippousi, S.  A. Papadimitriou, D.  N. Bikiaris, et  al., Novel core-​ shell magnetic nanoparticles for Taxol encapsulation in biodegradable and biocompatible block copolymers:  Preparation, characterization and release properties. Int. J.  Pharm., 448:1 (2013), 221–​30. [265] J. M. Shen, T. Yin, X. Z. Tian, F. Y. Gao, and S. Xu, Surface charge-​switchable polymeric magnetic nanoparticles for the controlled release of anticancer drug. ACS Appl. Mater. Interfaces, 5:15 (2013), 7014–​24. [266] Y. Jiao, Y. Sun, X. Tang, Q. Ren, and W. Yang, Tumor-​targeting multifunctional rattle-​type theranostic nanoparticles for MRI/​NIRF bimodal imaging and delivery of hydrophobic drugs. Small, 11:16 (2015). 1962–​74 [267] A. Singh, F. Dilnawaz, S. Mewar, U. Sharma, N. R. Jagannathan, and S. K. Sahoo, Composite polymeric magnetic nanoparticles for co-​delivery of hydrophobic and hydrophilic anticancer drugs and MRI imaging for cancer therapy. ACS Appl. Mater. Interfaces, 3:3 (2011), 842–​56. [268] R. R. Oliveira, F. S. Ferreira, E. R. Cintra, L. C. Branquinho, A. F. Bakuzis, and E. M. Lima, Magnetic nanoparticles and rapamycin encapsulated into polymeric nanocarriers. J. Biomed. Nanotechnol., 8:2 (2012), 193–​201. [269] B. Kirthivasan, D. Singh, M. M. Bommana, S. L. Raut, E. Squillante, and M. Sadoqi, Active brain targeting of a fluorescent P-​gp substrate using polymeric magnetic nanocarrier system. Nanotechnology, 23:25 (2012), 255102. [270] Y. Namiki, T. Namiki, H. Yoshida, et al., A novel magnetic crystal-​lipid nanostructure for magnetically guided in vivo gene delivery. Nat. Nanotechnol., 4:9 (2009), 598–​606. [271] S. Kumar, A. K. Jana, I. Dhamija, and M. Maiti, Chitosan-​assisted immobilization of serratiopeptidase on magnetic nanoparticles, characterization and its target delivery. J. Drug Target., 22:2 (2014), 123–​37.

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[272] Y. Chen, W. Wang, G. Lian, et al., Development of an MRI-​visible nonviral vector for siRNA delivery targeting gastric cancer. Int. J. Nanomed., 7 (2012), 359–​68. [273] M. Heidari Majd, D. Asgari, J. Barar, et al., Tamoxifen loaded folic acid armed PEGylated magnetic nanoparticles for targeted imaging and therapy of cancer. Colloids Surf. B, 106 (2013), 117–​25. [274] M. Kempe, H. Kempe, I. Snowball, et al., The use of magnetite nanoparticles for implant-​ assisted magnetic drug targeting in thrombolytic therapy. Biomaterials, 31:36 (2010), 9499–​510.

15

5

Modeling the In-​Flow Capture of Magnetic Nanoparticles Bart Hallmark, Nicholas J. Darton, and Daniel Pearce

5.1 Introduction Many of the applications of magnetic nanoparticles (MNPs) that have been described so far in this book involve either the manipulation of nanoparticles within a suspension or the immobilization of nanoparticles from a suspension onto a particular surface. The motivation for this can be, for example, to deliver cytotoxic drugs to cancerous cells or to achieve hyperthermia to destroy a tumor. Characterization of the immobilization and capture of MNPs from a suspension can be carried out experimentally, as has been done in a number of studies [1, 2]. Accurate experimental studies are, however, not without their limitations due to the complexity of some of the systems of interest and often idealized, in vitro, systems have to be used [1]. Data obtained from idealized experiments, however, can be of great use since it allows insight into the fundamental physical behavior underlying nanoparticle manipulation or capture; once this is understood, mathematical models can then be created and validated that can predict the manipulation or capture of nanoparticles in more complex systems. For a model to successfully describe the behavior of MNPs under the combined effect of magnetic field and fluid flow, a number of different physical mechanisms have to be accounted for. These include the nature of the material within the nanoparticles, the nature of the fluid flow, the nature of the magnetic field, and other effects, such as the adhesion of particles to surfaces and particle agglomeration. Incorporating these effects into one physical model is, therefore, a potentially complex task! This chapter will describe the basic physics that quantifies each of the key physical mechanisms such that simple models of nanoparticle capture can be created. In doing so, a brief discussion of both existing computer codes and key achievements in this field will also be given.

5.2

Physical Mechanisms Underlying Nanoparticle Capture The schematic diagram shown in Figure  5.1 illustrates some of the key physical mechanisms that require consideration when modeling nanoparticle manipulation or capture.

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Figure 5.1  Schematic diagram illustrating key physical mechanisms underlying nanoparticle

capture.

Each of the physical mechanisms illustrated in Figure 5.1 will now be explored in turn and examples will be given of the types of simplifying assumptions that have been made in models detailed in the literature. There are other effects, such as the colloidal diffusion of nanoparticles, which have been assumed to be negligible in many analyses: any attempt to create a model must, however, examine effects such as this and appropriate, justified, decisions must be made as to the merits of their inclusion or exclusion.

5.2.1

The Nature of the Fluid and the Fluid Flow The simplest assumptions that can be made are that the fluid is Newtonian, flows at steady state, has a plug flow velocity profile, and the flow domain is two-​dimensional (2D), corresponding to either an infinitely wide slit or a cylindrically symmetric pipe. Numerical models of magnetic nanoparticle capture that use these assumptions include those of Iacob et al. [3] and Rotariu and Strachan [4]. Using these assumptions, the velocity can be assumed to be the same at every point in the flow. This is not a physically realistic set of assumptions, but it can be justified when the motion of the particles due

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Figure 5.2  Schematic diagram of a parabolic flow profile, corresponding to a steady, laminar,

Newtonian flow in an axisymmetric tube.

to the applied magnetic field is significantly larger than the motion of the particles due to the fluid flow. If the motion of the nanoparticles due to the fluid flow and the motion of the nanoparticles due to the externally applied magnetic field are of a similar order of magnitude, then the nature of the fluid should be taken into account. The next simplest assumptions are that the fluid is Newtonian and flows at steady state in a laminar fashion through a cylindrical geometry. Under these conditions, it can be shown that the velocity profile of the fluid is parabolic, as shown schematically in Figure 5.2. In Figure 5.2, the radial velocity profile v (r ) is given by Eq. (5.1) as a function of the capillary radius, R, the radial coordinate, r, the pressure difference across the capillary length, ΔP, the capillary length, L, and the fluid viscosity, η:

v (r ) =

−ΔP 2 2 ( R − r ) . (5.1) 4L η

Simple laminar flow has been used by a number of authors to describe capillary flow in the study of magnetic nanoparticle capture; for example, see Voltairas et al. [5] and Hallmark et al. [6, 7]. Increasing the complexity of the description of the fluid flow can be attained by sequentially relaxing the remaining assumptions, namely that of a Newtonian fluid flowing at steady-state through a two-​dimensional (2D) cylindrically symmetric geometry. In terms of the examination of blood flow, relaxation of the Newtonian assumption is both of interest and of relevance. Moving the description of the fluid to that of a generalized Newtonian allows the viscosity of the fluid to vary as a function of shear rate, while retaining the simplicity of a fluid that does not exhibit viscoelasticity or viscoplasticity. One of the simplest generalized Newtonian fluids is the power law fluid,

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Figure 5.3  Plot of normalized velocity as a function of normalized radius for fluids of different

power law indices.

where the radial velocity profile, v (r ), depends on two fluid parameters, the consistency index, kP, and the power law index, n. This is shown in Eq. (5.2): 1



n +1  ΔP  n  n   nn+1  v (r ) = −     R − r n  . (5.2)   2 LkP  n + 1

When n = 1, Newtonian fluid behavior is recovered. If n < 1, then the fluid becomes shear thinning and the velocity profile is closer to plug flow. If n > 1, then the fluid becomes shear thickening (or dilatant) and has a “sharper” velocity profile. A graph showing typical normalized velocity profiles for a power law fluid is given in Figure 5.3. Other generalized Newtonian models describe fluids that display yielding behavior; below certain shear stresses some fluids behave essentially as a solid, but subsequently flow once a critical shear stress has been reached. Commonly used models include the Bingham fluid [8], which is solid below its yield stress and once flowing behaves as a Newtonian fluid, and the Herschel–​Bulkley fluid [9], which behaves as a power law fluid once the yield stress has been exceeded. For more information on generalized Newtonian fluid models, see the work of either Bird et al. or Steffe [8,10]. The generalized Newtonian characteristic of blood has long been known and studied [11–​13]. However, until the work of Haverkort et al. [14] all models were based on an

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underlying assumption of constant blood viscosity. Haverkort’s study incorporated and adapted the works of Ballyk and Johnston to produce a power law description of the rheology of blood. Work by Shaw et  al. [15] supported the requirement for accurate modeling of blood rheology by constructing a simple numerical model and adjusting the fluid characteristics. The study is based on the work of Merrill et al. [11], who found that the Casson model [16] holds satisfactorily for blood flowing in tubes of diameter 130–​1300 μm. The Casson model, developed for the prediction of flow behavior of pigment-​oil suspension [16], describes the behavior of a two phase, solid-liquid, suspension and has characteristics of both yield stress and a shear-thinning viscosity. For micro-​tubes of diameter 20–​100 μm, the Herschel–​Bulkley fluid model [9] can be used [11]. The study by Shaw found that the rheology of the blood plays a vital role in determining the trajectory of the particles and that the tendency of a particle to be captured by the magnet decreases as the rheology of the blood becomes more shear thinning in nature. Removal of the remaining assumptions of steady-​state flow and simple, symmetric, geometry require the solution of the Navier–​Stokes equations. The Navier–​Stokes equations, shown in vector form in Eq. (5.3), are capable of describing the motion of a Newtonian, incompressible, fluid in any arbitrary geometry:

 ∂v  ρ  + v.∇v  = −∇p + η∇2 v + ρ g + Fv . (5.3)  ∂t  In Eq. (5.3), v is the velocity vector, p, the pressure, ρ, the fluid density, η the fluid viscosity, g, the gravitational acceleration vector, and Fv, the vector of externally applied body forces. The Navier–​Stokes equations are a coupled set of non-​linear partial differential equations and are routinely solved computationally by using either finite element or finite volume methods. Finite difference methods can also be used, but tend to be less useful due to the mathematical complexity of dealing with complex geometries and the difficulty of applying certain, commonly used, boundary conditions [17]. Many computational fluid dynamics codes, such as Fluent®, Comsol Multiphysics®, and StarCD®, are also capable of solving heat and mass transfer problems in parallel with fluid flow problems, and are hence useful tools. The assumptions of steady-​state plug or laminar flow regimes were removed and a fuller description of the hydrodynamics was produced by both Ganguly et  al. [18] and Li et  al. [19]. The fluid in these models is treated as an incompressible, Newtonian, single-​phase fluid at steady state. The inclusion of solving the Navier–​ Stokes equations enabled the recirculation effects downstream of immobilized slugs of nanoparticles to be modeled. The study by Ganguly et al. found that the result is a rigidly bound core region of nanoparticles followed by a wash away region downstream of the slug. A model of flow in mammalian vasculature, represented as a highly branched, fractal system, has also been simulated [20]. The simplest departure from a tube is the examination of a flow in a single, Y-​shaped branch. The model of Avilés et al. [21] examined the collection efficiency of different implanted magnetic systems on a bifurcation in the carotid artery. The fluid flow in this more complex system was modeled using the 2D

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Navier–​Stokes equations, subject to a pulsatile inlet flow, a non-​linear magnetic constitutive equation (similar to those previously described), and subsequently evaluated forces on discrete particles. The combination of the pulsatile flow and the associated complex geometry produced a flow pattern that was both time-​dependent and non-​ linear, resulting in the manifestation of helical vortices. It was found that these helical vortices assisted the capture of the MNPs, presumably by increased particle convection in directions normal to the primary flow. It is interesting to note that magnetically induced secondary flow effects have been simulated in complex geometries without the introduction of nanoparticles [22]. Other time-​dependent studies include those by Mahmoudi et al. [23] and Mardinoglu et  al. [24] in which both authors modeled the fluid flow as a sinusoidal function. Mahmoudi et  al.’s work modeled the effect of the pulsatile flow on the capture of ferrofluids containing superparamagnetic nanoparticles, whereas Mardinoglu et  al.’s work built on the work of Cregg et al. [25] and modeled the effect on the capture of 25 discrete particles by a magnetic stent implant. This work concluded that the system performance can decrease by as much as 10% due to the effects of pulsatile blood circulation. Arguably the most complex model in the literature is that of Haverkort et al. [14]. This study produced computational simulations of magnetic nanoparticle motion and capture in the complex geometries of the left coronary artery and the carotid artery. In addition to this, the simulations were performed using the Navier–​Stokes equations in a time-​dependent three-​dimensional (3D) domain.

In modeling the capture of MNPs from flow, it is important to consider the nature of the flow field that conveys the nanoparticles. Assumptions of increasing complexity and accuracy can be made, ranging from one-​dimensional (1D) steady plug flow of Newtonian fluid to unsteady 3D flow of Newtonian, or non-​Newtonian, fluid. Simple mathematical expressions can be obtained to describe flow fields corresponding to assumptions of low complexity, whereas numerical solutions of the continuity and momentum equations are required for the more complex cases.

5.2.2

The Nature of the MNPs There are two general approaches used to model nanoparticles: the first is to assume that the particles behave as a continuum ferrofluid and the second is to examine the general behavior of ensembles of discrete particles. The first approach has been used with much success, for example, by Li et al., [19,26] and by Păltânea et  al. [27]. Commercial finite element packages, including Comsol Multiphysics®, contain numerical solvers that allow the specification of problems that involve solving the Navier–​Stokes equations to describe the motion of two fluid phases. For problems involving MNPs, one of these fluid phases is assumed to be a ferrofluid, coupled to Maxwell’s equations that describe a particular magnetic field architecture (e.g. see Munir

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et al., 2009 [28]). Due to use of the finite element approach, solutions are attainable for arbitrarily complex geometries in either two or three dimensions. The ability to perform simulations of this nature with commercially available software has immense utility to explore a wide range of relevant research problems and could serve to accelerate research progress in this subject. Simpler analytical approaches that involve examination of particle ensembles have the ability to explore the fundamental effects of nanoparticle behavior as they are exposed to magnetic fields and as they are captured; for example, the concepts of nanoparticle aggregation will be introduced and discussed in Section 5.2.4. It is also useful to have alternative approaches to gain insight into the behavior of MNPs such that either simplified analytical calculations or numerical solutions can be obtained to assist with experimental design or to act as a precursor to more complex, and potentially time-​consuming, ferrofluid-​based simulation. The remainder of this section will examine how to calculate the motion of nanoparticles and nanoparticle aggregates that are subject to an applied external magnetic flux. There are two important aspects to consider when examining the nature of the nanoparticles: first, their magnetic response and second, their motion under an externally applied magnetic field. The constitutive relationship between the magnetic dipole induced in a nanoparticle, m, and the applied external magnetic flux, B, is a function of the magnetic properties of the material within the nanoparticles. In general, due to its size, a magnetic nanoparticle can be modeled as a point dipole that experiences a magnetic force, Fm, that is proportional to its own magnetization and to the applied external field gradient [29]; this is shown in Eq. (5.4):

Fm = ( m ⋅ ∇) B. (5.4) If the solution of nanoparticles is highly concentrated, then the resultant magnetic dipole induced in the particles is also affected by the presence of magnetic interactions between nanoparticles. The induced magnetic dipole can be modeled in a number of ways for weak externally applied magnetic fields, but one commonly used in previous modeling work [30–​32] is the spherical cavity model [33]. For strong externally applied magnetic fields, it is assumed that the material within the nanoparticles becomes magnetically saturated. The induced magnetic dipole, therefore, can be written as shown in Eq. (5.5) in terms of the particle volume, Vp, and the vacuum permeability, μ0. The remaining term in this equation, a, is termed the demagnetization factor and is given in Eq. (5.6):





m=

3Vp α

µ0

B (5.5)

 χ Mµ  α = min  v , s 0  . (5.6)  3 + χv 3 B 

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In Eq. (5.6), Ms is the saturation magnetization of the nanoparticles. It has furthermore been assumed that the volumetric susceptibility difference between the magnetic material contained within the nanoparticle and the fluid in which the nanoparticle is immersed, ∆χ , is approximately the same as the initial Langevin susceptibility of the nanoparticles [33, 34] such that ∆χ ≈ χ v. For large values of the susceptibility, the demagnetization factor approaches three for all cases other than saturation. (Note: the demagnetization factor can also be affected by the shape of the nanoparticle). A number of assumptions can now be made to gain an expression that yields the magnetic force vector, Fm, as a function of a term that contains nanoparticle physical characteristics and a term that contains the applied magnetic flux. If non time-​varying ∇× B = 0, then Eqs. (5.5) and (5.6) can be substituted into fields are assumed such that ∇×t Eqs. (5.4), yielding

Fm =

3Vp α

µ0

1  ∇  B ⋅ B . (5.7) 2 

Further manipulation of Eq. (5.7) yields a more practical expression, which is given in Eq. (5.8):

Fm =

Vp a 2 μ0

( ). (5.8)

∇ B

2

A key assumption that was made during this analysis was that the magnetization of a nanoparticle is only dependent on the externally applied magnetic field. Cregg et al. [25,35] improved the modeling of magnetic forces by including magnetic dipole-​dipole effects. Two magnetic dipoles exert a force on each other, which can be included in the magnetic force equation, thus an expression can be written for the change in the magnetic flux density at a nanoparticle due to the presence of another nanoparticle and vice versa. This work was extended in a second paper in which an expression for the magnetic dipole-​dipole interaction between a large number of spherical MNPs, taken to be sufficiently small to have a homogeneous magnetic flux throughout the particles, was produced. Now that an expression for the force on a nanoparticle has been derived, it is possible to calculate the motion of a single particle due to the combined effects of fluid flow and motion due to the externally applied magnetic field. This takes the form of a simple force balance, as shown in Figure 5.4 If a Cartesian coordinate system is assumed, then the magnetic forces on a particle in the x and y directions can be shown to be equal to the expressions given in Eqs. (5.9) and (5.10), respectively:

( )



Fm , x =

Vp α ∂ 2 B (5.9) 2 µ 0 ∂x



Fm , y =

Vp α ∂ 2 B . (5.10) 2 µ 0 ∂y

( )

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In-Flow Capture of Magnetic Nanoparticles

159

Figure 5.4  Schematic diagram illustrating the force balance on a magnetic nanoparticle.

Nanoparticles are small enough to justifiably assume that inertia can be neglected. Once a particle has been set in motion by the action of magnetic forces, therefore, hydrodynamic drag will act to balance the magnetic forces, hence resulting in zero acceleration. This results in the ability to directly equate drag forces and magnetic forces. The most commonly-used description of hydrodynamic drag is the Stokes drag, where the drag force in a given direction, D, depends on the nanoparticle velocity, v, the nanoparticle radius, rp, and the viscosity of the fluid surrounding the nanoparticle, η. This is shown in Eq. (5.11): D = 6 πrp ην. (5.11)



Expressions for the velocity of the nanoparticle can now be obtained by equating Eqs. (5.9) and (5.10) with Eq. (5.11). This substitution is best done with reference to the diagram shown in Figure 5.5. As can be seen in Figure 5.5, the motion of the particle depends on both the applied magnetic force and the nature of the fluid flow. If it is assumed that the fluid flow is laminar and flowing in the x direction, then the nanoparticle velocity in the y direction can be written as shown in Eq. (5.12) and for the x direction, as shown in Eq. (5.13): νy =





νx =

( )

rp2 α ∂ 2 B (5.12) 9 ηµ 0 ∂y

( )

r2α ∂ −ΔP 2 2 2 B . (5.13) (R − r ) + p 4L η 9 ηµ 0 ∂x

A study by Cherry et al. [36] contains various extensions to include terms not found within other models. An empirical modification to the Stokes drag equation is derived therein, purportedly more accurate for higher particle Reynolds numbers (in medium-​ sized and large arteries) than the analytical Stokes expression. The hydrodynamic lift force is, however, generally ignored in the literature, without justification. Cherry et al. use the lift formulation developed by Saffman [37] and note that this model does not

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Figure 5.5  Schematic diagram of the motion of a nanoparticle subject to both magnetic forces

and hydrodynamic drag forces.

incorporate the virtual mass effect or the Basset force, both of which are insignificant for high particle densities and when particle accelerations are small. Additionally Brownian diffusion as well as gravitational and buoyant forces acting on the nanoparticles are included, all of which were considered to have a negligible effect in other studies. Nanoparticles can be modeled as an additional liquid phase, a ferrofluid, or as an ensemble of discrete particles in a carrier fluid. Particle motion can be modeled by considering the force balance resulting from magnetic forces and hydrodynamic forces. Calculation of this force balance, and the resultant particle motion, is relatively straightforward for discrete particles, whereas numerical methods capable of calculating multiphase flow behavior are typically required for ferrofluid approaches.

5.2.3

The Nature of the Externally Applied Magnetic Field The analysis in the previous section revealed that the motion of the nanoparticles is directly proportional to a function that involves the gradient of the applied magnetic flux (Eqs. (5.12) and (5.13)). A  crucial part of any model, therefore, is the accurate representation of this gradient, and there are two broad approaches that can be used to achieve this. The first approach is to solve Maxwell’s equations using appropriate simplifications for the geometry of the magnet and the physics specific to the scenario being examined. Since Maxwell’s equations are a set of coupled, partial differential equations, they will

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In-Flow Capture of Magnetic Nanoparticles

161

require a numerical solution for anything other than the simplest of scenarios; this can be achieved in a similar way to the solution of the Navier–​Stokes equations that were discussed in Section 5.2.1. If this approach is taken, then it is not uncommon to either write a code or choose a finite element modeling package in which the solution of both the Navier–​Stokes equations and Maxwell’s equations can be undertaken simultaneously, hence allowing coupling between the magnetic forces derived from the field predictions of Maxwell’s equations with the body force terms in the Navier–​Stokes equations. Examples of this approach are given by Mahmoudi et al. [23] and by Păltânea et al. [27]. Despite the rigor of this first approach, the complexity of its implementation may discourage its use, hence it is useful to explore an alternative that is inherently more approximate but simpler. Darton et  al. [1, 2, 38] carried out experiments in which the magnetic flux components from a rare-​earth magnet were mapped using a Hall probe and subsequently fitted to the sum of three independent Gaussian distributions to approximate the spatial representation and strength of the magnetic flux. The plots shown in Figure 5.6 show the absolute magnetic flux, defined in Eq. (5.14), as a function of distance along a line parallel to the edge of the magnet for two different perpendicular distances away from the edge of the magnet. The expression for the sum of the three Gaussian distributions is given by Eq. (5.15):

B = Bx2 + By2 + Bz2 (5.14)



3   ( x − µ i )2   Gi B ( x) = ∑  exp  −   , (5.15) 2σi2   i =1    σi 2π

where σi is the standard deviation of the ith Gaussian distribution, µ i is the mean of the ith distribution, and Gi is a pre-​multiplication factor. Interpolation between data sets to obtain predictions of absolute magnetic flux at intermediate y-​positions has to be done with care since the force on a nanoparticle is dependent on the magnetic field gradient at a given point. Therefore, the linear interpolation of the absolute magnetic flux will yield the false result of a constant gradient! One approach that has been used instead with some success [6] is to linearly interpolate the Gaussian parameters, Gi, σi, and µ i , in the y direction to yield values for the magnetic flux for different locations perpendicular to the edge of the magnet. Interpolation in this manner allows the magnetic flux to be calculated as a function of x and y location, hence making it possible to approximate values for the magnetic flux gradients in these directions by using the following equations:



( )

∂ B

2

2

≈

∂x

2

B x , y − B x − δx , y δx

(5.16)

x, y



( )

∂ B

2

2

≈

∂y

x, y

2

B x , y − B x , y − δy δy

. (5.17)

y-​positions. Solid data points represent experimental data and the solid line the summation of three different Gaussian distributions (dotted lines) used to fit the data.

Figure 5.6  Schematic diagram showing the absolute magnetic flux of a rare-​earth magnet as a function of the x-​position for two different

162

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163

The quantities δx and δy in Eqs. (5.16) and (5.17) are small perturbations away from the desired x and y locations, respectively. Use of this approach has yielded a sufficiently accurate description of the external magnetic flux to allow models of nanoparticle capture to be created and fitted successfully to experimental data [6]. The motion of a magnetic nanoparticle is related to the applied magnetic flux. The magnetic flux can be evaluated by either numerically solving Maxwell’s equations, in an appropriate number of dimensions, or by fitting experimental measurements of magnetic flux to a suitable analytical expression. The resultant magnetic flux can then be used to evaluate the force balance on a particle either directly, in the case of modeling discrete particles, or by its inclusion as a body force term in the momentum equations in the case of the ferrofluid approach.

5.2.4

The Aggregation of Nanoparticles under an Applied External Magnetic Field The magnetically induced aggregation of nanoparticles to form larger structures is known to exist due to observation in experimental studies [39–​44]. There are two different ways in which this is accounted for in the literature. One method, based on the work of Cregg et al. [25] involves accounting for the magnetic dipole-​dipole and hydrodynamic interactions between the nanoparticles. These interactions result in the nanoparticles approaching each other and, as the distance below the nanoparticles falls below a defined critical distance, the nanoparticles are given the same position for the remainder of the simulation [36]. The volume of the cluster is then recalculated by summing the volume of the agglomerated particles and a new radius is calculated based on this volume. The second method, used by Hallmark et al. [6], is based on a kinetic theory derived in the work of Kendall and Kosseva [45]. The expression produced links the aggregate diameter directly to the applied magnetic field and the initial nanoparticle diameter. Of these two methods, the Kendall growth law [45], given by Eq. (5.18), is the simpler of the two to apply in a model since this method allows the aggregate radius, ra, to be directly linked to the applied magnetic field, hence allowing the approximate aggregate size to be independent of parameters that may change during calculation:



ra =

36rp φ  1 1 +  2.12 kB T ln  m  − 8 K L ( H ε  φ

)

2

 rp 3  

, (5.18)

where rp is the initial nanoparticle radius, T is the temperature in Kelvin, φm is the packing fraction of the nanoparticles, φ is the volume fraction of nanoparticles in suspension, kB is the Boltzmann constant, KL is the Kendal fitting parameter, and ε is the adhesion energy. The magnetic field, H, can be back-​calculated from the applied magnetic flux, B, the vacuum permeability, μ0, and the magnetization response, M,

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as shown in Eq. (5.19). The magnetic field, H, can then be calculated from Eq. (5.20) by choosing the greater of the two terms within the parentheses: H=



B − M (5.19) µ0

 B (3 + χ v ) B  H = max  , − M s  . (5.20)  µ 0 (3 + 4 χ v ) µ 0 



The packing fraction, φm, is equal to

π 3 2

under the assumption that the nanoparticles

are spherical. Magnetically induced nanoparticle aggregation has been demonstrated to occur experimentally. Models of increasing complexity can be used to describe this behavior, ranging from using empirical growth laws that link together the aggregate diameter with the applied magnetic field to considering the nanoparticle magnetic dipole-​dipole and hydrodynamic interactions that cause nanoparticles to aggregate once they come within a critical distance of each other.

5.2.5

The Capture of Nanoparticles or Nanoparticle Aggregates The physics that has been described so far in this chapter provides a sufficient framework to predict the motion of MNPs under the combined effects of flow and an externally applied magnetic field. Of crucial importance to applications such as magnetic directed therapy is the ability to predict whether or not a nanoparticle or nanoparticle aggregate will be immobilized; even though the resultant trajectory of a nanoparticle may cause it to come into contact with a capillary wall, this does not necessarily mean that the nanoparticle will be held there. Theoretically establishing whether a nanoparticle will be immobilized is challenging due to difficulties in determining the coefficient of static friction. Some studies in the literature [46] have outlined the specific challenges in determining this parameter, whereas some authors [3] have accordingly avoided this term altogether. Further studies [1, 47] have also discovered that the adhesion properties of nanoparticles on various surfaces, ranging between vascular endothelium and polyethylene, are strongly dependent on the diameter of the nanoparticle or the nanoparticle aggregate. Depending on the level of accuracy required in a model, a simpler approach may be necessary! One simpler, more empirical, approach is to examine the angle between the resultant force that would act on an immobilized particle and the flow direction of the fluid. This is shown diagrammatically in Figure  5.7. The resultant force has two major contributions: the shear force acting on the surface of the nanoparticle due to fluid flow and the force on the nanoparticle due to the externally applied magnetic flux. The angle

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Figure 5.7  Schematic diagram of how the capture angle, θc, would vary in three different

nanoparticle locations as a result of different magnitudes of magnetic forces.

between the resulting force and the direction of fluid flow is termed the capture angle, θc, and a particle is defined to be captured once this angle exceeds a critical value. This approach is adapted from one that examined particle immobilization in cross-​flow filtration [48]. The determination of the capture angle requires the calculation of the hydraulic shear force acting on an immobilized nanoparticle Fh, and the x and y direction magnetic forces, Fm,x and Fm,y. An expression for the capture angle in given in Eq. (5.21):  Fm, y  θc = tan −1  . (5.21)  Fh + Fm, x 



An evaluation of the shear force on an immobilized particle can be obtained from simulation of the fluid flow in the geometry of interest or by use of simpler analytical approximations. One such approximation [1] is given for a nanoparticle of radius rp that is immobilized on a “bed” of nanoparticles in a tubular capillary of radius R subject to laminar flow of a Newtonian fluid, with volumetric flow rate Q and viscosity η, where the “bed” of nanoparticles has a specified thickness, th. This expression is shown in Eq. (5.22):

Fh =

4 ηQ π 3 rp2   2 R − h −1  2  π R − R cos  R  + ( R − th ) th ( 2 R − h ) 

3 2

. (5.22)

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The use of the capture angle approach has the advantage of being able to give insight into differing nanoparticle behaviors that occur when a nanoparticle contacts a capillary wall. These behaviors are dependent on the magnitude of the flow, the strength of the applied external magnetic flux, and the physical properties of the nanoparticles or nanoparticle aggregates. The first behavior mode can be represented by particle A in Figure 5.7. The trajectory of this particle has resulted in it contacting the wall of the capillary, but with a capture angle that is smaller than the critical capture angle. This particle is, therefore, not immobilized and is able to “roll” along the capillary wall in the flow direction. “Rolling” nanoparticles have been discussed in previous studies in the literature [47]. As the particle “rolls” closer to the magnet, the magnitude of the force due to the externally applied magnetic flux will increase, as will the capture angle until it reaches the critical capture angle. At this point, the particle will be immobilized and will hence define the most upstream location in the capillary (with reference to the capillary exit or other suitable datum) where nanoparticle capture is attainable. The second mode of behavior is denoted by nanoparticle B in Figure 5.7. The trajectory of this nanoparticle has resulted in the particle contacting the wall in a region of very high externally applied magnetic flux. Hence, the capture angle is greater than the critical capture angle as soon as it contacts the capillary wall. The particle, therefore, will be immediately immobilized. The limiting case is when the trajectory of the particle results in the nanoparticle contacting the wall with exactly the critical capture angle. The particle will be immobilized, but this location will represent the most downstream location in the capillary (with reference to the capillary exit or other suitable datum) where nanoparticles can be captured. Any perturbation that results in a slight decrease in the capture angle will result in this particle being washed away by the flow. The final mode of behavior refers to nanoparticle C in Figure 5.7. The trajectory of this nanoparticle has brought it into contact with the capillary wall with a capture angle less than the critical capture angle. This particle will not be immobilized and will hence continue to be conveyed through the capillary by the flow. Consideration of these three different nanoparticle behaviors gives further insight into two distinct regimes of nanoparticle capture that can occur; these two regimes are illustrated schematically in Figure 5.8. The regime denoted by A  in Figure  5.8 has been termed total capture [6]. In this regime, all the nanoparticles either arrive at the wall with a capture angle less than the critical capture angle but then “roll” along the wall as previously described until they become immobilized or they arrive at the wall with a capture angle greater than the critical capture angle and are, hence, immediately immobilized. The most upstream point of nanoparticle capture will correspond to where the critical capture angle has just been achieved and the most downstream point of capture will vary according to the relative magnitude of the fluid flow and the externally applied magnetic flux. The second regime, termed partial capture, which is denoted by B in Figure  5.8 represents a scenario where either the flow is too fast or the externally applied magnetic flux too weak (or, quite possibly, both!) for all the particles to arrive at the capillary wall. Some of the particles that do contact the wall will either “roll” along the wall until they

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Figure 5.8  Schematic diagram of the regimes of total capture (A) and partial capture (B) of

nanoparticles in a flow system.

are immobilized or they will be immobilized immediately, as previously described. A key difference, however, is that there will always be a “dividing” particle trajectory, denoted by the bold dashed line, that will result in a particle arriving at the wall at exactly the critical capture angle. Any particles that arrive at the capillary wall downstream of this position will continue with the fluid flow and any particles that arrive at the capillary wall upstream of this position will be immobilized. With increased fluid flow rates and decreased externally applied magnetic fluxes, fewer nanoparticles will reach the wall and hence be immobilized, but the most downstream position of immobilized nanoparticles will not change significantly and will correspond to the location of the critical capture angle. Experimental validation of these concepts was carried out by Darton et al. [2] and Hallmark et al. [6]. The optical measurement of nanoparticle deposits captured from fluid flows in in vitro systems has yielded data consistent with the concepts of partial capture and total capture. The plot, shown in Figure 5.9, gives a comparison between experimental data and model predictions of the location of the most upstream and the most downstream positions of a captured deposit of nanoparticles in a tubular capillary subject to Newtonian laminar flow, as a function of volumetric fluid flow rate. The numerical model that was created used only the physical concepts that have been outlined in this chapter. The transition between total and partial capture can be seen to occur at a flow rate of 0.8 ml/​min in this particular experiment, as the essentially constant value of external flux density measured at the most downstream position of the nanoparticle deposit illustrates that no further movement of the deposit was observed. The interaction between a nanoparticle, or nanoparticle aggregate, and a capillary wall is complex. A  simple method of approximating this behavior is to assume that particles or aggregates become immobilized once the relative angle between the capillary wall and the direction of the resultant magnetic force on the particle exceeds a critical value, termed the critical capture angle. The critical capture angle can be used as a fitting parameter in models of nanoparticle capture.

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Figure 5.9  Plot of the positions of the most upstream and downstream location of a

nanoparticle deposit as a function of fluid flow rate. Data points represent experimental measurements and lines simple numerical simulations.

5.3

Concluding Comments This chapter has outlined some of the physical phenomena that need to be taken into account when modeling the motion of MNPs under the combined influence of fluid flow and an externally applied magnetic field. The breadth of the literature pays testament to the multiplicity of successful approaches that can be taken, ranging from relatively simple analytical and numerical models through to complex, fully coupled, finite element simulations of ferrofluid flow. Each approach has its particular strengths, and sometimes certain weaknesses. Simulation is a very powerful tool to both assist understanding of the fundamental behavior and, subject to suitable validation, to test in silico the effectiveness of new designs of capture systems based on specific nanoparticle physical properties, flow geometries, and magnetic field architectures. Choosing the correct level of simulation is an important task for the engineer or scientist, and it is up to the creator of any new simulation to carefully decide what their specific objective is, what level of complexity is required, and hence, what simplifying assumptions can be made.

Sample Problems Question 1 List the differences between the assumptions that have to be made in modeling of magnetic capture of discrete particles in a plastic tube and the actual capture of magnetic particles in human subjects?

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Question 2 Qualitatively describe the difference between magnetic capture of nanoparticles in low and high-​flow regimes. Sketch a graph of the capture. References [1]‌ N. J. Darton, B. Hallmark, X. Han, S. Palit, N. K. Slater, and M. R. Mackley, The in-​ flow capture of superparamagnetic nanoparticles for targeting therapeutics. Nanomed. Nanotechnol., 4:1(2008),  19–​29. [2]‌ N. J. Darton, B. Hallmark, T. James, P. Agrawal, M. R. Mackley, and N. K. H. H. Slater, Magnetic capture of superparamagnetic nanoparticles in a constant pressure microcapillary flow. J. Magn. Magn. Mater., 321:10(2009), 1571–​4. [3]‌ G. Iacob, O. Rotariu, N. J.  C. Strachan, and U. O. Häfeli, Magnetizable needles and wires–​modeling an efficient way to target magnetic microspheres in vivo. Biorheology., 41:5(2004), 599–​612. [4]‌ O. Rotariu and N. J. C. Strachan, Modelling magnetic carrier particle targeting in the tumor microvasculature for cancer treatment. J. Magn. Magn. Mater., 293:1 (2005), 639–​46. [5]‌ P. A. Voltairas, D. I. Fotiadis, and L. K. Michalis, Hydrodynamics of magnetic drug targeting. J. Biomech., 35:6(2002), 813–​21. [6]‌ B. Hallmark, N. J. Darton, T. James, P. Agrawal, and N. K.  H. Slater, Magnetic field strength requirements to capture superparamagnetic nanoparticles within capillary flow. J. Nanoparticle Res., 12:8(2010), 2951–​65. [7]‌ B. Hallmark, N. J. Darton, X. Han, S. Palit, M. R. Mackley, and N. K. H. Slater, Observation and modelling of capillary flow occlusion resulting from the capture of superparamagnetic nanoparticles in a magnetic field. Chem. Eng. Sci., 63:15(2008), 3960–​5. [8]‌ R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of polymeric liquids. Volume 1 –​ Fluid Mechanics, 2nd edn (New York, NY: John Wiley and Sons Inc., 1987). [9]‌ W. H. Herschel and R. Bulkley, Konsistenzmessungen von Gumni-​Benzollosungen. Kolloid Zeitschrift., 39(1926), 291–​300. [10] J. Steffe, Rheological Methods in Food Process Engineering, 2nd edn (East Lansing, MI: Freeman Press, 1996). [11] E. W. Merrill, A. M. Benis, E. R. Gilliland, T. K. Sherwood, and E. W. Salzman, Pressure-​ flow relations of human blood in hollow fibers at low flow rates. J. Appl. Physiol., 20:5 (1965), 954–​67. [12] P. D. Ballyk, D. A. Steinman, and C. R. Ethier, Simulation of non-​Newtonian blood flow in an end-​to-​side anastomosis. Biorheology., 31:5 (1994), 565–​86. [13] B. M. Johnston, P. R. Johnston, S. Corney, and D. Kilpatrick, Non-​Newtonian blood flow in human right coronary arteries: steady state simulations. J. Biomech., 37:5 (2004), 709–​20. [14] J. W. Haverkort, S. Kenjeres, and C. R. Kleijn, Computational simulations of magnetic particle capture in arterial flows. Ann. Biomed. Eng., 37:12(2009), 2436–​48. [15] S. Shaw, P. V. S. N. Murthy, and S. C. Pradhan, Effect of non-​Newtonian characteristics of blood on magnetic targeting in the impermeable micro-​vessel. J. Magn. Magn. Mater., 322:8 (2010), 1037–​43. [16] N. Casson, A flow equation for pigment-​oil suspensions of the printing ink type. In C. C. Mill, ed., Rheology of Disperse Suspensions (New York, NY: Pergamon Press, 1959) pp. 84–​104. [17] T. J. Chung, Computational Fluid Dynamics, 2nd edn (Cambridge: Cambridge University Press, 2002).

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[18] R. Ganguly, A. P. Gaind, S. Sen, and I. K. Puri, Analyzing ferrofluid transport for magnetic drug targeting. J. Magn. Magn. Mater., 289 (2005), 331–​4. [19] X. L. Li, K. L. Yao, and Z. L. Liu, CFD study on the magnetic fluid delivering in the vessel in high-​gradient magnetic field. J. Magn. Magn. Mater., 320:11 (2008), 1753–​8. [20] G. Jayalalitha, V. Shanthoshini Deviha, and R. Uthayakumar, Fractal model for blood flow in cardiovascular system. Comput. Biol. Med., 38:6 (2008), 684–​93. [21] M. O. Avilés, A. D. Ebner, H. Chen, A. J. Rosengart, M. D. Kaminski, and J. A. Ritter, Theoretical analysis of a transdermal ferromagnetic implant for retention of magnetic drug carrier particles. J. Magn. Magn. Mater., 293:1 (2005), 605–​15. [22] S. Kenjereš, Numerical analysis of blood flow in realistic arteries subjected to strong non-​ uniform magnetic fields. Int. J. Heat Fluid Flow., 29 (2008), 752–​64. [23] M. Mahmoudi, M. A. Shokrgozar, A. Simchi, et  al., Multiphysics flow modeling and in vitro toxicity of iron oxide nanoparticles coated with poly (vinyl alcohol). J. Phys. Chem. C, 113:6 (2009), 2322–​31. [24] A. Mardinoglu, P. J. Cregg, K. Murphy, M. Curtin, and A. Prina-​Mello, Theoretical modelling of physiologically stretched vessel in magnetisable stent assisted magnetic drug targeting application. J. Magn. Magn. Mater., 323:3–​4 (2011),  324–​9. [25] P. J. Cregg, K. Murphy, A. Mardinoglu, and A. Prina-​Mello, Many particle magnetic dipole–​dipole and hydrodynamic interactions in magnetizable stent assisted magnetic drug targeting. J. Magn. Magn. Mater., 322:15 (2010), 2087–​94. [26] X. L. Li, K. L. Yao, H. R. Liu, and Z. L. Liu, The investigation of capture behaviors of different shape magnetic sources in the high-​gradient magnetic field. J. Magn. Magn. Mater., 311:2 (2007), 481–​8. [27] V. Păltânea, G. Păltânea, and D. Popovici, Numerical approach for an application of magnetic drug targeting in cancer therapy. Rev. Roum. Sci. Techn., 53 (2008), 137–​46. [28] A. Munir, J. Wang, and H. S. Zhou, Dynamics of capturing process of multiple magnetic nanoparticles in a flow through microfluidic bioseparation system. IET Nanobiotechnol., 3:3 (2009), 55–​64. [29] Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, Applications of magnetic nanoparticles in biomedicine. J. Phys. D Appl. Phys., 36:13 (2003), R167–​81. [30] H. Chen, A. D. Ebner, A. J. Rosengart, M. D. Kaminski, and J. A. Ritter, Analysis of magnetic drug carrier particle capture by a magnetizable intravascular stent: 1. Parametric study with single wire correlation. J. Magn. Magn. Mater., 284 (2004), 181–​94. [31] H. T. Chen, A. D. Ebner, M. D. Kaminski, A. J. Rosengart, and J. A. Ritter, Analysis of magnetic drug carrier particle capture by a magnetizable intravascular stent: 2. Parametric study with multi-​wire two-​dimensional model. J. Magn. Magn. Mater., 293:1 (2005), 616–​32. [32] E. J. Furlani and E. P. Furlani, A model for predicting magnetic targeting of multifunctional particles in the microvasculature. J. Magn. Magn. Mater., 312:1 (2007), 187–​93. [33] G. A.  van Ewijk, G. J. Vroege, and A. P. Philipse, Susceptibility measurements on a fractionated aggregate-​free ferrofluid. J. Phys. Condens. Matter., 14:19(2002), 4915–​25. [34] J. Connolly, T. G. St Pierre, and J. Dobson, Experimental evaluation of the magnetic properties of commercially available magnetic microspheres. Biomed. Mater. Eng., 15:6(2005), 421–​31. [35] P. J. Cregg, K. Murphy, and A. Mardinoglu, Inclusion of magnetic dipole–​dipole and hydrodynamic interactions in implant-​assisted magnetic drug targeting. J. Magn. Magn. Mater., 321:23(2009), 3893–​8.

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[36] E. M. Cherry, P. G. Maxim, and J. K. Eaton Particle size, magnetic field, and blood velocity effects on particle retention in magnetic drug targeting. Med. Phys., 37:1 (2010), 175–​82. [37] P. G. Saffman, The lift on a small sphere in a slow shear flow. J. Fluid Mech., 22:2 (2006), 385–​400. [38] N. J. Darton, B. Hallmark, P. Agrawal, T. James, V. H.  B. Ho, and N. K.  H. Slater, On the magnetic field architecture required to capture superparamagnetic nanoparticles in a microcapillary flow. J. Nanoparticle Res., 12:1 (2010), 307–​17. [39] C-​J. Chin, S. Yiacoumi, C. Tsouris, S. Relle, and S. B. Grant, Secondary-​minimum aggregation of superparamagnetic colloidal particles. Langmuir, 16:8(2000), 3641–​50. [40] B. D. Korth, P. Keng, I. Shim, et  al., Polymer-​coated ferromagnetic colloids from well-​ defined macromolecular surfactants and assembly into nanoparticle chains. J. Am. Chem. Soc., 128:20 (2006), 6562–​3. [41] R. J. Wilson, W. Hu, C. Wong, et  al., Formation and properties of magnetic chains for 100 nm nanoparticles used in separations of molecules and cells. J. Magn. Magn. Mater., 321:10 (2009), 1452–​8. [42] C. Neto, M. Bonini, and P. Baglioni, Self-​assembly of magnetic nanoparticles into complex superstructures: Spokes and spirals. Colloids Surf. A Physicochem. Eng. Asp., 269:1–​3 (2005), 96–​100. [43] A. Yu Zubarev and L.  Yu Iskakova, Condensation phase transitions in ferrofluids. Phys. A Stat. Mech. Appl., 335:3–​4 (2004), 325–​38. [44] A. Yu Zubarev and L. Yu Iskakova, To the theory of rheological properties of ferrofluids: Influence of drop-​like aggregates. Phys. A Stat. Mech. Appl., 343:15 (2004), 65–​80. [45] K. Kendall and M. R. Kosseva, Nanoparticle aggregation influenced by magnetic fields. Colloids Surf. A Physicochem. Eng. Asp. 286:1–​3 (2006),  112–​6. [46] W. Maass, M. Duschl, H. Hoffmann, and F. J. Friedlaender, A new model for the explanation of the saturation buildup in the transverse HGMS-​configuration. Appl. Phys. A, 32:2 (1983),  79–​85. [47] V. R. S. Patil, C. J. Campbell, Y. H. Yun, S. M. Slack, and D. J. Goetz, Particle diameter influences adhesion under flow. Biophys. J., 80:4 (2001), 1733–​43. [48] M. R. Mackley and N. E. Sherman, Cross-​flow cake filtration mechanisms and kinetics. Chem. Eng. Sci., 47:12 (1992), 3067–​84.

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Sensing Magnetic Nanoparticles

6.1

Hall Effect Biosensors Adarsh Sandhu and Paul Southern

6.1.1

Introduction to the Hall Effect The majority of classical electromagnetism was described during the nineteenth century, yet at this time, there was little use for a device that could sense magnetic fields. In actual fact, the necessity to directly measure and quantify the magnitude of a magnetic field has limited use in today’s technological environment. Where the usefulness lies is the ability to directly measure the orientation of a magnetic field and/​or the electrical current (more accurately, the charge carrier velocity) induced by an externally applied magnetic field using the phenomenon known as the Hall effect. Discovered in 1879 by Edwin Hall while studying for his doctorate at Johns Hopkins University [1], the Hall effect and subsequent advancements have led to major scientific discoveries, including several Nobel prizes [2, 3]. More impressively, Hall’s findings predate J. J. Thompson’s discovery of the electron by almost 20 years –​a concept that plays an important role in quantifying the effect. Although it was an outstanding achievement at the time, it had no immediate impact on science and technology until the mid-​twentieth century during the evolution of the semiconductor industry. Nowadays, Hall effect sensors are ubiquitous in industry, covering a wide range of applications, with billions of these devices fabricated every year [4]. Although there are many other magnetic sensing devices, for example, fluxgate magnetometers and superconducting quantum interference devices (SQUID), Hall effect sensors will often be chosen above others due to their compactness, reliability, robustness and production cost. Typical applications for Hall effect sensors include the following: 1 . switches: contactless switches for robust applications in industry [5]; 2. magnetic microscopy: non-​invasive, high-​sensitivity measurement of magnetic surfaces using micro-​Hall sensors [6]; 3. motor control: detection of the rotor position in brushless fans for feedback [7]; 4. mobile phones: orientation sensors using the earth’s magnetic field [7]; 5. automotive: fuel ignition timing and sensing of wheel rotation for anti-​lock braking systems [8]; and 6. biological sensing: detecting functionalized magnetic particles for bioassays [9, 10].

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Figure 6.1  Hall effect experimental set-​up.

It is apparent from this brief introduction that Hall effect sensors are an important and mature tool for a variety of industries, and still receive significant research interest for the development of future devices. The following section will describe the underlying physics of the Hall effect and associated electrical characteristics.

6.1.1.1

Quantifying the Hall Effect When Hall first observed the effect, he was using a magnetic field of approximately 1 Tesla powered by a battery consisting of 20 Bunsen cells, a thin gold leaf film and a galvanometer set-​up as shown in Figure 6.1. Where the Hall effect differs from magnetic induction, an already well known effect at the time of discovery, is that a static magnetic field applied in the direction perpendicular to the film will result in a small steady state voltage appearing across the film at right angles to the flowing current. In a similar fashion to magnetic induction, the polarity of the voltage will change depending upon the direction of the applied static field. Hall constructed his hypothesis based upon Ampère’s finding that a current carrying wire experiences a perpendicular force when placed in a magnetic field. Hall reasoned that if the current was the component experiencing the force rather than the wire, then an imbalance of current across the wire would lead to a potential difference, thus explaining the observations in the thin gold film. From a quantitative approach, this can be described by the Lorentz force, which describes the action upon a charged particle from an electromagnetic field, as shown in Eq. (6.1):



F = q ( E + v × B ) , (6.1) where F is the force vector acting upon a particle of charge q moving with velocity v in the presence of an electric field E and magnetic field B. Deconstructing Eq (6.1), there are two components that affect the resultant force on the charged particle. First, the electric field provides a directional force proportional to the strength of the field

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and charge of the particle. The effect of the magnetic field is a little more complicated and only acts upon a moving charge. The expansion of the cross product term is written below:

(

Fx = q vy Bz − vz By

)

Fy = q(vz Bx − vx Bz ) (6.2) Fz = q(vx By − vy Bx ).



In the simplest case, the force acting upon a charged particle moving perpendicular to the magnetic field will be at right angles to both vectors, as shown in Figure  6.1. The resultant force due to the magnetic field can be calculated by performing the cross product of v� ( − vx , 0, 0 ) and B� (0 , 0 , Bz ): x v × B = − vx 0



y z 0 0 = vx Bz y. (6.3) 0 Bz

The Lorentz force impacts the flow of the charge carriers and creates an imbalance of charge across the plate, giving rise to a potential drop. In the case of constant field conditions, the net force is reduced to zero as the magnetic and electric forces balance each other out: q ( E + v × B ) = 0. (6.4)



Rearranging Eq. (6.4) and solving for E, the Hall electric field is given by E H = −v × B. (6.5)



Additionally, the Hall voltage can be defined as a function of the width of the plate: VH = − w.(v × B ). (6.6)



This quantitative approach to describe the Hall effect has shown that the Hall voltage is dependent on three variables: the width of the plate (w), the charge carrier velocity (v), and the applied magnetic field (B).

6.1.1.2

Material Selection One of the most important factors in governing the sensitivity of a Hall sensor is the effect of the charge carriers and the selection of materials used to build the probe. In metals, the transfer of charge is a property of free conduction electrons that drift along the direction of an applied electric field. In the absence of an electric field, there is sufficient thermal energy to reduce the net motion to zero and thus reduce the overall transfer of charge to zero. It is a common assumption that electricity (charge carrying electrons) travels at speeds close to that of light; however, this is far from the truth. A  simple calculation based upon the properties of copper will show how the drift velocity of conduction electrons is indeed rather slow.

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The first step is to estimate the charge carrier concentration (N), and since copper has an electron configuration, that leaves a single free conduction electron, this can be calculated based upon the density of copper: N=



6.02 × 1023 mol −1 × 8.96 g.cm −3 NA = 8.49 × 1022 cm−3, (6.7) ρ= 63.55 g.mol −1 M

where N A = 6.02 × 1023 mol −1 is Avogadro’s constant ρ = 8.96 g.cm −3 is the density of copper at room temperature M = 63.55 g.mol −1 is the atomic mass of copper. In order to derive an estimate for the drift velocity, one must use the SI convention of current defined as the charge transfer of 6.24 × 1018 electrons per second, more commonly known as the Ampere. Adopting these values in a practical application, such as supplying 10 A of current to power a kettle or toaster, the drift velocity of the electrons can be calculated: v=



10 A I = = 0.074 cm.s −1 , (6.8) −19 eNA 1.60 × 10 C × 8.49 × 1022 cm −3 × 0.01 cm 2

where I = 10 A is the current required to power a kettle or toaster e = 1.60 × 10−19 C is the charge of an electron (1 e = 6.24 × 1018 ) N = 8.49 × 1022 cm−3 is the charge carrier concentration as estimated above A =1 mm2 or 0.01 cm2 is the cross-​sectional area of standard household electrical wire. Although an electric field propagates through a wire at approximately 50% of the speed of light, the drift velocity of the electrons is slow in comparison –​around 150 billion times slower! Given that the Hall voltage is proportional to the charge carrier velocity, it is often more convenient to define the Hall voltage as a function of the charge carrier concentration by substituting Eq. (6.8) into Eq. (6.6): VH = −



wIB IB =− , (6.9) eNA eNd

where d is the depth or thickness of the plate. From this derivation, an estimation of the Hall voltage from Hall’s first experiment can be calculated: VH == −

0.06 A × 1T IB = = 50 μV, (6.10) −19 eNd 1.60 × 10 C × 8.60 × 1028 m −3 × 90 × 10 −9 m

where B = 1 T I = 0.06 A e = 1.60 × −19 C is the unit charge for the carrier, i.e. an electron

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N = 8.60 × 1028 m −3 is the approximate volumetric charge density for gold d = 90 × 10 −9 m is the typical thickness for gold leaf. At the time of discovery, 50 µ V was a small yet discernible voltage to measure, and through careful experimental practice, Hall managed to collect enough statistically relevant data to prove his findings. However, in order to make the Hall voltage large enough for an everyday practical application, one must consider the impact charge carriers have on the magnitude of this effect. Eq. (6.9) demonstrates that the Hall voltage is inversely proportional to the density of charge carriers; thus, to increase the effect for a given field and current, one must use a suitable material with a lower charge carrier density. Fortunately, the semiconductor industry has provided a wide range of materials that offer charge carrier densities orders of magnitude lower than standard metals. Previously, electrons were considered as the primary charge carrier, as is the case for most metals; however, for semiconducting materials, the charge carriers fall into two distinct categories: negative carriers, or electrons, and positive carriers, known as holes, with the associated semiconducting materials known as p-​type and n-​type materials, respectively. In order to produce the desired electrical effect, semiconductors are deliberately doped with impurities, which lead to a thermally stable material with a well-​known charge carrier concentration. As a comparison between a metal and semiconductor-​based Hall probe, the following calculation shows a large increase in Hall voltage response using an n-​type silicon based probe: VH == −



0.006 A × 1 T IB = = 150 mV V, (6.11) −19 eNd 1.60 × 10 C × 5.0 × 1021 m −3 × 50 × 10 −6 m

where B = 1 T I = 0.006 A is the bias current e = 1.60 × −19 C is the unit charge for the carrier, i.e. an electron N = 5.0 × 1021 m −3 is a typical carrier concentration for n-​type doped silicon d = 50 × 10 −6 m is an example thickness for a silicon Hall probe. Even at a tenth of the bias current, the silicon-​based Hall probe example offers 3,000× the sensitivity to that of gold metal film under similar conditions. Manufacturers are not limited to using silicon for Hall effect devices, and there is a wide variety of semiconductor materials to suit the users requirements. Table 6.1 compares the sensitivity of typical materials used in commercially available Hall sensors.

6.1.1.3

Design Considerations Up to this point, generalizations have been made about the physics of the Hall effect and, to some extent, has provided an adequate solution to quantify the effect. In reality, there are many other factors that determine the sensitivity and stability of a Hall effect probe. One particular concern from a user’s perspective is the thermal stability of devices given that they are commonly used in the automotive industry, where devices can be exposed to temperatures exceeding 100 °C. The effect of temperature is twofold,

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Table 6.1  Comparison of Hall sensitivity measured by the output voltage VH for a given bias current and field. Material

Sensitivity (mV.mA −1 .kG −1)

Silicon (Si)

1.0

Indium arsenide (InAs)

2.0

Indium antimonide (InSb)

5.0

first, affecting a property known as the input/​output resistance, and second, the mobility of the charge carriers. The former increases resistance with increasing temperature, thus reducing the bias current (if driving at constant voltage), whereas the latter increases charge mobility. Other factors from a manufacturing perspective include effects from piezoresistive stresses applied to the Hall effect plate during packaging and misalignment of the Hall contacts with the latter leading to a permanent offset Hall voltage in zero field. While lithographic techniques provide fabrication of devices with sub-​micron accuracy, there are intelligent layout techniques that can partially eliminate stress and temperature effects. For example, it is possible to arrange a four Hall effect cells in a 2 × 2 configuration, leading to neighboring sensors canceling out each other’s errors, thus creating a highly balanced system [11]. Probably the most well-​known application for Hall probes in consumer electronics is their use as an orientation sensor, that is, as a three-​axis compass using the earth’s magnetic field as reference. This is yet another prime example where layout plays an important role in order to overcome the “limitations” of planar complementary metal oxide semiconductor (CMOS) fabrication used in manufacturing Hall sensors. As described previously, Hall sensors sensitivity are limited to the axis perpendicular to the flow of charge carriers and therefore, in a traditional sense, would require a three sensors to be arranged along each axis. This, however, can be overcome by using flux concentrators placed in the vicinity of the Hall sensor, which bend the magnetic fields from a parallel orientation to a perpendicular one, as shown in Figure 6.2 [12]. Utilizing this method, it is possible to combine a series of Hall sensors and flux concentrators to build a device that can realize a true three-​axis relationship with the earth’s magnetic field [13].

6.1.1.4

Advantages of Hall Sensors Accuracy, reliability, and repeatability are key components when building a sensor. It has been shown that Hall probes are inherently sensitive to static magnetic fields, and the choice of materials can have a dramatic impact upon the sensitivity of a device. Unlike optical or mechanical switches, Hall sensors are solid-​state devices requiring no moving parts and hence, immune to a variety of environmental conditions, such as humidity, dust, and vibration. Unlike their inductive sensor cousins, Hall probes do not rely on a changing magnetic flux and lend themselves well to proximity-​based applications whereby a local magnetic field could act as a switch or threshold, as shown in Figure 6.3 [14]. That said, Hall sensors still operate over a wide range of frequencies from dc to hundreds of megahertz [15].

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Figure 6.2  Parallel field measurement using flux concentrators.

Figure 6.3  Examples of Hall sensor arrangements for proximity detection.

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Hall Sensors for the Detection of Magnetic Nanoparticles for Medical Diagnostics Silicon-​Based Bio-​Hall Sensors The critical components (processors and memory chips) of modern electronic equipment, such as high-​performance laptop computers, are made using silicon. Recently, the proliferation of smartphones and demand for ever novel functions has led to the fabrication of Hall effect magnetic field sensors for use as “electronic compasses” in the iPhone [16]. Thus, silicon electronics offer a wide range of applications, from traditional memory and processing to magnetic sensing. The possibility of using silicon Hall sensors for medical diagnostics was demonstrated in 2002 by groups in Europe [17] and the USA [18]. These experiments showed that so-​called CMOS Hall sensors  –​that could be readily mass produced  –​were able to detect a single 2.8 µm diameter superparamagnetic Dynabeads® [19]. These reports inspired researchers to devise methods for the detection of smaller superparamagnetic beads (SPBs) using Hall sensors made using compound semiconductors, such as GaAs/​AlGaAs heterostructures multilayers of InSb and InAs thin films, which offered much higher sensitivity than silicon.

6.1.2.2

Bio-​Hall Sensors Using Compound Semiconductors Using the set up shown in Figure 6.4, which is similar to that reported in reference [17], Sandhu et  al. demonstrated the potential of exploiting the high electron mobility of indium antimonide (InSb) thin films for biosensing by fabricating 4.5 μm × 4.5 μm InSb Hall sensors with 320 nm thick InSb layers grown by molecular beam epitaxy (MBE). The mobility and electron density of the InSb Hall sensors were 17,453 cm2V−1s−1 and 3.6 ×1012 cm−2, respectively. Sandhu et  al. also reported on the fabrication of arrays of Hall sensors using GaAs/​AlGaAs heterostructures [20]. Arrays are necessary for multiplex detection. The detection of sub-​100  nm diameter superparamagnetic beads using In As-​based heterostructure Hall sensors has also been reported [21].

6.1.2.3

Integrated Current Lines for Rapid Detection Detection speed is an important factor to consider for actual applications of Hall sensors for point-​of-​care medical diagnostics. The integration of “current lines” with Hall biosensors is a novel means of decreasing the time taken for an antibody-​antigen type of reaction between proteins on beads and their counterparts on solid substrates. Magnetic field gradients produced by current passed through current lines enable the capture and collection of magnetic beads onto the surfaces of Hall sensors, thereby reducing detection time compared with Brownian motion mediated processes (Figure 6.5). Passing currents through the gold microstrips can lead to the generation of heat. Thus, the design of the current lines necessitates maximizing the action of field gradients at low currents. We typically used currents of several milli-​amperes to manipulate magnetic beads ranging from tens of nanometers to several micrometers in diameter. Figure 6.6 shows typical gold microstrips integrated with Hall sensors, where a dc current is passed through the circular gold strip patterns and an external magnetic field applied parallel

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Figure 6.4  (a) InSb thin film Hall effect biosensor set up. The detection process consists of

applying an alternating drive field Hac [4.4 mT at 670 Hz] along the x direction, a time invariant dc magnetic field Hdc [32 mT] along the z direction, and extracting the Hall effect voltage signal due to the magnetic bead using lock-​in electronics. As in reference [17], the presence of a magnetic bead is indicated by a change in the Hall voltage after the application of Hdc.

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Figure 6.5  Design of current lines for generating magnetic field gradients by passing currents

through Au microstrips for capturing magnetic beads onto the surfaces of Hall sensors to reduce detection time.

to the surface with a permanent magnet [22]. The action of the external field caused the beads at the edge of the circular strip to move over the center of the Hall sensor. Hall effect biosensors are promising for point-​of-​care medical diagnostics. The issues to resolve include defining an application that is commercially viable and that exploits the unique physical properties of these sensors.

6.2

Spin Valve and Tunnel Magnetoresistance Sensors Susana Cardoso de Freitas, Simon Knudde, Filipe A. Cardoso, and Paulo P. Freitas This section focuses on the use of magnetoresistive (MR) sensors for nanoparticle detection. The MR effect will be explained and demonstrated for two well-​established technologies: spin valves (SV) and spin dependent tunnel magnetoresistance (TMR). The practical integration of these sensors for magnetic nanoparticle detection is described. Finally, considerations on the minimum detectable field are discussed in terms of sensor noise and signal-​to-​noise ratio (SNR).

6.2.1

The Magnetoresistive Effect and Magnetoresistive Sensors MR sensors represent a well-​established technology for magnetic field detection at room temperature, with sensitivities that can reach pT (10–​12T) under some sophisticated

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Figure 6.6  (a) Microbeads before applying current and (b) the accumulation of microbeads after

passing a 10 mA current thought the current line. (c) The beads move in an counterclockwise direction after passing a 10 mA through the ring of 20 μm diameter. (d) The beads are moved by applying an in-​plane dc magnetic field. Change in position of microbeads after 5 s of applying an in-​plane dc magnetic field while maintaining the counterclockwise current through the ring. The location of Hall sensor is indicated by the dotted lines.

designs. The detection principle relies on the direct measurement of the magnetic field, which is converted into an electric signal (voltage) on the sensor, with a linear relationship to the magnetic field. The relation between resistivity and magnetization (magnetoresistance effect) was discovered in 1857 by Thomson [23] and explained with the quantum spin-​orbit interaction by Potter in 1974 [24]. In 1985, studies on surface magnetism and magnetic interactions across thin antiferromagnetic (AF) and non-​magnetic (NM) layers lead to the discovery of the giant magnetoresistance (GMR) effect [25, 26]. This was the start of spintronics. The technological advances in thin film deposition and lithography systems

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Figure 6.7  The three types of MR sensors most commonly used in technological applications.

allowed the practical demonstration of functional devices in 1991 by both industry and research institutes [27, 28]. Three major families of MR sensors have been developed and are presently used as field sensors, namely anisotropic magnetoresistance (AMR), GMR, and Tunneling magnetoresistance (TMR) sensors, as represented in Figure 6.7. They have in common the use of thin ferromagnetic (FM) films (typically NiFe, CoFe soft magnetic alloys, less than 10 nm thick), compact size (with dimensions from several μm to tens of nm), and compatibility with microfabrication techniques used in the semiconductor industry. These features have been the keys of success for large-​scale production and universal integration in many areas, from magnetic disk head recording technologies, magnetic random-​access memory (MRAM), and magnetic field sensors in general (domestic, industrial, space, biomedical, etc.). The impact of MR technology on a global scale led to A. Fert and P. Grünberg being awarded the Nobel Prize in Physics in 2007, which motivated even further the research and technological investment carried out by an increasing community worldwide. The MR effect relies on the property that some materials have to see their resistance modified under the presence of an external magnetic field. Figure 6.8 illustrates the base geometry where the MR effect can be used for the detection of a magnetic field in its vicinity: the field rotates the magnetization of the FM layer, therefore modifying its resistance.1 The MR ratio is normally a figure of merit when describing these sensors, and is quantified by the ratio between the maximum resistance state and the minimum resistance state, MR (%) =



Rmax − Rmin ×100, (6.12) Rmin

normalized by the minimum resistance. The maturity of MR-​based devices at present allows establishing ranges for the MR values achieved with each of the three technologies (see Table 6.2). However, other characteristics need to be considered when selecting the MR materials for a specific application: these include, for example, the linear range of operation,2 A good review of the physical principles and material requirements for MR sensors can be found in [29]. The ideal sensor has a unique and linear relation between resistance and magnetic field, therefore the linear range covers the field values that generate a linear variation on the sensor resistance.

1 2

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Figure 6.8  Basic structure of a MR sensor, consisting of a magnetic film whose resistance value depends on the relative orientation between the magnetization and the magnetic field at its vicinity.

Table 6.2  Some key properties of MR sensors (with dimensions of ~10 μm2), which need to be evaluated as an ensemble while selecting the best type of MR technology for a particular application. AMR

GMRa

TMR

MR ratio

2–​6%

6–​20%

70–​300%b

Field linear range

Down to ±1mT

Down to ±1mT

Down to ±2mT

Materials cost

Low

Expensive

Expensive

Thermal treatments (under magnetic fields)

Not required

Usually ~280°C

Usually ~340°C

Electrical robustness against electrostatic discharge

Very good

Very good

Fair

Note: the values presented here are for a particular family of GMR sensors: the SVs (to be described in Section 6.2.1.2 (Spin Valves)).

a

Note that the values were selected from sources demonstrating functional sensors, and unpatterned materials may have reported better properties.

b

materials cost, thermal treatments required, and electrical robustness against electrostatic discharge.

6.2.1.1

Anisotropic Magnetoresistance (AMR) AMR is an intrinsic property of FM materials by which they have different resistance values when the electrical current is parallel or perpendicular to the material’s axis of magnetization. A good review of the physical principles can be found in [30, 31]. The AMR effect is very well documented, with experimental data obtained in thin films (several nanometers thick), typically based on Co, Fe, Ni, and their alloys. Figure 6.9

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Figure 6.9  AMR effect measured in a thin film.

illustrates the geometry of an AMR sensor, consisting of a single thin film, which, under an external applied magnetic field, shows a maximum resistivity when the current is parallel to the magnetization direction (R||) and a minimum resistivity when the current is perpendicular to the magnetization direction (R⊥), following

R = R⊥ + Δ R cos2 θ. (6.13) The linear range of the response of the resistance to external fields is not centered at H = 0, but at fields promoting the magnetization to be at an angle of π/​4 instead. From a practical aspect, the sensor is not operational without any field applied (H = 0) and requires a bias field to set the magnetization at π/​4. This disadvantage was overcome with the integration of biasing schemes, that is, integrated strategies to force the sensing layer to be at π/​4, for example, current lines in a “barber pole” geometry [32] or soft adjacent layer [33] biasing schemes. Many sensors have been developed based on AMR due to its simplicity and easy integration, and presently, these sensors can operate with MR ratio around 5%. The application of AMR sensors as read heads in the magnetic storage industry was an important motor driving research and promoting the fast implementation of these devices in global markets. AMR sensors are based on NiFe and other soft magnetic materials and show MR up to ~5%. The R(H) response is not linear around H = 0, requiring linearization schemes.

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Figure 6.10  (a) Schematics of a GMR multilayer sensor. (b) Characteristic response of a GMR: the spacer thickness is tuned to have a fully antiparallel orientation at the remanent state (H = 0). For strong fields, all layers are in the parallel state (θ = 0°) and the resistance is a minimum, being a maximum when the layers are antiparallel (θ = 180°, at H = 0).

6.2.1.2

Giant Magnetoresistance (GMR) A novel structure was inspired by the studies on Fe/​Cr/​Fe layers by Grünberg [26] and Fert [25], demonstrating the GMR effect. For these multilayers, the FM layers are coupled antiferromagnetically3 through an NM spacer (Figure 6.10), so they are spontaneously antiparallel at zero fields [34]. By applying an external magnetic field to this system, the magnetization orientations in two consecutive layers can be changed from antiparallel (AP) to parallel (P). The lower resistance state will be achieved in the P state with θ = 0°, and the higher resistance state in the AP state with θ = 180°, which results on a sensor characteristic with a non-​linear dependence on the magnetic field near zero fields. The physical mechanisms can be completely understood upon simulation of the multilayer structure response under external magnetic fields [35, 36]. The MR ratios achieved with GMR multilayers based on CoFe/​Cu or CoFe/​Pt can surpass 100%. However, these structures require large magnetic fields (over 10 mT, typically) to rotate all layers into parallel alignment, and alternatives had to be sought, therefore giving space for the SV concept to be developed.

In ultrathin (few nm) ferromagnetic (FM)/​NM multilayers, interface roughness gives origin to virtual magnetic poles that tend to reorient minimizing the stray field energy. As a consequence, the coupling between adjacent FM layers depends on the thickness of the NM layer, resulting in a periodical switching from ferromagnetic (parallel) to antiferromagnetic (antiparallel) alignment. This is modeled with the Ruderman–​ Kittel–​Kasuya–​Yosida (RKKY) interaction [34].

3

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Figure 6.11  (a) SV sensor schematics, where the two FM layers are separated by a non-​magnetic thin film, (b) SV film materials and thicknesses for a simple stack, (c) magnetic response of a simple stack SV under fields large enough to rotate also the pinned layer above the Hexch field, and (d) magnetoresistance curve obtained for an unpatterned sample, showing a fast resistance changea and an MR ratio of ~10%. However, the curve is not linear, and requires adjustment of the geometry for the sensor to be linearized. a  When compared to GMR, the SV sensors can see their resistance changed under small applied fields H, therefore having a more sensitive response to smaller fields (fast response).

GMR sensors are based on antiferromagnetically coupled multilayer thin films and show MR values up to 100%. Similar to AMR, the transfer curves are not linearly centered at H = 0. Contrary to AMR, large fields are needed to obtain the total magnetization alignment, therefore the maximum attainable MR ratio.

Spin Valves (SV) Increasing demands in sensitivity required improved MR sensors, so in 1991, an “engineered” structure was proposed by IBM [37]:  the SV sensor. The SV structure consists of two FM layers (e.g. CoFe, NiFe) separated by an NM layer (Figure 6.11(a)). However, in an SV, one FM layer is the free layer (or sensing layer) and sees its magnetization rotating under an external magnetic field, while the other FM layer is the

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reference layer, and has a fixed magnetization.4 The sensor output response can be formulated with ΔV = − MR.



RI w. cos(θ free θ pinned ) (6.14) 2h

[38] showing a linear dependence of R with the cos (θf – θp), averaged over the sensing area. It will be seen in Section 6.2.2 that by optimizing the geometry and for certain material characteristics, this equation can become linear in H. This is a major improvement for the SV over a GMR multilayer, which allows an integrated sensor biasing and linearization scheme. In an SV, one of the FM layers (reference layer) is in contact with a pinning layer (e.g. MnIr, MnPt), which is an AF material able to induce a strong exchange coupling field (Hexch). Therefore, under external fields H smaller than Hexch, only the free layer is able to rotate, as if it were a compass needle. Figure 6.11(b) shows a typical SV structure, based on thin layers (few nm) of soft magnetic materials (NiFe, CoFe) and a Cu spacer, while in Figure 6.11(c), the magnetic characteristics of an SV stack, measured by a vibrating sample magnetometer (VSM), is depicted. The signature of two magnetic layers is visible by the two steps in the magnetic moment: for large external magnetic fields (H > Hexch), both free and pinned layers are aligned with the field, therefore a maximum moment (±Msat) is measured, equal to the sum of free and pinned layer individual moments. Under small fields (below the exchange pinning field, Hexch), only the free layer can rotate with H, inverting its magnetic moment from positive to negative, following the direction of H. This is visible in the transport curve R(H) in Figure 6.11(d), where the free layer switching occurs near H = 0. The variation in resistance is in this case ~10% (although up to 21% MR values have been reported so far). The shift of the curve is caused by the FM coupling field (HN) between the two FM layers (typically less than 1 mT (or 10 Oe), mediated by the spacer thickness (magnetostatic coupling, Hf) and roughness (HN, Néel coupling) [39]. SV sensors are based on two FM layers (one is free and another is exchange-​biased) separated by an NM spacer and show MR values up to 20%. Unpatterned materials show R(H) sharp responses near H = 0. Sensor linearization requires additional geometry with microfabrication. The use of SV sensors relies on the ability to integrate such thin film structures in a functional device with controlled output response under external magnetic fields. These issues will be discussed in Section 6.2.2. Challenging applications (such as read head sensors in hard disks since 1994) are based on the SV principle, and the reliability of the SV sensors made them the successors of AMR in hard disk sensors until 2005, when the TMR effect started to be exploited in the magnetic recording industry.

A good description of the physical mechanisms and material optimization can be found in [48–​50]; in particular, reference [51] describes in detail the energy minimization equations and biasing mechanisms.

4

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Figure 6.12  Schematics of MR sensors comprising two FM layers (free and pinned) separated by (a) an oxide spacer (TMR sensor) and (b) a metallic, NM spacer (SV sensor).

6.2.1.3

Tunnel Magnetoresistance (TMR) In parallel with the development of GMR and SV sensors, the studies on spin dependent tunneling by Jullière in 1972 [40] were the seed for a new generation of MR devices, based on FM (FM1)/​insulator/​FM (FM2) layers. The film structure can be very similar to the one optimized for an SV sensor, being different mainly in the spacer between the two FM films (Figure 6.12). The spin dependent tunneling is originated from an imbalance in the electric currents carried by the spin-​up and spin-​down electrons, which travel between FM layers through an insulating barrier by the tunnel effect (see Figure 6.13) [41]. The structure of a magnetic tunnel junction (MTJ) is a sandwich of two thin FM layers separated by a thin insulating spacer layer (e.g. Al2O3 or MgO, 1 nm thick) which forms a tunnel barrier (Figure 6.13). When a bias voltage is applied across the barrier, finite current flows through the junction because of quantum-​mechanical tunneling. The model assumes that electrons at FM1 Fermi level will tunnel into free equivalent spin states at FM2 Fermi level (e.g. spin up electrons in FM1 will tunnel to spin up band in FM2). In Figure 6.13, one can see that in the parallel state spin up electrons are the majority spins in both FM electrodes, therefore spin-​up electrons will have also a large density of states (N ↑1 and N ↑2) available when tunneling from one layer to the other. However, when one of the layers reverses its magnetization (antiparallel state), the spin up is now a minority band for the FM2 electrode, thus reducing the probability of a majority electron from FM1 to occupy that state. This reduces the current, corresponding to a larger tunnel resistance. Here, the MR ratio defined in Eq. (6.12) can be obtained from this resistance change, and can be calculated from the spin polarization of the FM electrodes (P1 and P2, respectively, for FM1 and FM2), defined in



P1 =

N ↑1 ( EF ) − N ↓1 ( EF ) N ↑1 ( EF ) + N ↓1 ( EF )

;

P2 =

N ↑2 ( EF ) − N ↓2 ( EF ) N ↑2 ( EF ) + N ↓2 ( EF )

. (6.15)

Finally, the TMR can be calculated with

TMR =

R/ / − R4 2 P1 P2 = . (6.16) R4 1 + P1 P2

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Figure 6.13  Energy bands of a biased tunnel junction, in parallel and antiparallel states.

TMR ratio values up to 70% [42] and 600% [43] have been reported, respectively, for Al2O3 and MgO barriers combined with FM electrodes based on CoFe/​CoFeB films. In particular for MgO/​CoFeB structures, for sensor applications at room temperature, and which aim to detect low magnetic fields (below 2 mT), more complex structures are needed (e.g. including thick buffer layers, or complex annealing schemes for MgO/​CoFeB crystallization over an exchange bias MnPt antiferromagnet), and the quality of the spin transport at the interfaces is compromised, with the consequence of reducing the measured TMR values in the final microfabricated devices. The figures of merit for an MR sensor include not only the resistance change (TMR), but also a linear response, which depend mainly on the material properties (as will be seen in Section 6.2.2). The model could be experimentally demonstrated in the 1990s, with the measurements of tunnel junctions with MR signals at room temperature (not only at very low temperatures) [44, 45], and opened a very exciting era among researchers working in the area. For the current to pass across the barrier, these devices need to be patterned into current perpendicular to plane (CPP) devices, compared with the other MR sensors, which are generally current in plane (CIP). How this is done will be explained in Section 6.2.2. A comparison between CPP and CIP is shown in Figure 6.14, together

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(a)

(b)

(c)

Figure 6.14  (a) Geometries used for GMR and SV devices (CIP) and MTJ devices (CPP), (b) MTJ device resistance as a function of the external field, and (c) layer structure of an MTJ device.

with an example of an MTJ device output curve. Similarly to the SV devices shown in Figure 6.11(d), the linearization of the R(H) response requires the understanding of the biasing mechanisms and internal balance of the sensing layer energy (see Section 6.2.2). A distinctive property of an MTJ, or any tunneling device, is the exponential decrease of the tunneling current with the thickness of the tunnel barrier [46]. From a device perspective, this is interesting, since the resistance of an MTJ can be varied over many orders of magnitude simply by varying the thickness of the insulating spacer layer, as can be seen in Figure 6.15.5 A consequence is that sensors with the same dimensions (Area = w × h) can have tunable resistances, by changing the barrier thickness, therefore not compromising its spatial resolution. This breakthrough was significant because MTJs can achieve higher MR signals than SV sensors, and are the most important sensors used today in the magnetic storage industry. Other applications are also profiting from TMR technology (e.g. current sensors and biochips). Since 1990, the number of contributions in this area has increased tremendously, and can be found with details in review papers [47–​50].

For a CPP device (as an MTJ), the resistance depends on the area, A. Therefore, the control parameter is the resistance-​area product, R × A, which should be a constant for each MTJ stack.

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Figure 6.15  MTJ sensor resistance can be tuned precisely with the oxide barrier thickness, ranging within several orders of magnitude. (Adapted from [47]).

MTJ sensors based on two FM layers (one is free and another is exchange-​biased) separated by a NM ultra thin oxide can show MR values up to 600% at room temperature (300% only, upon proper linearization). Sensor linearization requires exchange biasing schemes and complex thin film stacks, and only after microfabrication, the internal coupling fields would allow a linear R(H) response. MTJ sensors need to be patterned in a CPP geometry, defining a junction area of few μm2.

6.2.2

MR Sensor Linearization The sensor characteristic curve (transfer curve) directly represents the output voltage (or resistance) dependence on the signal field, therefore an unique relation between R and field must be obtained for a good transducer. MR sensors (SV and MTJ) must be properly biased to produce a linear response to external magnetic fields, which is achieved if the pinned and free layers are orthogonal to each other. This is achieved by controlling the magnetization configurations, which are a consequence of all magnetic field sources at the sensing layer, such as magnetostatics, field anisotropy, demagnetizing fields and sense current fields (HJ). Moreover, coherent rotation of the sensing layer is dependent on the material properties (e.g. crystalline anisotropy, Hk), and also shape and dimensions of the thin film (thickness t, length L, and width w). Equation (6.14) can be studied for the situation where a linear dependence with the external field, H, exists, resulting in

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Figure 6.16  Illustration of the coupling fields at the sensing layer and the impact of patterning on the sensor transfer curve.



(

)

cos θ free θ pinned = cos 90° =

H + HJ + H f H keff

. (6.17)

Thus, Eq. (6.14) can be rewritten as

ΔV = − MR.

R I H + HJ + H f w. . (6.18) 2h H keff

Here, the effective anisotropy field is Hkeff = Hk + Hdem, thus including also the demagnetizing fields. Figure 6.16(a) shows magnetic fields at the sensing (free) layer, including the external field (H), the field created by the current density J (HJ), anisotropy field (Hk), demagnetizing field (Hdem) and FM coupling fields (Hf). Figure 6.16(b) shows the effectiveness of shape anisotropy in the sensor curve linearization, when compared with the unpatterned material transfer curve.

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Figure 6.17  Some strategies used for sensor linearization.

A linear R(H) dependence can be achieved if the pinned and free layers are orthogonal to each other. References [32, 38, 39] provide a good overview of the mechanisms for magnetization rotation, including the discussion of the energy terms and coupling between layers in FM thin films. For sensor dimensions in the micrometric scale, the calculation of the sensor response can be made using a mono-​domain model with coherent magnetization rotation (Stoner–​Wohlfarth model). However, this model is not accurate for nanometric dimensions or if edge effects need to be included, and micromagnetic modeling needs to be considered instead [51, 52]. Several strategies can be used to promote a linear response, free of hysteresis (Figure  6.17). One is to make use of the internal demagnetizing field through shape anisotropy, and reduce the size and aspect ratio of the sensor. Also, an external magnetic field created by on-​chip integrated permanent magnets can be used [53]. It can also be accomplished by adding additional exchange biasing layers, located near the free layer. Upon optimized annealing, it is possible to set the free layer with a weak pinning, orthogonal to the reference layer [54, 55]. This strategy is used for MgO-​based MTJ sensors, where the demagnetizing fields created by the low magnetization FM films (CoFeB) are not enough to promote a linear response. Linearization is naturally obtained when the sensing layer has superparamagnetic behavior –​a linear and hysteresis free response of the magnetization –​by reducing the thickness of the free layer. Thin magnetic layers with thicknesses below 1.5 nm can indeed present a superparamagnetic behavior, and have been successfully used in MgO based TMR sensors [56].

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Figure 6.18  Ideal MR sensor transfer curve, with a linear dependence of the voltage (or resistance) with the external magnetic field, H. The curve is centered at H = 0, and free of hysteresis. The sensor sensitivity is defined as the slope of the curve within the linear range.

The main characteristic of the MR sensor transfer curve shown in Figure 6.18 is the field sensitivity, which can be measured experimentally from the slope of the transfer curve. The linear range is optimized as a function of the H keff values (geometry and material dependent), while the maximum resistance variation (thus, the MR ratio) is intrinsic of the FM/​spacer/​FM structure and interfaces.

6.2.3

Detecting Magnetic Nanoparticles MR sensors have been successfully used for nanoparticle detection, in many areas of applications, and create a new family of devices named spintronic biochips, whose success relies on the capability to manipulate nanoparticles/​beads with magnetic properties in platforms integrating chips with MR sensors and microfluidic channels. The particles should have no magnetic moment at the remanent state, to avoid clusters within the microfluidic channels. Therefore, the MR sensors cannot detect their presence unless an external magnetic field, H, sets a magnetic moment in the particle, enabling it to act as a dipole. As a consequence, the magnetized particle will create its own magnetic fringe field (Hb), which will be detected by the MR sensor. Figure 6.19 illustrates this mechanism. Several authors have described how magnetic nanoparticles (MNPs) can be detected with MR sensors [57–​59], including the equations for the nanoparticle fringe field in the sensor plane. When an MR sensor is used for the detection of the fringe fields created by nanoparticles (Hb), then the sensor output voltage (Eq. (6.18)) can be rewritten as (for SV and MTJ sensors, respectively)



SV sensor output: ΔVSV = MR.

Rsq I 2h

w.

Hb + H J + H f H keff

(6.19a)

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Figure 6.19  Principle of detecting nanoparticles using MR sensors: upon magnetization of a superparamagnetic bead, its dipolar moment creates a fringe field (Hbead) that is able to rotate the sensor free layer magnetization, and therefore modify the sensor resistance.



MTJ sensor output:ΔVMTJ = TMR.

R A I Hb + H J + H f . . (6.19b) 2wh H keff

In Eq. (6.19(a)), Rsq is defined as ρ/​t, where ρ is the SV resistivity. Also, the quantity RA (resistance-​area product) shown in Eq. (6.19(b)) is constant for each barrier thickness. The strategy used for magnetic bead detection combines several steps [49]: (1) define a convenient method to magnetize the beads without affecting the magnetic orientation of the sensing layer;(2) select a method for bringing the particles into the sensor area using a microfluidic channel or spotting; and (3) obtain a highly sensitive sensor able to detect small signals due to low concentrations, low magnetic moment, or small particles. The magnetization of the nanoparticles can be done using a current line (coil) or a permanent magnet. In either case, using an in-​chip (integrated) or discrete (external) solution would depend on the geometry available and nanoparticle susceptibility, affecting the intensity of the field H required. Besides the nanoparticles, the highly sensitive MR sensors can also be affected by the applied field H, as Figure 6.20 illustrates. For this selected configuration, an external permanent magnet is used to magnetize nanoparticles flowing inside a microchannel, integrated in a dynamic magnetic cytometer [60] or separator [61]. Usually, several sensors are addressed sequentially, therefore the particle magnetization should be stable along the path inside the microchannel (several millimeters long). Uniformity issues limit the choice of magnetization schemes to a large permanent magnet located under the MR chip to induce a magnetization in the nanoparticle perpendicular to the sensor plane [62]. The impact of this external solution on the sensor performance (R(H) response) is depicted in Figure  6.20(b), where a reduced sensitivity or curve offset

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(a)

(b)

Figure 6.20  (a) Schematics of the geometry used for the nanoparticle magnetization using an external permanent magnet underneath the sensor. (b) The magnetic field components in the plane of the sensor (transverse and longitudinal) affect the free layer magnetization, with the consequent degradation of the sensor R(H) response. Optimum performance will be set when the field from the magnet (B = μ0.H) is purely vertical [62].

occurs whenever there is a small longitudinal or transverse component in the sensor plane, respectively. Several configurations have been explored for nanoparticle detection with MR sensors, where the particles are diluted in a circulating fluid (dynamic detection) or by spotting or confining them over the sensor area. The architecture shown in Figure 6.21 was developed for single particle detection and counting at particle velocities up to 20 mm/​s, compatible with cell detection or bacteria detection in blood or milk samples [62]. From the sensor output voltage monitored over time, several peaks could be observed out of the noise level. Comparing the experimental pulse shape and amplitude, it is possible to determine the magnetic orientation of each particle and also the height of the particle trajectory in the channel. Bipolar and unipolar pulses (with amplitudes between 5 and 200 μV) have been measured with SV sensors (Figure 6.22), and from fitting the data one could extract the tilting angle of the particle’s moment, indicating the rotational behavior of the particles within the fluid [60]. Another geometry uses SV and MTJ sensors for detecting surface bonded-​ biomolecules labeled by MNPs (Figure  6.23). In this configuration, biomolecular probes (e.g. DNA strands and antibodies) are initially immobilized on top of the sensors [63]. After washing, if the probe and target molecules are complementary, the magnetic

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Figure 6.21  One possible configuration for nanoparticle detection is based on a dynamic detection of particles flowing in a microchannel, with an external magnet to set the magnetization of the particles in a direction perpendicular to the plane. While approaching from the sensor region, the particles will affect the free layer magnetization.

particles will stay immobilized on top of the sensor. On the contrary, if probe and target molecules are non-​complementary the magnetically labeled targets will be washed out. As previously, the detection of the immobilized magnetic particles requires a homogeneous magnetic field over the sensor area. In general, an external coil or an integrated current line connected to a DC and/​or AC current source generates a DC and/​or AC magnetic field. AC or DC+AC magnetic fields are the most advantageous configurations since lower noise levels can be achieved due to the reduction of the 1/​f noise of the sensor [63].6 A typical static detection signal is depicted in Figure  6.24. The experiment starts with the measurement of the sensor’s output signal due to the external magnetic field. At this stage, the sensor’s surface is covered only with a buffer solution containing no magnetic particles. Measuring the sensor resistance at this point would show a constant value and represents the sensor baseline signal. The sensor resistance is the same as obtained from the linear transfer curve at H = 0. After the acquisition of this baseline signal over ~100 s, the buffer solution is replaced by a solution containing magnetically labeled molecules. As the magnetic particles are settling down over the sensor surface a signal variation is observed. This is associated with the sensor resistance change due to

A discussion on the limits of detection and the impact of the sensor area on the detectivity of DNA biochips can be found in [49].

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Figure 6.22  Dynamic detection of MNPs using a permanent magnet to set the particles field perpendicular to the flow direction. Rotation of the particles can be recognized from the sensor output pulse shape, which changes from the expected bipolar pulse to unipolar pulse (in case of a 90° rotation). Reprinted with permission from [60]. Copyright [2009], AIP Publishing LLC.

the fringe field created by the particles, following Eqs. (6.19(a)) and (6.19(b)). At some point, there will be a full coverage of particles over the sensor leading to a saturation signal and allowing biomolecular recognition to occur. After a washing step, unbound particles will be removed from the sensor’s surface, leading to a binding signal caused by the presence of the immobilized particles. In this particular case, for a biasing current of 8 mA and magnetizing the 250 nm particles with an external DC magnetic field of 18 Oe, it was possible to achieve a binding signal of 2 mV. The limits of detection can be explored, for low DNA concentration detection. This strategy has been consolidated by several groups providing a reliable tool, with prototypes under validation aiming for commercialization [64–​65].

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Figure 6.23  One possible configuration for nanoparticle detection is based on a static detection of particles immobilized over a functionalized layer over the sensor. The proximity to the sensor allows small magnetic fields to be used (when compared with the situation represented in Figure 6.21), therefore in-​plane fields can be used (created by an integrated current line, or small electromagnet near the chip).

Figure 6.24  Detection of nanoparticles immobilized over the sensor area, for an experiment with DNA probes. The binding signal is proportional to the number of targets bound, thus to the concentration.

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Figure 6.25  Geometry used for experiments requiring single nanoparticle actuation for DNA strand stretching with a magnetic tweezer.

MR sensors have been used to detect the vertical movement of single MNPs attached to DNA [66]. Figure 6.25 shows the geometry used for this detection, where the magnetic nanoparticle is integrated in a magnetic tweezer based on a current loop to stretch the DNA strand. Additional on-​chip current loops were microfabricated, to generate a magnetic field gradient on the magnetic nanoparticle anchored to the bottom of the cavity using a single DNA molecule. As a consequence, a magnetic force can actuate the stretching of the DNA strand. On a 3 μm diameter magnetic bead, the resulting average vertical magnetic force generated by a 40 mA current is F = 1.0 pN. Figure 6.26 shows an example of the output of a MgO-​based MTJ sensor when the DNA strand is vertically stretched. The vertical displacement of the bead, Δ, can be estimated by the difference of positions when the bead is actuated. When the bead Bead Bead = 8.7µVrms to ΔVUP = 9.3µVrms . is pulled up, the sensor signal increases from ΔVDOWN Assuming that the DNA is immobilized at the center of the gold pad, the DNA extension corresponds to the DNA length,  DNA = 1.5μm (5 kbp), corresponding to a verBead tical separation of zUP = 3.6μm . Detecting single molecule displacements requires improved electronics to minimize the impact of random in-​plane fluctuations in the output signals.

6.2.4

Reaching the Detectivity Limits: Sensor Noise Very weak magnetic field detection is required in a large number of applications. While SQUID is a key tool to perform these thanks to its ability to detect fields as low as 10–​14 Tesla, the cryogenic temperature operation of these sensors demand complex and expensive systems to maintain and operate. The architecture of these systems also imposes a minimum distance between the SQUID and the source of the magnetic field, limiting its spatial resolution. The development of MR sensors over recent years has shown them to be an alternative to SQUIDs for low-​field magnetic field detection. The minimum field that can be measured will determine the usefulness of the sensor for various applications; this minimum field is determined by the SNR, hence the necessity to understand well the noise

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Figure 6.26  Sensor output change during bead vertical displacement. The bead is actuated with the current loop, upon changing the current progressively (Adapted from [66]).

of these sensors. The frequency of operation is a key parameter in the detectivity: while the signal may not depend on the frequency, most of the dominant noises do.

6.2.4.1

White Noise White noise is noise that does not depend on frequency. In this category we find the thermal noise due to the random thermal motion of electrons. This noise is present in any electronic component. It is given by



SVThermal (V 2 / Hz ) = 4 K B TR, (6.20) where KB is the Boltzmann constant, T the temperature and R the resistance of the device. Thermal noise is directly proportional to temperature and vanishes at 0 K. The thermal velocities of electrons are high compared to the net drift velocities (the current) and are thus independent of the presence of a current. Shot noise is another type of white noise, and is the consequence of the discrete nature of electric charge flow. While flowing through a continuous conducting element, the electrical current behaves like an incompressible fluid. However, at a discontinuity, the current will be made out of a small number of electrons tunneling through the discontinuity; this will give rise to fluctuations in the voltage, which is dependent on the number of electrons, and thus on the current intensity. Shot noise is given by

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SVShot (V 2 / Hz ) = 2eIR 2 (6.21)



and is present only when the electrical media is not continuous. Shot noise is thus present in MTJ sensors but not in AMR/​GMR/​SV sensors. Although having larger MR ratios, a TMR sensor has intrinsically more noise than an SV sensor.

6.2.4.2

Non-​White  Noise The most common frequency dependent noise is 1/​f noise [67]; like thermal noise, it is present in every electrical component. Its origin is, however, not always well understood. In electronics, it is related to the trapping of charge carriers in crystal defects. Electrons (or holes) are captured by those defects and then released through a random probability law that favors energy concentration at low frequencies. This noise can be noticeable when current flows through the device. As 1/​f noise is present in all active as well as passive electronic components, it is thus also present in every type of MR sensor. Although a first principles calculation of that noise has not yet been provided, phenomenological models provide accurate equations to describe 1/​ f noise. Those models combine the known characteristics of 1/​f noise with phenomenological parameters measured in experiments. In the case of SV sensors, 1/​f noise is given by



SV1/ fSV (V 2 / Hz ) =

γ I 2 R2 , (6.22) NC f

where f is the frequency, N c is the number of charge carriers taking part in the current I, R is the resistance of the device, and γ is the phenomenological Hooge’s parameter that quantifies the magnitude of the noise for a certain device. For MTJ sensors, 1/​f noise is described by a slightly different expression, considering that the number of charge carriers going through the device must be proportional to the area of the device’s tunnel barrier:

SV1/ fMTJ (V 2 / Hz ) =

α H I 2 R2 , (6.23) Af

where A is the MTJ sensor area and α H is the modified Hooge parameter. Hooge’s parameter is not a constant characterizing each type of device, but the agglomeration of all the known dependencies of 1/​f noise. For example, in an MTJ sensor, it is a function of the magnetic field, the temperature, and the product of R and A (most commonly noted as R × A as it is a key characteristic of MTJ sensors). Values for this parameter can be found for MR sensors based on AlOx barriers [68–​69] and MgO barriers [70]. The correlation between 1/​f noise and the magnetic field means that for MR sensors, part of the noise is due to its magnetic properties and not only crystal defects as in regular electronic components.

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For practical integration of SV and MTJ sensors for nanoparticle detection, one needs to consider the SNR, which will define the limits of detection in either case. The magnetic field detectivity (i.e. the spectral noise SV calculated in units of T Hz ) corresponds to the magnetic field that a sensor can measure with an SNR = 1, and is generally defined by Eqs. (6.24) and (6.25), in the case of SV and TMR sensors, respectively. These equations are valid for low frequencies, where 1/​f noise is dominant over thermal noise and shot noise (in case of MTJ):





SV − SV =

γ I b 2 .R 2 NC f ΔH = ΔR MR Ib ΔH

SV − MTJ =

α H I b2 .R 2 A f ΔH = ΔR TMR Ib ΔH

γ NC . f

αH A. f

)

(

Hz (6.24)

(

Hz . (6.25)

in units of T

in units of T

)

The detection of very small magnetic fields under the 1/​f noise frequency range is only possible upon proper control of the following points: 1. The magnetoresistance (TMR or MR) needs to be as large as possible in order to maximize the output signal of the sensor. 2. The sensor sensitivity is highly affected by the linear range, ΔH, which must cover the field values induced by the nanoparticles. Therefore, for small concentrations, or low magnetization beads, ΔH should be as small as possible. One strategy is to incorporate magnetic flux guides in magnetic field sensors, when a large sensor footprint is not an issue. 3. The detectivity improves for larger sensor areas, A. As an alternative, several sensors can be connected in series and parallel configurations for improved performance [71]. However, increasing the area is not compatible with applications requiring good spatial resolution. 4. The quality of the thin films (in particular, the sensing layer magnetic configuration) may affect the values obtained for γ/​NC (for SV) or Hooges’ parameter αH (for MTJ). Therefore, 1/​f noise would benefit from improved deposition techniques and sensor patterning under minimum edge roughness and pinning centers [72]. 5. At lower frequencies, it is more difficult to detect weak magnetic fields, thus o­ perating at larger frequencies can be an option, if the bead fringe field and sensor  biasing can be set at selected frequencies [73, 74]. This is not an option for the detection of the small fields from biological activities (e.g. brain or heart). Table 6.3 includes some examples where MR sensors have been optimized for ultra-low field detection, therefore overcoming the noise.

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Table 6.3  Indicative values for the minimum fields detectable by the three types of MR sensors described in the text: AMR, SV, and MTJ. Notice the values are obtained for low frequencies (1 Hz), under the 1/​f dominant regime.

6.2.5

Sensor type

Comments

Detectivity @1Hz (T/​√Hz)

Ref.

AMR –​ bridge

Honeywell commercial AMR HMC1001

100 pT

[75]

GMR –​ bridge

NVE commercial GMR with flux concentrators

4 nT

[75]

SV

SVs with flux concentrators

7–​20 nT

[76]

SV

SVs with MEMs with flux concentrators

40–​600 nT

[74]

MTJ –​ bridge

NVE commercial

~4 nT

[75]

MTJ –​ series

MTJ series

16.2 nT

[71]

MTJ

MgO barrier with flux concentrators

155 pT

[70, 77]

Competing Technologies and Technological Development Detection of biomolecular hybridization is playing an important role for healthcare, biomedical research, and the pharmaceutical industry. Of particular interest is, for example, the detection of DNA-​DNA hybridization for the detection of mutations, genetic diseases, or pathogen microorganisms. MR devices offer a good alternative to more conventional equipment for biomolecular hybridization recognition, such as fluorescent marker devices that use optical or laser-​based fluorescence scanners to detect fluorescent marked biomolecules. Here, the fluorescent markers are replaced by magnetic markers. The advantages of MR sensors are their high sensitivity and spatial resolution, fast response, and low background noise, since biological samples are NM. Because the detection is transmitted to the system as an electric signal, it is also easy to integrate the device into an electronic system connected to a computer and automate the measurement. The whole device being compact and cheap, MR sensor-​based biochips are a competitive alternative to more traditional systems for the analysis of a small number of different biological analytes. Advantages of MR sensors for biological detection are high sensitivity and spatial resolution, fast response, and low background noise. Due to tremendous progress on deposition equipment and precision characterization tools, which allow an improved control and accuracy of thin film materials in large area substrates, it has been possible to consolidate the integration of MR thin films into several technological products currently in the market (e.g. CMOS embedded

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electronic circuits). Several characteristics of MR sensors have made them competitive when compared with other magnetic field sensors. For example, fluxgates, which require more power for less resolution, and SQUIDS, which are expensive and require low temperatures, hence imposing a minimum distance between the sensor and what has to be measured, and thus a reduction of the spatial resolution. MR sensors are being used in biomedical applications for DNA, antibody, and cell detection. By marking the biological sample with nanometer-​size magnetic beads, one can detect the component of interest with a sensor, as well as actuate and manipulate them thanks to controlled magnetic gradients (magnetic tweezers). MR sensor enabled biochips were first developed using GMR sensors at NRL/​NVE in 1998. The first results using single SV sensors were obtained by Stanford and INESC-​MN in 2001, and a portable diagnosis platform for biomolecular hybridization was demonstrated in 2008 by INESC-​MN. The advantage of the magnetic approach compared to optical/​fluorescence methods is the low magnetic background noise of the biological sample, coupled to the field sensitivity of MR sensors, which allows the detection of a small number of beads. MR sensors can be fully integrated with large-​scale electronics (eg. CMOS), for compact integration with fast, multiplexing electronics.

6.3

Magnetoimpedance Biosensors Galina V. Kurlyandskaya

6.3.1

Introduction to Magnetoimpedance Biosensors Magnetic sensors were introduced long ago to the field of biomedical research focused on the development of advanced diagnostic tools. There are two principal types of biomedical applications: analysis of electric and magnetic properties of living systems closely related to their functionality and analysis of the requested specific properties of the bioanalytes. In the present work, we understand magnetic biosensors as diagnostic tools related to the second objective. In general, magnetic biosensors can be classified as detection methods employing markers [78] and marker-​free detection methods [79, 80]. A magnetic biosensor is a compact analytical device incorporating a biological, a biologically derived material associated with a physicochemical magnetic transducer or transducing microsystem [81]. A magnetic sensor is a device that measures changes in a magnetic field, that is, a magnetic transducer converts a magnetic field variation into a change of frequency, current, and voltage. For a long time, the development of magnetic biosensors was suppressed because of their limited sensitivity and/​or big size. The description of the first “magnetic biosensor”

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was reported in 1998 by Baselt et al. [78], introducing the idea of adapting a magnetic field sensor for biosensing in a GMR prototype fabricated with the well-​controlled technology of a computer hard disc. The authors developed a method of detection of superparamagnetic labels and simultaneous characterization of many individual molecular recognition events called the “bead array counter concept” [78]. Since then, many attempts have been made aiming to develop a magnetic field-​based sensor adapted for biosensing using different physical phenomena, including giant magnetoimpedance (GMI) [81]. What was the reason, the driving force for making these efforts? The detection principle for a GMR or GMI biosensor is detecting stray fields of magnetic markers “attached” to biomolecules of interest via appropriate biochemistry and translating them into an electronic signal. Figure 6.27(a–​b) illustrates magnetism-​related sensing steps. First, the magnetic field detector based on the magnetoresistance effect is calibrated in the uniform external magnetic field, that is, the field dependence of the resistance is measured for the initial state (Figure 6.27(a)). If superparamagnetic labels are present in the test solution, the application of the external field results in the appearance of magnetic moments of each one of the spherical labels, which can be easily calculated as stray fields of the magnetized microspheres [82] (Figure 6.27(b)). As a result, for the same value of the external field, Hext, the effective field affecting the resistance value differs from the Hext value in the absence of the superparamagnetic labels. If biochemistry is used for immobilization, a magnetic label with a functionalized surface will appear at a certain distance dx from the surface of the magnetic sensitive element. Two parameters are crucial for the quantitative interpretation of the change in the electric output signal of a magnetic sensitive element: the shape of the magnetic label and the distance between the sensor surface and the magnetic label. The stray field B ( d x ) is generated by a single magnetized microsphere with a magnetic moment (m) symmetric with respect to a sphere center and it follows the power law [83]:

B (d x ) =

µ 0 3n ( n ⋅ m ) − m 4π dx

with n =

dx . (6.26) dx

The dx distance between the sensor surface and a magnetic label is a decisive parameter. It strictly depends on the types of biocomponents and diameter of the magnetic label, as shown in Figure 6.27(c). One should of course, remember that Figures 6.27(b–​ c) describe only one magnetic label for simplicity. Usually, many molecular recognition events and magnetic labels are involved in a real biosensing process. It is also worth mentioning that, in practice, a differential sensor set-​up with a reference sensor in

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Figure 6.27  (a) Schematic description of magnetic biosensor functionality in the case of the external magnetic field, Hext, applied in the plane of the sensitive element. Initial calibration of the magnetic sensitive element for field interval under consideration: U1 is a voltage drop created at the ends of the sensitive element to calculate the resistance for each field value in the absence of magnetic labels in the test solution. (b) U2 is the voltage drop enabling the calculation of the resistance in the presence of magnetic labels in the test solution. (c) In the absence of an external magnetic field, the superparamagnetic label has zero net magnetic moment, and U3 is the voltage drop when the magnetically labeled test biocomponent is immobilized by the receptor.

the bridge configuration can be employed in order to compensate for both thermal and electrical shifts between a reference sensitive element in the initial state and sensitive element with immobilization [78]. Two of the most important characteristics of the magnetic field detector are the sensitivity with respect to external magnetic fields, that is, the signal per unit field, and magnetic field resolution, that is, the smallest field that will trigger a response from the sensor [78, 81].

6.3.2 Magnetoimpedance Examples of typical available sensitivities and resolutions for magnetic sensors of different types are widely discussed in the literature [81, 84–​86]. The magnetoimpedance (MI) phenomenon consists of the change of the total impedance of an FM conductor, Z, under the application of an external magnetic field when a high frequency alternating

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current, I = I0 e2πift, flows through it. I0 is the maximum value or amplitude of the alternating current and t is the time. We can write Z(f)  =  R(f) +iX(f), where R and X are the real and imaginary parts of the impedance, respectively, and f is a frequency of the sinusoidally alternating current [86], with the magnitude of the impedance given as |Z|2 = |R|2 + |X|2. The impedance in certain FM conductors strongly depends on the external field, that is, Z = Z(H). The simple explanation of the dependence of MI in a uniform ferromagnet on the external field is based on the classical skin effect [86, 87]. The skin effect is an effective reduction of the cross section through which the high frequency AC current flows owing to the generated eddy currents. At a low frequency, the driving current passes over the entire cross section of the sample, but as the frequency increases, it concentrates closer to the surface of the sample. The dependence of the impedance of an FM FeNi wire on the value of the external magnetic field was discovered and described on the basis of changes in the magnetic permeability of a soft magnetic material and the skin-​depth by Harrison et al. [87]. The dependence of the impedance of a homogeneous cylinder under the application of an external magnetic field was theoretically described by Landau and Lifshitz [88]. After its discovery in 1935 [86], the MI effect was forgotten until 1991, when Makhotkin et al. developed a magnetic field sensor with a sensitive element in the shape of FeCoSiB ribbon, operating on the MI principle [89]. In 1994, GMI was rediscovered by Beach et al. [90] and Panina et al. [91]. There were many technological applications proposed and put into practice for GMI magnetic field sensors based, first of all, on their extremely high sensitivity (up to 500%/​Oe) and resolution up to 10–​7 Oe being at least an order of magnitude higher than the resolution of GMR magnetic field sensors of 10–​2 Oe having sensitivities below 1%/​Oe [84, 85]. Figure 6.28(a) shows typical two-​peaks type [92] GMI curves of the impedance and its part changes in the [FeNi(170 nm)/​Ti(6 nm)]3/​Cu(250 nm)/​[FeNi(170 nm)/​Ti(6 nm)]3 GMI multilayer: the impedance is small in high fields (saturated state), it increases with decreasing field and reaches a maximum near the anisotropy field:

Ha =

2 K1 a( M ⋅ a ), (6.27) µ 0 M s2

where K1 is the first anisotropy constant, μ0 is the magnetic field constant, Ms is the saturation magnetization, a is a unit vector in the direction of the easy magnetization axis, and M is a magnetization vector of the computational cell. The obtained multilayers are characterized by well-​ defined transverse magnetic anisotropy and low coercivity. Two branches of the MI curves are always measured reflecting the hysteresis of the magnetization processes: “up” for increasing and “down” for decreasing magnetic fields. To present the results, the GMI ratios, ΔZ/​Z, ΔR/​R and

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Figure 6.28  (a) Field dependence of the GMI ratios (both “up” and “down” branches are shown) for [FeNi/​Ti]3/​Cu/​[Ti/​FeNi]3 multilayers deposited onto a COC flexible substrate at a frequency of 175 MHz. Inset shows the same responses for a smaller field range: the highest sensitivity of about 30%/​Oe (arrow marked) corresponds to the real part of the impedance. (b) Frequency dependence of the maximum values of GMI ratios and GMI sensitivities for [FeNi/​Ti]3/​ Cu(LCu)/​[Ti/​FeNi]3 multilayers deposited onto glass substrates. (c) The highest sensitivity of about 110%/​Oe corresponds to a frequency of 30 MHz for a central copper lead thickness of LCu = 500 nm.

ΔX/​X, can be used instead of the change of the total impedance and its parts. The GMI ratios can be defined as

 Z ( H ) − Z ( H max ) ΔZ = 100 ×  (6.28a) X Z ( H max )



ΔR [ R( H ) − R( Hmax )] (6.28b) = 100 × R R( H max )



ΔX [ X ( H ) − X ( Hmax )] , (6.28c) = 100 × X X ( H max )

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where Hmax is the maximum applied field. The GMI sensitivity can be defined as 

6.3.3

 ΔX  ΔX / X  ΔZ  ΔZ / Z  ΔR  ΔR / R S ;S  and S  withh ΔH = 0.1 Oe. = = =    R  X   Z  ΔH ΔH ΔH (6.29)

Improving GMI Sensor Sensitivity Up to now, the majority of GMI multilayered structures have been deposited onto glass substrates, but recently, biological applications have demanded the introduction of polymer substrates [93]. Figure 6.28(a) shows the dependence of GMI ratios of [FeNi/​Ti]3/​Cu/​ [Ti/​FeNi]3 multilayers deposited by rf-​sputtering onto a cyclo olefin copolymer (COC) flexible substrate with increasing external fields for a small field range. One can see (using Eq. (6.29)) that the highest sensitivity of about 30%/​Oe and the linear response (arrow marked) corresponds to the real part of the impedance at a field of about 5.5 Oe. Figure  6.28(b) shows the frequency dependences of GMI ratios and GMI sensitivities for glass substrates and different thicknesses of the Cu lead. One can see that the frequency of the exciting current is an important parameter determining the GMI value: in each case, there is an interval corresponding to the maximum of GMI ratio or GMI sensitivity. The sensitivity of GMI elements of 10 mm × 500 μm × 0.5 μm size obtained for a flexible substrate (not shown here) is at least an order of magnitude higher compared to a typical GMR sensitivity of 1%/​Oe. The extra high sensitivity/​resolution of MI detectors not only allows the required measurement to be performed in a more precise way, but also enables accurate detection in the conditions in which utilization of the magnetic detectors with less sensitivity is not at all effective:  it allows the detection of magnetic labels at concentrations too small to detect by many other types of magnetic sensors. In magnetic biosensing this means the possibility to increase significantly the distance between the surface of the magnetic sensitive element and a label, and also an opportunity to measure particular spatial distributions of magnetic labels, for example, MNPs inside living cells or nanoparticle-​loaded tissues [94, 95]. All the steps represented in Figure 6.27 are not limited to GMR-​based sensors only. Any kind of magnetic field sensitive element with sufficient sensitivity, including GMI, can be employed in this configuration. There are possibilities to control the spatial distribution of the nanoparticles with respect to the magnetic sensitive element by light, temperature, external stress, electric or magnetic fields, pH, ionic strength, different salt types, solvents, or a combination thereof. The above-​mentioned properties are typical for a relatively new class of functional materials, hydrogels [96, 97], which can be proposed as functional complements of GMI biodetectors when combined with MNPs (ferrogels). Hydrogels are water swollen three-​dimensional networks composed of

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primarily hydrophilic polymer chains. They are water insoluble but able to swell rapidly in water or biological fluids. Due to significant water content, their flexibility is very similar to the flexibility of natural tissues [97]. The shape of the magnetic label is a very important parameter for magnetic biosensing result quantification. It is not only due to the magnetic response, but also because a spherical shape minimizes chemical agglomeration and non-​specific binding. It is important to have biocompatible spherical MNPs to ensure an intracellular uptake [100, 101]. Commercial magnetic spheres widely used in magnetic separation and biosensing are composite materials. As an example, one can mention Dynabeads® M-​450, which are 4.5 μm diameter superparamagnetic polystyrene (PS) beads consisting of nanometer-​ sized iron oxide particles embedded in a polymer matrix [98]. Precisely due to the difficulty in controlling the shape and space distribution of the nanoparticles embedded into a polymer matrix, obtaining the same magnetic moment for each one of the magnetizable beads is the most difficult task to achieve.

6.3.4

Magnetic Nanoparticle Synthesis MNPs can be synthesized by many different techniques [99–​101]. Although visible progress has been made in fabricating spherical nanoparticles, the shape is still one of the most difficult parameters to control. In addition, modern drug delivery technologies demand a rather large amount of uniform material, a goal difficult to achieve using traditional chemical techniques. One of the relatively new techniques for spherical nanoparticle fabrication is the method of electric explosion of wire (EEW) [102, 103]. It is an efficient, ecologically safe and highly productive method based on the thermal dispersion of material in gas, providing production rates up to 200 g/​h, for a small energy consumption of about 25 kWh/​kg. EEW ensures a fabrication of both magnetic and NM nanoparticles with an average particle size of 20–​100 nm and a high degree of sphericity [102–​104] (Figure 6.29). One of the difficulties of practical applications of nanoparticles is connected with the fact that the air-​dry assemblies of MNPs almost exclusively consist of aggregates formed by individual nanoparticles forced toward each other by strong magnetic interaction. Therefore, the necessary process of fractionation is very difficult and challenging. Beketov et al. [104] described the preparation, fractionation, and step-​by-​step characterization of ensembles of MNPs of magnetite produced by EEW using different chemical and physical techniques. They succeeded at fabricating de-​aggregated spherical

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Figure 6.29  Transmission electron microscope image of Fe3O4 spherical nanoparticles prepared by the electrophysical EEW technique (courtesy I.V. Beketov and A.P. Safronov, Ural Federal University, Russian Federation).

magnetite nanoparticle ensembles with a narrow size distribution and the potential basis for the creation of on-​purpose designed magnetic ferrofluids.

Ferrofluids are stable colloidal suspensions of MNPs in a chemically inert carrier liquid.

Good ferrofluids are stable with respect to gravitational forces and magnetic field gradients, and show no agglomeration under the effect of dipolar or Van der Waals interactions. The size of the particles is strictly limited by these conditions. Stability with respect to the field gradient is the most demanding factor leading to a general rule: the size of the nanoparticles of the ferrofluid should typically not exceed 10 nm. Two strategies were developed for the separation of nanoparticles:  coating with a polymer layer (ferrofluids with surfactants) and electrical charging of the particles for repelling due to Coulomb interaction (ionic ferrofluids). The composition of a typical surfactant ferrofluid is about 5% magnetic solids, 10% surfactant, and 85% carrier liquid, by volume. For biomedical and pharmaceutical applications, aqueous ferrofluids have been developed [105, 106].

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Figure 6.30  Optical microscopy: Dynabeads® M-​450 on an amorphous ribbon surface. Magnetic domain structure of amorphous ribbon is also revealed by the simultaneous application of the ferrofluid.

6.3.5

GMI Biosensor Prototypes The first reported GMI biosensor prototype was tested, precisely, with a commercial ferrofluid [107]. The measurements were performed without immobilization of MNPs, and the concept of “free” (non-​immobilized) magnetic labels was introduced, meaning that magnetic particles were not fixed at the surface of the sensitive element by molecular recognition events or specific interactions (Table 6.4).

Figure 6.30 shows an example of the surface of a GMI ribbon-​based sensitive element with both ferrofluid and magnetic Dynabeads® M-​450 on an amorphous ribbon surface in zero field, but after the application of an in-​plane magnetic field in the diagonal direction. The possibility of detecting “free” labels in the case of GMI is a consequence of the extra-​high sensitivity of GMI sensors. There have been more studies of both low-​ frequency magnetization behavior [108, 109] and GMI responses of magnetic sensitive elements in the presence of ferrofluids, including the measurements of the concentration dependence of certain parameters of GMI curves, such as the Z value in a certain magnetic field [110]. Even so, GMI responses of a ribbon covered by liquid ferrofluid and a ribbon covered by the remains of the ferrofluid after it has dried are different, that is, in a ferrofluid, nanoparticles can interact with each other and form complex structures, making the exact interpretation of the model measurements with a ferrofluid rather difficult.

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Figure 6.31  Cross section of thin FeNi film-​based GMI sensitive element: (a) with opened and (b) with closed magnetic flux.

It is important to mention that, in a GMI biosensor, there are three magnetic fields present: the magnetic field created by the flowing current, a biasing field created by an external field source, and the stray fields of the particles. Therefore, for two different magnetic materials (sensor nucleus, magnetic or magnetizable particles) involved in the same sensing process in GMI devices, there is a need to develop synergistic pairs of materials to define the combinations with the best performance. The capacity of the GMI amorphous ribbon-​based sensor to detect a magnetic layer deposited onto its surface is not something surprising. Cerdeira et al. [111] proposed the GMI modification by deposition of thin Fe layers in thicknesses of 10–​240 nm onto the surface of a CoFeMoSiB amorphous ribbon. The details of similar discussions on the surface anisotropy or additional deposited magnetic layer roles can be found in [112–​115]. An additional NM layer with high conductivity can also be useful for controlling the high frequency current distribution over the cross section of the GMI sensitive element (Figure 6.31). The enhancement of the GMI effect in Co65Fe4Ni2Si15B14 amorphous ribbons was reported recently by Chaturvedi et  al. [115] in the case of coating with NM carbon nanotubes (CNTs). CNTs were grown in commercial porous alumina templates by a chemical vapor deposition without the use of metal catalysts. It was shown that the presence of CNTs on the ribbon surface increased the GMI effect, which varied with the concentration of the CNTs. The supposition about observed sensitivity was described as follows: the presence of CNTs on the ribbon surface can reduce stray fields created by surface irregularities and close up the magnetic flux path, resulting in the enhancement of the GMI effect [115]. Despite the technological advantages of GMI sensitive elements based on thin film or magnetic multilayered structures, there have been few studies of such prototypes [110, 116].

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Table 6.4  Magnetic GMI biosensor and closely related prototypes used to date. Publication year

Type of MI sensitive element

Type of analyte/​marker

Immobili-​ zation

Ref.

2003

Co67Fe4Mo1.5Si16.5B11 amorphous ribbon

Ferrotec ferrofluid (liquid)

No

[107]

2003

Fe73.5Cu1Nb3Si13.5B9/​Cu/​ Fe73.5Cu1Nb3Si13.5B9 GMI multilayer

2.8 μm diameter superparamagnetic beads

No

[116]

2005

Co67Fe4Mo1.5Si16.5B11 amorphous ribbon

Dynabeads® M-​450

No

[117]

2005

CoFeSiB glass-​covered amorphous microwires

Co/​PS microparticles

No

[118]

2007

Co67Fe4Mo1.5Si16.5B11 amorphous ribbon

Dynabeads® M-​450

No

[97]

2007

CoFeSiB glass-​covered amorphous microwire array

Estapor beads

No

[119–​120]

2007

Co64.5Fe2.5Cr3Si15B15 amorphous ribbon

Non-​specific Fe3O4 nanoparticles

Inside HEK 293 cells

[94]

2009

Co-​reach microwire

Maghemite nanoparticles

Inside rat prostate cancer cells

[95]

2009

Co64.5Fe2.5Cr3Si15B15 amorphous ribbon; FeNi/​Cu/​FeNi GMI multilayer

Non-​specific Fe3O4 nanoparticles; Dynabeads® M-​450

No

[110]

2010

GMI-​microchannel system with patterned Metglass ribbon

200 nm size superparamagnetic nanoclusters

Yes

[121]

2011

FeCoCrSiB amorphous ribbon; [FeNi/​Ti]3/​Cu/​[FeNi/​Ti]3 GMI multilayer

Chemicell beads; Dynabeads® M-​450

Flow in microfluidic system

[122]

2011

CoFeSiBNb microwire with microfluidic system

Ferrofluid

Flow in microfluidic system

[123]

2011

GMI-​microchannel system with patterned Co-​based amorphous ribbon

RGD-​Fe3O4@ chitosan nanoparticles

Yes

[124]

2012

Co65Fe4Ni2Si15B14 amorphous ribbon

Carbon nanotubes

No

[115]

2014

[FeNi]/​Cu]4/​FeNi/​Cu/​[FeNi/​Cu]4/​ FeNi meander

No

[126]

2014

[FeNi]/​Cu]4/​FeNi/​Cu/​[FeNi/​Cu]4/​ FeNi meander

No

[127]

Ni nanoparticles covered by polymer

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The first one reported by Bethke et al. [116] employed both the “free” magnetic labels concept and perpendicular GMI configuration for the design of their prototype (flowing high-​frequency alternating current and external magnetic field are perpendicular to each other). The GMI sensitive element consisted of a well-​known three-​ layered MI structure [84, 85] of two magnetic layers separated by a conductive lead (Figure 6.31) [116]. The GMI response was measured in ethanol flow. The external magnetic field was applied in the normal direction, and superparamagnetic markers of 2.8 nm size were injected. Although the effect was as small as ΔZ/​Z ≈ 0.08% without markers and ΔZ/​Z ≈ 0.01% with markers, there was no doubt of the capacity of the prototype to detect 2.8 μm diameter magnetizable superparamagnetic beads placed in ethanol. The next GMI biosensor prototype based on a Co67Fe4Mo1.5Si16.5B11 amorphous ribbon without a protecting layer was designed and tested for Dynabeads® M-​450 [117]. Prior to the measurements with magnetic labels, a sensor prototype was carefully calibrated with a fluid bath to achieve the best performance. The orientation dependence of the MI effect was studied for an external magnetic field applied in plane of the ribbon for a number of orientations. The best MI responses were obtained for longitudinal orientation. The frequency of 3.5 MHz and driving currents of 1.5 to 7.5 mA were selected as optimal. Commercial suspension of Dynabeads® M-​450 (containing 4 × 108 beads/​ml in PBS with a pH of 7.4, 0.1% bovine serum albumin, and 0.02% sodium azide) was used for the preparation of test solution of 4 × 105 beads/​ml, that is, about 0.013 beads/​μm of the surface of the sensitive element. Clear differences between the MI responses with Dynabeads® and without them were found for both 3 and 4.5 mA currents. The best sensitivity for this concentration was achieved in a field interval of –​4 to +4 Oe and for the current of 3 mA at a frequency of 3.5 MHz [117]. The next reported GMI biosensor prototype was based on glass-​coated microwires [118, 119]. They have shown the dependence of the impedance response of a GMI-​ sensitive element on the concentration of Co magnetic microparticles (of about 2 μm size) covered by a PS layer of about 5 μm. The covering was used both to prevent the agglomeration of the particles and to facilitate their functionalization. The magnetic labels used in this study [118] had shown significant remanence (remanent magnetization to saturation magnetization ratio of 0.18) and a rather high coercivity of 500 Oe. It seems that the authors made an effort to follow the rule that works well for GMR sensors for single-​bead detection: the highest sensitivity is achieved when the size of the sensor matches the bead size. Therefore, for a sensitive element of 25 μm in diameter, the big Co/​PS particles of about 12–​15 μm in diameter dispersed in dodecyl sulfate (1% in distilled water) were selected. The obtained sensitivity was as good as 25–​30 magnetic particles/​μl. Although this was the first reported study for the measurement of the change of impedance of the GMI-​sensitive element on the concentration of the magnetic particles, this result is difficult to evaluate because the details of the measuring conditions were not reported. Here, like in the case of the

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first GMI multilayer sensitive element [116], the designers had to decide between the most sensitive longitudinal geometry of GMI and the desirable strong stray field of the markers. Next came the microwire array for GMI detection of magnetic particles reported by Chiriac et al. [120]. They used a glass-​coated microwire array. The optimal measurement conditions and the influence of a liquid suspension of commercially available Estapor beads on the GMI response of the array were studied. Three different concentrations of Estapor beads were used. The relative change in MI response depended on the number of active microwires. The highest variation of 35% was found for 10 active microwires, for a current intensity of 10 mA.

6.3.6

GMI Sensing of Living Systems As the next step, some tests with grown in vitro Cos cells were done to study the state of living systems with an unprotected GMI sensitive element and in the presence of magnetic fields. A colony of living cells was divided in two parts and conserved for about 30 min at 0°C. The first part was introduced into the fluid bath and a complete GMI curve was measured. Another part was kept at 0°C without applying an external magnetic field. Afterward, both parts were conserved for about 30 min at 0°C and treated with a contrast agent, and a number of apoptotic cells were counted by optical microscopy separately for each group [81].

It was found that the conditions of the GMI measurements do not have much effect on the state of the cells in the experimental group compared to the control one (the difference between the numbers of surviving cells in both groups was less than 15%). This possibility of working with grown in vitro cultures gave the basis to propose another application of GMI biosensor prototypes [97] based on the fact that surface-​modified superparamagnetic nanoparticles can be a subject of intracellular uptake.

The calibration of the GMI CoFeCrSiB amorphous ribbon covered and uncovered by a gold layer-​based prototype was done with cells in PBS in a fluid bath [94]. Afterward, iron oxide non-​specific superparamagnetic nanoparticles of 30 nm were introduced into human embryonic kidney (HEK-​293) cells by intracellular uptake. The next step was to measure GMI after the consequent removal of free MNPs. The induced voltage difference represented the quantity of nanoparticles participating in the uptake. The resulted fringe fields from the nanoparticles were detected via the MI change in the ribbons. The gold covering is considered to be an improvement due to its biocompatibility and because of the biocorrosion process prevention. The MI responses in both cases were dependent on the presence of nanoparticles inside the cells and on the value of the external magnetic field.

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Figure 6.32  Accumulation of magnetizable superparamagnetic Dynabeads® M480 in the channel of the microfluidic chip.

6.3.7

GMI Sensors in Microfluidic Systems There were also special efforts to make microfluidic systems incorporating a GMI sensitive element [121, 123]. Several technological difficulties associated with such a detection mode were revealed and some of them solved by the utilization of rather new solutions earlier not applied to GMI magnetic field sensors. Figure  6.32 shows an example of the accumulation process of magnetizable Dynabeads® M-​450 in the channel of the microfluidic chip designed and fabricated in IKERLAN-​IK4 Technological Research Centre, Spain. In order to adapt a thin film sensitive element to the microfluidic chamber and to increase the sensitivity significantly in the future, they used GMI multilayered sensitive elements deposited onto flexible substrates of the same copolymer as the material of the microfluidic chip [122]. A different design was proposed for a microfluidic microsystem integrating a GMI wire sensor that successfully detected the passage of MNPs. The GMI sensor consisted of a CoFeSiBNb microwire of 40 μm in diameter and was 1  cm long [123]. Very interesting GMI prototypes with patterned amorphous ribbon meander sensitive elements have been reported recently [121, 124]. A microchannel system allowed quick and parallel genotyping of the human papilloma virus of the types 16 and 18. Compared to the conventional fluorescent detection method, GMI demonstrated a number of advantages, like shorter test times or the expectation that the process can be simplified and replaced by a commercially available syringe pump. The effort to measure concentration dependence of superparamagnetic beads (non-​ immobilized Dynabeads® M-​480) was reported in 2009 [110]. The obtained sensitivity of about 2 μΩ/​bead was not very high due to excessive noise of the non-​shielded prototype. The obtained difference between GMI ΔZ/​Z ratio without beads and with them in concentration 4.4 × 107 beads/​ml was about 6.5%. Again, despite the best compatibility with semiconducting electronics and advantages of well developed thin film technologies [86, 92, 93, 125, 126], one should admit that GMI thin film-​based biosensors are still very rare. This situation cannot be explained by just taking into account commercial arguments: GMR sensors, having had an earlier start, are dominating the corresponding

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Hext

dz dy Uy or Uz Figure 6.33  Magnetic labels are initially positioned on a surface of a functional polymer at a distance dy from the surface of the magnetic sensitive element. After specific treatment (like water adhesion by hydrogel), the average distance is increased up to dz. This change in distance is reflected in the change of the average stray field value affecting the output signal of the sensitive element: the voltage drop at the ends of the sensitive element changes from Uy to Uz.

market. It looks like there is still a lack of technological development and that theoretical approaches related to GMI biodetection is opposing the development of GMI biosensors with enhanced sensitivity. One of the strategies could be the development of GMI thin film elements with a specially modified surface of the sensitive elements up to the formation of special lithographic structures for an enhancement of the sensitivity to stray fields [93]. Figure  6.33 shows a hypothetical experiment that can be performed exclusively with a magnetic field detector having an enhanced sensitivity as compared to a GMR sensor. This new configuration with magnetizable nanoparticles in fact is neither label free nor a magnetic label-​based sensitive element. In such a configuration, which is still under development, the distance/​spatial distribution of the nanoparticles with respect to the magnetic sensitive element can be controlled by light, temperature, external stress, electric or magnetic fields, pH, ionic strength, different salt types, solvents, or a combination thereof [127]. In 1935, Harrison et al. proposed MI as “a novel method of measuring or detecting small changes in a magnetic field” [87]. Nowadays, many applications of GMI have been proposed in different fields, ranging from the research laboratory, through navigation and to pharmaceutical factories and hospitals, including devices already commercially available on the market. Although GMI-​based biosensors are still under laboratory development, there is hope, supported by the latest publications, of making them a widely spread advanced diagnostic tool.

Acknowledgments Galina V. Kurlyandskaya would like to thank A.P. Safronov, I.V. Beketov, A.V. Svalov, S.O. Volchkov, A. García-​Arribas, E. Fernández, and A.A. Svalova for special support.

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Sample Problems Question 1 Estimate the drift velocity of conduction electrons within a silver conductor on an electrical lead for a kettle or toaster with an applied current of 10 A. Question 2 Compute the fringe field created by 50  nm diameter magnetite particles (χ = 0.7), magnetized parallel to the sensor plane with a field of 1.2 kA/​m (15 Oe). Assume the particles are approximated to a magnetic dipole, placed 0.2 μm vertically from an MR sensor with area of 2 × 6 μm2 (I = 1 mA, MR = 10%, R = 900 Ω). Determine the maximum field at the surface of the sensor, when the particle is vertically located over the sensor, and also the average field over the sensor area. Question 3 What is a magnetic biosensor? Question 4 What is magnetoimpedance? Question 5 What are the most important characteristics of a magnetic field detector? References [1]‌ E. H. Hall, On a new action of the magnet on electric currents. Am. J. Math., 2:3(1879), 287–​92. [2]‌ K. von Klitzing, Discovery of (integer) quantum Hall effect. Nobel Lecture. (1985). [3]‌ R. Laughlin, H. Störmer, and D. Tsu, Discovery of a new form of quantum fluid with fractionally charged excitations. Nobel Lecture. (1998). [4]‌ R.E. Popovic, Z. Randjelovic, and D. Manic, Integrated Hall-​effect magnetic sensors. Sens. Actuators A Phys., 91:1(2001),  46–​50. [5]‌ J. E. Lenz, A review of magnetic sensors. Proc. IEEE, 78:6 (1990), 973–​89. [6]‌ A. Oral, S. J. Bending, and M. Henini, Real-​time scanning Hall probe microscopy. Appl. Phys. Lett., 69:9 (1996), 1324–​6. [7]‌ C. Schott, F. Burger, H. Blanchard, and L. Chiesi, Modern integrated silicon Hall sensors. Sensor Rev., 18:4 (1998), 252–​7. [8]‌ A.B. Frazier, Zhixiang Liub, Li Tianc, and J. Parhamd, Miniaturized linear magnetic position sensors for automotive applications. IEEE Sensors, 2 (2002), 1565–​70. [9]‌ G. Mihajlović, P. Xiong, S. von Molnár, et al., Detection of single magnetic bead for biological applications using an InAs quantum-​well micro-​Hall sensor. Appl. Phys. Lett., 87:11(2005), 112502. [10] M. Bando, T. Ohashi, M. Dede, et  al., High sensitivity and multifunctional micro-​Hall sensors fabricated using InAlSb/​InAsSb/​InAlSb heterostructures. J. Appl. Phys., 105:7 (2009), 07E909.

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7

Magnetic Nanoparticles for Magnetic Resonance Imaging Contrast Agents Nohyun Lee and Taeghwan Hyeon

7.1 Introduction Magnetic nanoparticles (MNPs) such as iron oxide nanoparticles have received enormous attention in various fields because of their unique properties [1]. Currently, MNPs are employed for diverse biomedical applications such as magnetic resonance imaging (MRI) [2], magnetic hyperthermia [3], targeted delivery of genes and drugs [4], biosensors [5], protein separation [6], and amplified protein assays [7]. Among these applications, MNPs have been most intensively investigated for their applications as MRI contrast agents. In comparison with other noninvasive imaging modalities such as computed tomography (CT) and positron emission tomography (PET), MRI can provide excellent anatomic details with high spatial resolution without use of radioisotopes or X-​rays. However, the sensitivity of MRI is still insufficient to detect subtle changes in a tissue, which is critical for early diagnosis of diseases [8]. In order to improve the visibility of internal organ structures in MRI, contrast agents are administered orally or intravenously. Although contrast agents themselves do not produce MRI signals, they generate a contrast effect by changing MRI signals of nearby water protons. Since the MRI contrast effect is dependent on the magnetic property, either paramagnetic or superparamagnetic materials can be used as MRI contrast agents. Thus far, paramagnetic metal ions (e.g. Gd3+ and Mn2+) and various nanoparticles (e.g. Fe3O4, FePt, and Gd2O3) have been employed in MRI. Among them, iron oxide nanoparticles have distinct advantages, including long circulation time, high biocompatibility, and superior sensitivity. Iron oxide nanoparticles (e.g. ferumoxide) prepared via a coprecipitation method was clinically approved for the detection of liver lesions and lymph node metastasis [9]. Although ferumoxide and similar iron oxide-​based contrast agents are no longer used in clinical situations, recent development of MNPs is expected to produce advanced MRI contrast agents with higher sensitivity, targetability, and multifunctionality [10]. In fact, the process of synthesizing uniform-​sized MNPs has experienced significant development during the past ten years [11]. Such progress has enabled fine control of the magnetic properties of nanoparticles by tuning their sizes and compositions. In addition, recently developed MNPs have clearly defined surface structure, which can be easily modified by various methods, such as ligand exchange, encapsulation with

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Magnetic Nanoparticles for MRI Contrast Agents

229

Table 7.1.  NMR relaxivities of contrast agents based on MNPs Nanoprobes

Magnetic core

Core size (nm)

Overall size (nm)

Coating

160

Dextran

Relaxivity (mM–​1s–​1)

Ref.

r1

r2

10.1

120

[23]

Ferumoxide (Feridex®)

Fe3O4, γ-​Fe2O3

4.5

Water-​soluble iron oxide nanoparticle (WSION)

Fe3O4

12

DMSA

218

[21]

Ferrimagnetic iron oxide nanoparticle (FION)

Fe3O4

58

DSPE-​ mPEG2000

324

[22]

Extremely small iron oxide nanoparticle (ESION)

γ-​Fe2O3

3

29.2

[17]

Mn-​doped magnetism-​ engineered iron oxide nanoprobes (MnMEIO)

MnFe2O4

12

DMSA

358

[24]

Co-​doped magnetism-​ engineered iron oxide nanoprobes (Co-​MEIO)

CoFe2O4

12

DMSA

172

[24]

Ni-​doped magnetism-​ engineered iron oxide nanoprobes (Ni-​MEIO)

NiFe2O4

12

DMSA

152

[24]

Zn-​doped ferrite

Zn0.4Mn0.6Fe2O4

15

DMSA

860

[25]

Cannonball

Fe/​Fe3O4 core/​ shell

16

DMSA

312

[32]

Fe@MnFe2O4 MNP (Fe@ MnFe2O4 MNP)

Fe/​MnFe2O4 core/​shell

16

DMSA

356

[33]

Iron/​iron oxide core/​shell nanoparticle

α-​Fe/​FeO4 core/​ 16 shell

DMSA

324

[29]

Rhodamine-​dye-​doped silica (DySiO2)-​(Fe3O4)n

multiple Fe3O4 nanoparticles

9

45

DMSA

397

[40]

Fe3O4-​mesoporous silica nanoparticles (Fe3O4-​MSN)

multiple Fe3O4 nanoparticles

8.5

87

PEG

76.2

[39]

14 nm superparamagnetic iron oxide nanoparticle (SPIO-​14)

Fe3O4

13.8

28.6

DSPE-​mPEG 1000

385

[42]

5 nm superparamagnetic iron oxide nanoparticle (SPIO-​5)

Fe3O4

4.8

14.8

DSPE-​mPEG 1000

130

[42]

15

PEG

4.77

amphiphilic surfactants, and formation of inorganic shells [12]. Thus, various kinds of MRI contrast agents based on MNPs have been developed (Table 7.1). In this chapter, we will review the principles of MRI contrast agents and show how MRI contrast effects can be controlled through modification of MNPs.

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Nohyun Lee and Taeghwan Hyeon

7.2

Basic MRI Principles and Properties of MNPs

7.2.1

Basic Principles of MRI MRI is based on nuclear magnetic resonance (NMR) that uses the magnetic properties of atomic nuclei. Among the various available atoms, such as 1H, 3He, 13C, 19F, 17O, 23Na, 31 P, and 129Xe, NMR signals of 1H is usually used owing to its abundance in our body and its high sensitivity. Thus, a typical MR image showing anatomic details consists of NMR signals of hydrogen atoms of water and fat in a body. However, MRI using other atoms also has enormous potential. For example, background-​free MR images can be obtained with 19F-​based contrast agents because the amount of endogenous 19F is negligible. Sodium is involved in most biological processes, and 23Na MRI is able to provide information on cellular metabolism. In a strong external magnetic field, a proton aligns either parallel or antiparallel to the magnetic field. Immediately after the application of an external magnetic field, the populations of parallel and antiparallel spins are the same. Over time, more spins align parallel to the magnetic field because the energy state of the parallel spin is lower (Figure 7.1(a)). The energy difference between the two states is given by the equation ΔE = γhB0/​2π, where γ is the gyromagnetic ratio, B0 is the external field, and h is Planck’s constant. Because the energy difference is proportional to an external magnetic field, more protons align parallel at a higher magnetic field, resulting in higher sensitivity. In clinics, 1.5 T and 3 T MRI systems are available. Theoretically, the signal-​to-​noise ratio (SNR) for a 3 T MRI system is doubled in comparison with a 1.5 T MRI system because the NMR signal is proportional to the square of the external magnetic field (B0) while noise increases linearly. Indeed, the actual improvement in SNR is less than the theoretical expectation due to the greater susceptibility effect. In addition, the spatial resolution and imaging speed can be improved in a high magnetic field. However, the specific absorption rate (SAR), defined as the amount of radiofrequency (RF) energy deposited in tissues, is proportional to the square of the external magnetic field. Unregulated absorption of RF energy can lead to an increase in the body temperature of a patient, which prevents clinical applications of high-field MRI scanners. Although protons in a strong magnetic field create net magnetization (M0), this longitudinal magnetization (Mz) parallel to the applied field is very small compared with the external magnetic field, and thus, it is very difficult to detect. To generate a detectable signal, the magnetization of protons should be flipped into the transverse plane perpendicular to the applied field by the application of a resonant RF pulse (ω0 = γB0, where ω0 is the Larmor frequency). When the RF is irradiated, the number of protons in the high-​ energy state (antiparallel spins) increases (Figure 7.1(a)). Thus, the overall longitudinal magnetization is decreased. In addition, protons that rotate freely prior to applying the RF pulse begin to precess in phase with each other, creating transverse magnetization. By varying either the strength or duration of the RF pulse, the flip angle can be controlled according to the equation θ = γB1τ, where θ is the flip angle, B1 is the magnetic field of the RF pulse, and τ is the duration of the RF pulse. When the populations of parallel spins and antiparallel spins are the same, longitudinal magnetization no longer exists, and only the transverse magnetization remains. The magnitude of the transverse

231

Magnetic Nanoparticles for MRI Contrast Agents

231

Figure 7.1  (a) In a magnetic field B0, protons are parallel (low energy) or antiparallel (high

energy) to the magnetic field. When an RF pulse is irradiated, the population of the protons in a high-​energy state increases (decrease in longitudinal magnetization), and the protons begin to precess in phase (increase in transverse magnetization). When the RF pulse is turned off, the protons return to their initial state. During relaxation, longitudinal magnetization recovers (b) and transverse magnetization decays (c).

magnetization equals that of the longitudinal magnetization (M0) before the application of the RF pulse. When the RF pulse is turned off, the protons return to their initial state, which is called relaxation (Figure 7.1(a)). There are two relaxation processes: longitudinal relaxation and transverse relaxation. Longitudinal magnetization increases slowly as the protons realign with the axis of the external magnetic field according to the equation, Mz(t)  =  M0(1 – e–​t/​T1), where T1 is the relaxation time (Figure  7.1(b)). In addition, R1 relaxivity refers to the rate at which Mz recovers to M0, and it is given as R1 = 1/​T1. At the same time, transverse magnetization decays rapidly as the spins get out of phase (Figure  7.1(c)). Owing to spin-​spin interaction and external magnetic field inhomogeneity, transverse magnetization decay is much faster than longitudinal magnetization recovery. The T2 relaxation process is given as Mxy(t)  =  M0e–​t/​T2, where T2 is the relaxation time. R2 relaxivity refers to the rate at which Mxy decays (R2 = 1/​T2). T2 is related to the spin-​spin interaction. Protons that align parallel and/​or antiparallel with the external magnetic field create the difference in the magnetic environment. Although this difference is very small, it affects the relaxation of nearby protons. In addition, external magnetic inhomogeneity also affects the relaxation process. Although magnetic

23

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field homogeneity is very important to produce an MRI scanner, there are still some variations. Thus, protons in different locations are exposed to a different magnetic field, resulting in spin dephasing. R2* relaxivity indicates the rate of transverse magnetization decay by spin–​spin interaction and external magnetic inhomogeneity (R2* = 1/​T2* = R2 + γΔB, where ΔB is the local magnetic inhomogeneity). Since it is almost impossible to achieve perfect magnetic homogeneity, T2* is always shorter than T2. In a spin-​echo sequence, which is widely used in clinical NMR imaging, the effect of the external magnetic field inhomogeneity is eliminated using a refocusing RF sequence. During the relaxation process, the protons emit energy, which is absorbed from the RF pulse, in the form of RF waves. Since the magnetic component of return signal induces the current in the receive coil, an MR image can be produced from the RF waves. The receive coil should be positioned at right angles to the external magnetic field, B0. If the external magnetic field goes through the coil, the induced current is so enormous that the tiny current induced by the RF waves cannot be detected. In a clinical MRI scanner, the direction of the external magnetic field, also called the z direction, corresponds to the head-​to-​foot direction of the patient. Thus, the receive coil is positioned at right angles either to the left-​right direction of the patient (x direction) or to anterior-​ posterior direction (y direction). The received signal is then transferred to a computer, which reconstructs the raw data into MR images. To acquire spatial information, an RF pulse should be applied multiple times. TR (the repetition time) means the time interval between RF pulses. Because only transverse magnetization can be measured, the signal is maximized immediately after applying the RF pulse (t = 0, Mz = M0), and the longitudinal magnetization recovers according to the equation Mz(t) = M0(1 –​ e–​t/​T1). If an additional RF pulse is applied at time TR, the longitudinal magnetization that recovers during the interval is flipped into the transverse plane. At t = TR, the longitudinal magnetization is given as M(TR) = M0(1 –​ eTR/​T1). In addition, since it is impossible to measure the signal immediately after the application of the RF pulse, a short time period, referred to as TE (the echo time), is required. During the short period of TE, the transverse magnetization decays according to the equation Mxy(t) = M0e–T​ E/​T2. Considering the effects of both TE and TR, the MRI signal intensity is given by I = M0(1 –​ e–​TR/​T1)e–​TE/​T2. By varying TR and TE, the effect of T1 or T2 on MR images can be controlled. For example, the T1 effect can be enhanced using short TR because a tissue with short T1 can recover enough longitudinal magnetization between TR. Likewise, the T2 effect can be enhanced using long TE because transverse magnetization of a tissue with short T2 can decay sufficiently. At 1.5 T, typical values of TR and TE used to obtain T1-​weighted images are 500 ms and 20 ms, respectively; and the typical values to obtain T2-​weighted images are TR = 2000 ms and TE = 80 ms. In fact, neither the T1 effect nor the T2 effect can be eliminated perfectly. Instead, T1-​weighted MR images or T2-​weighted MR images can be obtained by controlling TR and TE. Because many different contrasts can be created using only two parameters, TR and TE, it is not easy to choose a suitable contrast in a particular situation. In general, a T1-​weighted image provides a clear delineation of anatomical structures, while a T2-​weighted image is preferably used for pathology since most pathology produces bright contrast due to edema.

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7.2.2

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MRI Contrast Agents Since each tissue has different T1 and T2 values, MR images containing anatomical details can be obtained using suitable MRI parameters. However, visibility, such as subtle changes in diseased regions, can be improved using contrast agents. Contrast agents can alter the MRI signal by changing the relaxation rates of water molecules according to the equation Ri = Ri0 + riC, where Ri0 is the relaxation rate in the absence of the contrast agents, ri is the relaxivity of the contrast agents, and C is the concentration of contrast agents. As shown in the equation, the relaxivity, which indicates the ability of contrast agents to alter the relaxation rates, is the slope of the relationship between relaxation rates and concentration of the contrast agents. There are two types of MRI contrast agents: T1 contrast agents and T2 contrast agents. In fact, most contrast agents can enhance both the R1 and R2 relaxation rate simultaneously. An increase in the R1 relaxation rate results in signal enhancement (positive contrast). Conversely, an increase in the R2 relaxation rate leads to signal attenuation (negative contrast). Although positive contrast is usually preferred in a clinical situation, not all of the MRI contrast agents can be used as positive contrast agents. While the enhancement of the R1 relaxation rate by T1 contrast agents is similar to that of the R2 relaxation rate, T2 contrast agents enhance the R2 relaxation rate to a much greater extent than the R1 relaxation rate. In addition, T2 contrast agents shorten the T2 relaxation time so significantly that MRI signal intensity is decreased even in the T1-​weighted MR images. Thus, it is very difficult to employ T2 contrast agents as positive contrast agents. Although a dark MRI signal by T2 contrast agents is sometimes confused with the signals from other pathogenic conditions, such as bleeding, calcification, and metal deposition (intravascular or extravascular hemolysis, hemochromatosis, cirrhosis, etc.), the sensitivity of T2 contrast agents is much higher than that of T1 contrast agents. Currently, paramagnetic gadolinium complexes are used in most contrast-​enhanced MRI in clinical settings [13]. While they are typically employed as extracellular fluid agents or blood pool agents, an organ-​specific gadolinium agent, PrimovistTM has been recently introduced. Furthermore, macromolecular gadolinium contrast agents show great promise for improving the quality of MRI angiography and in the quantification of blood vessel permeability. However, several issues remain to be resolved. First, the sensitivity of gadolinium complex is insufficient for target-​specific imaging or molecular imaging applications. Second, the gadolinium ion is very toxic. To avoid the toxic effect, gadolinium ions are chelated by multidentate ligands, such as 1,4,7,10-​tetraazacyclododecane-​ 1,4,7,10-​tetraacetic acid (DOTA) and diethylene triamine pentaacetic acid (DTPA), and the Gd-​complexes are rapidly excreted through the kidney following intravenous injection. However, gadolinium ions are sometimes leached from the chelates, inducing severe side effects [14]. Third, owing to their short circulation time, the imaging time of gadolinium complexes is short, and therefore, it is very difficult to obtain high-​resolution MR images that require long scan times. Owing to high biocompatibility and tunable magnetic property, iron oxide nanoparticles can address the limitations of gadolinium-​based contrast agents. The following sections deal with the magnetic properties of iron oxide nanoparticles, and subsequently show how to control or to optimize their MRI contrast effects.

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7.2.3

Properties of MNPs In ferro- or ferrimagnetic materials, magnetic dipoles tend to align spontaneously even in the absence of an external magnetic field. As a result, magnetic poles exist at the end of the magnetic body, creating a magnetic field. Within the magnetic body, an internal magnetic field in the opposite direction of the outside field is generated, resulting in magnetostatic energy. To minimize this magnetostatic energy, bulk magnetic materials have a multiple-​domain structure, wherein regions with the same magnetization are divided by domain walls. The magnetostatic energy and the domain-​wall energy are proportional to the volume of the magnetic body and interfacial area between domains, respectively. Therefore, below a critical size, a magnetic domain is not generated because more energy is required to generate a domain wall than to support the magnetostatic energy. The critical radius for single-​domain spherical nanoparticles is given by



rc =

9A µ0 Ms2

  2rc    ln  a  − 1 , (7.1)  

where A is the exchange stiffness constant, μ0 is the permeability of free space, Ms is the saturation magnetization, and a is the lattice constant. Under this condition, a particle has only one magnetic domain (single-​domain particle), and all of its magnetic spins are aligned in the same direction. The critical diameter of the transition from multi-​domain to single-​domain varies from a few nanometers to a few hundred nanometers depending on the magnetic properties of materials. For magnetite, which is usually used as T2 MRI contrast agents, the estimated critical diameter is approximately 130 nm [1]. Since the direction of magnetization of a single-​domain particle can be altered only by spin rotation, the highest coercivity can be observed at the critical diameter. However, for smaller MNPs, the coercivity begins to decrease (Figures 7.2(a) and (d)) [15]. When the size of the nanoparticles is too small, their magnetization can be easily flipped by thermal energy. Under this condition, nanoparticles do not show any magnetization in the absence of an external magnetic field, like a paramagnetic material, and the coercivity becomes zero. However, since the magnetic moments within a nanoparticle are aligned, the nanoparticles exhibit huge magnetization when an external magnetic field is applied (Figure  7.2). This unique property of MNPs is referred to as superparamagnetism. The transition temperature is called the blocking temperature (TB), and is defined by the equation TB = KV/​25kb, where K is the magnetic anisotropy constant, V is the volume of a single particle, and kb is the Boltzmann constant. The blocking temperature depends on the magnetic anisotropy and the size of the particle. The magnetic response of superparamagnetic nanoparticles in an external magnetic field can be estimated using the Langevin equation:

M 1 = coth α − , (7.2) Ms α

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Figure 7.2  (a) Size dependent magnetic properties of nanoparticles from superparamagnetism

to ferromagnetism. (b) M-​H curve of extremely small MNPs showing an almost linear relationship without magnetic saturation. (c) M-​H curve of superparamagnetic nanoparticles. Superparamagnetic nanoparticles do not show remanent magnetization in the absence of an external magnetic field. If an external magnetic field is applied, they show magnetic saturation. (d) M-​H curve of ferromagnetic nanoparticles. Ferromagnetic nanoparticles shows remnant magnetization and coercivity. Reproduced from Ref. [10] with permission from The Royal Society of Chemistry.

where α is the ratio of magnetic to thermal energy (α = μ0mH/​kBT), μ0 is the permeability of empty space, H is the magnetic field, and m is the magnetic moment of a particle. In a low magnetic field, the magnetic energy is very small compared with thermal energy (μ0mH/​kBT ≪ 1). Thus, the Langevin equation can be expressed as M/​Ms = μ0mH/​3kBT, which means that magnetization is linearly proportional to the magnetic field, like a paramagnetic material. However, the slope of superparamagnetic nanoparticles is much steeper than that of paramagnetic materials because of the huge magnetic moment of the superparamagnetic nanoparticle. At a high magnetic field, the magnetic energy is very high (μ0mH/​kBT ≪ 1), and the Langevin equation is given as M/​Ms = 1, representing the saturation of magnetization. In addition to size, the surface atoms also affect the magnetic properties of nanoparticles. Because spin-​spin exchange coupling is reduced at the surface, the surface spins are not perfectly aligned, known as the spin canting effect [16]. This effect is most pronounced for smaller nanoparticles owing to the extremely high surface-​to-​ volume ratio. For example, more than 90% of spins in 3 nm iron oxide nanoparticles are canted. Thus, compared with larger nanoparticles, an extremely small iron oxide

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nanoparticle (ESION) exhibits reduced magnetization, and magnetic saturation appears at a very high magnetic field (Figure 7.2(b)) [17].

7.3

Control of the MRI Relaxivity of MNPs

7.3.1

Size-​Dependent MRI Relaxivity Since the magnetic properties of an MNP are dependent on the size of the nanoparticles, MRI relaxivity can be tuned by size control of the nanoparticles. While size control of MNPs was difficult using conventional coprecipitation methods, a recently developed thermal decomposition method enabled the synthesis of uniformly sized nanoparticles ranging in size from a few nanometers to tens of nanometers [15, 18]. As explained above, MNPs are mainly used as T2 contrast agents because they create local magnetic inhomogeneities in the presence of an external magnetic field, leading to acceleration of dephasing of nearby proton precessions. According to the outer sphere spin-​spin relaxation approximation that describes the interaction of MNPs with protons, the R2 relaxation rate of a solution containing nanoparticles is given by



 64 π  2 γ N A M µ 2C rD , (7.3) R2 =   135000  where γ is the proton gyromagnetic ratio, NA is Avogadro’s number, M is the particle molarity (moles/​L), μC is the magnetic moment of the nanoparticle, r is the effective radius of the nanoparticles, and D is the diffusion coefficient of water molecules [19, 20]. From the equation, the R2 relaxivity of MNPs is proportional to the square of their magnetic moments and inversely proportional to their size. At first glance, the size and magnetic moment of the nanoparticles have opposite effects on the relaxivity. However, since the magnetic moment is also proportional to the volume of the nanoparticles (cube of the size of nanoparticles), the r2 relaxivity of the nanoparticles increases with their size. The size effect on the r2 relaxivity of nanoparticles was investigated using superparamagnetic iron oxide nanoparticles [21]. For example, water-​soluble iron oxide nanoparticles (WSIONs) in the size range of 4 to 12 nm exhibited size-​dependent magnetization and T2 contrast effects (Figure 7.3). The r2 relaxivities of WSIONs with sizes of 4, 6, 9, and 12 nm were 78, 106, 130, and 218 mM–​1s–​1 at 1.5 T. It is also noteworthy that since the magnetic properties of the nanoparticles prepared via the thermal decomposition method are superior to those of the nanoparticles synthesized using coprecipitation methods (e.g. Combidex), the r2 relaxivity of water-​soluble iron oxide (WSIO) with similar core size (4 nm) is higher. Although the T2 contrast effect increases with the size of the nanoparticles, most nanoparticles that have been used as T2 contrast agents are smaller than 20 nm. Because larger nanoparticles are not superparamagnetic, they exhibit remanent magnetization even in the absence of external magnetic field, resulting in agglomeration. Owing to lack of colloidal stability, these ferrimagnetic iron oxide nanoparticles (FIONs) have

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Figure 7.3  (a) Transmission electron microscopy (TEM) images of WSIONs of 4, 6, 9, and

12 nm. Size-​dependent T2-​relaxation time (b) and magnetization (c) of WSION. Reprinted with permission from Ref. [21]. Copyright 2005 American Chemical Society.

received less interest compared with superparamagnetic nanoparticles. In nature, magnetotactic bacteria have magnetosomes that contain FIONs to navigate along geomagnetic field lines. Recently, FIONs whose shape and size are similar to those of magnetosomes were successfully used as biocompatible T2 MRI contrast agents [22]. Owing to their excellent magnetic properties, the r2 relaxivity of FIONs at 1.5 T was 324 mM–​1s–​1, which is much higher than that of superparamagnetic iron oxide nanoparticles. Although the low colloidal stability of FIONs prevents their use in in vivo applications that require intravenous injection, they are ideal agents for MRI tracking of transplanted cells. In fact, FIONs are able to label various kinds of cells easily without any treatment to facilitate cellular uptake. Using a high Tesla MRI, single cells labeled with FIONs were readily detected. Furthermore, FIONs can be used for the monitoring of transplanted pancreatic islets. When pancreatic islets labeled with FIONs were transplanted intrahepatically, they were detected as multiple dark spots with a clinical MRI scanner under similar MRI conditions as humans, not only in a rat model, but also in a swine model. In addition, immune rejection of transplanted islets was also immediately detected using MRI; internalized FIONs were released from destructed islets, resulting in a decrease in the number of dark spots representing transplanted islets in MR images.

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Although MNPs are used mainly as T2 contrast agents, very small MNPs such as ultrasmall superparamagnetic iron oxide nanoparticles (USPIOs) can be used as T1 contrast agents [23]. Because strong magnetic fields by usual MNPs perturb the T1 relaxation process, reduced magnetization of smaller nanoparticles is advantageous for T1-​weighted MRI. As the size of nanoparticles decreases, the r2/​r1 ratio, which is used to determine whether to use nanoparticles as T1 contrast agents or T2 contrast agents, also decreases. Consequently, ESIONs with very weak magnetization are ideal materials to use as T1 contrast agents [17]. Although the r1 relaxivity of ESIONs ( 100 nm), the diffusion time is longer than the echo time, making the refocusing pulses that maximize remaining transverse magnetization effective. Thus, the R2 relaxation rate decreases with the size of the cluster whereas the R2* relaxation rate remains constant. For example, r2 relaxivity of micelles containing multiple MnFe2O4 nanoparticles was much smaller than their r2* relaxivity, demonstrating the importance of size control of the magnetic cluster [37]. In addition, T2*-​weighted imaging of cells labeled with MNPs is more sensitive than T2-​ weighted imaging because the nanoparticles are aggregated within endosomes and/​or lysosomes after endocytosis [38]. To employ the magnetic clusters as MRI contrast agents, the clustering should be finely controlled to prevent loss of colloidal stability. Simple crosslinking of MNPs is not suitable because the uncontrollable crosslinking reaction usually produces very large aggregates with a broad size distribution. Thus, various templates have been utilized to control aggregation. Among them, silica nanoparticles have been widely used owing to their high biocompatibility, multifunctionality, facile synthesis, size uniformity ranging from a few nanometers to several micrometers, and versatile functional groups [39]. For example, r2 relaxivity of iron oxide nanoparticles increased by three times via preparation of core-​satellite nanoparticles (DySiO2-​(Fe3O4)n), in which multiple iron oxide nanoparticles were attached onto a dye-​doped silica nanoparticle [40]. Since the MNPs synthesized using the thermal decomposition method have a compact structure, the overall size of the DySiO2-​(Fe3O4)n nanoparticles was approximately 45 nm. This multifunctional nanoparticle can be used as a dual-​imaging probe for the detection of polysialic acids (PSA). Recently, a mesoporous silica nanoparticle (MSN) has been intensively studied owing to its potential as a drug delivery vehicle. Since the chemical properties of

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MSNs are similar to those of a dense silica nanoparticle, a multifunctional drug delivery vehicle can be easily prepared. For example, multifunctional nanoparticles (Fe3O4-​MSN) were synthesized via assembling multiple iron oxide nanoparticles onto a uniform dye-​doped MSN [41]. Owing to the clustering of MNPs, the r2 relaxivity of Fe3O4-​MSN is approximately three times higher compared to free iron oxide nanoparticles. It is well k​ nown that nanostructured materials can accumulate in tumors owing to leaky blood vessels and poor lymphatic drainage, referred to as the enhanced permeation and retention (EPR) effect. Thus, after intravenous injection of Fe3O4-​ MSN, a tumor was detected using MRI and fluorescence imaging. Furthermore, the anticancer drug doxorubicin was successfully delivered to the tumor, inducing a therapeutic effect. Although the above examples show a successful increase in r2 relaxivity by clustering of MNPs, the relaxivity is still less than the theoretically estimated value, which is due to the small number of MNPs in a nanocomposite. Recently, nanocomposites that have high magnetic content were reported [34]. The nanocluster consists of multiple 16-​nm sized MnFe2O4 nanoparticles encapsulated within a thin silica shell. The nanocluster has such a compact structure that its average size was approximately 68 nm. Owing to its high magnetic content and optimal size within SDR, the r2 relaxivity of the nanocluster was 695 mM–​1s–​1, which is close to the theoretically estimated maximum r2 value of 759 mM–​1s–​1 (Figure 7.6(b)).

7.3.5

Effect of Coating on the MRI Relaxivity of MNPs The relaxation of protons is affected by the magnetic field generated by MNPs. Since the strength of the magnetic field decreases with distance from the nanoparticles, a nanoparticle coating should be optimized to achieve high relaxivity [42]. Considering the effect of a coating, which keeps water molecules from approaching the surface of nanoparticles, the R2 relaxation rate is given by



R2 =

1  256 π 2 γ 2  * 2 2 =  V M s a D (1 + L a ) , T2  405 

(7.6)

where γ is the proton gyromagnetic ratio, V* is the volume fraction of the nanoparticle, Ms is the saturated magnetization of the nanoparticle, a is the radius of the nanoparticle core, D is the diffusion coefficient of water molecules, and L is the thickness of an impermeable surface coating. According to the equation, the R2 relaxation rate is inversely proportional to the coating thickness of the nanoparticles. However, the coating effect cannot be explained solely by the thickness, as the surface ligand can interact with water molecules. The interaction also affects the relaxation process of protons because diffusion of water molecules is hindered by the ligands or they can even be immobilized owing to strong interactions, such as hydrogen bonds. Recently, the coating effect of phospholipid-​polyethylene glycol (PEG)-​encapsulated iron oxide nanoparticles was

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Figure 7.7  (a) Magnetic field generated by 14 nm iron oxide core. Solid line and dashed lines indicate the boundary of the lipid layer and PEG coating layer, respectively. Starting from the center, the dashed lines represents PEG550, PEG750, PEG1000, PEG2000, and PEG5000. (b) T2 relaxation time of 14-​nm and 5-​nm iron oxide nanoparticles with different PEG lengths. Reprinted with permission from Ref. [42]. Copyright 2010 American Chemical Society.

investigated by varying the molecular weight of PEG [42] (Figure  7.7). When the molecular weight of PEG decreased from 5,000 to 1,000 Da, the r2 relaxivity of 14-​nm sized iron oxide nanoparticles increased by 2.5 times to 385 mM–​1s–​1. However, the r2 relaxivity did not increase further when the size of PEG was further decreased to 500 Da. This can be partly explained by the immobilization of water molecules by PEG. It is well k​ nown that each ethylene glycol subunit of PEG is tightly associated with two to three water molecules by hydrogen bonds. Since smaller PEG is able to interact with fewer water molecules, the relaxivity does not increase. Because the R2 relaxation rate is sensitive to the nanoparticle surface, it can be used to develop MRI contrast agents that can detect enzyme activity and target molecules. For example, Feridex coated with dextran shells was used to detect activity of dextranase [43]. Since dextranase cleaved the dextran shell of Feridex, the R2 relaxation rate was increased by allowing water molecules to diffuse closer to the nanoparticle surface. In addition to enzyme activity, binding of a target molecule to nanoparticles was detected as a reduction in the R2 relaxation rate because the overall size of the shell including the target molecule increased [44]. Compared with MNP clustering, which results in an increase in the R2 relaxation rate, ligand binding is more sensitive and kinetically faster. According to the previous report, 5.3 fmol of Bacillus anthracis plasmid DNA, 8 pmol of cholera toxin B subunit, and a few cancer cells in blood could be detected using a decrease in the R2 relaxation rate [44]. Surface modification of nanoparticles is very important for successful biomedical applications because coating of nanoparticles affects their interaction with biological

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systems as well as MRI relaxivity. Therefore, various methods have been proposed including encapsulation with amphiphilic surfactants, ligand exchange, and formation of inorganic shells. Amphiphilic ligands, such as pluronic polymers and PEG-​phospholipid, can stabilize the hydrophobic nanoparticles through hydrophobic interactions in aqueous solvents [45]. The encapsulation method can be applied to various kinds of nanoparticles prepared by thermal decomposition in hot organic solvents. Furthermore, diverse biocompatible ligands are available because the amphiphilic surfactants have been developed as drug delivery vehicles. In the ligand exchange method, initial non-​ polar ligands are replaced by polar ones to endow nanoparticles with biocompatibility and colloidal stability in aqueous conditions. For successful ligand exchange, the affinity of polar ligands to the nanoparticle surface should be sufficiently high. Among various anchor groups, including phosphate, carboxylate, amine, and catechol, the catechol group, such as derivatives of 3,4,-​dihydroxyl-​L-​phenylalanine (DOPA), show superior efficacy to stabilize iron oxide nanoparticles due to chelation of surface iron by 1,2-​ enediol [46]. In addition to organic ligands, inorganic shells, such as silica, have been used for the functionalization of MNPs. Silica has several distinct advantages, including high biocompatibility, chemical inertness, and facile functionalizations. Recently, multifunctional nanostructures consisting of iron oxide nanoparticles and dye-​doped silica nanoparticles have been developed for bimodal imaging and drug delivery [41].

7.4

Toxicity of MNPs Since MRI contrast agents are injected into patients in a clinical situation, their toxicity is a very important issue. For example, Gd-​based MRI contrast agents can induce a severe side effect known as nephrogenic systemic fibrosis (NSF) in people with kidney failure [47]. Although MRI contrast agents based on MNPs have been shown to be safe in most reports, studies on their long-​term toxicity are still lacking. After injection, the circulation time and biodistribution of nanoparticles are dependent on their size, charge, and surface properties. When the overall size of nanoparticles is smaller than 5.5 nm, their circulation time is very short because they are excreted through the urinary system [48]. However, nanoparticles larger than 200 nm are rapidly cleared by the reticuloendothelial system (RES). Thus, the optimal size of nanoparticles for targeted NMR imaging is known to be ~10–​100 nm. The injected nanoparticles accumulate mainly in the liver, spleen, bone marrow, and lymph nodes. After cellular uptake, MNPs are located within endosomes and lysosomes, where they are slowly degraded by low pH and hydrolyzing enzymes [49]. During their degradation, harmful elements can be released, inducing toxicity. For example, magnetic FePt encapsulated with CoS2 were degraded after cellular uptake and led to apoptosis of the HeLa cells [50]. Consequently, in vitro cytotoxicity studies and acute in vivo toxicity studies are not sufficient to show the long-​term safety of nanoparticles, and it is necessary to study the final fate of nanoparticles, their metabolism pathways, and excretion of each component.

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Iron-​based contrast agents are ideal for clinical utilization because they are biocompatible and the metabolic pathway of iron is well studied [51]. After degradation, most iron ions are stored within ferritin and hemosiderin, and used for biological processes that require iron sources. In rats, the median lethal dose (LD50) of iron oxide nanoparticles is 400 mg/​kg. Considering the dose of iron oxide nanoparticles for MRI is 2.5 mg/​kg, the LD50 is very high. However, most studies have been performed with dextran-​coated iron oxide nanoparticles. Although iron oxide nanoparticles prepared via thermal decomposition have superior properties, it is uncertain whether they have the same metabolic pathway.

7.5 Conclusion Owing to high biocompatibility and magnetic moment, superparamagnetic iron oxide nanoparticles prepared have been used as T2 MRI contrast agents. In addition, recent advances in nanotechnology have enabled the fine control of MNPs in terms of size, composition, and surface functionalization. Iron oxide nanoparticles smaller than 3 nm (ESION) can be used as biocompatible long-​circulating T1 contrast agents owing to their reduced magnetization. Iron oxide nanoparticles larger than 20 nm (FION) enable extremely sensitive MRI of single cells and transplanted pancreatic islets. The relaxivity of MNPs can be improved by controlling their composition or preparation of ferromagnetic nanoparticles. Clustering of superparamagnetic nanoparticles also increases r2 relaxivity while maintaining colloidal stability. Because the highest r2 relaxivity of MNPs appears in SDR, and the relaxivity decreases beyond SDR, the overall size of the cluster should be controlled. The coating of MNPs also affects the relaxivity because surface ligands exclude water molecules from the magnetic core (reducing r2 relaxivity) or increase the residence time by forming hydrogen bonds (increasing r2 relaxivity). Because the sensitivity of MNPs is much higher than that of gadolinium-​based T1 contrast agents, their potential is enormous. Recently, many efforts have been devoted to combining the progress of molecular biology with nanotechnology. After the biocompatibility of nanoparticles is addressed, such efforts will enable early diagnosis, multimodal imaging, and personalized therapy.

Sample Problems Question 1 What is the main advantage of the heat-​up method to develop nanoparticle-​based MRI contrast agents? Question 2 Discuss the advantages of superparamagnetic nanoparticles as an MRI contrast agent compared with ferrimagnetic nanoparticles.

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Question 3 Is it possible to observe both T1 and T2 contrast effects with the same nanoparticles?

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[34] T-​J. Yoon, H. Lee, H. Shao, S. A. Hilderbrand, and R. Weissleder, Multicore assemblies potentiate magnetic properties of biomagnetic nanoparticles. Adv. Mater., 23:41 (2011), 4793–​4797. [35] J. M. Perez, L. Josephson, T. O’ ‘Loughlin, D. Högemann, and R. Weissleder, Magnetic relaxation switches capable of sensing molecular interactions. Nat. Biotechnol., 20:8 (2002), 816–​20. [36] R. A. Brooks, T2-​shortening by strongly magnetized spheres: A chemical exchange model. Magn. Reson. Med. 47:2 (2002), 388–​91. [37] U. I. Tromsdorf, N. C. Bigall, M. G. Kaul, et  al., Size and surface effects on the MRI relaxivity of manganese ferrite nanoparticle contrast agents. Nano Lett., 7:8 (2007), 2422–​7. [38] C. V. Bowen, X. Zhang, G. Saab, P. J. Gareau, and B. K. Rutt, Application of the static dephasing regime theory to superparamagnetic iron-​oxide loaded cells. Magn. Reson. Med., 48:1 (2002), 52–​61. [39] J. E. Lee, N. Lee, T. Kim, J. Kim, and T. Hyeon, Multifunctional mesoporous silica nanocomposite nanoparticles for theranostic applications. Acc. Chem. Res., 44:10 (2011), 893–​902. [40] J-​H. Lee, Y-​W. Jun, S-​I. Yeon, J-​S. Shin, and J. Cheon, Dual-​mode nanoparticle probes for high-​performance magnetic resonance and fluorescence imaging of neuroblastoma. Angew. Chem. Int. Ed., 45:48 (2006), 8160–​2. [41] J. E. Lee, N. Lee, H. Kim, et  al., Uniform mesoporous dye-​doped silica nanoparticles decorated with multiple magnetite nanocrystals for simultaneous enhanced magnetic resonance imaging, fluorescence imaging, and drug delivery. J. Am. Chem. Soc., 132:2 (2010),  552–​7. [42] S. Tong, S. Hou, Z. Zheng, J. Zhou, and G. Bao, Coating optimization of superparamagnetic iron oxide nanoparticles for high T2 relaxivity. Nano Lett., 10:11 (2010), 4607–​13. [43] D. Granot and E. M. Shapiro, Release activation of iron oxide nanoparticles: (REACTION) a novel environmentally sensitive MRI paradigm. Magn. Reson. Med., 65:5 (2011), 1253–​9. [44] C. Kaittanis, S. Santra, O. J. Santiesteban, T. J. Henderson, and J. M. Perez, The assembly state between magnetic nanosensors and their targets orchestrates their magnetic relaxation response. J. Am. Chem. Soc., 133:10 (2011), 3668–​76. [45] B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, In vivo imaging of quantum dots encapsulated in phospholipid micelles. Science, 298:5599 (2002), 1759–​62. [46] D. Ling, W. Park, Y. I. Park, et al., Multiple-​interaction ligands inspired by mussel adhesive protein: synthesis of highly stable and biocompatible nanoparticles. Angew. Chem. Int. Ed., 50:48 (2011), 11360–​5. [47] M. A. Perazella, Current status of gadolinium toxicity in patients with kidney disease. Clin. J. Am. Soc. Nephrol., 4:2 (2009), 461–​9. [48] H. S. Choi, W. Liu, P. Misra, et  al., Renal clearance of quantum dots. Nat. Biotechnol., 25:10 (2007), 1165–​70. [49] A. S. Arbab, L. B. Wilson, P. Ashari, E. K. Jordan, B. K. Lewis, and J. A. Frank, A model of lysosomal metabolism of dextran coated superparamagnetic iron oxide (SPIO) nanoparticles: Implications for cellular magnetic resonance imaging. NMR Biomed., 18:6 (2005),  383–​9.

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8

Magnetotactic Bacteria and Magnetosomes Dennis A. Bazylinski and Denis Trubitsyn

8.1

Introduction and History In the early 1960s, Salvatore Bellini, while examining water samples collected from several freshwater environments near Pavia, Italy, observed large numbers of bacteria swimming in a consistent, single, northward direction. He speculated that the apparent magnetic behavior of the cells was due to an internal “magnetic compass” and published his findings in 1963 in papers now translated and republished in 2009 [1, 2]. Magnetic behavior in prokaryotes was independently rediscovered in 1974 by R. P. Blakemore, who referred to these organisms as magnetotactic bacteria and was the first to reveal Bellini’s “magnetic compass” as the presence of magnetosomes within cells of magnetotactic bacteria [3]. Magnetotactic bacteria are defined as motile prokaryotes whose swimming direction is passively influenced by the earth’s geomagnetic and external magnetic fields [4]. This behavior is due to the presence of magnetosomes (Figure 8.1), which consist of a magnetic mineral crystal surrounded by a lipid bilayer membrane known as the magnetosome membrane [4, 5]. All known magnetotactic bacteria are microaerophiles that might also be facultatively anaerobic or obligate anaerobes. These organisms are predominantly found at the boundary between oxic and anoxic water or in sediment where oxygen has become depleted [4, 6]. These prokaryotic microbes display a great diversity in their cell morphology, physiology, and phylogeny [6]. The isolation and cultivation of these organisms has been repeatedly shown to be difficult due to their fastidious nature and lack of appropriate enrichment media. However, the recent isolation of new strains of magnetotactic bacteria, the development of new techniques for genetically manipulating these strains, such as the creation of solid growth medium on which magnetotactic bacteria can form individual colonies, and the sequencing and annotation of several magnetotactic bacterial genomes has led to great progress in our understanding of magnetosome biomineralization processes at the molecular, genetic, and (bio)chemical levels. The purpose of this chapter is to briefly review some of this recently derived information and the burgeoning numbers of commercial and medical applications of magnetotactic bacteria and their magnetic inclusions.

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Figure 8.1  Transmission electron microscopy (TEM) image of a typical magnetotactic bacterium

collected from a fish hatchery pond near Bozeman, MT, USA. The cell is helical in morphology, i.e. a spirillum. The solid arrow indicates the chain of magnetite magnetosomes, while the hashed arrows indicate the two flagella (cell is bipolarly flagellated). The inset shows a high-​ magnification TEM image of the magnetosomes. White arrows point to twinned crystals.

8.2

Magnetotactic Bacteria: Diversity, Phylogeny, and Physiology Magnetotactic bacteria do not represent a concise taxonomic group of organisms and the only consistent traits they all share are that: (1) they are motile by means of flagella, regardless of how the flagella are arranged on the cell; (2) they have a Gram-​negative type of cell wall and Gram-​positive magnetotactic bacterium have never been identified; (3) atmospheric levels of oxygen are toxic to them, that is, it kills and/​or inhibits their growth; and (4) they all have the ability to biomineralize magnetosomes, which are intracellular, membrane-​bounded crystals of a magnetic mineral iron oxide or sulfide [4, 6]. These organisms are extraordinarily diverse in morphology, physiology, and phylogeny (their evolutionary relationships). The diverse nature of magnetotactic bacteria was noted even in early studies, prior to the isolation of axenic cultures, as numerous different cell morphologies were observed from water samples from natural environments. These so-​called morphotypes include coccoid-​to-​ovoid cells, rods, vibrios, and spirilla, as well as a group of multicellular forms referred to as multicellular magnetotactic prokaryotes (MMPs) [4, 6, 7]. Although morphology is obviously not the best way to determine actual biodiversity of magnetotactic bacteria, phylogenetic studies based on 16S ribosomal RNA gene (16S rDNA) sequences of the different types of cultured and uncultured strains confirm an extensive biodiversity of these microorganisms, that is, they have been found to belong to a number of different major prokaryotic groups. Thus far, all currently recognized magnetotactic bacteria are associated phylogenetically with five major lineages within the domain Bacteria, with three lying within the Proteobacteria phylum. Most known cultured and uncultured magnetotactic bacteria belong to these latter three groups, which include the Alpha-​, Gamma-​, and Deltaproteobacteria classes of the Proteobacteria [6]. Other uncultured species belong to the Nitrospirae phylum [6, 8–​12] and one to

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Table 8.1  Phylogenetic distribution of magnetotactic bacteria with their associated cell morphotypes and magnetosome crystal morphologies and compositions. The phyla/​classes are in order of most (earliest diverging phylogenetic group) to least (latest diverging phylogenetic group) deeply branching on the Bacteria lineage. Note that the magnetotactic bacteria of the earliest diverging groups contain bullet-​shaped crystals of magnetite, suggesting that the first magnetosomes contained this type of magnetite crystal. Greigite magnetosomes appeared to have developed later only in the Deltaproteobacteria class of the Proteobacteria phylum. Phylum/​class

Cell morphotypes

Magnetosome crystal morphology

Magnetosome crystal composition

Omnitrophica (formerly candidate phylum OP3; part of the Planctomycetes-​Verrucomicrobia-​ Chlamydiae superphylum)

Rods

Bullet-​shaped

Magnetite

Nitrospirae

Rods, ovoid cells

Bullet-​shaped

Magnetite

Proteobacteria/​Deltaproteobacteria

Rods, vibrios

Bullet-​shaped

Magnetite, greigite

Proteobacteria/​Alphaproteobacteria

Spirilla, rods, vibrios, cocci

Cubo​octahedral and elongated prismatic

Magnetite

Proteobacteria/​Gammaproteobacteria

Rods

Cubo​octahedral and elongated prismatic

Magnetite

the candidate division OP3, part of the Planctomycetes-​Verrucomicrobia-​Chlamydiae (PVC) superphylum [13]. None have yet been found to be phylogenetically affiliated with the Archaea. While members of all five groups are known to biomineralize magnetic iron oxides, some in the Deltaproteobacteria also produce iron sulfides either exclusively or with iron oxides, the predominant type of mineral formed being apparently dependent on environmental conditions (e.g. concentration of O2 and/​or H2S) (Table 8.1). Magnetotactic bacteria are worldwide in distribution and ubiquitous in chemically and redox-​stratified sediments and water columns of almost all types of aquatic habitats [4, 6]. The occurrence of these gradient-​loving organisms is dependent on opposing gradients of oxygen from the surface and reducing compounds from the anoxic zone (e.g. sulfide) with a concomitant redox gradient in sediments or water columns resulting in an interface referred to as the oxic-​anoxic interface (OAI), also known as the oxic-​ anoxic transition zone (OATZ) [6]. While in most cases magnetotactic bacteria have been observed at the OAI of chemically stratified water columns or sediments [14], it is clear that different species of magnetotactic bacteria occupy different positions within the OAI that are dependent on specific chemical/​redox conditions. Magnetite-​ producing magnetotactic bacteria are generally found quite close to the OAI, while greigite-​producing species are found below the OAI in the sulfidic anoxic zone [6, 14]. Most cultured and uncultured magnetotactic bacteria are mesophiles restricted to habitats with pH values near neutrality, although several extremophilic species have recently been described. Moderately thermophilic uncultured species have been found

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in several hot springs in northern Nevada, USA, with a probable upper growth limit of about 63°C [15] and in California, USA [16], while several strains of obligately alkaliphilic magnetotactic bacteria have been isolated from different aquatic habitats in California, including the hypersaline, extremely alkaline Mono Lake [17]. The alkaliphilic isolates appear to be strains of the non-​magnetotactic, dissimilatory sulfate-​ reducing bacterium Desulfonatronum thiodismutans [18], and have an optimal growth pH of about 9.0. Magnetotactic bacteria have not yet been identified in strongly acidic habitats, such as acid mine drainage. Aspects of the diverse physiologies of known magnetotactic bacteria have been determined experimentally with cultured strains, as well as from genomic data, and inferred from the ecology, elemental analysis, and genomic information of uncultured types. All known magnetotactic bacteria are obligate microaerophiles, facultatively anaerobic microaerophiles, or obligate anaerobes [4, 6]. All cultured strains are mesophilic with optimal growth temperatures of ~30°C although, as mentioned above, a few uncultured, moderately thermophilic species have been identified [15, 16]. Different types of general metabolism are present in magnetotactic bacteria, including chemoorganoheterotrophy, where the electron donor and carbon source(s) are organic; chemolithoautotrophy, where the electron source is inorganic (e.g. S2–​) and the carbon source is CO2; and even chemoorganoautotrophy, where the electron source is organic but the carbon source is CO2 (e.g. formate, as an electron donor, is oxidized to CO2, which is then used as the carbon source) [19]. Metabolism is respiratory in most species; only one species, Desulfovibrio magneticus, is capable of growth through fermentation (pyruvate to acetate and hydrogen) [19, 20]. Many species metabolize sulfur compounds in some way, for example, many members of the alpha-​and gammaproteobacterial magnetotactic bacteria oxidize reduced sulfur compounds (e.g. sulfide and thiosulfate) as electron donors supporting chemolithoautotrophy [21–​26], while those in the Deltaproteobacteria are sulfate-​ reducing bacteria, reducing sulfate as a terminal electron acceptor to sulfide [17, 20, 27]. Magnetospirillum species and Magnetovibrio blakemorei, both Alphaproteobacteria, respire with nitrate as a terminal electron acceptor, the former organisms being denitrifiers reducing nitrate to dinitrogen gas [28–​30]. Interestingly, there appears to be a strong positive correlation between nitrate reduction, denitrification, and magnetite synthesis in Magnetospirillum species [29, 31, 32]. In Magnetospirillum gryphiswaldense, both the periplasmic nitrate reductase nap and the cytochrome cd1 nitrite reductase NirS are required for anaerobic growth, and are involved in redox control of magnetite biomineralization [29, 32]. All species tested are capable of nitrogen fixation [19, 24–​26, 30, 33] except strain SS-​5 of the Gammaproteobacteria [25] and Magnetospira strain QH-​2, the latter whose genome lacks the genes for this process [34]. Autotrophy is a relatively common feature in many magnetotactic bacteria and is mediated generally through the Calvin–​Benson–​ Bassham cycle, the pathway that plants use to fix carbon during photosynthesis using the key enzyme ribulose-​1,5-​bisphosphate carboxylase/​oxygenase for most species in the Alpha-​and Gammaproteobacteria [21, 24, 25, 30], while one, Magnetococcus marinus, an alphaproteobacterium, utilizes the reverse or reductive tricarboxylic acid cycle

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[22, 26]. Autotrophic growth also occurs in the alkaliphilic, hydrogen-​oxidizing, sulfate-​ reducing strains of magnetotactic bacteria phylogenetically similar to Desulfonatronum thiodismutans [17] although the pathway has not yet been determined. These physiological features demonstrate that magnetotactic bacteria have significant potential in the cycling of key elements, including iron, sulfur, nitrogen, and carbon in natural habitats [19].

8.3

The Bacterial Magnetosome: Composition, Size, Arrangement, and Morphology Magnetosomes are intracellular, membrane-​bounded crystals consisting of the magnetic minerals magnetite (Fe3O4) and greigite (Fe3S4) [4, 6]. While most magnetotactic bacteria biomineralize only one magnetosome mineral, some are able to synthesize both magnetite and greigite [27, 35–​37]. Magnetite produced by magnetotactic bacteria is generally considered to be of high purity, lacking other metal ions, although trace amounts of some (e.g. titanium) have been found in some uncultured magnetotactic bacteria [38], while significant amounts of metal contaminants (e.g. copper) have been found in greigite magnetosome crystals of some uncultured magnetotactic bacteria [39]. Irrespective of mineral composition, virtually all individual magnetosomes crystals lie between 35 and 120 nm in diameter [4, 6, 40] which places them in the stable single magnetic domain size range [40–​43]. Single magnetic domain crystals of magnetite and greigite are the smallest particles, consisting of these minerals that would still be permanently magnetic at ambient temperature. Smaller, superparamagnetic crystals do not have stable, remanent magnetization (the magnetic induction or magnetism remaining in a material in a zero magnetic field after exposure to a strong external magnetic field) at ambient temperature, are not magnetic, except in the presence of a strong magnetic field, and would therefore not function for magnetotaxis in a bacterium. Larger particles tend to form multiple domains, reducing the remanent magnetization of the crystal. Through the synthesis of single magnetic domain crystals, magnetotactic bacteria have maximized the magnetic remanence per unit volume of mineral [43, 44]. Magnetosomes are usually arranged as one or more chains within the cell [4, 6, 40, 43]. While magnetic interactions between individual magnetic magnetosomes within the chain might be important in causing each magnetosome moment to orient parallel to one another, thereby minimizing the magnetostatic energy of the chain and maximizing the magnetic dipole moment of the bacterial cell [43], cytoskeletal elements might also play a major role in magnetosome chain formation and anchoring the chain within the cell [45, 46]. In the chain arrangement, the total magnetic dipole moment of the bacterium is the sum of the moments of the individual magnetosomes, which ultimately causes the cells to passively align along the earth’s geomagnetic field lines as they swim [43, 44]. The morphology of magnetosome crystals is typically consistent within a single species of magnetotactic bacterium [4, 6]. This is more applicable to magnetite-​ producing magnetotactic bacteria than those that biomineralize greigite magnetosomes

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Figure 8.2  TEM images of the general morphological types of magnetite crystals in

magnetotactic bacteria. (a) Cuboctahedral crystals from an uncultured Magnetospirillum species; (b) elongated prismatic crystals from cultured Magnetovibrio blakemorei; (c) fts anisotropic crystals from uncultured Candidatus Thermomagnetovibrio paiutensis; and (d) dts anisotropic crystals from a cultured alkaliphilic, sulfate-​reducing magnetotactic bacterium phylogenetically related to the non-​magnetotactic Desulfonatronum thiodismutans.

as several different morphologies of greigite have been observed in some uncultured cells. Three main magnetosome crystal morphologies, regardless of composition, have been observed:  (1) cuboctahedral (equidimensional; appear roughly cuboidal); (2)  elongated prismatic (appear rectangular in projection); and (3)  bullet-​or tooth-​ shaped (often referred to as anisotropic; that is, having properties that differ according to direction or are directionally dependent) (Figure 8.2) [4, 6]. Bullet-​shaped crystals have been subdivided into those with one pointed end and one flat end, referred to as flat-​top-​shaped (fts); and those with a point at each end, referred to as double-​triangular-​ shaped (dts), which appear as two isosceles triangles sharing a common base [47]. Both projected triangles in dts crystals appear to have the same width, although one triangle is often longer in mature crystals. The cuboctahedral, equilibrium form of magnetite is known to occur in inorganically formed magnetites [48]. However, the presence of elongated prismatic and elongated anisotropic habits in magnetosome crystals indicates anisotropic growth conditions, such as a temperature or chemical concentration gradient, or an anisotropic ion flux causing these crystals to grow at a different rate in one direction over another. In other words, the growth of these crystals is not centrosymmetric [49]. The chemical purity of magnetosome crystals and their intracellular arrangement of magnetosomes in the cell, as well as the strict control over the size and crystal

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morphology are hallmark features of a biologically controlled mineralization [50]. The unusual non-​equidimensional forms (i.e. elongated prismatic and bullet-​shaped) of magnetite found in ancient sediments on earth and in extraterrestrial materials (e.g. meteorites) have been used as evidence for the past presence of magnetotactic bacteria and are referred to as magnetofossils [50–​54]. There is a significant correlation between phylogenetic groups of magnetotactic bacteria and their magnetosome mineral composition and crystal morphology that might have important evolutionary implications (Table 8.1). All known species within the most deeply branching phylogenetic groups containing magnetotactic bacteria, which include the candidate division OP3, the Nitrospirae, and the Deltaproteobacteria, biomineralize bullet-​shaped crystals of magnetite in their magnetosomes [13, 17, 47], although some Deltaproteobacteria also produce greigite [27, 37] or only greigite [7]. Magnetotactic bacteria in the later diverging groups, the Alpha-​ and Gammaproteobacteria, biomineralize only cuboctahedral and elongated prismatic crystals of magnetite [19, 25, 55]. This finding suggests, given this correlation and the large amount of variation and number of crystal flaws in bullet-​shaped magnetite crystals, that these crystals represent the first mineral phase in magnetosomes, that is, the most primitive magnetosomes [56, 57]. The magnetosome membrane, the organic portion of the magnetosome, is the locus of control over the biomineralization of magnetosomes in magnetotactic bacteria [58]. Like the outer and cytoplasmic membranes in Gram-​negative prokaryotes, the magnetosome membrane consists of fatty acids, glycolipids, sulfolipids, phospholipids, and proteins [59, 60]. However, based on fatty acid similarities and electron cryoelectrontomography studies, the magnetosome membrane appears to derive from the cytoplasmic membrane [45, 60, 61]. Despite this, many specific proteins are only found in the magnetosome membrane and these are thought to mediate magnetosome biomineralization.

8.4

Function of Magnetosomes: Magneto-​Aerotaxis The intracellular magnetosome chain conveys a permanent magnetic dipole moment to the cell, which causes it to experience a torque in a magnetic field tending to passively align the cells along the earth’s geomagnetic field lines while they swim, behavior known as magnetotaxis [3]. Thus, cells behave like miniature, motile compass needles in a magnetic field [43, 44]. It should be noted that the suffix “-​taxis” is a misnomer as the cells do not swim toward or away from a magnetic field. In phototaxis or chemotaxis, for example, cells move either toward or away from light or different molecules, respectively. To understand the function of magnetotaxis, one must also understand the earth’s magnetic field. The direction of the earth’s geomagnetic field lines at any given location is the vectorial sum of the horizontal and vertical components of the geomagnetic field. At the equator, the geomagnetic field lines are flat because there is no vertical component and is due to only the horizontal component. As the location moves from the equator toward either pole, the geomagnetic field lines deviate from the horizontal at an angle, which increases to 90° at the poles where only the vertical

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component is present. Therefore, on most of this planet, the geomagnetic field lines are inclined. Several models have been proposed on how magnetotaxis is advantageous to magnetotactic bacteria in nature. However, in the most widely accepted model, magnetotaxis aids cells in finding an optimal position in vertical chemical and redox gradients. Simply put, magnetotaxis functions to make chemotaxis more efficient [62, 63]. In early studies, it was assumed that magnetotactic bacteria were generally microaerophilic (high levels of oxygen are toxic to them) and had a polar preference in their swimming direction, meaning that they either preferred to swim northward (north-​seeking behavior or polarity) or southward (south-​seeking behavior or polarity) [3, 64]. Because north-​seeking cells also swim downward due to the earth’s inclined geomagnetic field lines, magnetotaxis was thought to help guide the cells to deeper layers of aquatic habitats that are less oxygenated by swimming downward. Once the cells reached surface sediments, their presumed preferred microhabitat, they would cease swimming and become sessile, attaching to sediment particles until local oxygen concentrations changed. Strong evidence for this idea was mainly the observation at that time that magnetotactic bacteria in the northern hemisphere were primarily north-​ seeking in the northern hemisphere and south-​seeking in the southern hemisphere. Thus, cells of either polarity swim along the earth’s inclined geomagnetic field lines downward in their respective hemispheres [65]. The model described above, however, was not consistent with results and observations of later studies. The most important findings that challenged the original model were: (1) the discovery of magnetotactic bacteria that did not appear to have a polar preference or that had lost this preference; (2) the observation of polar magnetotactic bacteria at the OAI in the water columns of natural habitats [14, 66]; and (3)  the isolation and pure culture of a polar magnetotactic bacterium, now known as Magnetococcus marinus [26, 60]. Cells of M.  marinus grown in semi-​solid gradient cultures form a band of cells at the OAI [60]. According to the original model, cells of polar magnetotactic bacteria, either in the environment or in culture, should continue to swim downward to the sediments or to the bottom of the culture tube, respectively. Because the magnetotactic bacteria examined in these studies were not only magnetotactic but also strongly aerotactic (as microaerophiles), the behavior of these organisms has been referred to as magneto-​aerotaxis rather than magnetotaxis [62, 63]. Two forms of magnetotaxis have been characterized [62, 63]. The first, axial magneto-​aerotaxis, describes the behavior of cells that lack a polar preference in their swimming direction and that use the magnetic field as an axis while swimming in both directions under oxic conditions. Polar magneto-​aerotaxis, by contrast, describes the behavior of cells that have a polar preference in their swimming direction under oxic conditions, they are either north-​or south-​seekers. Cells of both types grow as microaerophilic bands of cells in semi-​solid oxygen gradient media and are able to reverse their swimming direction. This reversal in swimming direction for both appears to be based on aerotaxis, although they seem to use a different taxis mechanism [58, 59]. Once cells are aligned along the earth’s inclined magnetic field lines, whether they use axial or polar magneto-​aerotaxis, their search for an optimal position in a vertical chemical/​

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Figure 8.3  Depiction of how magnetotaxis functions in magnetotactic bacteria. The long dark arrows indicate the earth’s inclined geomagnetic field lines that occur in most of the planet. A magnetotactic bacterium aligns along these magnetic field lines, as shown on the left, and swims up and down using aerotaxis to locate the OAI, its optimal position in an oxygen gradient within the water column or sediment. The magnetotactic cell therefore has a one-​dimensional search problem. A microaerophilic, non-​magnetotactic bacterium similar to Escherichia coli is shown on the right and would use a random walk also using aerotaxis to locate the OAI, except that this cell has a 3D search problem. Thus, magnetotaxis appears to make chemotaxis, in this case aerotaxis, more efficient.

redox gradient is reduced from a three-​dimensional (3D) search problem (would apply for non-​magnetotactic bacteria such as Escherichia coli) to one of a single dimension (Figure 8.3). In this way, magnetotaxis, the passive alignment of motile cells along geomagnetic field lines, increases the efficiency of chemotaxis (in this case aerotaxis) [62, 63]. However, though this model seems to fit some magnetotactic bacteria very well, particularly those sulfide-​oxidizing species that use hydrogen sulfide and oxygen as the electron donor and acceptor, respectively (both compounds are available in the small required amounts at the OAI in many aquatic environments), it does not explain some more recent observations. One intriguing finding is the presence of large numbers of south-​seeking polar magnetotactic bacteria in natural habitats of the northern hemisphere [67, 68]. This is surprising because in the magneto-​aerotaxis model described above, these organisms would be expected to continue to swim southward/​upward toward oxygen-​rich surface waters of the northern hemisphere and die, and therefore be selected against. In addition, there are many other questions that remain to be answered. For example, why do cells require magnetosomes for navigation when many obligately microaerophilic, non-​magnetotactic bacteria find their way to the OAI without them? It is possible

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that there are physiological explanations for magnetosome biomineralization, including energy conservation through iron reduction and/​or iron oxidation [69]; detoxification of free iron ions in the cell; and decomposition of toxic oxygen radicals produced during respiration, such as hydrogen peroxide [64, 70]. However, to date, no strongly convincing physiological function for magnetosomes has yet been found.

8.5

Genomics of Magnetotactic Bacteria The genome sequences of a number of cultured and uncultured magnetotactic bacteria are now complete, or nearly so, and are available for examination. Magnetosome biomineralization-​and magnetotaxis-​related genes have been identified in these genomes using two different strategies. These include (1)  isolating magnetosome membrane proteins and performing reverse genetics to obtain specific gene sequences that encode these proteins; and (2) bioinformatically cross-​comparing complete and partial genomes of different magnetotactic bacteria. Genomic analysis has and continues to provide valuable insight into how magnetosome genes are organized in different magnetotactic bacteria, as well as into the magnetosome genes common to groups of magnetotactic bacteria and how these genes evolved. Identified magnetosome-​related genes have been named the mam (magnetosome membrane) and mms (magnetic particle membrane specific) genes, and a selection of these and perhaps organism-​specific magnetosome genes, have been found in the genomes of every bacterium whose genome has been sequenced. The mam and mms genes are organized as clusters that are in relatively close proximity to one another within the genomes of almost all magnetotactic bacteria studied [6]. These clusters, in turn, are organized as a larger unit, a genomic magnetosome island (MAI), in some species. A  different guanine + cytosine content compared to the rest of the genome [71], and the presence of mobile elements and tRNA genes that act as insertion sites for integrases [72–​74] are characteristic of genomic islands [75, 76]. In M. gryphiswaldense, for example, the putative MAI is about 130 kb in size, contains three tRNA genes upstream of the mms operon, has a slightly different guanine + cytosine content to that of the rest of the genome and contains 42 mobile elements as transposases of the insertion sequence type and integrases [77]. Although putative MAIs are found in the genomes of other magnetotactic bacteria, such as other Magnetospirillum species, Magnetovibrio blakemorei, and Desulfovibrio magneticus [78–​80], the clusters of magnetosome genes in some species (e.g. Magnetococcus marinus) lack some or most of these features [81]. There is evidence that genomic islands are distributed to different bacteria through a process called horizontal gene transfer (HGT). In addition, they are known to undergo frequent gene rearrangements and therefore may be a major mechanism for the evolution of bacterial genomes [82]. Distribution of the MAI through HGT might explain the great phylogenetic diversity of the magnetotactic bacteria, while variations of the MAI in different magnetotactic bacteria may be the result of rearrangements within the MAI occurring over time [4, 6].

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Magnetosome genes comprise three clusters in Magnetospirillum:  the mamAB, mamGFDC, and mms operons [77]. Although they are conserved in all magnetotactic Alphaproteobacteria [83], only the mamAB cluster is present in other groups of magnetotactic bacteria [84]. Gene deletion studies in M.  magneticum and M.  gryphiswaldense have shown that only the mamAB cluster is absolutely essential for magnetite magnetosome biomineralization [85, 86]. Other operons or genes found in magnetotactic bacteria appear to have accessory functions in controlling the size and morphology of magnetite magnetosome crystals [46, 85, 86]. For example, the mamGFDC and mms operons appear to be specific to the magnetotactic Alphaproteobacteria [87], while the recently described mad (magnetosome-​associated deltaproteobacterial) genes seem to be specific to the magnetotactic Deltaproteobacteria and Nitrospirae [84]. The genetic determinants responsible for the minimal set of functions required for magnetosome chain formation in all magnetotactic bacteria are present within the mamAB operon. This operon contains ten genes (mamABEIKLMOPQ) that are conserved in all magnetite-​producing magnetotactic bacteria, while nine of these genes (mamABEIKMOPQ) are also conserved in greigite-​producing species [56, 84, 85]. Identifying the function of the protein products of these conserved genes is the key to the elucidation of the magnetosome biomineralization process. For many of these proteins, putative functions have been predicted and/​or assigned based on comparisons of similar proteins through BLAST searches and through mutagenesis experiments. Some examples follow. MamI and MamL are proteins specific to magnetotactic bacteria and have no known homologues in non-​magnetotactic species [88] and do not contain known domains or obvious sequence patterns. Experimental evidence, however, suggests that they could be involved in the invagination of the magnetosome membrane, the first step in magnetosome formation [89]. Identified functional domains in the remainder of this core set of proteins through in silico and/​or experimental evidence include (1) one tetratricopeptide repeat (TPR) (in MamA) that appears to participate in assembly of the magnetosome membrane through protein-​protein interaction [90–​92]; (2) at least one cation diffusion facilitator (CDF) domain necessary for iron transport and magnetosome membrane assembly (in both MamB and MamM) [93]; (3)  PDZ (named from three proteins:  postsynaptic density protein (PSD95), Drosophila disc large tumor suppressor (Dlg1), and zonula occludens-​1 protein (zo-​1) [94]) domains that mediate protein-​protein interactions (two in MamE and one in MamP) [83, 89, 95]; (4) a LemA domain (in MamQ) whose function is uncertain [85, 89]; (5) at least four magnetochrome domains (two in MamP, two in MamE and/​or MamT) that putatively ensure redox control and the stoichiometry of Fe(II)/​Fe(III) [96]; and (6) one or two actin-​like domains (in MamK) involved in magnetosome chain assembly and its positioning inside the cell [45, 46]. Some proteins contain multiple domains, such as the proteases MamE, which contains trypsin, magnetochrome, and PDZ domains, or MamO, which contains one trypsin and one TauE domain [85, 89]. Additional details regarding the roles of these proteins in magnetosome biomineralization are presented in the next section. In sum, these conserved proteins/​domains constitute the minimum set of genes required for the formation of magnetite and greigite magnetosomes in magnetotactic bacteria.

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8.6

Biomineralization of Magnetosomes Because little is known regarding the biomineralization of greigite magnetosomes, this section is mainly focused on the synthesis of magnetite magnetosomes. The biomineralization process involved in magnetite magnetosome synthesis is complex and consists of several steps, which occur simultaneously within the cell [4, 6, 58, 97]. Thus far, the process has been mainly studied in Magnetospirillum species, a group of Alphaproteobacteria that produce cuboctahedral crystals of magnetite [4, 6, 55, 69] because of the relative ease with which these microbes can be grown and because there are tractable genetic systems for species of this genus [89, 90, 98–​100]. The first stage in magnetite magnetosome synthesis in Magnetospirillum involves invagination of the cytoplasmic membrane and the formation of a membrane vesicle via the pinching off of the cell membrane. Whether the invagination truly pinches off or whether it remains as an invagination of the cytoplasmic membrane has yet to be resolved [45, 46]. The proteins that appear to play important roles in magnetosome invagination/​ vesicle formation include MamB, MamI, MamL, and MamQ, which are essential for the formation of the magnetosome membrane in Magnetospirillum magneticum [89]. Some may also be involved in the bending and shaping of the magnetosome membrane [97]. The mamA gene, previously stated to be present in the genomes of all magnetotactic bacteria examined, encodes a protein that exhibits high amino acid sequence similarity to proteins of the TPR protein family [101]. Because multiple copies of TPRs are known to form scaffolds within proteins to mediate protein-​protein interactions and to coordinate the assembly of proteins into multi-​subunit complexes [102], MamA might serve as a scaffolding protein to coordinate the assembly of oligomeric protein complexes that might occur during magnetosome synthesis and construction of the magnetosome chain [91, 92]. In the second stage of biomineralization, cells must take up iron continually for magnetosome synthesis. Cultured magnetotactic bacteria are extremely adept at iron uptake and have been shown to consist of greater than 3% iron on a dry weight basis, an amount several orders of magnitude over non-​magnetotactic bacterial species [64, 103, 104]. Iron uptake for magnetite synthesis in Magnetospirillum appears to occur relatively quickly [55, 103, 104], and both Fe(II) and Fe(III) are taken up by cells of magnetotactic bacteria for magnetite synthesis [103, 105, 106]. How iron is taken up by magnetotactic bacteria for magnetosome synthesis is not precisely known, but it is likely that there are several iron uptake systems in a single magnetotactic bacterium, as has been found in other non-​magnetotactic bacteria [107–​109]. Results from a number of studies have implicated siderophores, low molecular weight iron chelators [110], in iron uptake by some magnetotactic bacteria [107–​109], although a role in magnetosome synthesis has never been established. Other possible mechanisms for iron uptake in magnetotactic bacteria include a copper-​dependent iron uptake system in Magnetovibrio blakemorei [109] and an accessory role for the ferrous iron transport protein B gene (feoB1) in magnetosome formation in Magnetospirillum gryphiswaldense [111]. Once iron has been taken up by the cell, it must be transported to the interior of the magnetosome invagination/​vesicle, and a specific magnetosome membrane proteins

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appear to be involved in this process. The MagA protein was thought to play a significant role in iron transport to the magnetosome in Magnetospirillum magneticum [112] although there is evidence to the contrary [113]. MamB and MamM (and MamV in some species) are homologous proteins that function as cation-​diffusion-​facilitator-​ transporters that facilitate the influx or efflux of cadmium, iron, and zinc [114–​116] and are thought to be responsible for the transport of iron to the magnetosome membrane vesicle/​invagination [117]. The mamB and mamM genes are present in the genomes of all magnetotactic bacteria examined thus far, while mamV has only been found in M. magnetotacticum and M. magneticum [56, 78, 80, 81, 117]. Results from one study [105] demonstrated that, during magnetite biomineralization, the genes encoding ferrous iron transporter proteins were up-​regulated, whereas genes encoding ferric iron transporter proteins were down-​regulated in magnetotactic bacteria. However, there was surprisingly no change in the expression patterns of MamB and MamM. MamB and MamM have been shown to form heterodimers and to interact with other magnetosome proteins, suggesting that magnetosome formation likely involves coordinated interactions between many proteins and genes [93]. It has also been shown that the ferric uptake regulator (Fur) protein is involved in global iron homeostasis in M. gryphiswaldense, probably by balancing competing requirements for iron in essential biochemical reactions and magnetite biomineralization [118, 119]. In the last stage, there is controlled magnetite biomineralization which involves nucleation and maturation of the magnetite crystal within the magnetosome invagination/​ vesicle. Using evidence from Mössbauer spectroscopy, magnetite precipitation in magnetotactic bacteria was thought to occur through the reduction of hydrated ferric oxide(s) [103, 120, 121], although this seems now unlikely since cells of Magnetospirillum gryphiswaldense shifted from iron-​ limited to iron-​ sufficient conditions exhibited no delay in magnetite production [104]. This latter finding implies that no mineral precursors to magnetite in this organism exist [104, 122] during biomineralization or that they are unstable and transform to magnetite extremely quickly. A  ferritin-​like protein was shown to be present in the membrane fraction of cells of M. gryphiswaldense during magnetite biomineralization using Mössbauer spectroscopy [122]. No other intermediates were observed. Ferritins are ubiquitous intracellular proteins that store iron and the iron is released in a controlled fashion from the protein when required by the cell [123]. It has been proposed that iron contained within this ferritin-​like protein co-​precipitates soluble ferrous iron to form magnetite crystals in the cell membrane, which are then transported into the magnetosome invagination/​vesicle [123]. In another study, in which X-​ray absorption spectroscopy at cryogenic temperatures and transmission electron microscopic imaging techniques were used to chemically characterize and spatially resolve the mechanism of magnetite biomineralization in magnetotactic bacteria, it was shown that magnetite forms through phase transformation from a highly disordered phosphate-​rich ferric hydroxide phase, consistent with prokaryotic ferritins, through transient nanometric ferric (oxyhydr) oxide intermediates within the magnetosome organelle [124]. Two phases of iron, ferrihydrite and magnetite, were identified and quantified in a magnetic and structural study of magnetosomes of M. gryphiswaldense that used a combination of iron

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K-​edge X-​ray absorption near edge structure (XANES) and high-​resolution transmission electron microscopy [125]. The results suggest that ferrihydrite is the source of iron ions for magnetite biomineralization in M.  gryphiswaldense. In this study, two steps were distinguished in the biomineralization process:  in the first, iron accumulates in the form of ferrihydrite; and in the second, magnetite is rapidly biomineralized from ferrihydrite. Lastly, XANES analysis suggests the origin of the ferrihydrite is bacterial ferritin cores that are characterized by high phosphorus content and a poorly crystalline structure [125]. If ferrihydrite and/​or ferritins are precursors to magnetite in magnetotactic bacteria, until now, no proteins have been shown to be involved in their synthesis. The magnetosome protein MamP contains a self-​plugged PDZ domain fused to two magnetochrome domains and has recently been shown to function as an iron oxidase that contributes to the formation of iron(III) ferrihydrite, presumably eventually required for magnetite crystal growth in vivo [126]. Results from this study suggest that magnetochrome domains in proteins play an important role in iron biomineralization [126]. Specific magnetosome proteins may be important in magnetosome magnetite crystal maturation. FtsZ, a ubiquitous cytosolic protein in prokaryotes, is a tubulin-​like protein that polymerizes into an oligomeric structure that forms the initial ring at mid-​cell and plays an essential role in cytokinesis (cell division) [127]. A similar gene, called ftZ-​like, is present in the magnetosome gene island of Magnetospirillum and like FtsZ, the FtsZ-​like protein is able to form GTP-​dependent filaments in vitro [128]. When the gene for the FtsZ-​like protein was deleted in M. gryphiswaldense, while cell division was unaffected, the cells were non-​magnetotactic and possessed magnetite crystals that were significantly smaller than those of the wild-​type strain [128]. The same gene deletion mutation in M. magneticum did not result in changes in the size of magnetosome magnetite crystals [89]. Some magnetosome membrane proteins, including MamC (also known as Mms12 and Mms13), MamD (Mms7), MamF, MamG (Mms5), MamX, and Mms6, may be important in magnetosome magnetite crystal maturation, and they appear to control the shape and size of the crystals [60, 129–​132]. MamC, MamD, and MamG appear to be the most abundant of the proteins located in the magnetosome membrane, comprising about 35% of all proteins present in this structure [87]. Mms6 is an amphiphilic protein consisting of an N-​terminal leucine-​glycine-​rich hydrophobic region and a C-​terminal hydrophilic region containing numerous acidic amino acids [129, 133]. It has been shown to bind iron and influence the morphology of magnetite crystals precipitated chemically in vitro [129, 133]. The MamX protein, highly conserved in Magnetospirillum species, appears to play a significant role in controlling magnetosome magnetite crystal size, maturation, and crystal form. Cells of deletion mutants of mamX in M. gryphiswaldense, like those of ftsZ-​like deletion mutants described earlier, showed a very weak magnetotactic response and produced very small, irregularly shaped, superparamagnetic magnetosome magnetite particles [132]. Recently, however, MamX, as well as MamZ and MamH, has been shown to be involved in redox control of magnetite biomineralization in M. gryphiswaldense [134], thereby possibly affecting crystal size and maturation.

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Mass Culture of Magnetotactic Bacteria and Purification of Magnetosomes High yields of magnetotactic bacterial cells and thus magnetosomes from cultures are required for use of these materials in virtually all commercial and medical applications. In order to obtain these yields, cells of the desired strain must be grown in mass culture under conditions where growth and magnetite biomineralization is optimized. In all cases, the focus of studies involving mass culture involves modifications of growth media and the conditions under which cultures are incubated. Most studies involve Magnetospirillum species again because they represent the species that are the easiest to grow. When examining studies of this type, however, it is difficult to compare yields directly, as some studies report yields in different units and some only magnetosome yields where it is unclear whether magnetosome membranes are included in the yield values. Two general strategies have been used in studies involving the mass culture of magnetotactic bacteria, including (1)  the simple scaling up of batch cultures; and (2)  growing cells in a fermenter, where the oxygen concentration can be precisely controlled. It has been known for some time that microaerobic or anaerobic conditions are required for magnetite synthesis in magnetotactic bacteria [4], and thus controlling the level of oxygen is very important. Redox potential of the growth medium is also important as most species not only require low or no oxygen but also some type of reducing agent added to the growth medium. Thus, the choice of reducing agent used to poise the redox potential of the growth medium is also important and may also have an effect on magnetosome production [135]. Again, in almost all these investigations, Magnetospirillum species were the organisms under study which biomineralize cuboctahedral crystals of magnetite [4, 6]. The problem with this is that many magnetotactic bacteria synthesize elongated prismatic crystals which appear to have different magnetic and physical properties that might make them more advantageous than cuboctahedra in specific applications but have not been tested because of the lack of growth experiments on these latter organisms. Matsunaga et al. [136] grew cells of Magnetospirillum magneticum in a 1,000 liter fermenter and obtained a then highest magnetosome yield of 2.6 mg per liter of culture. The same group performed culture optimization experiments using fed-​batch cultures of the same organism but did not obtain higher yields of cells or magnetosomes [137, 138]. A recombinant Magnetospirillum magneticum strain harboring the plasmid pEML was grown in a pH-​regulated fed-​batch culture system, where the addition of fresh nutrients was feedback controlled as a function of the pH of the culture [139]. Here, the magnetosome yield was improved by adjusting the rate of addition of the major iron source, ferric quinate at 15.4 mg per minute, resulting in a magnetosome yield of 7.5 mg per liter. Different iron sources and the addition of various nutrients and chemical reducing agents (e.g. L-​cysteine, yeast extract, polypeptone) also had significant effects on magnetosome yield by M.  magneticum grown in fed-​batch culture [140]. More precise control over the growth of Magnetospirillum species was

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achieved using an oxygen-​controlled fermenter [104, 141]. Three species were grown using this method, M. gryphiswaldense, M. magnetotacticum, and M. magneticum, and magnetite yields of 6.3, 3.3, and 2.0 mg per liter per day were obtained from each species, respectively [104]. Using a similar type of fermenter, except that dissolved oxygen was controlled to an optimal level using the change of cell growth rate rather than from a direct measurement from the sensitive oxygen electrode, Sun et al. [142] obtained a cell density measured as an optical density at 565 nm (OD595) of 7.24 for M. gryphiswaldense after 60 h of culture incubation. The cell yield (dry weight) was 2.17 g per liter and the yield of magnetosomes (dry weight) was 41.7 mg per liter and 16.7 mg per liter per day. By decreasing the amount of carbon and electron source (lactate) in the same fermenter, Liu et al. [143] later reported growth and magnetosome yields of OD595 of 12 and 55.49 mg per liter per day, respectively, after 36 h of culture, again using M.  gryphiswaldense. Recently, it was shown that iron-​chelating agents such as rhodamine B and EDTA stimulated growth and magnetosome production in M. magneticum [144]. In a recent study in which Magnetovibrio blakemorei was used as a model magnetotactic bacterium for mass culture rather than a Magnetospirillum species, a new, different approach was used to obtain optimal growth and magnetosome yields. Silva et al. [145] used a statistics-​based experimental factorial design approach to determine the key components and amounts in growth medium for maximum yields. This study is significant for several reasons. First, M. blakemorei biomineralizes elongated prismatic magnetite crystals which might be superior to the cuboctahedral produced by Magnetospirillum species in certain applications. Second, it is the first attempt at mass culture of a marine magnetotactic bacterium. In the optimized growth medium designed in this study, maximum magnetite yields of 64.3 mg per liter in batch cultures and 26 mg per liter in a bioreactor were obtained [145]. Another approach to synthesizing high amounts of magnetosomes is to have them synthesized by a genetically tractable, non-​magnetotactic organism that is less fastidious (easier to grow) than a magnetotactic bacterium and that also has a very short generation time, for example, Escherichia coli. Kolinko et  al. (2014) recently reported the introduction and expression of all the mam genes of Magnetospirillum gryphiswaldense in one of the closest, non-​magnetotactic, phylogenetic relatives of Magnetospirillum, the photosynthetic alphaproteobacterium Rhodospirillum rubrum. The biomineralization of magnetosomes in a non-​magnetotactic recipient of the mam genes represent not only a significant step toward the production of magnetosomes to high yield but also toward the endogenous magnetization of organisms by synthetic biology [146]. A final challenge to obtaining enough magnetosomes for specific applications is the efficient purification of these inclusions. There are a number of reports describing the purification of magnetite magnetosomes from magnetotactic bacteria, all involving magnetic separation techniques [5, 147]. Washing magnetosomes tends to be a relatively tedious task, although there is one report of a more rapid procedure for magnetosome purification [148].

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Applications of Magnetotactic Bacteria and Magnetosomes During the last several decades, both chemically and biologically produced nanoparticles of numerous compositional and morphological types have proven amazingly useful in a plethora of scientific, commercial, and medical applications [149, 150]. Magnetic nanoparticles (MNPs), in particular, due to their physical properties, have been exploited in a number of applications [151, 152]. The ways magnetotactic bacteria and their magnetic inclusions are effective with regard to specific applications is the subject of this section. Cells of magnetite-​ producing magnetotactic bacteria, their magnetosomes, and magnetosome crystals have unusual and sometimes unique magnetic, physical, and optical properties that have been employed in numerous scientific and commercial applications. This section is focused on magnetite magnetotactic bacteria and magnetosomes since there are few cultured greigite-​producing strains and the mass synthesis of greigite by these strains is difficult at best. While a major problem in the past has been the mass culture of magnetite-​producing strains and the efficient harvesting of magnetosomes from cells, as discussed in the previous section, there has been a great deal of progress in these areas in the last decade. Magnetotactic bacterial cells, in some cases living or not, have been shown to be useful in many medical, magnetic, and environmental applications. They are very effective in cell sorting and separation because of the ease with which the resultant magnetic cells can be manipulated using magnetic techniques. Granulocytes and monocytes, after phagocytizing magnetotactic bacterial cells, have been successfully separated to high purity magnetically [153]. Magnetotactic bacteria can act as biosorbents for heavy metals [154]. Because of this and the fact that the magnetotactic cells can be magnetically removed from a suspension, the use of magnetotactic bacteria in the uptake and remediation of heavy metals and radionuclides from wastewater has been discussed and explored [149, 155–​159]. As polar magnetotactic bacteria exhibit a preferred direction of swimming under oxic conditions, they are useful in some specific applications in which the cells need to be guided to a target area. For instance, they have been used to determine south magnetic poles in meteorites and rocks containing fine-​grained (