Tribology of Graphene: Simulation Methods, Preparation Methods, and Their Applications 0128186410, 9780128186411

Table of contents :
Cover
TRIBOLOGY OF GRAPHENE: Simulation Methods, Preparation Methods, and their Applications
Copyright
About the Author
Preface
Acknowledgments
Organization of the Book
Abbreviations
Chemical abbreviations
1
1
Introduction to graphene
Introduction to graphene structure
Defects in graphene
Derivatives of graphene
Mechanical properties of graphene
References
2
2
Computer simulations and theoretical predictions
Simulation of mechanical properties
Sliding of graphene against graphene
Functionalized graphene
Sliding of various materials against graphene
Effect of environmental conditions on friction and wear
Graphene-based nanocomposites
Summary
References
Further reading
3
3
Preparation and characterization of graphene
Mechanical exfoliation
Epitaxial growth
Chemical vapor deposition
Plasma-enhanced chemical vapor deposition and pulsed laser deposition
Wet exfoliation
Synthesis of graphene oxide
Reduction of graphene oxide
Graphene-based composites
Analysis and characterization
Optical imaging
Fluorescence quenching
Atomic-force microscopy
Raman spectroscopy
X-ray photoelectron spectroscopy
Transmission electron microscopy
Summary
References
Further reading
4
4
Experimental tribology of graphene
Nanoscale friction of graphene
Nanoscale wear of graphene
Effect of ambient conditions on the nanotribology of graphene
Macroscopic friction and wear of graphene
Macrotribology of dispersed graphene
Effect of atmosphere and humidity on the macrotribology of graphene
Healing of friction-induced structural defects
Summary
References
5
5
Graphene oxide and functionalized graphene
GO and rGO under dry sliding conditions
GO/rGO coatings under water lubrication
Functionalized graphene
Self-assembly coatings
Hybrid coatings
Summary
References
6
6
Graphene-based composites
Polymer matrix composites
Graphene-reinforced metal composites
Ceramic matrix composites
Hybrid and multilayer composites
Summary
References
7
7
Graphene-based lubricants
Graphene-based dispersions in water
Graphene oxide
Graphene
Hybrid additives
Liquid dispersion-derived solid lubrication
Graphene-based additives in ionic liquids
Graphene-based additives in oils
Graphene
Graphene oxide
Reduced graphene oxide
Functionalized graphene
Hybrid additives and new lubricants
Graphene in greases
Summary
References
8
8
In conclusion: Perspectives
Index
A
B
C
D
E
F
G
H
I
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Back Cover

Citation preview

TRIBOLOGY OF GRAPHENE

TRIBOLOGY OF GRAPHENE Simulation Methods, Preparation Methods, and their Applications

OLEKSIY V. PENKOV

ZJU-UIUC Institute, International Campus, Zhejiang University

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States © 2020 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-818641-1 For information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Deans Acquisition Editor: Dennis McGonagle Editorial Project Manager: John Leonard Production Project Manager: Nirmala Arumugam Cover Designer: Mark Rogers Typeset by SPi Global, India

About the Author Oleksiy V. Penkov is currently an associate professor at the Zhejiang University/the University of Illinois at Urbana-Champaign Institute, Haining, China. He received his B.S. and M.S. degrees from the National Technical University “KhPI” (Ukraine). In 2007, he received his doctorate degree in physics and mathematics, with a specialty in solid-state physics. Since then, he stayed in Korea as a postdoc and research professor. During 2011–19, he was a research professor at the Center for Nano-Wear, Yonsei University. He joined the ZJU-UIUC Institute in 2019. His research interests cover several areas of physics, materials science, and mechanical engineering such as nano-layered coatings, tribology, and surface engineering.

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Preface Friction and wear are ubiquitous features of mechanical systems having contact between moving components. These phenomena are responsible not only for the degradation of mechanical durability and efficiency due to progressive loss of material, but also for excessive energy consumption. So, it is not surprising that significant efforts have been devoted to the creation of effective methods of control of tribological properties. One of the approaches is to use another material in the form of a coating on sliding components that provides low friction and wear. The fabrication of integral mechanical components using such materials in the bulk form could be complicated and not cost effective, or even impossible. A combination of different materials for the bulk and surface is highly attractive because it allows tailoring different physical and mechanical properties. In other words, surface modification by coatings can provide a unique combination of properties and multifunctionality and offer superior tribological features. Tribological behavior is essential on all scales of mechanical applications, from the nano to the macro. It plays a vital role in the performance of ultraprecision mechanical systems such as microelectromechanical systems (MEMS). Due to the small size and tight tolerance of MEMS devices, the effectiveness of mechanical components such as switches, gears, and actuators is strongly dependent on their frictional behavior while the wear resistance determines the mechanical and commercial viability of the device. Furthermore, classical methods for reducing friction with lubricating fluids cannot be employed in microsystems because of significant surface tension effects. Therefore, the tribological properties of the components must be optimized under dry sliding conditions to allow the development of reliable microdevices. Different types of thin coatings such as soft metals, organic compounds such as self-assembled monolayers, bilayer and multilayer hard coatings, diamond-like carbon films, and nanostructured coatings can be used to reduce friction and wear in microdevices. Nonetheless, despite reports of numerous proposed coatings, a universal method for reducing the friction and wear of these devices has not yet been identified. Thus, the discovery and investigation of new materials for nanoand microtribological applications are still ongoing. One such new material demonstrating high potential for tribological properties is graphene. During the last decades, graphene has attracted much attention in the materials

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community due to its exceptional features. In addition to its unique electrical properties, the mechanical properties of graphene are also impressive. Graphene has high levels of stiffness, strength, and thermal conductivity and is also impermeable to gas. The combination of the remarkable mechanical, thermal, chemical, and electrical properties of graphene sheets and their relatively low production cost distinguishes them from other materials used for nanoelectromechanical applications. Thus, graphene has been considered a promising material for applications in nanoelectronics and miniaturized devices. Moreover, due to its superior strength, graphene has excellent potential for use as an ultrathin protective coating for various macroscale components exposed to contact stress. Graphene derivatives such as functionalization graphene have opened new perspectives for use in industrial tribological applications due to their relatively low price. Besides solid lubrication, graphene materials can be used for the improvement of various types of composite materials from polymers to ceramics. They also demonstrated their performance as nanoadditives for different kinds of lubricants such as water, oils, greases, and ionic liquids. A minimal amount of graphene additive can enhance the durability of composite materials and the performance of lubricants. In this book, advancements made in the fabrication and applications of graphene materials for the reduction of friction and wear are reviewed. The aim is to provide a comprehensive overview of various types of graphenebased materials for tribological applications and gain a better understanding of their advantages and limitations. Oleksiy V. Penkov

Acknowledgments First and foremost, I would like to express my sincere gratitude to Prof. Dae-Eun Kim (Department of Mechanical Engineering, Yonsei University), who introduced me to tribology. He motivated me to write my first review paper (Tribology of Graphene: A Review), which finally evolved into this book. I am incredibly thankful to my teachers, advisors, and former colleagues from the National Technical University “Kharkiv Polytechnic Institute,” and especially the X-ray optics lab. Thank all of you for bringing me to science. I acknowledge hundreds of researchers cited in this book. This book would not be possible without their fantastic theoretical and experimental work. I must also record another special tribute to my family. My parents, thank you for your love and constant support as I satisfy my own curiosity. My wife Evgeniya, thank you for your unfailing love, sacrifice, and encouragement to realize my dream as well as your consideration in my everyday life.

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Organization of the Book This book is organized into eight chapters, each of which has a list of references. Chapter 1 introduces the structure of graphene and its derivatives, basic definitions, and nomenclature. In Chapter 2, the results of computer simulations of the mechanical and tribological performance of graphene are discussed. Chapter 3 provides a brief overview of the preparation and characterization methods for graphene, its derivatives, and graphene-based composites. Chapter 4 evaluates the tribological performance of graphene from the nano- to the macro scale. Chapter 5 discusses the possibility of replacing graphene with cheaper derivatives in different tribological applications. Chapter 6 is an overview of the utilization of graphene reinforcement for improvement of composite materials. Chapter 7 discusses the performance of graphene-based nano-additives in lubricants, including water, oils, greases, and ionic liquids. Chapter 8 summarizes the overall content of the book and discusses the future direction in the tribology of graphene.

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Abbreviations

AFM AIREBO APCVD CMS CNT CQD CVD DFT DLC DV EHL EHT EPD ESCA ESD FEM FG fG fGO FTIR GIC GNP GNR GNS GO GONR HAADF HIP HOFG HOPG HRTEM HT IL ISS LPCVD LST MC MD MEMS/NEMS MG

atomic force microscopy adaptive intermolecular reactive empirical bond order potential atmospheric-pressure chemical vapor deposition computer modeling and simulation carbon nanotube carbon quantum dots chemical vapor deposition density functional theory diamond-like carbon divacancy elastohydrodynamic lubrication epoxy-hydroxyl-terminated rGO electrophoretic deposition electron spectroscopy for chemical analysis electrodynamic spraying deposition finite elements method fluorinated graphene functionalized graphene functionalized graphene oxide Fourier transform infrared spectroscopy graphite intercalation compound graphene nanoplatelet graphene nanoribbons graphene nanosheets graphene oxide graphene oxide nanoribbons high-angle annular dark-field imaging hot isostatic pressing hydroxyl-functionalized graphene highly ordered pyrolytic graphite high-resolution transmission electron microscopy hydroxyl-terminated rGO ionic liquid internal shear strength low-pressure chemical vapor deposition laser surface texturing Monte Carlo molecular dynamics microelectromechanical systems/nanoelectromechanical systems multilayer graphene

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Abbreviations

ML MSM NDP OFGR oWNC PECVD PGO PLD QCM QC REBO rGO SAM SEM SPS STEM STM SW TEM XPS XRD

machine learning molecular structural mechanics nanodiamond particles oxyfluorinated graphene oxidized wood-derived nanocarbon plasma-enhanced chemical vapor deposition pristine graphite oxide pulsed laser deposition Quartz crystal microbalance quantum chemistry reactive empirical bond order potential reduced graphene oxide self-assembly monolayers scanning electron microscopy spark plasma sintering scanning transmission electron microscope scanning tunneling microscopy Stone-Wales defect transmission electron microscopy X-ray photoelectron spectroscopy X-ray diffractometry

Chemical abbreviations APS APTES APTMS BLG BMIMI BScB DDA DDP DMF EC EMIM EP ETA GPTS HBPE MAC MC NBR NMP ODA OHMimBScB OL OTA OTS PAO PA PDA PDMS PEEK PEG PEI PET PFDTS PFPE PF PI PMMA PPS PSS PTFE PTFE PU PVC

3-aminopropyltriethoxysilane 3-aminopropyltriethoxysilane 3-aminopropyltrimethoxysilan β-lactoglobulin 1-butyl-3-methylimidazolium iodide bis(salicylate)borate dodecyl amine alkyl phosphate N,N-dimethylformamide ethyl cellulose 1-ethyl-3-methylimidazolium epoxy ethanol amine 3-glycidoxypropyl-trimethoxysilane hyperbranched polyamine-ester multiply-alkylated cyclopentane monomer casted nylon acryl nitrile butadiene rubber N-methyl pyrrolidone octa-decyl amine 3-(hydroxypropyl)-3-methyl imidazolium bis(salicylate )borate oleate octylamine hydroxylated octadecyl trichlorosilane polyalphaolephin polyamide polydopamine polydimethylsiloxane poly(ether-ether ketone) poly(ethylene glycol) polyethyleneimine polyethylene terephthalate perfluorodecyltrichlorosilane perfluoropolyether phenol-formaldehyde polyimide poly(methyl methacrylate) polyphenylene sulfide poly(sodium 4-styrenesulfonate) poly(difluoro methylene) polytetrafluoroethylene polyurethane poly(vinyl chloride)

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Chemical abbreviations

PVDF PVP PWF SDBS TFSI UHMWPE ZDDP

polyvinylidene difluoride poly(vinyl pyrrolidone) polytetrafluoroethylene wax sodium dodecylbenzene sulfonate bis(trifluoromethyl sulfonyl)imide ultrahigh molecular weight polyethylene zinc cialkyl cithiophosphate lubricant additives

CHAPTER 1

Introduction to graphene Contents 1.1 Introduction to graphene structure 1.2 Defects in graphene 1.3 Derivatives of graphene 1.4 Mechanical properties of graphene References

1 5 7 9 9

1.1 Introduction to graphene structure Carbon is one of the most essential materials for organic life, and “graphene” is the name of one of the carbon allotropes. The word “graphene” consists of the prefix “graph,” which comes from graphite, and the suffix “ene,” which represents the carbon/carbon double bonds [1]. In general, the word “graphene” refers to a monolayer of sp2-hybridized carbon atoms packed into a two-dimensional (2D) honeycomb structure that is partially filled with π-orbitals above and below the monolayer [2]. The graphene monolayer is atomically flat with the Van der Waals thickness of 0.34 nm. This monolayer represents a building block for all other graphitic materials. Graphene can exist not only in the form of the single monolayer (sheet) but also in the multilayer form where several sheets are stacked together, forming a threedimensional (3D) structure (Fig. 1.1). Beside the forming of 3D graphite, graphene can be wrapped up into zero-dimensional (0D) fullerenes or rolled into one-dimensional (1D) nanotubes (Fig. 1.2) [3]. Initially, it was assumed that graphene could not be standalone because of the predicted thermodynamic instability of 2D crystals [2]. Nonetheless, the theoretical predictions about this material became real in 2004 when it was demonstrated that isolated 2D structures can not only be stable at room temperature and in the air, but also maintain macroscopic continuity [4]. Graphene is a fundamental element of a large group of 2D and 3D carbon forms that includes materials with very different properties, lateral sizes, and number of layers. The term “graphene” can be prefixed by “bilayer,” “fewlayer,” or “multilayer.” This classification is essential because the properties Tribology of Graphene https://doi.org/10.1016/B978-0-12-818641-1.00001-0

© 2020 Elsevier Inc. All rights reserved.

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Tribology of graphene

Fig. 1.1 Formation of 3D graphene from a 2D building block—three common graphite structures with different graphene stacking arrangements: hexagonal stacking (AA), Bernal stacking (AB), and rhombohedral stacking (ABC).

Fig. 1.2 A 2D graphene sheet is the base for other allotropes: 0D (fullerene) and 1D (carbon nanotube).

of mono-, bi- and multilayer graphene differ from the properties of graphite and each other [1, 2]. Besides, different names can be used for the same structures. For example, “multilayer nanosheet” has the same meaning as “fewlayer nanoplate.” The most commonly used terminology of graphene is summarized in Table 1.1.

Table 1.1 Nomenclature of graphene materials based on their dimensions. Parameter Aspect ratio A (length/width)

Number of layers n

Range Nomenclature

1 Single-layer; monolayer

2 < n < 10 Few-layer; multilayer

>10 Graphite

A < 10 Nano

A > 10 Micro

Lateral size D (nm)

D > 100 - Ribbon

Introduction to graphene

D < 100 - Flake - Sheet - Plate - Platelet

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There are three possible stacking configurations of few-layer graphene (Fig. 1.1): Bernal (AB), hexagonal (AA), and rhombohedral (ABC) [5, 6]. These stacking configurations differ in the relative orientation of the graphene layer stacks that may be crucial for some applications. For instance, the stacking order significantly affected the electronic structure of few-layer graphene [5]. Among the possible stacking configurations, the Bernal configuration has the lowest stacking energy [7]. This configuration is formed by stacking two graphene sheets rotated by 60 degrees relative to each other around the z-axis. In this case, the 3D unit cell has four atoms, and a third basis vector perpendicular to the graphene layer stacks is 0.6672 and 0.6708 nm at 4.2 and 297 K, respectively [8]. In the case of AA-stacked graphene, all carbon atoms in every sheet have the same x and y coordinates (Fig. 1.1). In the ABC structure, half the atoms are located directly below atoms in the adjacent layer and directly above the hexagonal ring centers while the other half of the atoms are directly above atoms and directly below hexagonal ring centers [9]. Even though the Bernal stacking is the most common configuration in single-crystal graphite, it was found that 15% of the exfoliated multilayer graphene is composed of micrometer-sized domains of rhombohedral stacking, rather than the usual Bernal stacking [10]. Stacking order may be crucial for the mechanical behavior of several-layer graphene, especially on the macroscopic level. For instance, different lengths of the upper and lower layers of graphene in the case of AB stacking led to a stress concentration at the boundary of the short layers of graphene [11]. Many properties of graphene are affected by chirality or orientation. Because graphene has a hexagonal lattice, there are two types of edges, called zigzag and armchair (Fig. 1.3). Zigzag and armchair edges also could be drawn

Fig. 1.3 Two types of edges in graphene: (A) zigzag and (B) armchair. The edges are indicated by bold lines.

Introduction to graphene

5

as “lateral” and “longitudinal” edges [12]. In the case of nanoribbons, “zigzag graphene” and “armchair graphene” definitions can be used. Here, the name is defined by the edge type along the longest dimension of a nanoribbon.

1.2 Defects in graphene Various types of structural defects may appear during the synthesis of graphene. Because sp2-hybridized carbon atoms can rearrange themselves into various polygons and form different structures, the formation of nonhexagonal rings may occur [13]. Such nonhexagonal structures could be considered as structural defects of the ideal hexagonal lattice. Depending on their configuration, nonhexagonal rings could produce curvature of the graphene sheet or leave it flat if the arrangement of polygons satisfies certain symmetry rules. Such behavior is attributed only to 2D structures and could not be found in bulk crystals [13]. Several experimental studies reported the existence of either native or physically introduced structural defects in graphene. The presence of defects is essential for the mechanical and tribological properties of graphene materials. Defects in graphene structure are referred to as intrinsic or extrinsic, depending on their nature. Intrinsic defects resulted in the form of perturbation of the original crystal structure without the presence of foreign atoms. Foreign atoms are denoted as impurities and constitute extrinsic defects [14]. Due to the reduced dimensionality of graphene, the number of possible defects is reduced in comparison to 3D materials. The 0D point defects in graphene are similar to one of the bulk crystals, line defects are different, and 3D defects do not exist. Graphene defects have certain mobility in the graphene plane. The migration mobility of various types of defects is governed by their activation energy and exponentially increases with temperature [14]. Several point defects of graphene such as mono- and di-vacancies, adatoms, and Stone-Wales (SW) defects are known. Defects in graphene are illustrated in Fig. 1.4. The monovacancy is the missing lattice atom; this is the simplest point defect in a graphene structure (Fig. 1.4A). The formation of the monovacancy led to the creation of nine- and five-membered rings, also called the 5-9 cluster. The formation energy of the monovacancy is about 7.5 eV [15]. Due to having a dangling bond, the monovacancy is highly reactive and can be quickly demolished. Divacancy (DV) in graphene has no dangling bond (Fig. 1.4B). Due to the lower energy of formation, it is much more stable and less reactive [16].

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Fig. 1.4 Schematics of point defects in graphene. (A) mono-vacancy; (B) di-vacancy; and (C) Stone-Wale defect (SW); the boundary of defects is indicated by bold lines.

It could be formed by the coalescence of two monovacancies or by the removing of two neighboring atoms. Thus, two pentagons and one octagon are built instead of four hexagons, forming a 5-8-5 cluster [14]. The formation energy of the divacancy is very close to one of the monovacancies [15]. But because of two missing atoms, the energy per atom would be significantly lower, making the formation of DV thermodynamically preferable [13]. Beside the 5-8-5 configuration, there are several other ways for a graphene lattice to accommodate two missing atoms. Moreover, this configuration is not energetically preferred. Other arrangements such as 555-777 or 5555-6-7777 have lower formation energy [14]. The elimination of more than two atoms may cause the formation of a larger and more complex configuration of defects. Because an even number of missing atoms allows the full recombination of dangling bonds, such defects are energetically preferable over defects having an odd number of missing atoms due to the remaining of the open bond [14]. The formation of large holes with unsaturated bonds is more likely in the case of simulations removing a large number of atoms. One of the exceptional properties of graphene lattice is the ability to reorder by establishing nonhexagonal rings without missing atoms [14]. The simplest example of such rearrangement is the formation of the SW defect (Fig. 1.4C). It forms due to a change of connectivity of two π-bonded carbon atoms, which led to a 90 degree in-plane rotation of the bond [17]. Four hexagons are transformed into two pentagons and two heptagons, forming a so-called 5-7-7-5 cluster. Thus, the formation of the SW defect does not involve any removed or added atom, and no dangling bonds are introduced [14]. The formation energy of the 5-7-7-5 defect is about 5 eV [18]. The formation of interstitial atoms as occurred in bulk crystals is not possible in graphene because adding an atom to any in-plane position such as the

Introduction to graphene

7

Fig. 1.5 Covered and uncovered step edges of graphene.

center of a hexagon would require excessively high energy. Thus, in graphene, adatoms are located in the third dimension. The energetically preferred position would be the top of a carbon-carbon bond (the bridge configuration). The formation of such a structure led to the changing of hybridization. Due to the appearance of some sp3 hybridization, the formation of two covalent bonds between the adatom and the underlying atoms in the graphene plane takes place [14]. One-dimensional defects such as dislocations and grain boundaries were observed in several experimental studies of graphene. Generally, these defects are tilt boundaries separating two domains with different lattice orientations. Such defects could be imagined as a line of point defects with or without dangling bonds [14]. The formation of line defects can occur in the case of simultaneous nucleation of graphene layers in different locations followed by their coalescence. This process is similar to the creation of grain boundaries in bulk crystals. The presence of atomic-scale steps is a ubiquitous feature of multilayer graphene. There are two types of step edges (Fig. 1.5). The first type is internal or covered steps, which formed during the graphene growth (Section 3.3). The second type is external (uncovered) steps usually created during the mechanical cleavage of HOPG (Section 3.1). The presence of dangling bonds on the exposed edges makes them chemically active. A higher work function was observed on the external steps compared with other internal steps due to step dipoles and adsorbates [19].

1.3 Derivatives of graphene Significant attention was first paid to pristine graphene because of its unique electronic properties. This made graphene a model system for the observation of a novel quantum phenomenon and the building block for future nanoelectronic devices [3]. Nevertheless, from a practical point of view,

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industrial applications are required to produce graphene in significantly large quantiles. One of the approaches to increase the production rate of graphene is fabrication by the reduction of graphene oxide (GO) because it demonstrated the potential of cost-effective, large-scale production of graphenebased materials [20]. Since it was first synthesized in the nineteenth century, GO has been a popular graphene derivative. GO is a single-carbon monolayer with randomly distributed aromatic regions (sp2 carbon atoms) and oxygenated aliphatic domains (sp3 carbon atoms) containing carbonyl, carboxyl, epoxy, and hydroxyl functional groups (Fig. 1.6). The presence of the functional groups makes GO hydrophilic [21]. GO is synthesized by the oxidation of graphite in the presence of a strong acid and an oxidizing agent. The oxidation process leads to a partial disruption in the sp2 hybridized structure of graphite and to an increase of the distance between its carbon layers, leading to final separation to sheets that are a single carbon atom thick [21]. Graphene oxide sheets are thicker than graphene due to the displacement of sp3 hybridized carbon atoms slightly above and below the original graphene plane and the presence of covalently bound oxygen atoms [3]. The level of the oxidation can be varied depending on the method, the reaction conditions, and the graphite precursor. Although extensive research has been done to reveal the chemical structure of GO, several models of this process are still being debated in the literature [20]. Reduced graphene oxide (rGO) is also a 2D single-atom-thick material. It is like graphene, but it has extra carbon ring domains, defects, and remaining oxygen-containing groups (-OH, -COOH, etc.) on the surface (Fig. 1.6). The initial goal of reducing GO was to fabricate graphene materials comparable to the structure and properties of pure graphene achieved by mechanical exfoliation.

Fig. 1.6 Comparison of the chemical structures of graphene, GO, and rGO.

Introduction to graphene

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1.4 Mechanical properties of graphene The mechanical properties of graphene are the main reason that it is a primary tribological material of the future. It has the highest strength and elastic modulus after carbon nanotubes. The exceptional mechanical properties of graphene are based on the stability of sp2 bonds forming the hexagonal lattice. That allows a graphene sheet to oppose in-plane deformations [22]. For the first time, the mechanical properties of free-standing monolayer graphene were measured by Lee et al. using the nanoindentation mode of AFM [23]. It was demonstrated that the monolayer graphene membrane had a Young’s modulus of 1 TPa. Hoverer, different stiffness values were obtained in some reports. This difference was attributed to the unrecordable crumpling of graphene sheets that may originate from point defects or uneven stress at the boundaries [22]. The transfer process used after the CVD process almost always causes wrinkling and damage, which also may reduce the mechanical properties. The shear modulus of CVD-grown monolayer graphene (Section 3.3) was measured by Lui et al. [24]. A value of 280 GPa was obtained. Defect-free monolayer graphene was considered by Hone et al. to be the most durable material ever tested [23]. Hoverer, the mechanical properties of graphene can be significantly affected by defects [25]. Depending on the type and concentration of defects, such as vacancy type or sp3-type, the strength and stiffness of graphene can be reduced significantly, as was observed for vacancies. In the opposite, the mechanical properties were maintained even at higher densities of sp3-type defects.

References [1] A. Bianco, H.M. Cheng, T. Enoki, Y. Gogotsi, R.H. Hurt, N. Koratkar, T. Kyotani, M. Monthioux, C.R. Park, J.M. Tascon, J. Zhang, All in the graphene family—a recommended nomenclature for two-dimensional carbon materials, Carbon 65 (2013) 1, https://doi.org/10.1016/j.carbon.2013.08.038. [2] A.K. Geim, K.S. Novoselov, The rise of graphene, Nat. Mater. 6 (2007) 183, https:// doi.org/10.1038/nmat1849. [3] V. Singh, D. Joung, L. Zhai, S. Das, S.I. Khondaker, S. Seal, Graphene based materials: past, present and future, Prog. Mater. Sci. 56 (2011) 1178, https://doi.org/10.1016/ j.pmatsci.2011.03.003. [4] K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, Two-dimensional atomic crystals, PNAS 102 (2005) 10451, https://doi. org/10.1073/pnas.0502848102. [5] K.F. Mak, J. Shan, T.F. Heinz, Electronic structure of few-layer graphene: experimental demonstration of strong dependence on stacking sequence, Phys. Rev. Lett. 104 (2010) 1, https://doi.org/10.1103/PhysRevLett.104.176404.

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[6] B. Partoens, F.M. Peeters, From graphene to graphite: electronic structure around the K point, Phys. Rev. B 74 (2006) 1, https://doi.org/10.1103/PhysRevB.74.075404. [7] R.R. Haering, Band structure of rhombohedral graphite, Can. J. Phys. 36 (1958) 352, https://doi.org/10.1139/p58-036. [8] N. Ferralis, Probing mechanical properties of graphene with Raman spectroscopy, J. Mater. Sci. 45 (2010) 5135, https://doi.org/10.1007/s10853-010-4673-3. [9] C.L. Lu, C.P. Chang, Y.C. Huang, J.H. Ho, C.C. Hwang, M.F. Lin, Electronic properties of AA- and ABC-stacked few-layer graphites, J. Phys. Soc. Jpn. 76 (2007) 1, https://doi.org/10.1143/JPSJ.76.024701. [10] H.L. Chun, Z. Li, Z. Chen, P.V. Klimov, L.E. Brus, T.F. Heinz, Imaging stacking order in few-layer graphene, Nano Lett. 11 (2011) 164, https://doi.org/10.1021/ nl1032827. [11] W. Dou, C. Xu, J. Guo, H. Du, W. Qiu, T. Xue, Y. Kang, Q. Zhang, Interfacial mechanical properties of double-layer graphene with consideration of the effect of stacking mode, ACS Appl. Mater. Interfaces 10 (2018) 44941, https://doi.org/ 10.1021/acsami.8b18982. [12] H. Zhang, T. Chang, Edge orientation dependent nanoscale friction, Nanoscale 10 (2018) 2447, https://doi.org/10.1039/C7NR07839K. [13] L. Liu, M. Qing, Y. Wang, S. Chen, Defects in graphene: generation, healing, and their effects on the properties of graphene: a review, J. Mater. Sci. Technol. 31 (2015) 599, https://doi.org/10.1016/j.jmst.2014.11.019. [14] F. Banhart, J. Kotakoski, A.V. Krasheninnikov, Structural defects in graphene, ACS Nano 5 (2011) 26, https://doi.org/10.1021/nn102598m. [15] A.A. El-Barbary, R.H. Telling, C.P. Ewels, M.I. Heggie, P.R. Briddon, Structure and energetics of the vacancy in graphite, Phys. Rev. B 68 (2003) 144107, https://doi.org/ 10.1103/PhysRevB.68.144107. [16] Z. Sahan, S. Berber, Divacancy in graphene nano-ribbons, Phys. E. 106 (2019) 239, https://doi.org/10.1016/j.physe.2018.09.029. [17] A.J. Stone, D.J. Wales, Theoretical studies of icosahedral C60 and some related species, Chem. Phys. Lett. 128 (1986) 501, https://doi.org/10.1016/0009-2614(86)80661-3. [18] J. Ma, D. Alfe, A. Michaelides, Stone-Wales defects in graphene and other planar sp2bonded materials, Phys. Rev. B 80 (2009)033407. [19] H. Lee, H.B. Lee, S. Kwon, M. Salmeron, J.Y. Park, Internal and external atomic steps in graphite exhibit dramatically different physical and chemical properties, ACS Nano 9 (2015) 3814, https://doi.org/10.1021/nn506755p. [20] S. Park, R.S. Ruoff, Chemical methods for the production of graphenes, Nat. Nanotechnol. 4 (2009) 217, https://doi.org/10.1038/nnano.2009.58. [21] M. Ionita, G.M. Vlasceanu, A.A. Watzlawek, S.I. Voicu, J.S. Burns, H. Iovu, Graphene and functionalized graphene: extraordinary prospects for nanobiocomposite materials, Compos. Part B 121 (2017) 34, https://doi.org/10.1016/j.compositesb.2017.03.031. [22] D.G. Papageorgiou, I.A. Kinloch, R.J. Young, Mechanical properties of graphene and graphene-based nanocomposites, Prog. Mater. Sci. 90 (2017) 75, https://doi.org/ 10.1016/j.pmatsci.2017.07.004. [23] C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (2008) 385, https://doi.org/10.1126/ science.1157996. [24] F. Scarpa, Shear modulus of monolayer graphene prepared by chemical vapor deposition, Nano Lett. 12 (2012) 1013, https://doi.org/10.1021/nl204196v. [25] A. Zandiatashbar, G.H. Lee, J.A. Sung, S. Lee, N. Mathew, M. Terrones, T. Hayashi, C.R. Picu, J. Hone, N. Koratkar, Effect of defects on the intrinsic strength and stiffness of graphene, Nat. Commun. 5 (2014) 1, https://doi.org/10.1038/ncomms4186.

CHAPTER 2

Computer simulations and theoretical predictions Contents 2.1 Simulation of mechanical properties 2.2 Sliding of graphene against graphene 2.3 Functionalized graphene 2.4 Sliding of various materials against graphene 2.5 Effect of environmental conditions on friction and wear 2.6 Graphene-based nanocomposites 2.7 Summary References Further reading

11 15 28 30 39 41 43 45 50

2.1 Simulation of mechanical properties For a long time, graphene was just an ideal model object. A variety of computer modeling and simulation (CMS) methods such as Monte Carlo (MC), molecular dynamics (MD), and quantum chemistry (QC) have been utilized for the investigation of various characteristics of graphene, including thermal conductivity and expansion, surface diffusion, and elastic modulus [1]. In general, CMS is a practical approach that uses computer models to investigate not only the interaction process between different materials, but also structural transformations that occurred during this interaction process [2]. The availability of simulation methods is especially crucial for graphene, where experiments encountered many limitations caused by the nanoscale of tribological systems. But it should be noted here that due to the nature of CMS, the scale of simulations is usually limited to a tenths of nanometers. This is because CMS methods deal with individual atoms and molecules, and the increasing size of the model requires significant computational resources. In the case of simulation of tribological phenomena, another limiting factor appears, which is a requirement to have an adequate model to describe an interaction between individual atoms of different elements. For instance, in the typical MD simulation, each particle is considered as Tribology of Graphene https://doi.org/10.1016/B978-0-12-818641-1.00002-2

© 2020 Elsevier Inc. All rights reserved.

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a single entity, and the interactions between various particles are modeled using their reactions to potential functions derived from classical physics [2]. Available potentials defined a variety of materials that can be used in simulations. Moreover, using various reactive potentials could give significantly different results even in similar models. Historically, early theoretical studies of graphene were mostly focused on the simulation of electrical or thermal properties. Later, many systematic pieces of research were performed on the mechanical properties of graphene. For instance, Young’s modulus was calculated using various approaches and simulation methods such as MD and ab initio DFT [2]. Depending on the reactive potentials used in MD simulations, the values of Young’s modulus reported by other researchers were in the range from 0.86 to 1.24 TPa [3–5]. Such a difference can be attributed to several factors. The first factor is a selection of the reactive potential. For example, AIREBO, Tersoff, Brenner, or bond-order Tersoff-Brenner potentials were used in different studies. The second factor is the size of a simulated specimen. For instance, increasing the specimen size from 0.1 to 0.35 nm led to an increase of Young’s modulus from 0.65 to 1.05Tpa, and its saturation [6]. Similar behavior was observed by Hao et al. for graphene nanoribbons [4]. When relatively large specimens were used (more than 2 nm), the mechanical properties were found to be independent of the specimen size [5]. Thus, the model used in CMS should be large enough to avoid the effects of its size. Many simulations demonstrated a significant difference in the mechanical properties of graphene depending on the direction of deformation. For instance, the zigzag graphene structure had a 30% higher strength and 60% higher fracture strain than the armchair structure [3]. Gao and Peng [7] also reported similar failure mechanisms and different mechanical properties of zigzag and armchair graphene. Their MD simulation showed that both zigzag and armchair graphene began to break at the outermost carbon atomic layers. Furthermore, Young’s modulus was found to be affected by temperature. Raising the temperature from 100 to 500 K increased the Young’s modulus of monolayer graphene from 0.94 to 1.1 TPa [6]. Dewapriya et al. also reported that Young’s modulus was slightly affected by temperature in the range of 1–300 K [8]. They reported values of 0.9 and 1.12 TPa for armchair and zigzag configurations, respectively. The small difference in the temperature behavior of the Young’s modulus of graphene again could be attributed to using different reactive potentials. Besides the effects of chirality and temperature, the mechanical properties of graphene are affected by the presence of structural defects.

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The presence of defects significantly reduced the failure strain and the inherent strength of single-layer graphene while it had a small effect on the Young’s modulus [9]. The impact of various defects on mechanical properties was carefully assessed by Zandiatashbar et al. [10]. In this work, different types of defects having a range of sizes were modeled in a single graphene sheet using MD simulation. It was demonstrated that both the elastic modulus and strength were almost insensitive to defects. Also, it was confirmed that graphene can be covalently bonded to a polymeric matrix without losing its reinforcing properties, which is very important for the design of graphene-based polymers. A simulation of defects in graphene using a molecular structural mechanics (MSM) approach showed that SW defects caused a smaller effect on mechanical properties in comparison with vacancies [11]. MSM is a continuum-based modeling technique in which CdC covalent bonds were replaced with energetically equivalent beam elements. An investigation of 100
100 nm2 graphene sheets revealed that mono- and divacancy reduced the axial stiffness of graphene significantly. In the case of monovacancy, it was dropped by 60% at the defect concentration around 12%. Divacancies caused an even higher reduction of the stiffness. Moreover, vacancies—and especially divacancies—led to a significant deterioration of mechanical properties. The effect of SW defects was less significant. The same concentration of SW defects reduced the axial stiffness by several percent. The fracture of graphene sheets having SW defects was also investigated at different temperatures using MD [12]. It was also demonstrated that the structural defects and vacancies in graphene could lead to a significant reduction in strength. In particular, introducing four vacancy defects into a 5
5 nm2 graphene sheet caused a decrease of fracture strength from 100 to 60 GPa. SW defects caused a 50% lowering of fracture strength. Besides, it was demonstrated that the fracture strength of graphene was dependent on temperature and loading direction. Raising the temperature from 300 to 900 K led to a 20% drop of the fracture strength. In the studies discussed above, relatively simple stretching of graphene was simulated. Further advances in the development of CMS methods allowed performing more complicated but also more realistic simulations. For example, simulation of the indentation of suspended graphene membranes with a tip became available. Kim et al. [13] performed a simulation of single- and multilayer graphene membranes with a rounded Si tip having a diameter of 5 nm (Fig. 2.1). The width of the circular graphene layer was 17 nm, which allowed avoiding the size effect mentioned above. It was

14

Tribology of graphene

Fig. 2.1 (A) Visualization of the indentation process of a single-layer graphene sheet and a multilayer (six layers) graphene sheet. (B) Indentation curves for the different number of layers. (C) The indentation-induced crack opening for the single-, bi-, and four-layer graphene. (Adapted with permission from H.J. Kim, K.J. Seo, D.E. Kim, Investigation of mechanical behavior of single- and multi-layer graphene by using molecular dynamics simulation, Int. J. Precis. Eng. Man. 17 (2016) 1693, doi:https://doi. org/10.1007/s12541-016-0196-4. Copyright (2016) Springer Nature.)

demonstrated that the elastic modulus of graphene increased from 0.92 to 1.08 TPa and saturated as the number of graphene layers varied from one to four. The central region of the membrane was stretched significantly compared to the boundary region. Increasing the load led to fracture failure initiated in the central area (Fig. 2.1). In the case of multilayer graphene, the fracture was initiated at the topmost layer due to the friction between the surface of the membrane and the Si tip. Poisson’s ratio of graphene was calculated to be in the range from 0.149–0.416 [6, 14–16]. Such a significant difference was caused by using different approaches. In particular, the highest values were calculated using continuum mechanics [14]. The calculations that gave the largest values of Poisson’s ratio also predicted a relatively low Young’s modulus. Assuming such a discrepancy between Poisson’s ratio and Young’s modulus, these calculations can be considered as not trustworthy. Some simulations predicted that the Poisson’s ratio of graphene depended on the temperature and size of a graphene sheet. Reducing the scale from 4 to 1 nm increased the Poisson’s ratio from 0.17 to 0.22 [6]. A study of the anisotropy of Poisson’s ratio showed that it reduced the tensile force applied in the directions close to armchair or zigzag.

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The presence of defects in graphene structure reduced the Poisson’s ratio [6]. Moreover, some types of defects such as SW could lead to a negative value of Poisson’s ratio due to local wrinkling [17]. The negative Poisson’s ratio was also predicted for rippled graphene [18]. The out-of-plane ripples were generated in freestanding graphene with topological defects to release the in-plane deformation energy. During uniaxial tension, the ripples gradually became flat, causing the negative Poisson’s ratio [18]. It is worth noting that negative values of Poisson’s ratio are somehow “virtual” because they appeared when the amplitude of the out-of-plane deformations was close to the size of a graphene sheet. In other words, this phenomenon can be attributed only to specimens having a size of several nanometers. Various simulations predicted values of the fracture strength of graphene in the range of 90–137 GPa [3, 4, 9, 12, 19]. Fracture strength was also affected by both chirality and temperature. In general, it is 10%–20% lower in the zigzag direction compared to the armchair. Increasing the temperature from 1 to 900 K led to a 10% reduction of the fracture strength. The mechanical properties of graphene predicted by MD simulations are summarized in Table 2.1. Zhang et al. [21] used machine learning (ML) to predict the mechanical properties of monolayer graphene under various factors, including temperature, strain rate, vacancy concentration, and chirality. Several MD models were used for the calculation of initial datasets. After the training, the ML systems were able to predict the mechanical properties depending on the input parameters. For instance, it was revealed that increasing the defectiveness and temperature deteriorated the mechanical properties. At the same time, the strain rate had a positive effect. The authors calculated the Pearson’s correlation between each pair of factors and outputs, as shown in Fig. 2.2. The correlation coefficient ranges from 1 to 1, corresponding to the most substantial negative and positive correlations.

2.2 Sliding of graphene against graphene One of the first tribological simulations of graphene was reported by Verhoeven et al. [22]. In this work, the friction between a finite, nanometersized, rigid graphite flake and a rigid graphite surface was investigated using a modified Tomlinson model. The simulation showed near-zero friction (superlubricity) or high friction depending on the commensurability between the two layers (Fig. 2.3A). The results of these simulations were in good agreement with the experimental findings of Dienwiebel et al.

16

Table 2.1 Summary of mechanical properties of graphene reported by different authors. Potentials

Type of simulated experiment

Conditions (temperature, number of layers etc.)

Young’s modulus, TPa

Brenner

Uniaxial tensile

100–500 K, monolayer

Fracture strength, GPa

AIREBO

300 K, monolayer

Tersoff TersoffBrenner AIREBO

300 K, monolayer 300 K, monolayer 1 K, 300 K, monolayer

Second REBO

Indentation

300 K, 1–6 layers

AIREBO AIREBO

Uniaxial tensile

300 K, monolayer 300 K, monolayer

Tersoff AIREBO

300 K, monolayer 1 K, 300 K, monolayer

Value

Ref.

0.95 (100 K) 1.1 (500 K) 0.89 (armchair) 0.83 (zigzag) 1.24 1.05/1.13

[6]

0.884 (armchair 1 K) 0.899 (armchair 300 K) 1.148 (zigzag 1 K) 1.111 (zigzag 300 K) 0.92 (monolayer) 1.06 (6 layers) 1.01 105 (armchair) 137 (zigzag) 175 113.9 (armchair 1 K) 107.5 (armchair 300 K)

[8]

[3] [4] [5]

[13] [19] [3] [4] [20]

Tribology of graphene

Property

Poisson’s ratio

97.4 (zigzag 1 K) 90.6 (zigzag 300 K) 127/123

TersoffBrenner AIREBO

300 K monolayer

AIREBO

300–900 K, monolayer

MD MD MD

300 K, monolayer 300 K, monolayer 300 K, monolayer

90 (armchair) 107 (zigzag) 125 (300 K) 92(900 K) 0.22 0.17 0.19

[9] [6] [12] [6] [15] [16] Computer simulations and theoretical predictions

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18

1.00 Chirality 0.75 Defect

0.50

Strain rate

0.25

Temperature

0.00

Fracture strength

Young’s modulus

–0.75 Fracture strain

Young’s modulus Temperature

–0.50

Strain rate

Fracture strength

Defect

–0.25

Chirality

Fracture strain

Friction (pN)

Fig. 2.2 Pearson’s correlations between input layer features and output layer targets. (Reprinted from Z. Zhang, Y. Hong, B. Hou, Z. Zhang, M. Negahban, J. Zhang, Accelerated discoveries of mechanical properties of graphene using machine learning and high-throughput computation, Carbon 148 (2019) 115, doi:10.1016/j.carbon.2019.03.046. Copyright (2019), with permission from Elsevier.)

(A)

400 350 300 250 200 150 100 50 0 –20

40 60 80 0 20 Rotation angle F (degrees)

(B)

Fig. 2.3 (A) Illustration of commensurate and incommensurate interfaces. (B) Average friction force versus rotation angle of the graphite sample around an axis normal to the sample surface. (A: Adapted with permission from O. Hod, Interlayer commensurability and superlubricity in rigid layered materials, Phys. Rev. B 86 (2012) 075444, doi:10.1103/ PhysRevB.86.075444. Copyright (2012) by the American Physical Society; B: Reprinted with permission from M. Dienwiebel, G.S. Verhoeven, N. Pradeep, J.W. Frenken, J.A. Heimberg, H.W. Zandbergen, Superlubricity of graphite, Phys. Rev. Lett. 92 (2004) 126101, doi:10.1103/PhysRevLett.92.126101. Copyright (2004) by the American Physical Society.)

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published in 2004 (Fig. 2.3B) [23]. Since that time, many researchers proposed various models of superlubricity of graphene and many computer simulations of the tribological behavior of graphene have been conducted. In the simulations, the tribological behavior of graphene is revealed by a variation of different parameters such as the normal force, sliding velocity, and the number of graphene layers. They allowed us to obtain a clear insight into the frictional and wear processes of graphene, helping us to understand the fundamental mechanisms. For instance, AFM probing experiments were simulated using tightbinding (TB) atomistic simulation [20]. Graphene flakes were slid against an infinite rigid graphene sheet. The fully atomistic model included quantum mechanics with the chemistry of bond breaking, the bond formation, and the flexibility of the flake. To reproduce the real AFM experiment, the normal force was applied to the graphene flake, and the flake was rotated in-plane relative to the substrate honeycomb structure for a given angle. A different rotation angle reproduced the other kind of graphene stacking–AA, AB, or incommensurate. It was found that the frictional force depended on the rotating angle and the flake size. Moreover, the significant stick-slip phenomenon was observed. It was demonstrated that larger flakes experienced a lower friction force due to reducing the role of boundaries. Reactive atoms located at the edges of the flakes were responsible for adhesion to the substrate. Increasing the number of these boundary atoms increased friction. Atomic-scale friction of the monolayer graphene sheet during a peeling process was simulated by Sasaki et al. [24]. In this case, the stick-slip phenomenon was also found. It was demonstrated that there is a difference in the sliding process between the armchair and zigzag types of sliding edges. Besides the effect of orientation, the friction of graphene against graphene depends on its thickness (number of layers). It was demonstrated by Xu et al. [25] that the friction force dramatically dropped with the decrease in the number of graphene layers. This result seems counterintuitive because increasing the number of layers increased the number of weak interlayer interfaces. Thus, with a larger number of layers, the system should be easier to shear. For instance, such behavior was predicted by FEM simulations for nanolayered periodical structures [26]. Nonetheless, the simulation showed that the friction force for multilayer graphene increased. To explain this phenomenon, a model of friction in few-layer graphene was proposed. The model was composed of a few connected springs and oscillators. Each ball represented one graphene layer as an oscillator while the top

20

Tribology of graphene

layer was represented by a block moving at velocity V. The bottom layer was represented by a fixed block that has periodic interaction potential E with the undermost oscillators. Springs of stiffness K described the effective interaction between neighbor layers. Intralayer motions of atoms were neglected. Reactive empirical bond order (REBO) potential [27] was used for the description of interactions inside graphene layers, and the Lennard-Jones [28] potential was used for interlayer interactions. Several graphene layers were stacked together; the bottom layer was rigid and the top layer was driven with constant velocities. The frictional behavior was attributed to the stick-slip phenomenon. It was claimed that the weak interlayer binding and strong intralayer bonds caused stick-slipping. Reducing the number of layers decreased the stiffness of the whole structure, causing a decline of the average friction force. It was also observed that lowering the interlayer distance increased friction. This observation supported the proposed model. Also, it is in good agreement with other studies [29–31]. It should be noted that these results are valid only for the sliding of graphene against graphene. As will be shown in Section 2.6, the effect of the number of layers is opposite for the sliding of another material against graphene. The effects of interlayer distance and in-sheet defects on the interlayer friction of graphene were systematically studied by Guo et al. [31]. Increasing interlayer friction with decreasing of the interlayer distance was also observed. It was found that in the case of incommensurate stacking, ultralow friction could exist in a significantly expanded range of interlayer distances. Also, superlubricity was insensitive to vacancy defects in the graphene sheets. As discussed in Section 3.3, a significant amount of graphene can be produced in the form of micro- or nanosheets rather than continuous monolayers. Thus, the development of simulation methods for multisheet graphene is vital. Such a model was developed by Kavalur and Kim [32]. In this study, the frictional behavior of multigrain graphene was compared to one of monolayer graphene. For the first time, the pristine-to-pristine model consisting of four single-crystal graphene layers in the A-B-A-B stacking order was developed. This model had multiple layers and provided friction between infinite layers. This system exhibited a typical stick-slip behavior and a relatively large friction force. The pristine-to-multigrain system consisted of two pristine graphene layers in A-B stacking, whereas the top substrate had two multigrain layers. Various configurations of grain shapes, boundaries, and sizes were evaluated. It was found that the most multigrain configuration demonstrated persistent negligible friction.

Computer simulations and theoretical predictions

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Nevertheless, for several configurations, significantly higher friction was observed due to the commensurate interface. The interaction between graphene layers as a function of the misorientation angle was investigated by Xu et al. [33] in detail. The stepwise behavior of friction force was found. It was attributed to the alternating appearance of AB and AA stacking. Also, there were transition areas between AB and AA stacking, and most incommensurate configurations in these transition areas provided very low friction. The negative effect of commensurate interfaces could be illuminated by the generation of strain in a graphene layer [34]. Because tension or compression changed the distance between atoms in the layer, the condition of commensurability also changed, and the commensurate interface was transformed to an incommensurate state. It was confirmed by the simulation that tensile and small compressive strains did not affect the incommensurate interface, mitigating the stick-slip behavior. At the same time, inducing strain led to a nonmonotonic variation of the friction of the commensurate interface. In particular, 5% tensile strain reduced the friction force from 0.6 to 0.05 pN/atom. Small compressive stresses also reduced the friction, but at the particular level formation of buckling occurred in the front of the sliding graphene flake, causing increased friction. The frictional behavior of small graphene flakes against a perfect, infinite graphene layer was also studied by van Wijk et al. [35]. In this model, 24 hexagonal graphene flakes having 29 atoms each were randomly distributed between two large graphene sheets. It was found that the presence of graphene flakes allowed reducing the friction between the top and bottom graphene sheets. The decreasing friction was attributed not only to the lower contact area, which reduces the adhesion force, but also to the fact that many flakes were moving independently. The flakes slipped at different times, resulting in more smooth sliding of the top layer, and average friction force was reduced. The aspect ratio is another important parameter in the case of sliding of graphene flakes. Besides the fact that friction force was strongly dependent on the edge orientation, friction increased with the length of the edge perpendicular to the sliding direction [36]. At the same time, friction was less dependent on the length of the edge parallel to the sliding direction. It was also attributed to the interaction between the leading edge of the flake and the substrate. The following equation to relate the dimension of the flake with the friction force was derived [36]:
Ffri ¼ ðμp + τs Þ λ? l? + λk lk + A (2.1)

22

Tribology of graphene

where μ is the friction coefficient, p is the contact pressure, τs is the interlayer sliding strength, λ is a factor accounting for the edge effect, l is the length of the edge, and A is the contact area. The product of l and λ gives the friction force generated by the edge. From the experiments, the interlayer friction coefficient was found to be on the order of 105–104 [37], and the interlayer sliding strength τs was on the order of 0.01 MPa [38]. Even though Eq. (2.1) looks quite simple, its parameters depend on many factors such as commensurability, temperature, sliding velocity, etc. Thus, all these factors are present there in a hidden form. Simulation multiasperity contact also revealed the importance of orientation in the sliding of a graphene flake against a graphene sheet [39]. In this work, the sliding of a rigid diamond tip having four asperities coated with separated graphene flakes was investigated. The tip was slid against several graphene sheets attached to a rigid substrate (Fig. 2.3A). Thus, the model had four contact points. Two different cases were compared (Fig. 2.3B). In the first case, all the four flakes on asperities had a random misfit in the orientation (incommensurate contact). In the second case, all the flakes had the same orientation (commensurate contact). Definite slip-stick was observed for the commensurate contact (Fig. 2.4C). Also, the average friction was much higher in this case. With increasing the normal load, the friction force also increased almost linearly (Fig. 2.4D). In the opposite, the friction force showed no significant change in the case of incommensurate contact. Moreover, the integral friction force was significantly lower in this case. This occurred because randomly oriented graphene flakes led to overall incommensurate contact in the case of multiasperity contact. As a result, “all the asperities can neither synchronously attain commensurate contact, nor trigger the slip process at the same time, which will lead to smooth sliding and minimum energy dissipation” [39]. A comparison of results for separated flakes [35] and a continuous single multigrain sheet [32] also revealed that increasing the degree of freedom is beneficial. Separated flakes could rearrange and rotate during sliding, adapting to the sliding interface and providing “collective superlubricity.” This self-adaptation allowed minimizing the slip-stick due to the formation of the incommensurate interface. Then the grains were joined together, and such adaptation was not possible, causing high friction in some configurations. These findings correlated with the results of the shear stress calculated for AB-stacked bi-layer graphene sheets [29]. It was demonstrated that the maximum shear stress is direction-dependent; it was observed for 120degree rotation symmetry. It is important that the shear stress was also

Computer simulations and theoretical predictions

23

6.03°

V

21.04°

13.09°

(A) 26.93°

(B) 5

Mean friction (nN)

Friction (nN)

4 3 2 1 0 0

(C)

5

10 15 20 25 30 Sliding distance (Å)

Commensurate contact Randomly oriented contact

3.0

Commensurate contact Randomly oriented contact

35

2.5 2.0 1.5 1.0 0.5

(D)

50

100

150 200 250 300 Load (nN)

350

Fig. 2.4 Simulation results of the randomly oriented multiasperity contact model. (A) Side view of the system. The yellow atoms represent the rigid upper base with four diamond bumps. The blue atoms denote the graphene flakes wrapped on the asperities. The green atoms represent the graphite substrate, and the bottom gray atoms indicate the fixed layer. (B) Top view of the system. The graphene-coated diamond hemispheres represent the asperities on the microsphere. The orientation angles are chosen randomly between the graphene flakes and the underlying graphite substrate. The atoms of the graphene flakes are color-coded based on the Z direction coordinate of these atoms. (C) Friction force with the sliding distance of the randomly oriented multiasperity model in comparison with the commensurate model, with an applied load of 320 nN. (D) Friction force with a function of applied load for the two models. (Reproduced from S.W. Liu, H.P. Wang, Q. Xu, T.B. Ma, G. Yu, C. Zhang, et al., Robust microscale superlubricity under high contact pressure enabled by graphene-coated microsphere, Nat. Commun. 8 (2017) 14029, doi:10.1038/ ncomms14029.)

dependent on interlayer distance. The shear stress increased in orders of magnitude when the interlayer distance was reduced from 0.36 to 0.3 nm. Similar results were obtained by Wijn et al. [30]. In their research, the system consisted of two infinite rigid plates with graphene flakes

24

Tribology of graphene

embedded between them. The surface of the plates was covered by singledomain or randomly oriented multidomain graphene layers. The quasisuperlubricity was achieved for the case of the disordered multidomain structure. It means that the tribological performance of multilayer graphene should be significantly affected by the normal load. The friction of graphene was affected by the stiffness of the substrate. This fact was concluded based on the results of MD simulations using a graphene-spring model [40]. In this model, a rectangular spring-supported graphene layer was located on a rigid substrate. A graphene flake was on the top of the graphene layer. Every atom in the graphene layer was linked to a linear spring in the y-direction. The normal force was applied to every atom of the flake. The flake was connected to the moving rigid connector using another spring. The simulation showed that friction increased with the rising of the normal load that was in a good argument with the result for the conventional bilayer graphene system. Also, it was demonstrated that the friction increased exponentially with the decreasing stiffness in both the commensurate and incommensurate cases. This fact was attributed to the stiffness-dependent deformation of the substrate. A softer substrate exhibited more considerable strain, causing a higher dissipation of friction energy. From the practical point of view, it means that superlubricity of graphene predicted by simulations can be entirely impeded on soft substrates such as polymers. The theoretical design of the graphene-graphene interface was proposed by Xu et al. [41] to suppress the nanoscale wear in the contact between two rough surfaces. It was demonstrated by means of the MD simulation that coating graphene on both contacting surfaces in a tribological interface allowed suppressing the fluctuations of contact pressure. Because the rapture of graphene under scratching was caused by atomic interlocking, coating the counter surface allowed minimizing the failure of graphene due to the smoothing of the distribution of the contact pressure (Fig. 2.5A–F). While the studies mentioned above dealt with rigid graphene or graphene attached to a rigid substrate, Smolyanitsky and Killgore [42] investigated the friction of a carbon nanotube (CNT) against suspended graphene. In this case, anomalous increasing of the friction force was observed when the CNT tip was retracted from the graphene surface. This unexpected finding was attributed to local upward displacement of the compliant graphene sheet due to adhesion to the tip. This produced an asperity that might be moved by the sliding tip. Movement of such asperity significantly raised the dissipation of frictional energy.

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Fig. 2.5 Simulation of contact pressure. First, second, and third rows show the morphology, three-dimensional surface, and two-dimensional contour of the pressure distribution, respectively, for (A) diamond tip, (B–D) diamond tip coated with monolayer graphene, two-layer graphene, and four-layer graphene. (E) Radially averaged pressure distribution profiles obtained through averaging the atomic stresses from the center of the contact region with radial bins of 1.7 Å spacing. (F) Changes in maximum atomic stress (the red line) and maximum averaged pressure (the green line) with the number of graphene overlayers on the tip. The applied normal load is 80 nN in all simulations. (Adapted with permission from Q. Xu, X. Li, J. Zhang, Y. Hu, H. Wang, T. Ma, Suppressing nanoscale wear by graphene/ graphene interfacial contact architecture: a molecular dynamics study, ACS Appl. Mater. Interfaces 9 (2017) 40959, doi:10.1021/acsami.7b11133. Copyright (2017) American Chemical Society.)

According to most simulations described above, the low friction of graphene occurred due to the weak interaction between individual layers, which has long been known. At the same time, these interactions are strong enough to prevent the natural exfoliation of graphene at a large scale [43]. Several studies have been devoted to the simulation of the mechanical cleavage of graphene (Section 3.1). Despite cleavage not being related directly to

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tribology, these studies were necessary for a general understanding of the wear behavior of multilayer graphene. Sasaki et al. [44] investigated the process of graphene formation under the sliding of the nanoscale tip against multilayered graphene (graphite). It was found that the transition from the tip friction to graphene sliding occurred in the [1230] direction. Also, ultralow friction between graphene layers was observed. Khomenko and Prodanov [45] found that effective exfoliation of monolayer graphene occurred when a highly adhesive tip was moved along the graphite substrate with low velocity. Sliding with high speeds caused the formation of small flakes attached to the tip. Sinclair et al. proposed a new forcefield with the aim of understanding the nanotribological behavior of graphene [43]. The new forcefield is called GraFF (A New Forcefield for Graphene and Graphite). It was developed to overcome some issues attributed to representing layer interactions in graphene by Lennard-Jones potentials. It was shown that the conventional potentials usually either undervalue the energy barrier of relative sliding of graphene sheets or overvalue the absorption energy of graphene. The propulsion of a 10 nm graphene flake slid against the graphite substrate by an STM tip was simulated (Fig. 2.6). The force was applied to each atom in the flake until it had been displaced, and the average distance traveled by the flake was measured. The kinetic energy of the sliding flake was converted to translation and formation energy. The travel distance of the graphene flake was much longer under the low temperatures. Also, the sliding length was shorter in the case of suspended graphene substrate in comparison to the graphite substrates. These findings were in excellent agreement with the experimental data obtained by Feng et al. (Section 4.1). As the authors rightly pointed out, the observed effects could not be reproduced with simple Lennard-Jones nonbonded interactions because of the underestimation of interlayer friction. Finally, Sinclair et al. used the GraFF for the investigation of graphene exfoliation. First, they compared the peeling and shearing modes of exfoliation. A peeling mechanism reproduced that used by the “Scotch tape” method of graphene preparation (Section 3.1). It was demonstrated that the work required for exfoliation was 40% lower in the case of peeling in comparison to shearing. This outcome was attributed to the interlayer friction. During the shearing, the flake would fall into different commensurate positions, and every time energy should be spent to overcome this barrier. In the opposite, during the peeling, the flake did not need to leave the commensurate position, and the energy required for flake bending was quite small. Thus, exfoliating graphite via peeling is the energetically favored mechanism [43].

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Fig. 2.6 Simulation of graphene-graphene interactions. (A) A representative trajectory from a large ensemble of simulations of a 10 nm graphene flake on a graphite surface after being pushed out of a commensurate position. In this instance, the trajectory lasted 500 ps until the flake was stationary. The flake travels from left to right, with a color corresponding to time (red at the start, blue at the end). A snapshot of the flake is shown every 50 ps. The flake slides and rotates freely when unaligned with the surface lattice and is only deflected when it is aligned. The internal kinetic energy of the flake is shown in (B). The flake loses energy, which is dissipated to the substrate in alignment events that are represented by dashed vertical lines in (B), until it comes to rest in a commensurate position. (C) Variation of interaction energy, rotation angle, and substrate temperature as a function of sliding time. (Reprinted from R.C. Sinclair, J.L. Suter, P.V. Coveney, Graphene–graphene interactions: friction, superlubricity, and exfoliation, Adv. Mater. 30 (2018) 1705791, doi:10.1002/ adma.201705791.)

A simulation of graphene exfoliation by pyrene-based molecules demonstrated that the molecules could act as wedges to exfoliate graphene from graphite well [46]. Due to the high interaction energies between the molecules and bilayer graphene, they penetrated between the layers. At the same time, the molecules demonstrated low friction against graphene, lower than the one between graphene layers. The high interaction energy and low friction explained that the experimental observations were pyrene-based molecules that acted as molecular wedges to exfoliate graphene from graphite (Section 3.4).

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2.3 Functionalized graphene The chemical modification of graphene significantly influenced its tribological performance. Depending on the ratio of hydroxyl and epoxide groups attached to the graphene sheet, the internal shear strength (ISS) of GO was varied significantly. For instance, introducing epoxide groups reduced the ISS from 78 to 17 MPa. ISS decreased significantly at low levels of functionalization because of a reduction in hydrogen bonding and an increase in the surface roughness. In addition to the investigation of chemical effects, the influence of topological defects was also evaluated [47]. The topological defects were represented by holes, islands, and fragments. The defective GO sheet was located between two intact layers. It was found that the presence of fragments did not influence ISS, but in the case of island defects, ISS was significantly lower. In other words, intercalated flakes increased interlayer spacing and lowered the ISS. The corrugation of the interfacial potential of graphene due to fluorination led to a dramatic reduction of friction [48]. The corrugation of potentials was caused by the intense local concentration of charge, located at fluorine sites. This outcome of MD simulation was consistent with the Prandtl-Tomlinson model [49], which consisted of a point mass driven over a periodic potential. In opposite, a simulation performed by Kwan et al. [50] demonstrated that the fluorination increased the out-of-plane bending stiffness of graphene. As a result, less-compliant fluorinated graphene exhibited higher friction. Such behavior was attributed to the domination of graphene friction by flexural phonons, which was modified by chemical treatment of the surface. These results were supported by tribological experiments performed in ultrahigh vacuum conditions [50]. In the opposite of fluorination, hydrogenation was found to significantly increase the friction [51]. The atomic-level analysis revealed that the increase in friction was caused by hydrogenation-induced roughness. Other mechanisms of the friction enhancement, such as adhesion and rigidity, were excluded based on the analysis using the Prandtl-Tomlinson model [49]. Besides, it was found that the friction did not monotonically rise with the increasing of the hydrogen coverage. The highest friction was observed while the coverage reached 7%. At this coverage, the friction was 20 times higher in comparison with nonhydrogenated graphene. Further increasing of hydrogenation led to reducing the friction, but it was five times higher. The nonmonotonic behavior of the friction was attributed to the competition between the raising of the number of hydrogen atoms in the

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contact and the reducing of the interlock due to the increase in separation between the tip and the substrate. These results demonstrated that hydrogenation could be an effective method of controlling the friction at the nanoscale [51]. Another model of improvement of tribological performance of functionalized graphene was proposed by Ko et al. [52]. It was postulated that the nanoscale friction of graphene is characteristically different from conventional solid surfaces. The friction mechanics of graphene were attributed to its intrinsic mechanical anisotropy. Graphene is stiff in the plane but flexible out of the plane. It was calculated based on the density-functional theory that the chemical modification of graphene not only reduced its adhesive properties down to 30, but also increased the out-of-plane elasticity up to 800%. Thus, the chemical treatment led to significant improvement of the tribological performance of graphene. In the case of several layers of GO, the mechanical properties were also significantly affected by the alignment of layers. It was demonstrated that a stronger interlayer interaction of aligned layers changed the fracture of layers [53]. In the case of the misaligned bilayer, the formation of decoupled and dissimilar cracks was revealed. In the opposite, aligned GO bilayers generally fractured with a significant number of common cracks shared by both layers. Despite that, no significant effect of misalignment on the strength and toughness was found. Increasing the number of layers to five and above caused significant local heterogeneity of thickness, causing a 60% reduction in the normalized fracture force and toughness. Besides, it was shown that the partial intercalation of GO led to the formation of anisotropic stress as well as stress concentration near the edges. These factors also may cause a significant reduction of toughness and strength of the multilayer GO. The comprehensive MCS study performed by Liu et al. [54] revealed that the variation of out-of-plane flexibility caused by vacancies had a minimal effect on friction. On the contrary, the chemical reactivity of dangling bonds at the uncovered step edges, the increasing of roughness caused by functional groups, and the Schwoebel barrier were much more critical for the nanoscale friction of graphene. Based on these findings, the friction-mechanism map for defective graphene was constructed (Fig. 2.7). According to the map, the frictional behavior of graphene could be described as follows [54]: (1) Multivacancies created step edges. These step edges performed as the geometrical barriers effected on the friction. If the size of a vacancy

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Fig. 2.7 Friction-mechanism map for defective graphene. (Reprinted from J. Liu, Y. Qi, Q. Li, T. Duan, W. Yue, A. Vadakkepatt, et al., Vacancy-controlled friction on 2D materials: roughness, flexibility, and chemical reactions, Carbon 142 (2019) 363. Copyright (2019), with permission from Elsevier.)

was larger than the contact area, the effect of the step edge was the most significant, and it caused the highest friction. (2) The presence of multivacancies could increase out-of-plane flexibility. Higher flexibility led to higher friction due to increasing the real area of contact. (3) The effect of roughness induced by introducing functional groups was more significant in comparison with out-of-plane flexibility. (4) Chemical bonding between the tip and vacancy edges caused the most significant enhancement of the friction.

2.4 Sliding of various materials against graphene The studies discussed in the previous sections dealt with friction on graphene-graphene interfaces. From the practical point of view, simulations of the interaction between graphene and other materials are more attractive. Although possible combinations of elements to be simulated are limited by the availability of adequately described reactive potentials, significant progress was achieved in this field. Simulations of sliding against different graphene structures were performed for various materials such as Si, Au, Cu, Pd, Al, Fe, and diamond. For instance, a simulation of copper

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and gold nanoparticles on a graphene sheet showed that the friction force depended on the counter material [55, 56]. Besides, local commensurability caused sawtooth dependency of the friction force on sliding time. Averaged friction force increased linearly with the contact area. Moreover, friction depended not only on the contact area, but also on the local structure of a material of a counterpart, in particular in the direction normal to the surface [57]. These simulation results were in good agreement with the experimental findings. Simulation of graphene nanoribbons (GNR) on gold demonstrated that the interior area of the GNR demonstrated superlubricity, and the overall friction force was generated by the front and tail regions of the GNR [58]. In other words, static friction was entirely edge-driven. As a result of the edge pinning, the static friction was independent on the GNR length. Similar results were obtained more recently by Zhu and Li [59]. The simulation of sliding of a graphene flake against a gold substrate demonstrated that the average friction forces per atom are smaller for a larger graphene flake. Friction was significantly affected by the orientation of the graphene flake. It was also found that friction was affected by the shape of a flake. Rectangular and circular flakes demonstrated significantly lower friction per one atom in comparison to a rectangular flake. Evidently, this result should also be attributed to the commensurability of edge atoms, similar to the conclusion made in refs. [55, 57, 58]. Later, the friction of the graphene flake between two metal layers was simulated by Ouyang et al. [60]. The goal of this simulation was to provide insight into the effect of commensurate-incommensurate transition on the frictional behavior of nanojunctions. It was found that the frictional behavior was determined by lattice mismatch and out-of-plane deformation of a graphene sheet. The author suggested that the morphology of the substrate should be close to that of the graphene sheet while the second confining surface should be incommensurate with the graphene. In this case, the superlubricity of graphene should be expected. Such a configuration could be achieved, for instance, by the CVD growth of graphene on the Cu substrate, and using Au or another metal as a counter surface. The friction of a diamond tip against graphene was significantly affected by its defectiveness and, especially, the type and location of defects [61]. In the case of a vacancy defect, the friction force linearly increased with the rising of the normal load, which is the normal behavior. But in the case of a Stone-Wales defect [62] located on the surface, the friction could even

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reduce with an increase of the normal force. When several defective graphene layers were stacked together, the friction force was increased in comparison to single-layer defective graphene. The presence of defects significantly reduced the wear resistance of multilayer graphene. According to Zheng and Duan [63], the critical normal load required for initiation of adhesive wear was 85%, 15%, and 11% of that of the intact graphene for the Stone-Wales defect, double vacancies, and a single vacancy, respectively. Such significant influence was attributed to the increasing of the chemical reactivity of graphene due to the formation of dangling bonds. In its turn, it increased the adhesion between a tip and the graphene surface. The simulation of the diamond tip slid against multilayer graphene attached to a rigid substrate demonstrated that the thickness dependence of friction was more significant for the rough substrate in comparison to a smooth one [64]. The substrate had the root mean square roughness of σ ¼ 0.3 nm, which was the typical value for the SiO2 surface used in many experiments. The friction force for the monolayer graphene on the rough substrate was seven times higher in comparison to the graphene on the flat substrate. For the five-layer graphene, the difference was around four times. Increasing the number of layers led to smoothing of the surface; the RMS of the top graphene layer reduced from 0.18 to 0.04 when the number of layers increased from 1 to 5. Thus, the observed dependence of friction could be attributed to the smoothing of the surface with the rising of the number of layers. Increasing of the substrate roughness raised the friction of monolayer graphene. Rising of the adhesion force between the graphene layer and the substrate strengthened the confirmation effect, leading to the higher roughness of the top surface and higher friction. Ye et al. [65] also revealed the reducing of friction force with increasing the number of layers. In this work, the formation of a wrinkle due to the siding of the tip was observed. The frictional behavior was directly correlated to the height of near-contact wrinkles that resist sliding, similar to the findings of Smolyanitsky and Killgore [42] for the case of CNT pushed against suspended graphene. It was found that this behavior was also affected by the size of a graphene sheet. For a smaller sheet, the formation of a wrinkle was more natural. As a result, reducing the friction was observed only when the graphene sheet was large enough (longer than 28 nm). The mechanism of thickness-dependent friction was also investigated in the study of scratching of multilayer graphene by a diamond tip [66]. On the

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contrary to the results of graphene-graphene sliding [25], the friction coefficient significantly dropped when the number of layers increased. This result was attributed to cross-linking between the graphene layers. It was postulated that the amount of cross-linking reduced when the number of layers increased. The cross-linking occurred during the scratching due to the disruption of graphene bonds by the tip. The compression of layers caused the formation of rebonding between layers. With the larger number of layers, the deformation of each individual layer was smaller, producing less distortion of the bonds and lower cross-linking. It is essential that in this simulation, the scratch depth was maintained the same for all specimens. Thus, the reduced friction should be attributed rather to lower deformation of each layer than to cross-linking. The cross-linking was the side effect resulting from the more extensive strain, and the observed relation between friction and the number of layers was caused by the better load support provided by multilayer graphene. Nevertheless, the study [66] demonstrated the theoretical tribological benefits of multilayer graphene, such as lower friction and better scratch resistance. Moreover, in the previous work [67], the authors also confirmed that the tip shape affected the friction. Three different shapes—hemispherical, square, and triangle—were compared. The effect of the shape increased with the rising of the scratch depth. The friction coefficient for the hemispherical tip was the lowest regardless of the scratch depth. Besides various point defects, grain boundaries also affect the tribological behavior of graphene. The interlocking between the tip and the graphene atoms located on the grain boundary led to a significant reducing of the critical load of failure [68]. Moreover, the wear resistance of graphene was affected by the orientation of grain boundaries relative to the sliding direction. Graphene with higher mismatch angles demonstrated less reducing of strength. Also, increasing the adhesion between graphene and a substrate allowed mitigating the weakening effects of grain boundaries. Frictional contact between graphene and a silicon tip was also evaluated by Li et al. [37]. The main goal of this simulation was reproducing some experimentally observed frictional behaviors of graphene, such as layerdependent friction and transient frictional strengthening. The second phenomenon was the gradual increase of the friction in the early beginning of sliding before reaching a steady-state value. Such behavior was observed in the experiment [69], where it was shown that it took place only in the case of low adhesion between graphene and substrate. It is interesting that it was not

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observed in earlier simulations, for instance, in [65, 70]. MD simulation revealed that such a variation of static friction was caused by readjusting the graphene shape due to its elasticity. In other words, the upward deformation of graphene occurred due to high adhesion between graphene and the tip, and low adhesion between the graphene and a substrate. The similar behavior was observed by Smolyanitsky and Killgore [42] and Ye et al. [65], as was discussed above. When graphene was suspended or the adhesion to a substrate was weak, the local upward displacement of the compliant graphene sheet caused the formation of a protrusion. Increasing the number of graphene layers raised the stiffness, and the size of the protrusion reduced. Lee et al. [37] demonstrated that for the case of weak adhesion, the friction force reduced from 8 to 4.5 nN when the number of graphene layers increased from one to four. The deformation caused by adhesion also reduced in the case of high adhesion force. This is why this phenomenon was not observed in many other simulations: they dealt with a large number of layers or highly adhesive or rigid substrates. Introducing preexisting wrinkles showed a strong dependence between friction and the contact area of monolayer-suspended graphene [37]. Thus, it was demonstrated that graphene friction could increase not only in the case of weak adhesion to a substrate but also due to substrate roughness. In both cases, the number of atoms in the contact increased, causing higher friction due to adhesion. The most recent advances in simulations allowed obtaining useful information, not only about the frictional behavior of graphene but also about its fracture and wear characteristics. One of the first studies of abrasive wear and failure of graphene was performed by Sandos-Rosado et al. [71]. A smooth spherical asperity was slid against graphene attached to a rigid substrate. Also, the behavior of graphene was compared to one of the DLC. It was found that local tearing of graphene under the asperity caused local failure. Delamination of graphene was found to not be critical for the failure mechanism. The adhesion force between graphene and the substrate was crucial for the disruption of graphene; for the higher adhesion force, more graphene bonds were broken during sliding. The abrasive wear of graphene depended on the sliding velocity. At low speeds, the frictional energy was dissipated due to the local pulling of graphene flaps from the substrate. When the speed was higher than 6 m/s, the flaps became damaged, causing an increase of the wear rate. Coverage of the substrate after

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the sliding of the asperity was higher in the case of low adhesion. It meant that the graphene could potentially recover its structure if it has weak adhesion to a substrate. Adhesion between a graphene sheet and a substrate is especially essential when a tip slides through the edge of the sheet. In this case, depending on the adhesion force, two scenarios are possible, as was demonstrated by Qi et al. [72]. If the adhesion was low, the sliding through the graphene edge caused peel-induced rupture of the graphene sheet. If adhesion was high, atom-byatom adhesive wear of graphene occurred. In this case, the mechanism of wear was similar to one observed by Sandoz-Rosado et al. [71]. The different studies [69, 71, 72] gave some contradictory predictions regarding the role of adhesion between the graphene and substrate. This might be because the authors focused on different aspects of the frictional process. Nevertheless, these contradictions could be resolved. On the one hand, the adhesion should be high enough to prevent the formation of protrusions and wrinkles during the sliding. On the other hand, it should not be too high to minimize tearing by the counter surface and allow self-recovery. Besides, adhesion between the graphene and the counter surface is also essential. For better wear resistance, it should be at least lower than the adhesion between graphene and the substrate. It seems that using multilayer graphene firmly attached to the substrate due to high adhesion is the best solution. The effect of adhesion between the counter surface and graphene was also evaluated in detail by Wang and Duan [73]. The authors varied the adhesion between the diamond tip and graphene by the passivation of the tip’s surface with hydrogen atoms. Thus, they were able to observe both adhesive and abrasive wear by changing the passivation rate. It was found that the critical contact pressure for adhesive wear was 42 GPa compared to 92 GPa for pure abrasive wear. After an evaluation of single-layer graphene, a tribological test of trilayer graphene was simulated, and the results were compared to the results for the 1-nm thick DLC layer [71]. The DLC was prepared by the melt-quench method [74, 75] and contained 86% of sp3 bonds. It was demonstrated that graphene sustained 8.5 higher normal load during indentation, and 2 times higher load during sliding and tearing compared to the DLC. This work demonstrated the potential of graphene as a solid lubricant. One of the first mechanisms of reducing friction and wear by graphene was proposed by Klemenz et al. [76]. The nanoindentation study of

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graphene-covered Pt demonstrated the main advantages of graphene as a solid lubricant. At low loads, both graphene and PT demonstrated elastic response accompanied by low friction. When the load increased, the plastic deformation of PT occurred (Fig. 2.8). If the graphene sustained, the friction remained low. At higher loads, the rapturing of graphene occurred, and the

Fig. 2.8 Simulation of wear process for a graphene-coated PT block, scratching with amorphous (A, C, E) and smooth indenters (B, D, F). At low normal forces, the substrates deform elastically, and the lateral forces FL are low and show clearly visible stick-slip (A, B). When the substrates deform plastically under the intact graphene layer, the lateral forces increase, and the stick-slip pattern disappears (C, D). Graphene rupture causes strong plastic deformation and the formation of wear tracks (E, F). (Adapted with permission from A. Klemenz, L. Pastewka, S.G. Balakrishna, A. Caron, R. Bennewitz, M. Moseler, Atomic scale mechanisms of friction reduction and wear protection by graphene, Nano Lett. 14 (2014) 7145, doi:10.1021/ nl5037403. Copyright (2014) American Chemical Society.)

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friction increased to the values of bare Pt. It is reasonable because the disrupted graphene could not isolate the Pt surface from the contact with the tip. Thus, it was demonstrated that could provide low friction and wear until it was not damaged. Graphene rapturing caused a loss of its low friction and wear properties. Moreover, the tribological performance of graphene would be affected by the mechanical properties of the substrate. Substrates such as soft metals or polymers are not able to provide enough support, and the plastic deformation of such substrates will cause a too-large deformation of the graphene layer and its fracture. Thus, graphene should demonstrate better tribological performance by being coated on harder substrates. Besides lower wear, a rigid substrate will help to maintain the lower friction, as was discussed in Ref. [40]. The nanoindentation of mono- and few-layer graphene on a monocrystalline metal substrate was affected by the chirality and grain boundaries of graphene [77]. Chirality, in this case, meant the tilt between the Ni(111) substrate and the armchair direction of graphene. The indentation response divided into the elastic, plastic, and graphene rupturing regime. For monolayer graphene, the load-bearing capacity was found to be slightly affected by the tilt angle. As for the four-layer graphene, the ultimate load increased from 3.2 to 3.7 μN while the tilt angle changed from 0 to 30 degrees. The presence of the grain boundary in monolayer graphene led to reducing the elastic limit from 168 to 134 nN. The ultimate load reduced from 1.1 to 0.9 μN. A combination of the tilt and grain boundary also improved the mechanical properties of graphene on Ni. In the case of Fe, the presence of graphene on the surface changed the pattern of dislocation nucleation [78]. Without the graphene layer, nucleation sites were formed at the free surface and glided into the subsurface due to high local stress caused by contact with asperities. As for the Fe coated with graphene, the dislocations nucleated in the subsurface region and moved to the surface due to the surface homogenization effect. Such behavior is typical for the ideal smooth contact. As a result, the graphene coating allowed increasing the critical contact load 300%. The authors also demonstrated that multilayer graphene smoothed the stress distribution in the case of rough contact. That finding was in excellent agreement with the previously reported results of graphene behavior in the rough contact discussed above [41]. Strengthening under nanoindentation due to the graphene coating was also predicted for Cu [79]. The mechanism of graphene fracturing under indentation was also investigated. MD simulation revealed that the

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fracturing involved three stages. The first stage was the formation of a decagon defect in the contact region. In the second stage, the decagon defect was extended. And finally, the creation of a pearl necklace-like structure occurred. Despite the breaking of graphene during the second stage, it retained its strengthening capability. The graphene layer also significantly affected the slip behavior of dislocations near the surface of Cu. Most of the dislocations slept parallel to the surface, which was different from the behavior of dislocations in pure copper. Moreover, it was demonstrated that graphene suppressed the plastic deformation of the Cu substrate and led to an increase of the nanohardness of the graphene/Cu system by 5.3 times [80]. This phenomenon might be attributed to reducing the dislocation’s mobility by the graphene coating. Further insight into the functionality of graphene as a solid lubricant on iron surfaces was provided by Restuccia and Righi [81]. It was demonstrated using density functional theory (DFT) that graphene was strongly bent to the iron surface and reduced its surface energy. Due to the passivation effect, graphene provided low adhesion and shear strength in the sliding contact between two iron surfaces. In particular, an 88% reduction in adherence and a 98% lowering of shear strength was predicted. An MD simulation of sliding of rough Au surfaces against each other demonstrated that heat dissipation and friction were reduced more than an order of magnitude if one of the surfaces was covered with a monolayer of graphene [82]. The replacement of monolayer graphene with a double layer further reduced the friction. It was shown that graphene could effectively prevent direct contact between Au asperities. High adhesion between graphene and the substrate was the key factor for structural stability and low friction. The performance of graphene nanoribbons was significantly lower due to their detachment and displacement, allowing direct contact between Au asperities (Fig. 2.9). The DFT simulation of the graphene layer between two parallel Ni(111) surfaces also confirmed that graphene screens the attractive forces between Ni atoms, leading to a reduction of adhesion and friction [83]. In the case of two graphene layers attached to each Ni surface, the adhesion reduced further. The adhesion and corrugation strength continued to decrease with increasing the number of layers. On the contrary, this effect was not confirmed for other metallic substrates such as Cu and Al. The significant reducing of lubricity for the Ni-graphene system was attributed to the coupling of Ni-3d and graphene π-orbitals.

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Fig. 2.9 Surface morphology evolution during sliding. The color scale denotes the atomic potential energy. Each column represents a different case. (A) δ ¼ 2 nm, (B) δ ¼ 12 nm, (C) δ ¼ 42 nm, (D) δ ¼ 90 nm, (E) δ ¼ 110 nm, (F) δ ¼ 120 nm. (Reproduced with permission from Z. Wang, Lubricity of graphene on rough Au surfaces, J. Phys. D 51 (2018) 435301, doi:https://doi.org/10.1088/1361-6463/aadfcb. © IOP Publishing. All rights reserved.)

2.5 Effect of environmental conditions on friction and wear Most of the earlier simulations of graphene friction and wear were performed in somewhat idealistic conditions. For example, endless graphene sheets were used or simulations were performed without an accounting of the effects of the atmosphere. This was a significant drawback because the real atmosphere, in particular humidity, could play a crucial role in the tribological behavior of graphene. Due to the development of simulation methods and the increasing of the available computational power, the simulation of more realistic systems became possible. For example, in 2018, Qi et al. [84] presented the results of an experiment and simulation for graphene in various environmental conditions. It was demonstrated that a humid environment could improve the wear resistance of graphene due to

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passivation of the dangling bond by condensed water. In their model, a monolayer graphene sheet was attached to a graphite substrate. The substrate was partially covered with graphene, and a diamond tip was slid across the edge of the graphene layer with or without water molecules. In the dry conditions, even under the normal load of 5 mN, string CdC covalent bonds were formed between tip atoms and nonterminated atoms at the edge of graphene, causing the pulling-up of the edge. Destruction of graphene was observed after the scratching. In opposite, in wet conditions, the edge of graphene remained intact after the scratching. It was attributed to the prevention of the formation of strong bonds between carbon atoms by water molecules and active suppression of adhesive wear. In the case of a ta-C tip slid against the three-layer graphene sheet, the friction was almost insensitive to the humidity in the range of 0%–15% [85]. Then, the humidity was raised from 15% to 75%, and the friction increased almost sevenfold. Further raising of the humidity to 100% led to a slight reducing of the friction. Thus, adsorbed water did not lubricate the interface, but rather increased friction until a threshold humidity level was reached. It was demonstrated that the formation of the water meniscus somehow affected the friction, but it was not the dominant factor. Instead, the nonmonotonic effect of the humidity was attributed to changes in the volume and location of adsorbed water at the interface. Under the low humidity, the water coverage was sparse, and solid-to-solid contact between the tip and film occurred. This contact was mostly governed by van der Waals interactions. Under the moderate humidity, adsorption increased, creating the pining sites along the contact area and leading to increasing the friction. Under the high humidity, the friction reduced due to the formation of a continuous layer of intercalated water molecules [85]. Thus, the main conclusions are in agreement with the findings made by Qi et al. [84]. To explain some experimental behavior of graphene on an SiO2 substrate, the corresponding MD model was built [84]. It was demonstrated that the chemical interaction between the substrate and edge atoms of graphene could lead to an effective substrate pinning effect. Extra edge pinning from the substrate effectively reduced the formation of bonds between the step edge and the tip. As a result, the adhesive wear was also suppressed under the normal load of 30 nN. According to the Hertzian contact model, this load corresponded to the shear stress of 6 GPa. The effect of the gas environment on the tribology of graphene was also investigated by Berman et al. [86]. It was demonstrated that graphene had extraordinary wear performance, especially in a hydrogen atmosphere. This

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phenomenon was attributed to passivation of the dangling bonds of raptured graphene with hydrogen. Hydrogen stabilized defects and protected the underlying surface from further damage. In the case of a nitrogen atmosphere, no such passivation occurred.

2.6 Graphene-based nanocomposites A computer simulation of graphene composites is much more sophisticated in comparison to the simulation of graphene/graphene or graphene/metal systems. First of all, the simulation of composites requires using much larger models, which include complex polymer molecules. Besides, the model size also should be relatively large for adequate representation of real materials. Due to these factors, the simulation of polymers requires a significant amount of computational resources. As a result, that kind of simulation became available almost 8 years later, with the first MD simulation of graphene. One of the early studies in this field was published by Zhang and Jiang [87] in 2014. In this work, the composite structures consisting of graphene or Go sheets separated by polymer layers were studied. It should be noted that such construction is quite different from the real nanocomposites, discussed in Section 6.1. Nevertheless, this work laid the foundation for understanding graphene/polymer composites. For instance, it was demonstrated that the stiffness of composites increased with increasing the density of polymer-graphene intercalations due to greater layer-matrix adhesion. Especially, the macroscopic mechanical properties of GO-based polymers were controlled by H-bond networks formed between GO sheets and polymer molecules. This conclusion was also supported by Skountzos et al. [88]. Their computations showed that the addition of a small number of graphene nanosheets into the PMMA matrix led to the significant improvement of the mechanical properties of the nanocomposite, primarily when functionalized graphene sheets were used. Multiscale finite element modeling of graphene-reinforced polymer composites also demonstrated the remarkable improvement of their mechanical properties, even if a low amount of reinforcements was used [89]. It was predicted that the Young’s modulus of a composite should linearly increase with increasing of the volume fraction of graphene reinforcement. Besides, the mechanical properties of composites are strongly dependent on the size of graphene flakes. In this simulation, increasing the size of graphene flakes from 3
3 to 10
10 nm2 increased the Young’s modulus 2.5 times for the same volume fraction.

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The first study of the tribological properties of a graphene/polymer composite was presented by Li et al. [90]. In this work, the sliding of an Fe nanorod against a graphene/polymer layer was simulated. The aim was to explore the mechanism of improved tribological properties of nanocomposites. The introduction of a graphene flake into the acrylic polymer matrix led to a 150% increase of the Young’s modulus. Shear modulus and hardness were improved by 27.6% and 35%, correspondingly. Besides, the friction coefficient and abrasion rate were reduced to 35% and 48% of the initial value. Such significant improvement was attributed to the stabilization of the chemical state of the polymer matrix due to the strong adsorption and bonding of the polymer chains by the graphene reinforcement via the electrostatic and van der Waals forces. Thus, during the tribological interaction, fewer polymer chains interacted with the nanorod, leading to lower adhesion. In its turn, reducing the adhesion force lowered both friction and wear. Using hydroxyl-functionalized graphene (HOFG) allowed a further significant reduction of the friction force [91]. Additional hydroxyl-function groups grafted on the graphene sheet increased the adhesion and bonding of polymer bonds, improving the reinforcement properties. An MD simulation of GO-reinforced styrene butadiene rubber revealed a 734% increase of the Young’s modulus when 5 vol% of GO was used [92]. In this case, the friction coefficient and abrasion rate were reduced by two and five times correspondingly. The improvement was also attributed to better adhesion between the GO reinforcement and the polymeric matrix. A different approach was used by Chen et al. [93]. In this work, the authors focused on the improvement of the mechanical properties of the graphene/polymer composites rather than the tribological behavior. Nevertheless, their results are essential for further understanding of graphene composites. By the MD simulation. It was found that the pullout of graphene, opposite to that of microfibers, is not only defined by friction. Instead, the pull-out force is revealed to be driven by a “crack surface adhesion” phenomenon. In other words, graphene cracking caused additional anchoring to the polymer matrix. Depending on the degree of functionalization, the crack-driven mechanism could be converted to friction-driven. Therefore, the crack-driven mechanism is more probable for pristine graphene. Improvement of mechanical properties of the SiC/graphene nanocomposite was also attributed to better adhesion between the ceramic matrix and single-layer graphene [94]. Comparison between single-layer and

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bilayer graphene revealed that the single-layer one tended to provide better reinforcement. Even in the case of the rigid ceramic composite structure, better interlocking between more-corrugated single-layer graphene and ceramic matrix led to a 37% improvement of Young’s modulus. As for the bilayer graphene, the interlayer slippage led to reducing of the mechanical properties. Thus, from the practical point of view, using SLG as the reinforcement in ceramic-based nanocomposites is preferable. Increasing the volume fraction of graphene also increased both the Young’s modulus and the fracture toughness. The mechanical properties were slightly sensitive to the temperature, as an increase from 100 to 500 K reduced them by 30%. While the mechanical properties of the graphene/polymer and graphene/ceramic composites increased with the rising of adhesion, the absolute opposite behavior was predicted for graphene/metal composites. Comparison of Ni/graphene and Cu/graphene nanocomposites performed by Montazeri and Mobarghei [95] revealed that the overall mechanical behavior of the nanocomposite was improved in the case of lower graphene/metal interactions. This was attributed to the facilitation of mechanical deformations in the case of stronger interfacial interactions. As a result, the stiffness of nanocomposites was reduced. The simulation of a Cu-graphene layered composite [96] showed that the distance between graphene layers was the crucial parameter for the mechanical properties of such composites. The best improvement was achieved when the graphene layers were separated with very thin (2 nm) copper lamellas. Increasing the lamella thickness reduced the mechanical properties of nanocomposites– the Young’s modulus and the fracture strain.

2.7 Summary Many theoretical studies were performed to get a better understanding of the mechanical and tribological behavior of graphene. The key factors affecting the mechanical properties such as the Young’s modulus, the Poisson’s ratio, and the fracture strength are chirality and defectiveness. In particular, graphene demonstrated better mechanical performance in the zigzag direction. The presence of defects did not affect the Young’s modulus, but it could significantly reduce the fracture strength. Increasing the number of graphene layers led to better mechanical performance. Also, the mechanical properties slightly deteriorated with increasing temperature.

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CMS showed that the reinforcement of various materials with graphene allowed improved mechanical properties. Adhesion between the composite matrix and reinforcement plays a vital role in such improvement. In the cases of polymer and ceramic matrices, better adhesion leads to better mechanical performance. The formation of chemical bonds did not affect the mechanical properties of graphene flakes. At the same time, low adherence is preferred for metal-graphene composites. Simulations of sliding of graphene against graphene predicted superlubricity in some situations. First of all, commensurability is a crucial factor. The friction affected by the orientation of graphene layers and the lowest values could be achieved in the case of the fully incommensurate interface. Using multiple flakes or multigrain graphene structures is preferable due to the possibility of self-alignment and reducing the negative effect of the stick-slip phenomenon. The friction of graphene could be reduced by increasing the number of layers and stiffness of the substrate. Friction also could be reduced by chemical modifications of graphene. Functionalization allowed not only reducing the adhesion of the surface but, in some cases, increasing the elasticity of graphene, leading to better tribological performance. In the case of sliding of different materials against graphene, the best tribological performance should be achieved in the case of defect-less multilayer graphene, firmly attached to a rigid and smooth substrate. The counter surface should also be smooth, and its material should have low adhesion to graphene. This could be achieved through the selection of proper materials, the functionalization of the graphene surface, or using various lubricants. The contact also should be incommensurate. These requirements are summarized in Fig. 2.10. In the next sections, we will discuss which deposition methods allow approaching this ideal model.

Fig. 2.10 The ideal graphene-based tribological system for low friction and wear.

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[86] D. Berman, S.A. Deshmukh, S.K. Sankaranarayanan, A. Erdemir, A.V. Sumant, Extraordinary macroscale wear resistance of one atom thick graphene layer, Adv. Funct. Mater. 24 (2014) 6640, https://doi.org/10.1002/adfm.201401755. [87] J. Zhang, D. Jiang, Molecular dynamics simulation of mechanical performance of graphene/graphene oxide paper based polymer composites, Carbon 67 (2014) 784, https://doi.org/10.1016/j.carbon.2013.10.078. [88] E.N. Skountzos, A. Anastassiou, V.G. Mavrantzas, D.N. Theodorou, Determination of the mechanical properties of a poly(methyl methacrylate) nanocomposite with functionalized graphene sheets through detailed atomistic simulations, Macromolecules 47 (2014) 8072, https://doi.org/10.1021/ma5017693. [89] Z. Guo, L. Song, G.B. Chai, Z. Li, Y. Li, Z. Wang, Multiscale finite element analyses on mechanical properties of graphene-reinforced composites, Mech. Adv. Mater. Struct. 1 (2018), https://doi.org/10.1080/15376494.2018.1447176. [90] Y. Li, S. Wang, Q. Wang, A molecular dynamics simulation study on enhancement of mechanical and tribological properties of polymer composites by introduction of graphene, Carbon 111 (2017) 538, https://doi.org/10.1016/j.carbon.2016.10.039. [91] Y. Li, S. Wang, Q. Wang, Enhancement of tribological properties of polymer composites reinforced by functionalized graphene, Compos. Part B Eng. 120 (2017) 83, https://doi.org/10.1016/j.compositesb.2017.03.063. [92] R. Chawla, S. Sharma, A molecular dynamics study on efficient nanocomposite formation of styrene–butadiene rubber by incorporation of graphene, Graphene Technol. 3 (2018) 25, https://doi.org/10.1007/s41127-018-0018-9. [93] S.J. Chen, C.Y. Li, Q. Wang, W.H. Duan, Reinforcing mechanism of graphene at atomic level: friction, crack surface adhesion and 2D geometry, Carbon 114 (2017) 557, https://doi.org/10.1016/j.carbon.2016.12.034. [94] M. Barfmal, A. Montazeri, MD-based design of SiC/graphene nanocomposites towards better mechanical performance, Ceram. Int. 43 (2017) 17167, https://doi.org/ 10.1016/j.ceramint.2017.09.140. [95] A. Montazeri, A. Mobarghei, Nanotribological behavior analysis of graphene/metal nanocomposites via MD simulations: new concepts and underlying mechanisms, J. Phys. Chem. Solid 115 (2018) 49, https://doi.org/10.1016/j.jpcs.2017.12.012. [96] S. Weng, H. Ning, T. Fu, N. Hu, Y. Zhao, C. Huang, X. Peng, Molecular dynamics study of strengthening mechanism of nanolaminated graphene/Cu composites under compression, Sci. Rep. 8 (2018) 3089, https://doi.org/10.1038/s41598-018-21390-1.

Further reading [97] O. Hod, Interlayer commensurability and superlubricity in rigid layered materials, Phys. Rev. B 86 (2012) 075444, https://doi.org/10.1103/PhysRevB.86.075444.

CHAPTER 3

Preparation and characterization of graphene Contents Mechanical exfoliation Epitaxial growth Chemical vapor deposition Plasma-enhanced chemical vapor deposition and pulsed laser deposition Wet exfoliation Synthesis of graphene oxide Reduction of graphene oxide Graphene-based composites Analysis and characterization 3.9.1 Optical imaging 3.9.2 Fluorescence quenching 3.9.3 Atomic-force microscopy 3.9.4 Raman spectroscopy 3.9.5 X-ray photoelectron spectroscopy 3.9.6 Transmission electron microscopy 3.10 Summary References Further reading 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

51 54 55 63 65 66 67 68 70 70 71 73 75 80 80 83 83 90

3.1 Mechanical exfoliation As follows from the theoretical studies discussed in Chapter 2, the successful utilization of graphene in tribological applications raises some specific requirements not only to the structure of graphene itself but also to the whole “graphene-substrate” system. The critical factors for the graphene structure are the graphene defectiveness, the number of layers, the grain size, the adhesion to the substrate, the stiffness of the substrate, etc. They are defined by a specific method of preparation/synthesis of graphene. Since the first invention of mechanical exfoliation of graphene from pyrolytic graphite in 2004, many approaches have been developed to fabricate Tribology of Graphene https://doi.org/10.1016/B978-0-12-818641-1.00003-4

© 2020 Elsevier Inc. All rights reserved.

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single- and multilayer graphene on different substrate materials. The variety of approaches include techniques such as chemical vapor deposition, liquidphase exfoliation, microcleavage, and oxidization reduction, as illustrated in Fig. 3.1A. The synthesis methods can be divided into two main groups, called top down and bottom up. Top-down approaches are grounded on the exfoliation of graphite. The first historical preparation method of isolated graphene specimens was mechanical exfoliation, proposed by Novoselov and Geim [1]. This method allowed preparing multilayer or single-layer graphene that would be suitable for device fabrication and the study of electronic properties. According to this method, graphene films were made by repeated peeling of small mesas of highly oriented pyrolytic graphite (Fig. 3.1B). This method is also well known as the “Scotch tape method” or microcleavage [2, 3]. It allows preparing films up to 20 μm in size [4]. Despite its initial simplicity, the Scotch tape method was further improved by various researchers. For example, Peng et al. proposed their own modified plan [5]. In their work, a fresh piece of adhesive tape was firmly pressed sticky-side down onto the HOPG surface for about 30 s. Then, the tape was peeled away with thick layers of graphene stuck to it. The part of the tape with graphite layers was refolded on a clean adhesive section of the same piece of tape. After that, the tape was unfolded and the mirrored layer of graphite remained on it. This process was repeated until a large portion of the tape became dark gray. Then, the graphene was transferred to the SiO2/Si substrate by pressing the tape with graphene flakes on it. Zhang et al. developed a micromechanical method to extract fragile graphene samples [6]. Initially, micropillars were fabricated on the HOPG surface using micropatterning, followed by masked anisotropic oxygen plasma etching. Then, individual pillars were removed from the substrate and attached to a micromachined silicon cantilever by a small amount of ultraviolet-sensitive epoxy. In the next step, cantilevers with graphite samples were mounted at the tips of the AFM device for transfer onto an SiO2/Si substrate. AFM tip slid in contact mode against the surface, leading to the shearing of graphene layers onto the substrate. The thickness of the graphene layers was in the range of 10–100 nm, and the lateral size was around 2 μm. These specimens were suitable for electrical experiments. The original Scotch tape method appeared to be extremely simple and effective and allowed the fast growth of graphene-related studies. It has a low entry barrier and does not require a significant investment or complicated

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CVD

53

Mechanical exfoliation (research, prototyping)

Quality

(coating, bio, transparent conductive layers, electronics, photonics)

SiC (electronics, RF transistors)

Molecular assembly (nanoelectronics)

Liquid-phase exfoliation (coating, composites, inks, energy storage, bio, transparent conductive layers) Price (for mass production)

(A)

(B) Fig. 3.1 (A) Summary of graphene production methods based on price and quality estimation. (B) The micromechanical cleavage technique (“Scotch tape method”) for producing graphene. Top row: Adhesive tape is used to cleave the top few layers of graphite from a bulk crystal of the material. Bottom left: The tape with graphitic flakes is then pressed against the substrate of choice. Bottom right: Some flakes stay on the substrate, even after removal of the tape. (A: Reprinted by permission from K.S. Novoselov, V.I. Fal’ko, L. Colombo, P.R. Gellert, M.G. Schwab, K. Kim, A roadmap for graphene, Nature 490 (2012) 192, https://doi.org/10.1038/nature11458. Copyright (2012); B: Reprinted from K.S. Novoselov, Nobel lecture: graphene: materials in the flatland, Rev. Mod. Phys. 83 (2011) 837. Copyright (2011) by the American Physical Society.)

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equipment. These factors have helped considerably to broaden the geography of graphene science [3]. This method allowed preparing high-quality graphene specimens with a low number of structural defects [1, 6–8]. Nonetheless, even though this method of mechanical exfoliation has led to numerous discoveries regarding the mechanical properties of graphene, it has two significant drawbacks: low production efficiency and the small size of graphene flakes. Because these limitations are crucial for the tribological applications of graphene, it was used only in some initial tribological studies [7].

3.2 Epitaxial growth Besides mechanical exfoliation and chemical reduction methods, several promising approaches for producing graphene sheets have been reported. In particular, they are chemical vapor deposition (CVD) and epitaxial growth from SiC [9]. Growth from SiC, which is also called SiC sublimation, has been attractive, first of all, for the semiconductor industry because it does not require transfer to another substrate for assembling the final devices [10, 11]. In this process, the sublimation of Si atoms from the substrate occurred during high-temperature heating of the SiC substrates under UHV conditions. As a result, the surface carbon atoms were rearranged into graphene layers. The thickness of the graphene layers depends on the temperature and processing time. The formation of few-layer graphene typically required annealing of the SiC surface at a temperature around 1200°C for several minutes [12]. Even though the synthesis of graphene on SiC substrates looks promising, several substantial disadvantages still limit its application. In particular, it was challenging to control the number of graphene layers. Another uncertainty involved the different epitaxial growth patterns on different SiC polar faces (i.e., Si-face or C-face). Also, the lattice mismatch caused abnormal rotational graphene stacking. The lattice mismatch can lead to delamination between different layers of graphene [11]. Moreover, it is very challenging to grow uniform graphene over a large area due to the occurrence of step bunching on the SiC surface [13]. The issue of nonuniformity was overcome by the gown of graphene on off-axis 3C-SiC(111), which is one of the polytypes of silicon carbide. 3C-SiC substrates could be synthesized in many ways in the form of bulk substrates or coatings [14]. It was demonstrated that the step bunching was eliminated

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during graphene growth due to the synergistic effect of periodic SiC step edges as graphene nucleation sites and the unique thermal decomposition energy of 3C-SiC steps [13]. Besides, several studies were focused on the optimization of synthesis conditions for conventional SiC substrates. For instance, high-quality epitaxial graphene was produced by flash annealing of 6H-SiC in a lead (Pb) atmosphere [15]. It was found that the three top bilayers of SiC are decomposed due to fast heating to
1400°C and cooling. In this case, the sublimation of Si atoms from SiC was accelerated by the Pb atmosphere.

3.3 Chemical vapor deposition While top-down methods are grounded on the exfoliation of graphite, bottom-up approaches use carbon molecules as building blocks. Usually, these molecules are obtained from external sources such as carbonaceous gases. CVD is related to bottom-up methods. It is still one of the most promising approaches for the large-scale production of graphene [7]. The successful synthesis of few-layer graphene films using thermal CVD was first reported by Somani et al. [15]. Films were grown on Ni foils using camphor pyrolysis with two horizontal furnaces. Camphor is evaporated in the first furnace at 180°C and pyrolyzed in the second furnace at 700–850°C with argon as the carrier gas. Ni sheets were kept on the alumina boat in the center of the second furnace. This method allowed covering relatively large areas (2  2 cm2 in the first experiments). This study opened the possibility of performing controlled and large-area synthesis of graphene [16]. Despite the first success, CVD suffered several severe downsides and unresolved issues such as the need for minimization of graphene folding and control of the number of layers. However, since the initial report, much progress has been achieved, allowing the deposition of a controlled number of graphene layers on various metal substrates. Moreover, it was demonstrated that graphene can be relatively easily transferred to other substrates after CVD synthesis. The transfer technique can provide high-quality graphene layers without additional mechanical or chemical treatments [16]. For example, Bae et al. demonstrated a roll-to-roll production of graphene films using the CVD method [17]. Initially, graphene was grown on 30-in. copper foils. Then, the copper foil was covered with a polymer layer to support the graphene. In the next step, the copper foil was etched, and the graphene layers were released and transferred onto a target substrate. A schematic of such a process is shown in Fig. 3.2.

Cu etchant

(A)

(C)

Graphene on target

(D)

Fig. 3.2 (A) Schematic of the roll-based production of graphene films grown on a copper foil. The process includes the adhesion of polymer supports, copper etching (rinsing), and dry transfer printing on a target substrate. Wet chemical doping can be carried out using a setup similar to that used for etching. (B) Copper foil wrapping around a 7.5-in. quartz tube to be inserted into an 8-in. quartz reactor. The lower image shows the stage in which the copper foil reacts with CH4 and H2 gases at high temperatures. (C) Roll-to-roll transfer of graphene films from a thermal release tape to a PET film at 120°C. (D) A transparent ultra large-area graphene film transferred on a 35-in. PET sheet. (Reprinted by permission from S. Bae, H. Kim, Y. Lee, X. Xu, J.S. Park, Y. Zheng, et al., Roll-to-roll production of 30-inch graphene films for transparent electrodes, Nat. Nanotechnol. 5 (2010) 574, https://doi.org/10.1038/nnano.2010.132. Copyright (2012).)

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Released polymer support

Target substrate

Graphene on Cu foil

(B)

56

Graphene on polymer support

Polymer support

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Depending on the substrate material used in the CVD process, the formation of graphene films may occur through two different mechanisms— reinfusion or surface activation on the catalyst. In the case of metals having intermediate or high solubility of carbon (>0.1 atomic%), such as Co and Ni, the synthesis occurred by reinfusion and involved two stages. The first stage is the diffusion of carbon atoms into the thin metal film during the high-temperature CVD process. Carbonaceous gaseous species such as CH4 decomposed on the hot surface, providing the source of carbon for the first stage. The diffusion was followed by the second stage, which is the precipitation of carbon from the bulk to the surface of the metal during cooling [18]. The surface activation occurred at high temperatures (900–1100°C) on the surfaces of thin metal films or foils. This mechanism has been primarily attributed to the limited solubility of carbon in some metals. In particular, it is realized in metals having very low carbon solubility (85%, 3 layers), and a low oxidation degree. The suspensions prepared by various exfoliation methods could be further used for deposition of graphene films by multiple techniques such as vacuum filtration, drop casting, spray coating, spin coating, or electrospray coating [52, 53].

3.6 Synthesis of graphene oxide The chemical conversion of graphite to graphene oxide was developed as an affordable production method of graphene-based single sheets in considerable quantities. GO can be produced from graphite using various oxidants such as concentrated nitric or sulfuric acids or potassium permanganate. The formation of GO from graphite includes the three following independent steps. The first step is the conversion of graphite into a graphite intercalation compound (GIC). The second step is the conversion of the GIC into oxidized graphite, which was defined as pristine graphite oxide (PGO). This step involves diffusion of the oxidizing agent into the preoccupied graphite galleries. This rate-determining step makes the entire process diffusivecontrolled. The third step is the conversion of PGO into conventional GO after exposure to water. This step involves the hydrolysis of covalent sulfates and the loss of all interlayer bonding [54]. In the case of the classical Hummers’ method [55], graphite oxidation was achieved by the harsh treatment of one equal weight of graphite powders in a concentrated H2SO4 solution containing three equal weights of KMnO4 and 0.5 equal weight of NaNO3. The Hummers’ method has significant advantages over previous techniques: (1) the reaction can be completed within a few hours; (2) KMnO4 was used to improve the reaction safety, avoiding the evolution of explosive ClO2; and (3) the use of NaNO3 instead of fuming HNO3 eliminates the formation of acid fog [56]. It was demonstrated that the appropriate oxidation time of graphite depended on the size and shape of the primary particles [57]. While the oxidation of the large agglomerations was completed in several days, the oxidation of flake powder was achieved within just 2 h. Thus, the oxidation time could be decreased by reducing the particle size (e.g., by grinding). This means that the small and flakey particles are more suitable for large-scale GO preparation. The oxidation degree of GO produced by modified Hummers’ methods could be controlled by adjusting the parameters of the process, such as the temperature and duration of different steps [58].

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Initially, the Hummers’ method received intense attention due to its high efficiency and satisfying reaction safety. However, it still has several significant drawbacks: (1) the oxidation procedure releases toxic gases such as NO2 and N2O4; and (2) the residual Na+ and NO3 ions are difficult to remove from the wastewater formed from the processes of synthesizing and purifying GO [56]. Thus, significant efforts were directed to developed ecofriendly methods of GO synthesis. Dimiev and Tour [54] found that excluding the NaNO3, increasing the amount of KMnO4, and performing the reaction in a 9:1 mixture of H2SO4/H3PO4 allowed improving the efficiency of the oxidation process. This improved method provides a more massive amount of hydrophilic oxidized graphene material as compared to the classical Hummers’ method or Hummers’ method with additional KMnO4. Chen et al. [56] also proposed an improved Hummers’ method without using NaNO3 for the synthesis of GO. This enhanced method eliminates the generation of toxic gases and simplifies the procedure of purifying waste liquid that allowed decreasing the cost of GO synthesis. Further improvement was achieved by Zaaba et al. [59]. In this method, the GO also was synthesized without NaNO3 and an ice bath, allowing the process to be carried out at room temperature. The size and number of layers are essential parameters that define the further applicability of GO. Typically, it allows producing GO flakes with a scale in the range from several micrometers to several hundred micrometers. Improvements of the Hummers’ method allowed producing single-layer graphene oxide with a high yield of 171  4% [60]. The solubility and stability of GO was significantly affected by the reduction process. Solutions of GO in NMP, ethylene glycol, and water presented significant long-term stability with solubility values reaching
8.7 μg/mL for NMP. Also, the dispersion behavior of GO changed after its reduction, introducing better interaction with solvents such as o-DCB (
9 μg/mL) and CN (8.1 μg/ mL) [61].

3.7 Reduction of graphene oxide GO could be further converted to rGO by chemical reduction using various reducing agents, including hydrazine and sodium borohydrate [47, 62]. Hydrazine was the most efficient reductant, but due to its toxic nature, there is a high demand to use green reductants for RGO synthesis. Thus, many efforts were directed to design green and ecofriendly processes of GO reduction [63]. Green reducing agents include organic acids, plant extracts, sugars,

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proteins, amino acids, and even microorganisms. For instance, the green reduction of GO using two different phytoextracts of Mangifera indica L. (dry mango leaf ) and Solanum tuberosum L. (potato) was demonstrated [64]. It was observed that the polyphenols in the plant extract act both as reducing and stabilizing agents. Thus, the resultant graphene possesses good solubility and stability in an aqueous medium. Nevertheless, among all the green reductants, ascorbic acid-AA (vitamin C) has achieved primary interest as it has proven to be an excellent alternative in synthesizing RGO, challenging the toxic yet potent reductants such as hydrazine [63]. Besides chemical methods, GO could be reduced physically, for instance, using UV irradiation or thermal reduction. For example, reducing GO carried out by UV irradiation of GO dispersion in the presence of N,Ndimethylformamide (DMF) was demonstrated by Wu et al. [65]. It was found that a stable dispersion of rGO was produced by UV irradiation of a GO solution in the presence of DMF. The rapid and mild thermal reduction of GO with the assistance of microwaves in a mixed solution of N,Ndimethylacetamide and water was demonstrated by Chen et al. [66]. The whole variety of graphene synthesis methods was summarized by Raccichini et al. [67] in the diagram shown in Fig. 3.5. Selection of the process plays a crucial role in determining the properties of the final product (Table 3.1). For example, the use of methods such as mechanical exfoliation, epitaxial growth on SiC, and bottom-up approaches are still mostly limited to fundamental research due to limited scalability and high production cost. Nonetheless, significant progress was achieved in the development of the bottom-up methods, and they look most suitable for realization in the ideal graphene-based tribological system described in Section 2.7.

3.8 Graphene-based composites Graphene-based composites are a broad class of materials utilizing graphene reinforcement and categorized by a composite matrix. In general, the composite matrix may be polymer, metal, or ceramic. A manufacturing process is mostly defined by the type of matrix. The fabrication of polymer-based composites is relatively simple because it does not require high temperature and pressures [68]. As a result, degradation of the reinforcement can be readily avoided. The graphene should not form aggregates and must be well dispersed to enhance the interfacial interaction with the matrix to maximize the advantage of graphene as an effective reinforcement for high-strength polymer composites. The most common method for preparing graphene-based

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Fig. 3.5 Schematic of the most common graphene production methods. Each method has been evaluated in terms of graphene quality (G), cost aspect (C; a low value corresponds to the high cost of production), scalability (S), purity (P), and yield (Y) of the overall production process. (Reprinted by permission from R. Raccichini, A. Varzi, S. Passerini, B. Scrosati, The role of graphene for electrochemical energy storage, Nat. Mater. 14 (2014) 271, https://doi.org/1038/nmat4170. Copyright (2014).) Table 3.1 Comparison of methods and properties of graphene. Method

Mechanical exfoliation (cleavage) Epitaxy CVD, intact CVD, transferred PECVD Chemical exfoliation, oxidation, reduction a

Dimension, up to

Adhesion

20 μm

Weak/moderate


200 mm
1 m
1 m
200 mm
100 mm

High High Weak Moderate/higha Weak

Depending on the material of substrate.

Durability a

High High Moderate/higha Low Moderate Low

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polymer composites is to mix both components into a solvent and evaporate it with or without vacuum conditions to form a composite. The most efficient distribution of components during the first step is achieved by bath or tip sonication [68–72]. Besides, polymer-based composites could be manufactured by in situ polymerization and melt mixing. The melt mixing technique uses a high temperature and shear forces to disperse the reinforcement phase in the polymer matrix. The high temperature liquefies the polymer phase and allows easy dispersion or intercalation of GO and reduced graphene sheets. In situ polymerization starts with the dispersion of GO or RGO in the monomer followed by its polymerization. Graphene-reinforced metal and ceramic composites are mostly produced by powder metallurgy techniques. The initial powder mixing is a critical step in ensuring the homogenous dispersion of graphene particles. Graphene should be uniformly dispersed in matrices without agglomeration to take advantage of the high surface area and nanostructure. A common problem with mixing graphene is the prevention of particle agglomeration, so the techniques of mixing ceramic/metal matrix powder and graphene powder require high energy to overcome the high surface energy of graphene that causes the agglomeration of graphene particles [73]. After preparation of a graphene-content mixture, it could be sintered using high temperatures and pressures.

3.9 Analysis and characterization 3.9.1 Optical imaging Different methods are used for the visualization of single- and few-layer graphene such as optical microscopy, scanning electron microscopy (SEM), high-resolution transmission electron microscopy (TEM), and their combinations. Initially, the optical microscope was primarily used because it is a cheap and nondestructive method. However, handling optical microscopy requires graphene layers laying on a thin dielectric layer such as SiO2 or Si3N4 [74]. High contrast between the graphene and the substrate can be obtained by choosing the appropriate optical properties and thickness of the dielectric layer. In this case, the visual contrast is based on the FabryPerot interference between the Si substrate and the dielectric surface layer. Another essential factor that defined contrast is the wavelength of the incident light. For instance, Blake et al. [75] used different narrowband filters to detect graphene sheets on SiO2 layers having different thicknesses. The authors show that graphene visibility strongly depends on both the light

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Fig. 3.6 Graphene crystallites on 300 nm SiO2 imaged with white light (A), green light, and another graphene sample on 200 nm SiO2 imaged with white light (C). Single-layer graphene is clearly visible on the left image (A), but even three layers are indiscernible on the right (C). Image sizes are 25  25 μm2. Top and bottom panels show the same flakes as in (A) and (C), respectively, but are illuminated through various narrow bandpass filters with a bandwidth of
10 nm. The flakes were chosen to contain areas of different thickness so that one can see changes in graphene’s visibility with the increasing numbers of layers. The trace in (B) shows step-like changes in contrast for one, two, and three layers (trace averaged over 10-pixel lines). This proves that the contrast can also be used as a quantitative tool for defining the number of graphene layers on a given substrate. The measured thickness of the GO sheet here is
1 nm. (Reprinted with permission from P. Blake, E.W. Hill, A.H. Castro Neto, K.S. Novoselov, D. Jiang, R. Yang, et al., Making graphene visible, Appl. Phys. Lett. 91 (2007) 063124, https://doi.org/10.1063/1.2768624. Copyright (2007) American Chemical Society.)

wavelength and the thickness of the SiO2 layer. It was found that by using monochromatic illumination, graphene can be isolated for any SiO2 thickness. Nevertheless, 300 nm and, mainly,
100 nm were observed to be most suitable for the visual detection of graphene (Fig. 3.6).

3.9.2 Fluorescence quenching It was reported in 2010 that graphene-based sheets could be made highly visible under a fluorescence microscope by quenching the emission from a dye coating [76]. As was mentioned in Section 3.4, optical imaging for graphene requires specific substrates. In contrast, the fluorescence quenching

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mechanism does not have such a limitation. In this case, graphene, reduced graphene oxide, or even graphene oxide sheets deposited on arbitrary substrates can be visualized with good contrast for layer counting. Also, this method could be used for direct observation of suspended graphene flakes in solution. The imaging mechanism involves quenching the emissions from dye-coated graphene, GO, and RGO. The contrast originated due to the chemical interaction between the dye and the graphene. The charge was transferred from the dye molecule to GO, which causes the quenching of fluorescence [76, 77]. The contrast depended on the material of the substrate and varied from 0.07 to 0.78 for glass and SiO2 correspondingly, which is enough for clear visualization [78]. Correlation between AFM and FQM images is shown in Fig. 3.7, where the FQM image is compared to the AFM image of the same area. Besides, this technique can be used for

(A)

(B)

2 µm

3 2 1 0

50 µm

0

1

2

3

4

X axis (µm)

5

6

Height (nm)

(C)

–1

Fig. 3.7 (A) Fluorescence image of a GO monolayer deposited on T4-functionalized, 300 nm thick SiOx. (B) AFM image of the area indicated in (A), showing the GO sheet partially folded over itself (z range 30 nm). (C) Height profile is taken across the black line in (B). The measured thickness of the GO sheet here is
1 nm. (Reprinted with permission from E. Treossi, M. Melucci, A. Liscio, M. Gazzano, V. Palermo, High-contrast visualization of graphene oxide on dye-sensitized glass, quartz, and silicon by fluorescence quenching, J. Am. Chem. Soc. 131 (2009) 15576, https://doi.org/10.1021/ja9055382. Copyright (2009) American Chemical Society.)

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visualization of the GO/RGO film on plastic substrates [79]. However, this technique is based on dye addition on the graphene surface. Even though the dye coating can be conveniently removed afterward by rinsing without disrupting the graphene layers, further use of the same sample might be limited due to the attachment of unwanted functional groups.

3.9.3 Atomic-force microscopy This technique is commonly used to determine the graphene layer thickness at the nanometer scale. The typical cross-sectional profile of mono- and fewlayer graphene is illustrated in Fig. 3.7. The vertical distance between the top surfaces of graphene layers is called “step high” (Fig. 3.7C). The sum of the step heights of all layers gives the total thickness of the graphene film. The step height of monolayer graphene equals its thickness. Various authors reported the thickness of the monolayer graphene in the range of 0.5–1.7 nm, depending on specimens and measurement conditions [80, 81]. Gupta et al. [82] demonstrated that the thickness of multilayer graphene linearly increased with the constant increment of 0.35 nm (Fig. 3.8). In their study, the thickness of the monolayer graphene was 0.86 nm. The 0.33 nm difference between the 0.35 increment and the thickness of the monolayer graphene was called the “AFM offset.” It was attributed to the different attraction forces between

Fig. 3.8 Effective nGL film height versus assigned n. The straight line is a least-square fit to the data. The apparent thickness of a graphene layer is t ¼ 0.35  0.01 nm, and the AFM offset parameter is t0 ¼ 0.33 nm (see text for discussion). (Reprinted with permission from A. Gupta, G. Chen, P. Joshi, S. Tadigadapa, P.C. Eklund, Raman scattering from highfrequency phonons in supported n-graphene layer films, Nano Lett. 6 (2006) 2667, https://doi.org/10.1021/nl061420a. Copyright (2006) American Chemical Society.)

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the tip and graphene compared to the tip and SiO2. Thus, the variation in the thickness of the monolayer graphene reported by various authors could be due to a slight difference of adhesion between tips, graphene, and substrates. The comprehensive comparison of measurement results of the thickness of monolayer graphene was performed by Shearer et al. [81]. It was demonstrated that using advanced AFM modes such as the PeakForce tapping mode allowed reducing the error in measuring the first layer from 0.3–1.3 nm to 0.1–0.3 nm. It was also concluded that the pressure applied to the AFM tip was the critical parameter for the accurate measurement of graphene because it mitigated the effect of the absorbate layer between a substrate and a graphene layer. Also, that observation meant that more precise results could be achieved in the dry or vacuum conditions. Despite the fact that the linear thickness increase of multilayer graphene with an increasing number of layers is intuitive, nonlinear behavior was also observed by some authors. For instance, Ptak et al. [83] found that in their experiment, the step high of exfoliated graphene transferred onto an SiO2 substrate reduced with increasing the number of layers. The thickness of monolayer graphene on SiO2 is around 0.8 nm. The step high reduced it to 0.5 nm for the second layer and reached
0.34 nm for the fifth layer. Thus, the step high of the fifth layer is equivalent to the interlayer distance of bulk graphite. The nonlinear behavior, in this case, could be attributed to the effect of water absorption from the atmosphere. Different AFM modes allowed the study of the electrical, mechanical, frictional, magnetic, and even elastic properties of graphene [16]. It is an indispensable instrument for the mechanical and tribological characteristics of graphene. For instance, AFM was used to measure the strength and Young’s modulus of graphene [79] as well as for simulation of its tensile and compressive properties [84]. Because of the extremely high lateral and vertical force resolutions of AFM, it is an excellent tool for investigating nanotribological phenomena [4]. Using an AFM device in the friction force microscopy (FFM) mode allows measuring the friction coefficient under various loads. After a friction test, wear can be immediately evaluated using a topography measurement mode. However, due to technical limitations, it is challenging to assess large areas of graphene by AFM. First, the maximum scanning area of most commercial devices is in the range from 50  50 to 100  100 μm2. Second, scanning large areas requires a compromise between image quality (resolution) and scanning time. Moreover, AFM imaging is mostly limited to topographic contrast. Thus, graphene oxide and the graphene layers cannot be distinguished in the normal direction.

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This issue could be overcome by AFM. In this case, phase imaging facilitated distinguishing between defect-free pristine graphene and the functionalized one. This method is based on the difference in the interaction forces between the AFM tip and the attached functional group. Paredes et al. demonstrated the tapping mode for determining the thickness of graphene sheets [85]. It was found that the unreduced graphene oxide has a thickness of
1.0 nm, and for chemically reduced GO it was 0.6 nm. This difference was attributed to the hydrophilicity of GO.

3.9.4 Raman spectroscopy Since the Raman spectrum of graphene was first measured in 2006 [86], Raman spectroscopy had become one of the most popular techniques for the characterization of disordered and amorphous carbons, fullerenes, nanotubes, diamonds, and carbon chains. Raman spectroscopy works for all graphene samples. Moreover, it can be used for the identification of unwanted byproducts, structural damage, functional groups, and chemical modifications introduced during the preparation, processing, or transferring of graphene. As a result, a Raman spectrum is indispensable for quality control and for comparing samples used by different research groups [86, 87]. The spectra of all carbon-based materials show only a few prominent features, regardless of the final structure. Identification of these features allows the characterization of graphene layers regarding the number of layers, strain, doping concentration, impact of temperature, and presence of defects. The Raman spectrum of graphite and multilayer graphene mainly consists of the set of peaks called D, G, and 2D. They are located around 1350, 1580, and 2700 cm1, correspondingly. A comparison of Raman spectra between pristine and defective graphene is shown in Fig. 3.9 [86]. The G band is associated with the double degenerated E2g phonon mode at the center of the Brillouin zone. This band arises due to the in-plane vibration of the sp2 carbon atoms [16]. The D band appears due to the breathing modes of six-atom rings and requires a defect for its activation. It represents disorder in the atomic arrangement or edge effect of graphene, ripples, and charge puddles [87]. The spectra of the pristine graphene do not show the D peak that confirms the absence of defects. The 2D band is the second-order peak, and it has almost double the frequency of the D band. Because it arises from a double-resonant electronic process, the 2D band is sensitive not only to the vibrational features of graphene but also to the electronic structure. As a result, Bernal (ABA) and Rhombohedral (ABC)

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Fig. 3.9 Raman spectra of pristine (top) and defective (bottom) graphene. The main peaks are labeled. (Reprinted by permission from A.C. Ferrari, D.M. Basko, A.C. Ferrari, D.M. Basko, Raman spectroscopy as a versatile tool for studying the properties of graphene, Nat. Nanotechnol. 8 (2013) 235, https://doi.org/10.1038/nnano.2013.46. Copyright (2013).)

multilayer graphene demonstrated clear differences in the shape and width of the Raman 2D peak [88]. Increasing the temperature led to the redshift of the G peak [89]. In the case of few-layer graphene and graphite, a significant change in the shape and intensity of Raman peaks was observed (Fig. 3.10). The 2D band splits into just two components for bulk graphite and multilayer graphene, and into four components for bilayer graphene. For multilayer graphene, an exact number of layers could be evaluated based on the distance between these components. It increased from
25.4 to 44 cm1 when the number of layers was raised from 3 to 10. The number of graphene layers also effects the relative intensity of the 2D peak and the position of the G peak. Increasing the number of layers from 1 to 6 increased the I(G)/I(2D) intensity ratio from
0.3 to
1 and shifted the G peak position from 1585 down to 1581 cm1 [90]. These findings allowed evaluating the spatial uniformity of the thickness of multilayer graphene by Raman mapping [22, 35]. The intensity ratio between the G band and the disorder-induced D band could be used for quantification of the defect’s density in graphene. In particular, the phenomenological model describing the relation between the ID/IG ratio and the graphene concentration was proposed for monolayer graphene by Lucchese et al. [91]. The ID/IG ratio as the function of the

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Fig. 3.10 (A) Plot of the ratio of the integrated intensities of the G and D0 peak versus the number of stacked layers (average value and standard deviation). (B) G line frequency vs. the number of stacked layers (average value and standard deviation). (C) G peak for HOPG (upper peak), double- (middle peak), and single-layer (lower peak) graphene. The vertical dashed line indicates the reference value for bulk graphite. (D) D0 peaks for an increasing number of graphene layers along with HOPG as a bulk reference. The dashed lines show the Lorentzian peaks used to fit the data; the solid lines are the fitted results. The single peak position for the single-layer graphene is at 2678.8  1.0 cm1. The peak positions of the two innermost peaks for double-layer graphene are 2683.0  1.5 and 2701.8  1.0 cm1. On the left, the value for splitting from the double-layer graphene up to HOPG is presented. All peaks are normalized in amplitude and vertically offset. (Adapted with permission from D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, L. Wirtz, Spatially resolved Raman spectroscopy of single- and few-layer graphene, Nano Lett. 7 (2007) 238, https://doi.org/10.1021/nl061702a. Copyright (2007) American Chemical Society.)

average distance between defects LD has a well-defined peak shape with the maximum around 3 nm. Reducing the LD from 25 to 6 nm led to a parabolic increase of the ID/IG ratio from 0.5 to
3.5 (right side of the peak). Then, the coalescence of defects started at LD
6 nm, the LD reduced further, and the ID/IG ratio lowered to 0.5 (right side of the peak). The ID/IG results on HOPG were different from those on monolayer graphene, showing an increase and saturation of ID/IG with decreasing LD. Thus, several-layer graphene should exhibit behavior lying between these two cases.

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The zigzag and armchair edges of graphene also could be distinguished based on the evaluation of the intensity of a disorder-induced Raman peak [92]. In particular, the armchair edge induced a sharp D peak while in the case of the zigzag edge, the peak was relatively weak; the intensity of the peak was approximately four times lower. This observation was explained based on the double-resonance theory applied to the one-dimensional defect. Because the D band is sensitive to defects, its relative intensity could be used for evaluation of the quality of the graphene films. It helps to estimate the spatial distribution of defects using Raman mapping. For instance, this approach was used by Won et al. [22] to evaluate graphene defectiveness during different stages of CVD growth on copper foils. In this work, the spatial distribution of I(D)/I(G) was plotted and compared to optical images. In combination with the evaluation of the I(G)/I(2D) ratio, this method allows obtaining all information about the uniformity of graphene films. Doping affected the Raman spectra of graphene. Increasing the charge carrier concentration led to decreasing the relative intensity and shift of the D and 2D peaks [93]. In particular, the ID/IG ratio reduced and the G peak position increased (blueshifted). Besides, the Raman spectra of graphene are sensitive to mechanical stress. Contrary to other factors, the presence of mechanical stress led to shifting the peak positions rather than a variation of their intensities. For instance, the compressive stress of several GPa led to a blueshift of the spectra in comparison to the bulk graphite [94]. Tensile stress led to the redshift of the 2D peak [95]. Under a 6% strain, the peak was shifted from 2682 down to 2676 cm1 . Raman spectroscopy can be used for evaluation of the mechanical properties of graphene. For example, compressive and tensile strain in the graphene layer can be evaluated based on a change in the G and 2D peaks with applied stress. The splitting of the G peak and the redshift was observed with an increase in strain, whereas the 2D peak also redshifted without splitting for small deformations around 0.8% [96]. Ni et al. found the opposite behavior for epitaxial graphene on an SiC substrate [94]. The blueshift of all the Raman bands of the epitaxial graphene occurred due to the compressive residual stress [16]. Raman spectroscopy allowed determining the Gruneisen parameters of suspended graphene sheets under uniaxial and biaxial strain [97]. Also, the effects of the graphene-substrate interaction on the strain and the relation between the mechanical and thermal properties were presented along with characterization of the thermal properties of graphene with Raman spectroscopy. The effect of various factors on the Raman spectra is summarized in Table 3.2.

Table 3.2 Effect of structural factors on Raman spectra of graphene. D peak

G peak

2D peak

ID/IG

IG/I2D

Ref.

Number of layers Defect concentration Doping Temperature Tensile stress Compressive stress

– Increasing – – – –

Redshift Widening/splitting Blueshift Redshift Redshift Blueshift

Widening/blueshift – Blueshift – Redshift Blueshift

– Increasing Reducing – – –

Increasing – – – – –

[90] [91] [93] [89] [95] [94]

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3.9.5 X-ray photoelectron spectroscopy X-ray photoelectron spectroscopy (XPS), also known as ESCA (electron spectroscopy for chemical analysis), is an ultimate tool for the examination of a surface. It is a quantitative spectroscopic technique that allows the evaluation of elemental composition and the chemical state of elements that exist within a material. First, it is an indispensable method for assessing the oxidation of graphene and its derivatives. In this case, primary attention should be paid to the carbon and oxygen peaks. The most representative carbon peak is C 1s, having a binding energy around 284 eV. The O 1s peak has a binding energy around 532 eV. The presence of chemical bonds between carbon, oxygen, and hydrogen leads to the appearance of satellite peaks. For example, Fig. 3.11 illustrates the variation of carbon and oxygen peaks during the high-temperature reduction of GO in the Ar atmosphere and the comparison to the graphite standard [98]. A change of the oxidation rate leads to a redistribution of intensities of these satellite peaks. Besides, XPS can be used to evaluate doping (functionalization) of graphene [99]. For instance, fluorine induces a significant chemical shift of the C 1s binding energy, allowing the quantification of composition and bonding type [100]. Nitrogen doping of graphene caused a shift of the N 1 s peak. Moreover, two predominant binding conditions of nitrogen in graphene could be distinguished [101]. XPS was used for monitoring the defect formation in graphene film during evaluation of the degradation mechanism under dry sliding [22]. In this case, the creation of the defects and voids in the continuous graphene film during the sliding test led to the oxidation of a substrate, causing the appearance of Cu-O peaks on the XPS spectra.

3.9.6 Transmission electron microscopy Transmission electron microscopy (TEM) is used to visualize nano-sized materials with atomic-scale resolution. Because graphene and GO/RGO are layers of several atoms thick, TEM should be one of the most suitable tools to allow resolving the atomic features of the graphene [16]. However, the use of traditional TEM is limited because the operation at high voltage damages the monolayer, whereas at the low operating voltage, the resolution is insufficient. The development of a new class of TEM devices with aberration correction in combination with a monochromator allowed overcom˚ ing this issue. It was demonstrated that such devices could provide 1 A resolution at an acceleration voltage of only 80 kV [102, 103]. For the first

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Fig. 3.11 Results of C 1 s and O 1 s spectra fitting into C and O chemical groups for XPS spectra recorded for (A) FL-GO, (B) FL-RGO, and (C) graphite standards. (Adapted from L. Stobinski, B. Lesiak, A. Malolepszy, M. Mazurkiewicz, B. Mierzwa, J. Zemek, et al., Graphene oxide and reduced graphene oxide studied by the XRD, TEM, and electron spectroscopy methods, J. Electron Spectrosc. 195 (2014) 145, https://doi.org/10.1016/j.elspec.2014.07. 003. Copyright (2014), with permission from Elsevier.)

time, the direct high-resolution images of the graphene lattice were demonstrated by Mayer et al. [102]. It becomes possible to observe every single carbon atom arranged in a hexagonal fashion. It was shown that the imperfection and topological peculiarities in graphene affected the electronic and mechanical properties, and this can be determined using an aberrationcorrected low-voltage TEM.

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Besides, the atomic lattice is visible in high-angle annular dark-field (HAADF) images acquired in a scanning transmission electron microscope (STEM) [103]. In this case, the electron beam focused onto a monoatomic layer of atoms, such as graphene. Bright contrast corresponds to atoms and dark contrast to the gaps between them. Such images are directly interpretable because they are a direct depiction of the ball-and-stick model of an atomic lattice structure. TEM was successfully used for the direct observation of structural defects in the monolayer graphene membrane [104]. The defects were generated under 300 keV electron-beam irradiation. Various defects such as monovacancy, divacancy, and Stone-Wales defects were observed (Fig. 3.12). It was shown how the transformation occurred step by step by nucleation and growth of low-energy multivacancy structures constructed of rotated hexagons and other polygons. Besides the point defects, a grain boundary is another type of defect that is especially pronounced in two-dimensional materials. Using TEM in combination with the scanning probe not only allowed visualizing these defects, but also demonstrated that the grain boundaries severely weaken the mechanical strength of graphene membranes [105]. It was shown that two crystals were stitched together by a series of pentagons, heptagons, and distorted hexagons. The grain boundary was not straight, and the defects along the boundary were not periodic. The last observation was quite crucial because the aperiodicity was contrasted with many theoretical models [105].

Fig. 3.12 Elementary defects and frequently observed defect transformations under irradiation. Atomic bonds are superimposed on the defected areas in the bottom row. Creation of the defects can be explained by atom ejection and reorganization of bonds via bond rotation. (A) Stone-Wales defect, (B) defect-free graphene, (C) V1(5-9) single vacancy, (D) V2(5-8-5) divacancy, (E) V2(555-777) divacancy, and (F) V2(5555-6-7777) divacancy. Scale bar is 1 nm. (Reprinted with permission from J. Kotakoski, A.V. Krasheninnikov, U. Kaiser, J.C. Meyer, From point defects in graphene to two-dimensional amorphous carbon, Phys. Rev. Lett. 106 (2011) 105505. Copyright (2011) by the American Physical Society.)

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3.10 Summary Since the first exfoliation of graphene flakes by the Scotch tape method, huge progress has been achieved in the development of advanced synthesis methods. Some of these methods are almost “perfect” regarding quality, and they are mostly used for research purposes due to their extreme cost. Other methods are not able to produce such “perfect” graphene, but they are cheap enough to be used in the industry. Thus, there is always a trade off between cost and scalability on the one hand and the quality of graphene on the other. Besides the general requirements to the “price/quality” ratio, tribological applications rise additional demands, such as substrate adhesion and area coverage. From the tribological perspective, the CVD-based methods seem to be the most promising, especially if the transfer to another substrate is not required. Besides a variety of synthesis methods, analytical techniques were developed. Raman spectroscopy is of the most interest because it is an ultimate informative and nondestructive method for graphene analysis. With a combination of in situ techniques, it could be an indispensable method for tribological studies of graphene. Other methods such as XPS and TEM could provide additional information about the chemical state and structure of graphene. AFM is widely used for the evaluation of mechanical and nanotribological properties of graphene, as was discussed in this chapter.

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[39] T. Aytug, M.S. Rager, W. Higgins, F.G. Brown, G.M. Veith, C.M. Rouleau, H. Wang, Z.D. Hood, S.M. Mahurin, R.T. Mayes, P.C. Joshi, T. Kuruganti, Vacuum-assisted low-temperature synthesis of reduced graphene oxide thin-film electrodes for high-performance transparent and flexible all-solid-state supercapacitors, ACS Appl. Mater. Interfaces 10 (2018) 11008, https://doi.org/10.1021/ acsami.8b01938. [40] M. Lukosius, J. Dabrowski, J. Kitzmann, O. Fursenko, F. Akhtar, M. Lisker, G. Lippert, S. Schulze, Y. Yamamoto, M.A. Schubert, H.M. Krause, A. Wolff, A. Mai, T. Schroeder, G. Lupina, Metal-free CVD graphene synthesis on 200 mm Ge/Si(001) substrates, ACS Appl. Mater. Interfaces 8 (2016) 33786, https://doi. org/10.1021/acsami.6b11397. [41] S. Chugh, R. Mehta, N. Lu, F.D. Dios, M.J. Kim, Z. Chen, Comparison of graphene growth on arbitrary non-catalytic substrates using low-temperature PECVD, Carbon 93 (2015) 393, https://doi.org/10.1038/srep14374. [42] A. Malesevic, R. Vitchev, K. Schouteden, A. Volodin, L. Zhang, G.V. Tendeloo, A. Vanhulsel, C.V. Haesendonck, Synthesis of few-layer graphene via microwave plasma-enhanced chemical vapour deposition, ACS Symp. Ser. 19 (2008) 305604, https://doi.org/10.1088/0957-4484/19/30/305604. [43] R. Vitchev, A. Malesevic, R.H. Petrov, R. Kemps, M. Mertens, A. Vanhulsel, H. C. Van, Initial stages of few-layer graphene growth by microwave plasma-enhanced chemical vapour deposition, ACS Symp. Ser. 21 (2010) 095602, https://doi.org/ 10.1088/0957-4484/21/9/095602. [44] W. Yang, G. Chen, Z. Shi, C.C. Liu, L. Zhang, G. Xie, M. Cheng, D. Wang, R. Yang, D. Shi, K. Watanabe, T. Taniguchi, Y. Yao, Y. Zhang, G. Zhang, Epitaxial growth of single-domain graphene on hexagonal boron nitride, Nat. Mater. 12 (2013) 792, https://doi.org/10.1038/nmat3695. [45] Y. Bleu, F. Bourquard, T. Tite, A.S. Loir, C. Maddi, C. Donnet, F. Garrelie, Review of graphene growth from a solid carbon source by pulsed laser deposition (PLD), Front. Chem. 6 (2018) 572, https://doi.org/10.3389/fchem.2018.00572. [46] C. Maddi, F. Bourquard, V. Barnier, J. Avila, M.C. Asensio, T. Tite, C. Donnet, F. Garrelie, Nano-architecture of nitrogen-doped graphene films synthesized from a solid CN source, Sci. Rep. 8 (2018) 3247, https://doi.org/10.1038/s41598-01821639-9. [47] S. Park, R.S. Ruoff, Chemical methods for the production of graphenes, Nat. Nanotechnol. 4 (2009) 217, https://doi.org/10.1038/nnano.2009.58. [48] Y. Hernandez, V. Nicolosi, M. Lotya, F.M. Blighe, Z. Sun, S. De, I.T. McGovern, B. Holland, M. Byrne, Y.K. Gun’Ko, J.J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A.C. Ferrari, J. N. Coleman, High-yield production of graphene by liquid-phase exfoliation of graphite, Nat. Nanotechnol. 3 (2008) 563, https://doi.org/10.1038/nnano.2008.215. [49] N. Liu, F. Luo, H. Wu, Y. Liu, C. Zhang, J. Chen, One-step ionic-liquid-assisted electrochemical synthesis of ionic-liquid-functionalized graphene sheets directly from graphite, Adv. Funct. Mater. 18 (2008) 1518, https://doi.org/10.1002/ adfm.200700797. [50] X. An, T. Simmons, R. Shah, C. Wolfe, K.M. Lewis, M. Washington, S.K. Nayak, S. Talapatra, S. Kar, Stable aqueous dispersions of noncovalently functionalized graphene from graphite and their multifunctional high-performance applications, Nano Lett. 10 (2010) 4295, https://doi.org/10.1021/nl903557p. [51] K. Parvez, Z.S. Wu, R. Li, X. Liu, R. Graf, X. Feng, K. Mullen, Exfoliation of graphite into graphene in aqueous solutions of inorganic salts, J. Am. Chem. Soc. 136 (2014) 6083, https://doi.org/10.1021/ja5017156.

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Further reading [106] K.S. Novoselov, V.I. Fal’ko, L. Colombo, P.R. Gellert, M.G. Schwab, K. Kim, A roadmap for graphene, Nature 490 (2012) 192, https://doi.org/10.1038/ nature11458.

CHAPTER 4

Experimental tribology of graphene Contents 4.1 Nanoscale friction of graphene 4.2 Nanoscale wear of graphene 4.3 Effect of ambient conditions on the nanotribology of graphene 4.4 Macroscopic friction and wear of graphene 4.5 Macrotribology of dispersed graphene 4.6 Effect of atmosphere and humidity on the macrotribology of graphene 4.7 Healing of friction-induced structural defects 4.8 Summary References

91 101 105 107 113 116 119 120 120

4.1 Nanoscale friction of graphene Because graphene is a nanomaterial, it is not surprising that most of the early studies were focused on its tribology at the nanolevel. The most suitable tool for that kind of study was atomic force microscopy. In particular, a custom-built AFM-like tool called the “Tribolever” was used by Dienwiebel et al. for the first investigation of graphite superlubricity [1]. In this experiment, atomic-scale friction between a tungsten tip and graphite surface was assessed. It was demonstrated that the ultralow friction of graphite occurred due to the incommensurability (Fig. 2.3) between rotated graphite layers. Later, the friction anisotropy of graphene was investigated by Yu et al. using AFM [2]. In this work, multilayer graphene with a thickness of 2 nm was prepared by micromechanical cleavage and transferred onto Si/SiO2 substrates. The measurements were performed in an ambient atmosphere with a relative humidity of 30%– 57%. Friction anisotropy with a periodicity of 60 degrees was observed. This friction anisotropy is consistent with the hexagonal periodicity of graphene. The friction along the armchair direction was higher than the one along the zigzag direction. The measured difference between these orientations was around threefold. These results were in some agreement with the theoretical Tribology of Graphene https://doi.org/10.1016/B978-0-12-818641-1.00004-6

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calculations, where almost a 10-fold difference was predicted. A 60 degree periodicity of friction was observed for the monolayer graphene transferred on an SiO2 grating [3]. Using the calibrated grating as a substrate allowed measuring the friction coefficient, which was switching from 0.066 to 0.087. The periodicity of friction was also attributed to the atomistic incommensurability. Due to the high expectations of the unique properties of graphene, it was fascinating to compare graphene with bulk traditional graphite. The first experimental comparison between the friction of graphite and graphene was performed by Lee et al. [4]. Graphene flakes on SiO2 substrates were prepared by the “Scotch tape method.” The flakes had different thicknesses and consisted of mono- or multilayer graphene (up to five layers). It was demonstrated that the frictional force of single-layer graphene was smaller than that on the SiO2 surface but more significant than that on graphite. Based on the force-distance relationship, it was suggested that the difference in friction between graphene and graphite is related to van der Waals forces. Increasing the number of graphene layers reduced the friction force significantly. The lowering was approximately five times in the case of five-layer graphene. Interestingly, the most significant decrease of friction occurred when the number of graphene layers changed from one to two. That fact was in excellent agreement with the findings of Dienwiebel. It means that at least two graphene layers are required to provide a solid lubricity through the sliding of graphene layers, one against other. When a graphene nanoflake slid against graphite under low temperature (as little as 5 K), it exhibited the superlubricity state, as was demonstrated in the experiment using the STM method [5]. In this experiment, the flake was initially lying on the substrate with a commensurate alignment with the underlying graphene layer. Then, the sliding was initiated by the STM tip, and the transition from the commensurate to incommensurate arrangement occurred (the superlubric state). This transition was followed by rapid sliding of the flake until it reached another commensurate position. The schematic of this phenomenon is shown in Fig. 4.1. The final commensurate alignment of the flake had the same, or it was rotated by 60 degrees. The average sliding distance of the flakes was much larger at 5 K than at 77 K (
95 and 30 nm, respectively). This observation indicated that the transaction from the superlubric to the commensurate ground state was triggered by thermal fluctuations. Later, this experiment was modeled by MD simulation, and the experimental outcome was confirmed (Section 2.2). Ultralow friction between incommensurate graphene surfaces was observed even under ambient conditions over a contact area of 100 nm2 [6].

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Fig. 4.1 Proposed mechanism for GNF sliding. Schematic illustration showing that a flake rotates out of the registry, reaching an incommensurate state (the superlubric state), where it can slide easily until another commensurate position is achieved with either the same orientation or rotated by 60 degrees. The commensurateincommensurate transition is driven by van der Waals interactions with the STM tip, and the return to the commensurate state is triggered by thermal fluctuations. (Adapted with permission from X. Feng, S. Kwon, J.Y. Park, M. Salmeron, Superlubric sliding of graphene nanoflakes on graphene, ACS Nano 7 (2013) 1718, https://doi.org/ 10.1021/nn305722d. Copyright (2013), American Chemical Society.)

In this case, a microscale graphite mesa was prepared lithographically and sheared using a pin. It was demonstrated experimentally that self-retraction of the mesa occurred caused by superlubricity. The self-retraction showed a six-fold symmetry. The size of the mesa was a crucial factor for superlubricity. In particular, 100% superlubricity was observed for contact areas below 1  106 nm2, and the probability dropped to 58% and 12% when the contact area was increased to 2.89  106 and 1  108 nm2, respectively. If the contact area exceeded 4  108 nm2, the superlubricity disappeared utterly. It was concluded that shearing occurred preferentially on the grain boundaries. Thus, the observed effect of the area on the probability of superlubricity should be attributed to the relation between the sizes of the mesa and the crystal grains inside it. Superlubricity between graphite and silica also occurred under ambient conditions [7]. In this case, it was induced by the formation of the transferred graphene layer on the asperities of the silica ball having a radius of 11.5 μm. As a result of the material transfer during the initial stages of sliding, the “silica-graphene” interface was actually converted to the “graphenegraphene” one (Fig. 4.2). During this transformation, the friction coefficient

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Fig. 4.2 (A) Illustration of the shear plane between the silica asperities and graphite at the initial stage. (B) Illustration of the transferred GNFs on the asperities of the silica surface and the shear plane after presliding. (C) Illustration of the common contact between silica asperities and graphite at the initial stage. (D) Illustration of the incommensurate contact between the transferred GNFs and graphite after presliding. (E) Frictional forces as functions of normal loads between eight different probes (random roughness) and HOPG after the presliding. The sliding speed was set as 2.4 μm/s. The inset is the roughness of the eight different probes over an area of 90,000 nm2. (Adapted from J. Li, T. Gao, J. Luo, Superlubricity of graphite induced by multiple transferred graphene nanoflakes, Adv. Sci. 5 (2018) 1700616, https://doi.org/10.1002/advs.201700616. Licensed under CC BY 4.0.)

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was reduced as low as 0.0003 from the initial value of 0.012. The low friction was robust and independent of the rotation angle, sliding velocities, and surface roughness. Moreover, ultralow friction was demonstrated under the contact pressure up to 700 MPa. The superlubricity should be, first of all, attributed to the incommensurate contact. Such behavior was earlier predicted by the MD simulations (Section 2.3). Using a graphene-coated microsphere prepared by the metal-catalystfree CVD method (Section 3.3) helped to improve these results even more [8]. First of all, using CVD allowed enhancing the adhesion between the graphene coating and the microsphere. Because the coating consisted of randomly oriented graphene nanograins, the overall incommensurability in the multiasperity contact was achieved. All these factors led to a low and robust friction coefficient of 0.003. The contact pressure under local asperities reached 1 GPa. Sliding against h-BN allowed reducing the friction coefficient down to 0.0025. This outcome could be attributed to the lower adhesion forces. The experimental findings were supported by MD simulations, discussed in Section 2.3. Mechanical exfoliation may induce strain during the transfer of graphene flakes onto a substrate and lead to the formation of wrinkles and other defects. Moreover, the creation of uneven mechanical stress may occur [9]. In other words, mechanical exfoliation and transfer could lead to the formation of anisotropic domains having different properties. The existence of such areas on exfoliated monolayer graphene that differ by their friction characteristics was experimentally demonstrated by Choi et al. [9]. Angledependent scanning showed the presence of periodical friction anisotropy. The friction anisotropy reduced with an increase in the normal load. Anisotropy was decreased significantly after thermal annealing at 200°C and wholly disappeared after annealing at 400°C. The heating and cooling of graphene restored its equilibrium state and relieved stress-induced ripples due to the negative thermal expansion coefficient [10]. The effect of wrinkles was also investigated by Long et al. [11]. It was found that the coefficient of friction perpendicular to the wrinkle direction was
194% compared to that of the parallel direction. The observed anisotropic friction originated from the formation of ripples and was explained by the puckering mechanism. Tripathi et al. also studied the effect of adhesion and various wrinkle structures on the friction of graphene [12]. Comparison of different wrinkle types showed that the folded wrinkles (horizontal) sustained at a fivefold higher normal load in contrast to the standing (vertical) one.

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The role of the graphene boundary in friction was also investigated [4]. It was found that friction increased when the AFM tip was slid through the interface between two graphene flakes. This rise was attributed to chemical forces induced at the graphene edges. This experimental observation matches theoretical predictions discussed in Section 2.3. The first attempt to establish the correlation between the mechanical and tribological properties of graphene of varying thicknesses was performed by Lee et al., also in 2009 [13]. It was also found that friction decreased while the number of layers increased from one to four, but the difference between one- and multilayer graphene was much less than that observed by Lee [4]. In this case, the difference between mono- and bilayer graphene was around 20%. Moreover, the friction was not dependent on the presence of a substrate. The last observation was in controversy with predictions of MD simulations. It was predicted that the friction of graphene on a rigid substrate should be reduced (Section 2.2). As the relationship between friction and the number of graphene layers was confirmed in several experimental studies, further investigations were performed to clarify this phenomenon. For example, in the case of graphene grown on SiC, the friction of monolayer graphene was two times higher in comparison to the bilayer one [14]. This difference was found not to originate from contact stiffness or differences in structural properties. A similar difference was demonstrated for a variety of experimental situations: for a wide range of normal loads, for silicon- and diamondcoated tips, and at different bias voltages compensating for differences in contact potential. Besides, the load-dependent transition from superlubricity to stick-slip sliding was illuminated in the case of bilayer graphene. It was demonstrated that the stick-slip occurred when the normal load exceeded
40 nN. Frictional experiments performed with tips having various apex sizes confirmed that friction decreases with an increasing number of layers [15]. These experimental results were supported by the MD simulations when the realistically rough substrates were used while simulations employing atomically smooth substrates resulted in the opposite trend. These observations were attributed to reducing the roughness of the topmost graphene layer with increasing the number of beneath layers. Lower surface roughness decreased the number of topographical corrugations that needed to be surmounted by the tip that led to smaller friction forces. Typically, the friction force of graphene linearly increased with the rising of the normal load, meaning that the friction coefficient is independent of

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the contact pressure [4, 7, 8, 16, 17]. At the same time, the friction of monoand multilayer graphene was found to be affected by the sliding velocity. At least in the range of 0.1–50 μm/s, the friction force of multilayer graphene increased
30% [18]. The intensive rise was observed when the sliding velocity increased to
20 μm/s, and then friction continued to grow slowly. Similar behavior was observed by Peng et al. [17] and later by Zeng et al. [19]. The velocity-dependent friction at low sliding velocities was attributed to the interaction potential between the tip and graphene. It was postulated that at high speed, the interaction was weaker than that at low velocity because the evolving of the strong tip–graphene contact interface required a longer time [19]. The logarithmic behavior of the velocity dependence of the friction was observed [4]. This phenomenon was attributed to the thermally activated stick-slip effect. Investigation of the frictional behavior of graphene by friction force microscopy on various substrates also confirmed the general trend of reducing friction with increasing the number of layers [20]. The response of graphene on SiO2 and frilly suspended graphene was studied. However, this trend was absent for graphene deposited on mica, where high adhesion between the film and substrate existed. These measurements suggested that mechanical confinement to the substrate played a vital role in the frictional behavior of graphene. The following mechanism was proposed to explain the observed phenomenon: “Loosely bound or suspended graphene sheets can pucker in the out-of-plane direction due to tip-graphene adhesion. This increases the contact area, and allows further deformation of the graphene when sliding, leading to higher friction. (Because) thinner samples have lower bending stiffness, the puckering effect and frictional resistance are greater. However, if the graphene is strongly bound to the substrate, the puckering effect will be suppressed, and no thickness dependence should be observed.” [20]. Another comparative study [21] showed that high purity multilayer graphene grown by CVD demonstrated twofold lower friction in comparison to a highly ordered pyrolytic graphite (HOPG). The results indicate that such a significant difference is attributed to the strong adhesion between graphene and the underlying Ni substrate. High adhesion led to reducing the real contact area between the AFM tip and surface due to the minimization of the “puckering effect” when weak adhesion caused a rise of the contact pressure in the tip-graphene interaction. Moreover, experiments with single-layer graphene transferred from a copper foil demonstrated ultralow friction in the regions having strong adhesion. At the same time, high

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friction was observed in the weak adhered areas of the graphene flake. Strong anchoring of graphene to a Ge(111) substrate allowed preserving the ultralow friction of graphene even after fluorination or oxidation [22]. It was demonstrated that this phenomenon related to the suppression of the molecular-level deformation of graphene due to the formation of the moire superlattice structure. Growth on liquid metallic substrates was initially considered a prominent method of synthesis of large-sized polycrystalline graphene (Section 3.3). Nonetheless, direct compression of tribological performance of graphene grown by conventional CVD and from the liquid phase demonstrated that the preliminary expectations were too optimistic [23]. In particular, liquid phase-grown graphene suffered from a high concentration of structural defects and wrinkling caused by different thermal expansion. As a result, such graphene demonstrated much higher friction in comparison with conventional CVD graphene. Thus, despite the ability to produce large-area graphene crystals, this method still requires optimization for overcoming the issues. Initially, the interest of researchers to grow graphene on Cu was caused by the possibility of relatively easy transfer to other substrates. But the comparison of graphene synthesized by reinfusion and surface activation showed that Ni-grown graphene was relatively more durable compared with Cu-grown graphene [24]. Better tribological performance of the Ni-grown graphene resulted from the formation of a tortoise shell-like pattern inside the wear track instead of an amorphous carbon layer with many defects formed in the case of the Cu-grown one. Another comparison of mono- and multilayer graphenes grown on Ni and Cu by CVD showed that the adhesion might depend on the number of layers [25]. In the case of the copper substrate, conversion from mono- to multilayer graphene led to
4 times growth of the adhesion. As for the Ni substrates, the multilayer graphene film exhibited almost 20 times higher adhesion. As expected, the adherence of mono- and multilayer graphene on SiO2 was the same. Besides, the experiment performed in the vacuum indicated that multilayer graphene on SiO2 possesses higher work of adhesion in comparison to the multilayer graphene on Ni. That was a surprising result assuming that in both systems sliding occurred between the same interfaces—graphene and the silicon tip. The experiment clearly demonstrated that a strong adhesion of the graphene sheet in respect to the substrate seems to be an essential ingredient to reduce the friction force in sliding contact [25]. These experimental findings are in excellent agreement with the

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theoretical predictions discussed in Chapter 2. Mainly, they support the model of the ideal graphene-based tribological system proposed in Section 2.7. Thereby, CVD-grown graphene demonstrated better tribological performance due to better adhesion to a substrate. Nonetheless, the effect of the substrate grain boundaries is another essential factor for such a type of graphene. High-temperature annealing leads to recrystallization and growth of grains. Several studies demonstrated that the tribological properties of graphene are significantly affected by the grain topology of the metal substrate. In the case of graphene grown on Ni, interboundary regions exhibited higher roughness and had more graphene layers in comparison to the surface of grains [26]. These factors led to lower friction in the interboundary areas. The friction coefficient was around 0.014. An investigation of the frictional behavior of graphene on various substrates such as SiO2, h-BN, bulk-like graphene, and mica was performed to examine the effect of the adhesion level [27]. The friction of graphene on SO2 decreased with an increasing number of layers. Interestingly, graphene demonstrated higher friction being transferred onto bulk graphite. It was shown that the ultraflatness of both the substrate and the graphene sheet is a necessary condition for strong adhesion between graphene and the substrate. In the case of graphene transfer, the initial morphology of graphene is crucial for adhesion. Thus, the frictional behavior of graphene could be tuned by adjusting the adhesion and morphology of both the graphene sheet and the substrate [27]. The posttransfer treatment of graphene flakes transferred onto SiO2 substrates had a negative effect [28]. Plasma treatment led to an increase in surface adhesion and higher friction. Thus, the plasmabased method could be effectively used for controlling the tribological performance of graphene. In general, the adhesion of graphene to substrates in the case of transfer is not high enough to provide excellent tribological performance. Nonetheless, adhesion could be improved by various surface methods. For example, direct voltage glow-discharge plasma treatment of SiO2 substrates before the graphene transfer allowed enhancing its adhesion [29]. In the opposite, plasma treatment of graphene after its transfer onto SiO2 negatively affected the graphene friction due to the formation of defects. A comparative study of different two-dimensional (2D) materials such as graphene, molybdenum disulfide (MoS2), niobium diselenide, and hexagonal boron nitride demonstrated a similar trend [30]. Friction monotonically decreased with increasing the number of layers in the case of low adhesion

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between films and the substrate. Strong bending to a substrate suppresses the trend. These observations indicate the existence of a universal characteristic of nanoscale friction for 2D materials. As was concluded in Chapter 2, the tribological performance of graphene should be better in the case of rigid substrates. An investigation of the nanotribological behavior of multilayer graphene on soft elastic PDMS substrates confirmed this conclusion in general. It was demonstrated that the friction of multilayer graphene on PDMS reduced almost three-fold when the thickness of the graphene increased from 2.3 to 9.6 nm [31]. At the same time, the contact pressure also decreased by threefold. In other words, the low friction on the soft substrate could be achieved if the graphene is thick enough to provide support and a small contact area. The improvement of the tribological performance of graphene on PDMS compared to one on SiO2 should be attributed to much higher adhesion rather than the elasticity of the PDMS substrate. Thus, opposite to the author’s declaration, their experimental finding supported the theoretical end empirical pieces of evidence of the better tribological performance of graphene on rigid substrates. Computer simulations discussed in Chapter 2 predicted the significant influence of structural defects on the tribological performance of graphene. It should be noted that producing defect-free graphene might be complicated; in most experiments, researchers deal with more or less defective graphene materials. It is not surprising that several studies were dedicated to the assessment of the role of various structural defects in the tribological behavior of graphene. For instance, besides the investigation of wrinkles, the role of edges and step edges was also studied by Tripathi et al. [12]. It was found that lateral deformation under sliding appeared higher at edges than at stepedge regions. Depending on the load conditions, the deformation may yield tearing, folding, or buckling. The initiation of wear for step edges occurred at the normal forces of 74 nN while edge wear started at lower loads (
57 nN). The basal layer of graphene significantly contributed to the load- and friction-bearing capacity of line defects. Airborne impurities could also increase the adhesion between the tip and the step-edge atoms, leading to higher friction as was predicted by the computer simulations (Chapter 2). Substrates play a vital role in graphene friction, not only due to mechanical properties or adhesion. For example, the substrate-regulated nanoscale friction of graphene on SiO2 layers with different thicknesses was observed by Munter et al. [32]. It was found that the friction forces increased two-fold when the thickness of the oxide layer increased from 90 to 300 nm. Moreover, graphene on 90 nm and 3000 nm thick SiO2 layers demonstrated a very

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different nonlinear variation of friction with the increase of the normal load. The large difference in friction was measured under relatively low normal loads. For instance, under the load of 10 nN, the friction forces were 0.4 and 1 nN for the thin and thick oxide layer, respectively. But under 50 nN, the friction force was 0.8 and 1.1 nN, respectively. First of all, graphene friction on the thin oxide layer exhibited much more considerable variation with the rising of the normal load. Second, the difference between the thin and the thick oxide layer was mitigated with increasing the normal load. Further investigation showed that the thickness of the oxide layer not only had an effect on friction forces, but also changed the energy dissipation between the graphene tip and the AFM probe. The experimental findings could be attributed to increased phonon scattering, which was responsible for lowering the vibrational reduction of nanoscale friction. This explanation was based on the results of DFT calculations performed by Fan et al. [33]. It was found that the graphene layer is mostly physically absorbed on the surface and impurities in the form of oxygen defects disturb the band structure of π-electrons, resulting in the hole doping of graphene. Increased hole doping in the graphene layer acts to efficiently dampen the excess phonons or lattice vibrations, generated through stick-slip events as the AFM probe slides over the graphene [34]. Increasing the thickness of the oxide layer led to enhanced hole doping, resulting in larger interfacial friction forces due to the mitigation of the vibrational reduction of friction. Recent experimental studies showed that the layer dependence of friction on graphene measured by AFM was a complex phenomenon [15]. In particular, it could be affected by various factors such as roughness and the correlation length of the interface, shape, and size of an AFM tip, in addition to effects such as electron-phonon coupling and puckering, as was discussed in previous paragraphs. Tables 4.1 and 4.2 summarize the experimental findings in the nano- and microscale friction of graphene.

4.2 Nanoscale wear of graphene Detectable nanowear of exfoliated multilayer graphene by a silicon AFM tip was observed after 100 reciprocating sliding cycles under the normal load of 5 μN [35] (Fig. 4.3). Assuming a wear depth of
45 nm, it could be concluded that the single layer of graphene was worn out under these conditions. Increasing the normal load led to linear growth of the wear depth. The wear depth increased with an almost constant interval of
0.3 nm,

102 Tribology of graphene

Table 4.1 Summary of experimental results on the nanotribology of graphene. Graphene preparation

Friction test conditions

Method

Substrate

Counter surface

Normal load

Conditions

Friction coefficient

Ref.

Mech. exfoliation Mech. exfoliation Epitaxy Mech. exfoliation Frictional transfer from HOPG CVD, transfer CVD Liquid Cu

Si SiO2 6H-SiC Si HOPG SiO2 Ni, intact SiO2

SiN Si SiC Si SiO2 Si Si Si DLC Si DLC

0.01–0.5 nN 1 nN 40 nN 3–30 nN 0–470 nN 100–400 nN 1–20 nN 1–12 nN

Air, Air, Air, Air, Air, Air, Air, Air,

0.025 0.06–0.15 0.2 0.02 0.0003 0.01 0.012 0.12 0.16 0.06 0.11

[4] [13] [14] [35] [7] [11] [26] [23]

CVD, transfer

RT RT RT RT RT RT RT RT

Table 4.2 Summary of experimental results on the microtribology of graphene. Graphene preparation

Friction test conditions Normal load/ contact pressure

Conditions

20 mN/ 220 MPa 0–0.5 mN

Air, RT, 45% RH Air, RT

Growth substrate

Substrate

Counter surface

CVD

Cu

Intact

Steel ball, 1 mm

Exfoliation

–

Si SiC

Diamond tip, 1 nm

CVD

SiO2

Fused silica lens/ 1 mm

5–10 mN

Air, RT

Epitaxy

Ni Cu Ni SiC

Intact PET

SiO2 ball, 7.7 mm

Air, RT

Epitaxy

SiC

Intact

Ruby ball, 0.5 mm

20 mN 40 mN 1 mN/350 MPa

CVD

SiO2

Intact

CVD

Graphene-coated SiO2 ball, 8 μm –

–

Graphene-coated SiO2 ball, 8 μm h-BN

Si

Si3N4 ball, 4 mm

Self-assembly

1.45 μN/1 GPa 1 μN 5–300 mN/ 140–560 GPa

Air, RT, 30%–60% RH UHV RT, 51% RH RT, 51% RH Air, RT

Friction coefficient

Ref.

0.2

[36]

0.03 0.03

[37]

0.15 0.2 0.05 0.08 0.18 0.08

[24]

0.003

[38] [39]

[40] [8]

0.0025 0.05

[41]

Experimental tribology of graphene

Method

103

104 Tribology of graphene

Fig. 4.3 (A) AFM image of wear tracks and (B) the cross-sections of wear tracks. (C) The wear depth of multilayer graphene as a function of applied loads. (Reproduced from L.Y. Lin, D.E. Kim, W.K. Kim, S.C. Jun, Friction and wear characteristics of multi-layer graphene films investigated by atomic force microscopy, Surf. Coat. Technol. 205 (2011) 4864, https://doi.org/10.1016/j.surfcoat.2011.04.092. Copyright (2011), with permission from Elsevier.)

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which was close to the step high of graphene. After the reciprocating sliding test under the normal load of 10 μN, six graphene layers were worn out. It was postulated that the wear occurred due to the breaking of in-plane carbon bonds and shearing of the interface. In general, the proposed mechanism was close to theoretical predictions (Section 2.2). Later studies of graphene nanowear confirmed these findings. Moreover, it was found that the dependence of friction from the normal load had two distinct regimes [42, 43]. In the first regime, when the normal loads were below approximately 10 μN, graphene was only strained and plastically deformed. In the second regime, when the normal loads exceeded 11 μN, graphene was cut and torn in an uncontrolled manner, leaving large bumps. Phase images confirmed that the increase of the normal load above 10 μN led to graphene peeling. Graphene exhibited low friction in the first regime. Besides, it was demonstrated that the 4 nm thick graphene flake provided adequate wear protection for the SiO2 surface. The tearing and delamination of graphene were observed under the normal loads higher than 10.5 μN. The wear was most probably controlled by the adhesion between the SiO2 substrates and the graphene flake. In particular, for the CVD graphene transferred onto SiO2, the critical load measured in the scratch test was just about 152 mN [43]. Improvement of the adhesion should definitely enhance the wear protective properties of graphene. The presence of step edges is crucial for the wear resistance of graphene. Under the usual conditions, uncovered steps exhibited higher friction than covered ones due to the exposition of the broken carbon bonds located on the edge [44, 45]. Besides, experimental evidence of the elastic straining of covered graphene edges that act like nanoscale springs was demonstrated [44]. Another experimental investigation of monolayer graphene transferred onto SiO2 substrates showed that while graphene exhibited extraordinary wear resistance in the interior region, it could be easily damaged at the step edge under a much lower normal load (
2 orders of magnitude smaller) [46]. With the support of MD simulations, it was postulated that the significant increase of wear at the step edges could be attributed to two primary mechanisms–atom-by-atom adhesive wear and peel-induced rupture.

4.3 Effect of ambient conditions on the nanotribology of graphene Experiments showed that monolayer and multilayer graphene exhibited significantly lower friction while the humidity was decreased from 75% to 7%

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[47]. In particular, a friction force under 50 nN and humidity of 75% was
2.5-fold compared to the 7% humidity. Under extremely dry conditions (RH ¼ 0.1%, dry nitrogen atmosphere) the friction was
5 times lower in comparison to 75% humidity. Friction force of the monolayer graphene under ambient conditions was
10 times smaller than one of the SiO2 substrate. Assuming the typical friction coefficient for SiO2 in the range of 0.15–0.25 [48], the friction coefficient for graphene should be in the range of 0.015–0.025. Reducing friction with an increasing number of layers was observed under dry and humid conditions. The aging of graphene under ambient conditions after an ultradry nitrogen environment during several days led to the twofold increase of the work of adhesion. In another study [49], the frictional behavior of graphene was found to exhibit a combination of two distinctive regimes under the normal load of 200 nN. In the first regime, while humidity increased from 5% to 50%, there was a very low increase of friction force from
5.9 to 8.2 nN. In the high humidity regime (50%–70% RH), the friction force increased from 8.2 to 16.5 nN. In the low/intermediary humidity regime (RH < 50%), the frictional behavior was dominated by water absorption. It was postulated that in the high humidity regime, meniscus/capillary condensation on graphene led to the friction increase. Similar behavior was observed by Hasz et al. [50]. The authors performed both experiments and MD simulations and demonstrated that the absorbed water did not lubricate the interface between graphene and the ta-C tip. The water instead increased the friction until a sufficient threshold humidity level (
60%–70%) was reached. Further increasing the humidity led to the slight reducing of friction. The observed trend was attributed to the change of amount and location of absorbed water at the interface. Under the low humidity, water exhibited very sparse coverage, allowing the solid-solid contact between the tip and the surface. In this case, weak van der Waals interactions dominated the friction. Incensing of the water adsorption led to the creation of pinning sites and the increase of the friction. At high humidity, the formation of the meniscus and a water film occurred. Increasing the distance between the tip and the surface under high humidity revealed that capillary adhesion was not the dominant effect for friction. Instead, the friction changed due to the intercalation of water molecules. The formation of the complete monolayer of water led to reducing the friction. The authors suggested that the increase of friction due to adsorbates could be mitigated if the adsorbates had weak interactions with the interfacial materials. Using a graphene-coated microsphere prepared by the metal-catalystfree CVD method (Section 3.3) helped to improve these results even more

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[8]. First of all, using CVD allowed enhancing the adhesion between the graphene coating and the microsphere. Because the coating consisted of randomly oriented graphene nanograins, the overall incommensurability in the multiasperity contact was achieved. All these factors led to a low and robust friction coefficient of 0.003, which was insensitive to relative humidity up to 51% RH. Despite the adverse effect of humidity on friction, a humid environment improved the wear resistance of graphene due to the passivation of dangling bonds of graphene located on the step edges [51]. Passivation of dangling bonds reduced adhesion between the tip and carbon atoms, leading to lower wear. In particular, a critical normal load before tearing the monolayer graphene on a graphite substrate increased from 120 under dry conditions to 268 nN under humid conditions. However, in the case of strong adhesion between graphene and the substrate, the adhesion effect was less significant. For the monolayer graphene transferred onto the SiO2 substrate, the variation of the critical normal load under dry or humid conditions was not observed. In other words, high humidity might help only in the situation where graphene was transferred to substrates with relatively low adhesion. The frictional behavior of graphene steps (Section 4.1) under different humidity could significantly affect the overall functioning of the graphene coating, especially if it is not uniform. Opposite to the behavior of graphene planes, the lateral force at the uncovered atomic step decreased with the increase of RH while the lateral force at the covered step was independent of RH [52]. Evaluation using scanning Kelvin probe microscopy demonstrated that uncovered steps possessed a higher work function than graphene planes. This behavior should be attributed to the existence of dangling bonds and oxygen-containing functional groups. The adsorption of a water molecule on hydrophilic oxygen-containing functional groups at an uncovered step reduced the lateral force under high RH due to a lower work function. Thus, the overall response of multilayer graphene to humidity would depend on its thickness, uniformity, and concentration of steps. It is counterintuitive, but lower uniformity could be beneficial at high RH conditions or under water lubrication.

4.4 Macroscopic friction and wear of graphene Some researchers said that graphene “is nanoscopically strong yet macroscopically weak.” This is because of the significant negative role of graphene steps, which is challenging to avoid on the macroscale [46]. This is especially true for exfoliated graphene. Nonetheless, several successful attempts at the

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tribological utilization of graphene on the macroscale were reported. The first results were reported by Kim et al. in the paper titled “Chemical Vapor Deposition-Grown Graphene: The Thinnest Solid Lubricant,” published in 2011 [24]. Graphene was grown on Cu and Ni substrates and transferred onto SiO2/Si substrates. It was demonstrated that multilayer graphene films exhibited a friction coefficient compatible with that of bulk graphene. CVD-grown graphene, being transferred onto PET substrates, exhibited a stable friction coefficient of 0.1 under the normal load of 20 mN [39]. Increasing the normal load to 40 mN led to the continuous rise of the friction coefficient from 0.1 to 0.2 during the sliding test. In this experiment, a fused silica lens with a diameter of 14.4 mm was used as a counter surface. The contact pressure was around 11 MPa. It was found that under the 40 mN normal load, graphene was damaged and partly torn out. Three different types of graphene were compared: Cu- and Ni-grown transferred onto SiO2, and Ni-grown remained on the Ni foil. Cu-grown graphene had one layer, and the Ni-grown one was multilayered. The friction force for all three specimens linearly increased with the rising of the normal load. The Cu-grown graphene exhibited slightly higher pull-off force at both the micro- and nanoscale. As for the friction coefficient, the Cu-grown monolayer graphene showed a value of about 0.22 and the Ni-grown one was 0.12. Such a significant difference could be due to a different number of layers. As was shown before, multilayer graphene generally demonstrates lower friction in comparison with the monolayer one. Raman spectra showed that the Ni-grown graphene had more defects. Thus, assuming that the transfer was performed on identical substrates, it could be concluded that the difference should be mainly attributed to the number of layers. But this conclusion would be wrong. Using the fused-silica lens as a counter surface allowed evaluating the wear mechanism. In the case of graphene transferred onto the SiO2 substrates, rubbing caused the detaching of graphene particles from the substrate and accumulation on the counter surface. Thus, the number of layers affects the friction, but in a different way: multilayer graphene just allowed the formation of a thicker tribofilm on the counter surface and inside the wear track, which was confirmed by XPS data [24]. Furthermore, as-grown graphene showed a friction coefficient of 0.03. Such significant improvement of the tribological performance in comparison to the same graphene transferred onto SiO2 should be definitely attributed to higher adhesion and the absence of additional defects produced during the transfer process. Moreover, even in the case of graphene transfer onto highly adhesive substrates such as PMMA, a friction coefficient