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j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / n a n o t o d a y

REVIEW

Theoretical approaches to graphene and

graphene-based materials

Teng Zhang

a,b

, Qingzhong Xue

a,b,∗

, Shuai Zhang

c

, Mingdong Dong

c,∗∗

a_{State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266555, Shandong, PR China}

b_{College of Science and Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong, China University} of Petroleum, Qingdao 266555, Shandong, PR China

c_{Interdisciplinary Nanoscience Center (iNANO), Centre for DNA Nanotechnology, Aarhus University, DK-8000 Aarhus C, Denmark}

Received 8 December 2011; received in revised form 14 March 2012; accepted 21 April 2012 Available online 29 May 2012

KEYWORDS Graphene; Composites; Modeling; Simulation; Properties

Summary Graphene with its peculiar and exceptional properties has been widely used in the preparation of next generation functional nanocomposites. However, future development of graphene and graphene-based composites crucially depends on the fundamental understand-ings of their hierarchical structures and dynamical behaviors provided by multiscale modeling and simulation. In the beginning of this review, some computational methods that have been applied extensively in the area of graphene and graphene-based composites are introduced, covering from Quantum Chemistry approach, Molecular Dynamics method to Monte Carlo sim-ulation technique. Then the applications of these methods to various aspects of graphene and graphene-based composites are discussed in some detail. Particular emphasis is laid on researches that explore the physical properties, interacting mechanisms, and potential appli-cations of graphene-based materials. Finally, future challenges and perspectives in modeling and simulation of graphene-based composites are addressed.

∗_{Corresponding author at: College of Science and Key Laboratory}

of New Energy Physics & Materials Science in Universities of Shan-dong, China University of Petroleum, Qingdao 266555, ShanShan-dong, PR China.

∗∗ _{Corresponding author. Interdisciplinary Nanoscience Center}

(iNANO), Centre for DNA Nanotechnology, Aarhus University, DK-8000 Aarhus C, Denmark.

E-mail addresses:xueqingzhong@tsinghua.org.cn(Q. Xue), dong@inano.au.dk(M. Dong).

Introduction

Graphene, the one atom-thick single layer graphite sheet has fascinated the whole scientiﬁc community since it was discovered in 2004 [1]. Generally, it is viewed as a two-dimensional (2-D) sheet composing of carbon atoms arranged in a honeycomb lattice structure. Correspond-ing Bloch states of graphene are formed mainly by the carbon valence pz orbital (the z-axis is perpendicular to the graphene plane) forming two bands (cones). The other three occupied valence states of carbon atoms form the deep-lying bands through sp2 _{hybridization; these} 1748-0132/$ — see front matter © 2012 Elsevier Ltd. All rights reserved.

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Figure 1 Mother of all graphitic forms.

are responsible for the structural robustness of graphene’s structure[2]. This unique structure gives rise to the intrigu-ing properties of graphene, such as high carrier mobility (∼10,000 cm2_{/V s)} _[1]_{, quantum hall effect at room}

tem-perature [3,4], good optical transparency (∼97.7%) [5], large theoretical speciﬁc surface area (2630 m2_/g) _[6]_,

high Young’s modulus (∼1 TPa) [7] and excellent ther-mal conductivity (TC) (∼3000 W/m K) [8]. Additionally, graphene is often viewed as the building unit of all the other graphitic carbon allotropes of different dimensional-ity (Fig. 1) [9]. So it is comprehensible that there is such an exponential growth of researches on graphene in both scientiﬁc and engineering communities during the last 10 years.

Currently, graphene can be synthesized from a variety of methods, including mechanical exfoliation of highly ori-ented pyrolitic graphite (HOPG)[1,9], reduction of graphene oxide sheets [10], chemical vapor deposition (CVD) on the surfaces of single metal crystals (such as Ni [11], Fe [12], etc.), and thermal decomposition of silicon carbide [13]. Due to the decrease in its preparation cost, by now graphene has been widely applied to various ﬁelds. Recently, graphene-based composites, including graphene interacting with polymer [14,15], inorganic surfaces [16,17], organic solvent[18], metal particles[19,20], biomaterials[21—23] and carbon nanotubes (CNTs)[24,25]have been successfully fabricated and are being intensively explored in applications such as transparent conductors[24,26], batteries [27,28], supercapacitors [6,29], fuel cells [19], sensing platforms [30,31], and so on. However, due to the tiny size of these low dimensional nano-structures and the lack of basic infor-mation about these materials, it is still a great challenge to characterize the structure and manipulate the fabrication of graphene and graphene-based complexes. This is the main obstacles toward a full-scale application of graphene-based composites. Fortunately, this conundrum can be overcome

by using computer modeling and simulation (CMS) method, which is qualiﬁed to address the structures, properties and other fundamental questions of graphene-based com-plexes. Anyway, CMS acts as a powerful complement to the experimental synthesis and characterization, synergistically unraveling new ways of designing and exploiting graphene-based materials[32].

In general, numerous theoretical investigations focusing on graphene and graphene-based complexes have been per-formed using CMS. First, distinct images and theoretical evidences can be provided by CMS, which might be use-ful for our experimental researches. For example, ‘‘ripple effect’’ observed on both suspended [33] and supported [34] graphene has been confirmed by A. Fasolino using Monte Carlo (MC) simulation [35], and they find that rip-ples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 ˚A, compatible with that of experimental findings [33]. N. Abedpour has reported that internal forces could be the reason for the observed ripple structure on suspended graphene through Molecu-lar Dynamic (MD) simulation[36]. The atomic scale rippled structures formed by monolayer graphene on 6H-SiC (0001) surface have been presented by C. Tang using the clas-sical MD and the simulated annealing techniques [37]. Secondly, the detailed information of a specific system that may hardly be obtained by experiment can be achieved through CMS. As a matter of fact, experimental investiga-tion of many nanoscale systems currently faces problems due to a certain lack of imaging tools: the nanoscale is too small for light microscopy and too large for X-ray crys-tallography; in certain cases it is too heterogeneous for NMR and too ‘‘wet’’ for electron microscopy [38]. CMS, on the other hand, can provide theoretical information such as electronic band structure[39,40], vibration model [41,42], TC [43,44] and diffusion mobility of atoms [45] and ion[46] on the surface of graphene. Additionally, the whole interacting processes between graphene and other materials become ‘‘visible’’ using this method [47,48]. Lastly, the results obtained from CMS can guide experimen-tal investigations to explore the potential applications of graphene-based materials. To be more specific, CMS is used to predict the properties and applications of graphene-based composites and provide novel ideas and theoretical confir-mation to the experimental research. For instance, recent theoretical investigations [49,50]have demonstrated that ‘‘metal doped graphene’’ can be excellent hydrogen storage media, pointing out a new way to explore high performance hydrogen storage material [49,50]. Since graphen flakes are now easily available, the merit and feasibility of this noble idea would be confirmed by experiment in the near future.

In this review, we intend to cover most of the theoretical investigations about graphene and graphene-based materials. Moreover, we highlight several research areas that explore the morphological structures, inter-acting mechanisms, physical properties, and potential applications of the graphene composites. It is convinced that a systematic review on the theoretical studies of graphene and graphene-based materials is an essential step towards a better understanding of graphene and will be useful in the fabrication of graphene compos-ites.

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Modeling and simulation techniques

Briefly, CMS is an effective approach that uses computer model to investigate the structural transformations of a defined material system as well as the interacting processes between different materials. It can also provide us with useful physical information of a specific system. Recent years, driven by the advances in high performance com-putational resources together with development of more efficient numerical algorithms, CMS has been widely used in modeling different scales of materials ranging from atoms, clusters to bulk materials. In this part, three widely used simulation techniques: Quantum Chemistry (QC) method, MD simulation method, and MC simulation method are dis-cussed in detail.

QC method

QC is a modeling and simulation technique that precisely predicts the physical properties of a deﬁned system. Based on quantum mechanics, the underlying methodology for a typical QC simulation is the computational solution of the noble electronic Schrodinger equation[51].

ˆ

H= E (1)

While ˆH stands for the Hamiltonian operator, and E are the wavefunction and energy of the system, respectively. However, since the electronic Schrodinger equation is a many-body problem, the computational complexity of the QC simulation grows exponentially with the number of elec-trons[52]. Thus the ability to obtain proper solutions to the Schrodinger equation for systems containing tens, or even hundreds of atoms is of crucial importance to the QC simulation. Two highly productive approaches namely wavefunction-based approach and density functional theory (DFT) have been widely applied in this ﬁeld.

Most of the wavefunction-based calculations are based upon Born-Oppenheimer approximation that separates the motions of electrons and atomic nucleus to simplify the Schrodinger equation. Various techniques and approxima-tions have been used in the wavefunction-based calculation, and the most effective and successful approach would be the import of the Hartree-Fork equation. In 1928, D. Hartree proposed the Hartree equation[51], which calculated the motion of each electron through mathematical iteration. Soon after that, in 1930 V. Fock further modiﬁed the equa-tion by taking the Pauli principle into consideraequa-tion. This equation, also known as the Hartree-Fock equation has been proved to be the basic method for dealing modern QC prob-lems[53].

= 1(1)2(2)3(3) . . . n(n) (2)

i(i) represents the electron wave function of each atom in the system. But the choice of a proper approximation to simplify the H-F matrixes is regarded as the main difﬁculty challenging the future development of wavefunction-based calculation. Despite this problem, wavefunction-based cal-culation has been widely used in a variety of materials including inorganic materials, polymer and biomacro-molecules.

Density functional theory which follows the Hohenberg— Kohn theorem is quite different from the wavefunction-based approach [54]. Speciﬁcally, DFT regards the total energy of the system as a function of electron density. This avoids the problem of calculating complicated Schrodinger equation that wavefunction-based calculation encounters, since the electron density depends on only three coordi-nates (as opposed to 3N coordicoordi-nates of N electrons), so DFT is considered computationally efﬁcient compared with wavefunction-based calculation. Under DFT calculations, the total energy of the system could be summarized as fol-lows[54,55]:

Et[]= T[] + U[] + Exc[] (3)

where T[] is the kinetic energy of non-interacting particles of density in a system, U[] is the classical electro-static energy due to Coulombic interactions, Exc[] includes

all many-body contributions to the total energy, in partic-ular, the exchange and correlation energy. However, the ﬁnal term in Eq. (3) Exc[] requires proper

approxima-tions for the DFT method to be computationally tractable. A simple and efficient approximation is the local density approximation (LDA), which is based on the well-known exchange-correlation energy of the uniform electron gas [56,57], and LDA assumes that the charge density varies slowly on an atomic scale. The next step of improving the approximation is to take the inhomogeneity of the electron gas into consideration, which can be achieved by introduc-ing an electron density gradient into the system; and this method is named as the generalized gradient approxima-tion (GGA)[58,59]. Some famous modi embedded into the QC software, such as PW91[60], PBE[61]and BLYP[62]are based upon the GGA method. Compared with LDA, GGA can greatly improve the computational accuracy, but it would cost more time than that of LDA. Since DFT method con-siders both the computational efficiency and accuracy, it has been an effective tool in the field of condensed mat-ter physics. Compared with other CMS method, QC provides more accurate results and is the only method available to provide information like band structure, density of state and so on, this endows QC an irreplaceable role in analyzing the ‘‘physical nature’’ of graphene.

MD simulation

Based on classical mechanics, MD is one of the widely used simulation techniques at molecular scale. For a typical MD simulation, each atom in the system is considered as a sin-gle entity and the interaction between different atoms are modeled as they react to potential functions derived from classical physics. The ﬁrst MD simulation for a condensed phase system was performed by Alder and Wainwright in 1957[63], who used a hard-sphere model to carry out calcu-lation of relaxations accompanying various non-equilibrium phenomena. After that, the application of MD has devel-oped so quickly that it gains popularity in many research areas. One proper explanation for the popularity of MD is that it allows us to study time dependent processes; and the simulation time for a typical MD can ranges from a few picoseconds to hundreds of nanoseconds. Meanwhile ther-modynamic properties of the system such as internal energy,

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pressure and heat capacities can be calculated from posi-tions, velocities and forces of each atom generated from MD.

A typical MD simulation involves the proper selection of interaction potentials, numerical integration, periodic boundary conditions and the controls of pressure and tem-perature to mimic physically meaningful thermodynamic ensembles [64]. To start a MD simulation, a set of initial conditions including positions and velocities of all particles are needed. Then the atoms would move according to the Newtonian equation of motion[65]:

mi ∂2_r i ∂t2 = − ∂ ∂ri Etot(r1,r2, . . . ,rN), i= 1, 2, . . . N (4)

mistands for the mass of the atom i, riis its position. For Etot, it represents the total potential energy which depends on the positions of atoms. The total potential energy that determines the interaction between different atoms is the most crucial part of the simulation. A set of suitable param-eters known as force-field are embedded into the algorithm to calculate the potential energy. Such a force field may be obtained by quantum mechanical calculations together with experimental data. To name a few, AMBER[65], GROMACS [66], COMPASS[67]and many other force fields are widely used in the MD softwares. To select a preferable force-field, accuracy, transferability and computational speed should be considered. In general, most of the force fields provide rela-tively similar results, but GROMACS is frequently adopted if the system contains gas and solvent[68], while AMBER and COMPASS are widely applied in the theoretical studies that explore the mechanical properties of graphene-based mate-rials[69,70]. The force-field of a molecular system mainly contains the following terms[71]

Etot= Enonbond+ Ecrossterm+ Evalence (5)

For Enonbond, it is composed of 3 parts

Enonbond= EvdW+ ECoulomb+ EH-bond (6)

EvdW stands for the attractive forces at long range, and it is

often represented by the Lennard-Jones potential. To save computational time, a speciﬁc cut-off distance usually not greater than 9.5 ˚A is used. The calculation of ECoulomb fol-lows the Coulomb law, Ewald summation and particle Ewald summation has been developed to deal with the problems resulting from periodic boundary conditions in the calcula-tion of electrostatic potential. Ecrossterm and Evalence which

represent the interaction between atoms through bond and angle are described by the following teams in the COMPASS force ﬁeld[71]

Evalence= Ebond+ Eangle+ Etorsion+ Eopp+ EUB (7)

Ecross—term= Ebond—bond+ Eangle—angle+ Ebond—angle

+ Eend—bond—torsion+ Emiddle—bond—torsion

+ Eangle—torsion+ Eangle—angle—torsion (8)

Though MD provides us with thermodynamic properties of a bulk material, the number of atoms it contains is still far less than that in bulk materials. So ‘‘super-cell’’ and ‘‘periodic boundary condition’’ approximation are used to

produce accurate results in correspondence with experi-mental ﬁndings. Some ensembles such as microcanonical (NVE), canonical (NVT) and isothermal—isobaric (NPT) are used to calculate the thermodynamic properties of speciﬁc system. The control of constant temperature and pressure can be achieved by introducing an appropriate thermostat (e.g., Berendsen, Nose-Hoover) and barostat (e.g. Ander-son, Hoover, and Berendsen) into the system, respectively [64]. Since MD simulations provide us with the opportunity to monitor the whole interacting process between graphene and other materials, it has been widely used to study time dependent properties of graphene-based materials and helps us to design graphene based nanostructures.

MC simulation method

Although MD has been proved to be an effective method at molecular scale since it can provide various thermodynamic properties of the system, it has some significant limitations in terms of application. The main difficulty is that MD takes considerable amounts of time since it computes the move-ments of all atoms precisely at all instants of time, but not all of the movements are of practical interests. MC simula-tion, on the other hand, focuses on the final configurations of the system can overcome some of these disadvantages.

Generally, MC simulation is a stochastic method that generates the equilibrium configuration of a specific sys-tem by randomly changing the orientations and positions of proper atoms, and properties of interest can be calcu-lated from the final positions of atoms. In a MC simulation, first an initial configuration of N-particle system is arranged. Then a new configuration is generated by changing the posi-tion of a specific atom. Afterwards, the Hamiltonians of each configuration are calculated. Finally, fixed prescribed rules embedded into the software are used for determining the final configuration of the system. In detail, it can be hypothesized that a new configuration can be achieved by arbitrarily or systematically changing the positions of par-ticular atoms. For example, one atom is initially located at i coordinate, then it is moved to a temporary new position j, and this motion is summarized as i→ j. Due to such atomic movement, changes in the Hamiltonian H of the system can be described as follows[64]:

H= H(j) − H(i) (9)

where H(i) and H(j) represent the Hamiltonian associated with the original and the new configuration, respectively. Whether or not the new configuration is a more preferable state is evaluated according to the following rules. First if H < 0 which means the atomic movement has brought the system to a state of lower energy, the new configuration will be accepted as the initial state and restart the atomic movement process. Otherwise, H≥ 0, evaluation of the new configuration is with a certain probability[64],

pi_→j∝ exp −H kBT (10)

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where kB stands for the Boltzmann constant. A random number between 0 and 1 is generated and the new conﬁg-uration is determined by the following rule:

≤ exp

−H kBT

, the move is accepted,

> exp

−H kBT

, the move is rejected.

Finally if the new conﬁguration is rejected, the calcu-lation process can be repeated by using some other atoms [64,72]. Even though MC approach can only provide equi-librium properties, due to its relatively high computational speed, it has been widely accepted in analyzing the dynam-ical processes of large systems. Specially, MC is skilled at dealing the interaction between graphene and vast numbers of gas and solvent moleculars.

Modeling and simulation of graphene

Electronic properties of graphene

Two-dimensional (2D) graphene is a zero-gap semiconductor with a pointlike Fermi surface and a linear dispersion at the Fermi level. Though graphene was just discovered within 10 years[1], monolayer, bilayer and multilayer graphite sheets which are regarded as graphene derivative have been inves-tigated for more than 50 years[73—75], and most of these theoretical studies are based on the QC techniques that we have mentioned previously. First most of the researchers have focused on the band structure of single layer and multilayer graphite, since band structure is an effective tool in analyzing the electronic performance of a speciﬁc material. Using tight-binding approach, theoretical band structure image for different layers of graphite are pre-sented separately [73—75]. It seems that, although most of the researchers have taken monolayer graphite sheet (graphene) as the simplest theoretical model for graphite, recent studies have found that graphene sheets with differ-ent number of layers exhibit quite differdiffer-ent band structures [76,77]. Generally a single graphene layer is a zero-gap semiconductor with a linear Dirac-like spectrum around the Fermi surface, while graphite shows a semimetallic behav-ior with a band overlap of about 41 meV. With tight-binding approach, B. Partoens and F. M. Peeters have investigated the electronic structure evolution from a single graphene layer into bulk graphite by computing the band structure of one, two, and three layers of graphene[76]. They con-clude that two graphene layers have a parabolic spectrum around the Fermi energy and are a semimetal like graphite; however, the band overlap of 0.16 meV is extremely small. Three and more graphene layers show a clear semimetal-lic behavior. For 11 and more layers the difference in band overlap with graphite is smaller than 10%. The research con-ducted by S. Latil shows that the band structure of these graphites not only depends on the number of graphene layers but also the stacking geometry, since different band struc-tures are presented in 4-layer graphite with different layer arrangements[77]. Considering the application of graphene

Figure 2 Band structure of (a) armchair and (b) zigzag ribbons with width N = 20.

in the nanoelectronic ﬁeld, these theoretical studies offer an effective way to tune the electrical properties of mul-tilayer graphene sheets by simply changing the number of graphene layers and the stacking geometry.

When graphene is etched or cleaved along a specific direction, a strip of graphene of nanometers in width can be obtained, this novel quasi-one-dimensional structure is known as graphene nanoribbon (GNR). Briefly, GNRs are geometrically terminated single graphene layers, but the ideal symmetry of graphene is broken by the edges of GNRs thus complicate the band structure of GNRs. A general, in-depth understanding of the band structure for different kinds of GNRs is of great importance since GNRs can be used as semiconductors[78], field-effect transistors[79]and so on. However this may hardly be achieved by the available experimental approach, so CMS is adopted to provide band structure images, electronic density and other basic infor-mation that may be useful in analyzing and explaining the electronic performance of GNRs. Firstly, researchers have focused on the edge state of GNRs since it contributes to the density of states near Fermi level on a nanometer scale. It is reported that the energy state difference is influenced by the shape of edges [80]. M. Fujita has discovered that for GNRs with hydrogen passivation at the edge, a zigzag ribbon shows a remarkably sharp peak of density of state at the Fermi level, while no such peak exists for an armchair ribbon. This energy state difference is recorded in Fig. 2. Nakada et al. have further investigated the edge state in graphene considering nanometer size effect and edge shape dependence[81]. They conclude that nanometer size effect is crucial for determining the shape of edge state, furthermore an edge shape with three or four zigzag sites per sequence is sufficient enough to show an edge state, when the system size is on a nanometer scale. After that, more detailed investigations on the electronic properties of GNRs including band gaps and band structures have been presented. It is predicted that GNRs with armchair shaped edges can be either metallic or semiconducting depending on their widths, while GNRs with zigzag shaped edges are metallic with peculiar edge states on both sides of the ribbon regardless of its widths[39,40]. Using Dirac equation method, L. Brey and H. A. Fertig have studied the electronic

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Figure 3 The variation of band gaps of Na-armchair GNRs as a function of width (wa) obtained (a) from TB calculations with

t = 2.70 (eV) and (b) from ﬁrst-principles calculations (symbols). (c) First-principles band structures of Na-AGNRs with Na= 12, 13, and 14, respectively.

states of GNRs with different atomic terminations [40]. They suggest that zigzag nanoribbon allows a particle-like and a hole-like band with evanescent wave functions confined to the surfaces while the electronic band structure of the armchair nanoribbons strongly depends on the width of GNRs. However, different from the former investigations based on simple tight-binding calculations and solutions of the Dirac’s equation [39,40], first-principles calculations suggest that both armchair and zigzag shaped GNRs are shown to have band gaps [82]. Another calculation done by Y. Li has further confirmed this finding, they report that band gaps shows a significant self-energy corrections for both armchair and zigzag GNRs, in the range of 0.5—3.0 eV for ribbons of width 2.4—0.4 nm[83]. Besides, using first-principle calculation, Y. W. Son [82] and V. Barone [84] propose that the band gap of zigzag GNRs would decrease with the increased ribbon width (recorded inFig. 3). More detailed investigations are needed in order to have a deeper understanding of the electronic properties of graphene.

Apart from shape, edge and other internal factors, band structure of graphene is also found to be sensitive to the external environment. Through the method of first-principles calculations, it is shown that the adsorption of atomic hydrogen on the surface of graphene opens up a sub-stantial gap in the electronic density of states[85], this kind of hydrogenated graphene (or graphane) has been reported by Geim in 2009 [86], and the band opening has been confirmed since they find graphane is an insulator. Besides, recent researches have demonstrated the ‘‘substrate effect’’ on the electronic structure variations of graphene both experimentally [87] and theoretically [88]. Ab initio investigation shows that graphene overlayered on SiC (0001) and SiC (000¯1) surfaces possess qualitatively different elec-tronic structures, while the former is metallic, the latter has semiconducting properties [88]. An interesting study performed by V. M. Pereira et al. has analyzed the effect of tensional strain on the electronic structure of graphene

[89]. They report that strain can generate a bulk spectral gap and this provides a new way to tune the transport char-acteristics and pinch off current ﬂows in graphene devices [89]. These CMS studies identify most of the inﬂuencing factors on the electronic properties of graphene, point out new and fantastic approach in tuning the electrical prop-erties of graphene and would be helpful for the fabrication of graphene based nanoelectronic devices.

Thermal properties of graphene

Besides electronic properties, another important factor con-tributed to the wide application of graphene in the area of nanoelectronics is the thermal transport properties of graphene and a full understanding of the thermal transport properties of graphene is crucial for developing any prac-tical graphene-based devices. Theoreprac-tically, 2 subareas are included in the theoretical investigations on the thermody-namic properties of graphene: one is a basic understanding of the phonon transfer mechanism and vibrational edge modes in graphene[41,42,90,91] while the other focuses on the acquisition of TC comparable to that of experimental results[43,44,92—97]. As is known to all, thermal transport properties mainly depend on the phonon dispersion rela-tions of the system, so the ﬁrst step towards a systematic study of the thermal properties is a full understanding of the phonon dispersion relations in graphene. A systematic study conducted by T. Yamamoto et al. has discussed the phonon transport properties of GNRs at low temperature using the method of Brenner’s empirical potential[90]. Phonon dis-persion relations are calculated for GNRs with armchair- or zigzag-shaped edges, and localized phonon modes are iden-tiﬁed at the edges of the ribbons. Intrinsic phonon modes of GNRs are further investigated in detail by M. Vandes-curen [41] and Y. Yamayose et al. [42]. According to M. Vandescuren[41], the existence of intrinsic phonon modes in GNRs are attributed to the edges of graphene, as they

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are localized at the GNR edges. The identification of the intrinsic phone modes and the investigation on the phone modes by using the method of CMS has contributed to a better understanding of the thermal properties of graphene. Recent experimental measurements of TC for a partially suspended graphene sheet have found that can be as high as 5300 W/m K at room temperature[98]. First principle cal-culations done by Kong et al.[43]and Nika et al.[44]have calculated the value in the range of 2000—6000 W/m K, corresponding with the experimental data [98]. Several research groups using different MD simulation technolo-gies suggest that to be highly dependent on the shape [44,93,94], edge type (armchair or zigzag)[93—95], defect [96], and edge roughness[93]of specific GNRs. Generally theoretical investigations involving the thermal transport properties of graphene are divided into two categories: (1) equilibrium MD (EMD) and (2) non-equilibrium MD (NEMD). The main difference between the two methods is that in the latter approach, experimental condition is mimicked by setting up temperature gradient across the system. Y. Xu et al. suggest that at room temperature the thermal con-ductance of zigzag GNRs can be up to∼30% larger than that of armchair GNRs[94], but W. J. Evans argues that the con-ductivity is essentially the same for GNRs with smooth zigzag and armchair edges[93], this difference might be induced by the size of GNRs. Y. Xu et al. have even proposed an anisotropy factor () to investigate the anisotropic behav-ior in graphene with the variation of width. The factor is defined as follows: = (/S)ZGNR (/S)AGNR − 1 (11)

where /S stands for the thermal conductance of speciﬁc GNRs. Fig. 4 shows the variation versus width at dif-ferent temperature [94]. Very remarkable decrease of TC is obtained when a tensile/compressive uniaxial strain is applied on GNRs which is shown inFig. 5 [97].

Besides edge charity, shape, TC of graphene might also be affected by other factors. Due to the ‘‘substrate effect’’ on the electronic properties of graphene, researchers are curi-ous about the variation of TC once graphene is bonded to a

Figure 4 The anisotropy factor () versus width (W) at 100 K (black square), 300 K (red circle) and 500 K (blue triangle). Reprinted ﬁgure with permission from[94]. Copyright 2009 by the American Institute of Physics.

Figure 5 Uniaxial strain dependence of TC of 20-armchair GNR and 10-zigzag GNR. The unstrained length is 11 nm. Reprinted ﬁgure with permission from[97]. Copyright 2009 by the American Institute of Physics.

substrate. The ‘‘substrate effect’’ has been proved by Z. Y. Ong and E. Pop[99], who ﬁnds an order-of-magnitude reduc-tion in TC of supported graphene on SiO2. They also indicate

that when the graphene-substrate van der Waals coupling is increased, heat flow along supported graphene increases as well, and can be modulated by up to a factor of three. Not only the substrate, but also the number of graphene layers would reduce the in-plane TC for multilayer graphene films [100]. This also highlights an interesting route for tuning the thermal transport in two-dimensional nanostructures like graphene, via carefully controlled layer arrangements envi-ronmental interactions. Some researchers also show that TC of GNRs is very sensitive to the chemisorptions on GNRs [101,102]. Q. X. Pei has investigated the TC of hydrogenated graphene using NEMD [101]. It is found that TC greatly depends on the hydrogen distribution and coverage. For ran-dom hydrogenation, TC decreases rapidly with increasing coverage up to about 30%. Beyond this limit, however, TC is almost insensitive to the coverage. For patterned hydro-genation with stripes parallel to the heat flux, TC decreases gradually with increasing coverage from 0% to 100%. Con-trarily, when the stripe direction is perpendicular to the heat flux, a small (5%) coverage causes a sharp (60%) drop in TC. They further explain that the deterioration of TC is due to the sp2_-to-sp3_{bonding transition upon hydrogenation,}

which softens the G-band phonon modes[101]. Similarly, S. K. Chien has revealed that TC is greatly inﬂuenced by the functional groups since a functional group coverage regime of as little as 1.25% of GNR atoms reduces the TC by about 50%[102]. Additionally, TC of GNRs with zigzag edges is more sensitive to the degree of functionalization than that with armchair edges[102]. Recent experiment has demonstrated that different carbon isotopes such as13_{C can be controllably}

introduced in graphene[103]. So J. N. Hu et al. have con-ducted a classical MD simulation to investigate the ‘‘isotope effect’’ on graphene[104]. They conclude that isotope mix-ing can reduce the TCs, with the superlattice distribution giving rise to more reduction than random distribution. The ‘‘chemisorptions effect’’ and ‘‘isotopes effect’’ sug-gest that pure graphene plate without doping and adsorption is the best for thermal transportation. Above all, different

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factors contributed to the variation of TCs have been identiﬁed which help us to establish the thermal transfer mechanism in graphene and at the same time guide our experimental studies in nanoscale engineering of thermal transport and heat management.

Mechanical properties of graphene

Recently, the mechanical properties of graphene have been studied extensively using both experimental and theoret-ical approaches. Experimentally, the Young’s modulus of graphene is calculated in the order of magnitude of 1 TPa [7,105]. For example a Young’s modulus of 1.0± 0.1 TPa is reported by Lee et al. using nanoindentation method [7]. Theoretically, a great number of systematic researches have been done on the mechanical properties of graphene. Taking the Young’s modulus as an example, the calculated value of the Young’s modulus and the simulation details are recorded inTable 1. Clearly, the results obtained from molecular sim-ulation are in well correspondence with the experimental ﬁndings. H. Bu et al. have conducted a systemic study on the mechanical behavior of GNRs with width ranging from 0.49 nm to 10 nm[107]. They suggest that the Young’s mod-ulus is insensitive to the GNR width, in accordance with the research done by Z. H. Ni et al.[114], but J. W. Jiang et al. argue that the Young’s modulus of graphene increases with increasing size and saturates after the size reaches a thresh-old value[115]. They also report that the Young’s modulus of graphene increases with the increasing temperature in the region [100,500] K and is insensitive to the isotopic dis-order in low disdis-order region (<5%) but decreases gradually after further increasing the disorder percentage[115]. This suggests that isotopic disorder is not an effective method to control the Young’s modulus of graphene, different from the case for the thermal properties of graphene, as we have just discussed in the former part. Through MD analysis, we have learned that the ultrastrong mechanical properties of graphene may be result from the ﬂexibility of bond and angle

Figure 6 Stress—strain relation of bulk graphene under uni-axial tensile test in the armchair direction (dashed line with circles) and the zigzag direction (solid line with squares) at 300 K. The inset ﬁgure shows the linear elastic behavior for the small strain range without chirality effects.

in graphene. Moreover, we can analyze the transformations of bond and angle under mechanical load directly, which is very helpful for our understanding of the mechanical properties of graphene. Besides Young’s modus, some other mechanical properties and the mechanical performance of graphene have been identiﬁed and discussed in detail. The anisotropic mechanical properties along different directions can be explained as follows: under conditions of same ten-sile loads, the edge bonds bear larger load in the longitudinal mode (LM) than in the transverse mode (TM), which causes fracture sooner in LM than in TM[114]. H. Zhao has inves-tigated the mechanical strength of graphene under uniaxial tensile test as a function of chirality by orthogonal tight-binding method and MD simulations coupled with AIREBO potential[116]. As can be seen fromFig. 6, with the strain

Table 1 Calculated value of the Young’s modulus by different research groups. Reference Young’s modulus (TPa) Method

[106] 0.86 MD simulation (adaptive intermolecular reactive bond order

(AIREBO) potential method)

[107] 1.24 MD simulation (empirical Tersoff potential)

[108] 1.05 ab initio DFT method

[109] 0.7 (equilibrium) MD simulation (Brenner potential)

1.0 (non-equilibrium)

[110] 3.81 (thickness: 0.0618 nm) MD simulation (Brenner potential)

3.21 (thickness: 0.0734 nm) 2.69 (thickness: 0.0874 nm)

[111] 1.25 (LDA) ab initio DFT method

1.23 (GGA)

[112] 1.06 MC simulation with the LCBOPII bond order potential

[113] 1.11 (thickness: 0.34 nm) ab inito DFT method

[114] 1.13 (longitudinal mode) MD simulation (bond-order Tersoff—Brenner potential)

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Figure 7 The structural evolution and the fracture mecha-nism of the (36, 11) armchair GNR under tensile load.

increases, the chirality dependence becomes obvious. The fracture strains are 0.13 and 0.20 in the armchair and zigzag cases, respectively, while the fracture strength, deﬁned as engineering stress on the material at the breaking point, are 90 and 107 GPa separately. They further explain that the reason why zigzag direction tension has a relatively larger fracture strain compared to the armchair direction tension is that the magnitude of the bond angle variation in the zigzag direction tension test is much larger than that in the arm-chair direction tension test[116]. Using quantum mechanics and quantum MD simulation, Y. W. Gao has revealed that zigzag GNRs and armchair GNRs share similar failure mech-anisms under tensile and compressive loading but different mechanical properties are found in zigzag GNRs and arm-chair GNRs subjected to mechanical load [117]. Fracture process under tension has been explored by H. Bu[107]and Z. H. Ni [114]. Fig. 7is a distinctive picture of the frac-ture process for an armchair GNR under critical tensile load. The shear modulus of zigzag and armchair GNRs has been calculated to be 0.213 and 0.228 TPa selectively[118]. The mechanical properties for graphene with monatomic vacan-cies [119], Stone-Wales dislocations and double vacancy defects[120]have been reported. Besides graphene under tensile stress, the elastic buckling behavior of defect-free single-layered graphene sheet has been discussed by A. S. Pour [121]. K. V. Zakharchenko et al. have presented a

temperature dependent shear modulus variation using MC simulation[112]. K. Min et al. have investigated the mechan-ical properties of graphene under shear deformation[122]. Using MD simulations, they have computed the shear mod-ulus, shear fracture strength, and shear fracture strain of zigzag and armchair GNRs at various temperatures. These simulations explains the ultrastrong mechanical properties of graphene and further conﬁrms its usage under tension load and shear deformation.

Y. Li has conducted a detailed analysis on the stretch-ability of GNRs with a small twist angle by MD simulation [123], after ‘‘spontaneous twist’’ has been recognized as a nature phenomenon on the surface of graphene[124,125]. Compared with tension simulation on untwisted GNRs, twist effect can help the C—C covalent bond go into large non-linear deformation, when the twisted GNR is under tension. Moreover, the breaking strain of a twisted GNR can be 37.6% larger than that of an untwisted one at room temperature. At the same time, the stiffness of twisted GNR can also be enhanced[123]. It seems that ‘‘spontaneous twist’’ has turned out to be an effective way to enhance the mechanical properties of graphene. The effect of chemical functional-ization on the mechanical properties of graphene has been identiﬁed by Q. X. Pei[106,126]. They ﬁnd that the Young’s modulus, tensile strength, and fracture strain of the func-tionalized graphene deteriorate drastically with H-coverage increasing up to about 30%. Beyond this limit, the mechan-ical properties then remain insensitive to the H-coverage. Though the Young’s modulus of graphane is smaller than that of graphene by 30%, the tensile strength and fracture strain show a much larger drop of about 65%. Furthermore, Q. X. Pei explains that this drastic deterioration in the mechanical strength arises from both the conversion of sp2_{to sp}3

bond-ing and an easy-rotation of unsupported sp3 _bonds _[106]_.

Due to the fact that CMS can support us with a very distinct picture of graphene under mechanical load and gives us the access to monitor the dynamic process of graphene under mechanical load, it has been an essential tool to analyze, explain, and predict the mechanical properties of graphene under different mechanical load.

Modeling and simulation of graphene-based

composites

As a material that attracts so much attention, graphene not only has extraordinary electronic, thermal and mechanical properties but also is capable of interacting with other kinds of materials to form different kinds of functional nanocom-plexes.

Graphene interacting with metal

Since the discovery of graphene, numerous researchers have focused on importing metal impurities into graphene with the purpose of tuning the electronic and magnetic prop-erties of graphene, and at the same time, expanding the applications of graphene. As a result it would be interesting to explore how metal atoms would perform on the surface of graphene and a large number of studies have been done which specially emphasize the structural transformations, electronic properties variation of different metal atoms

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Figure 8 The three adsorption sites considered: hollow (H), bridge (B), and top (T).

adsorbed and doped on graphene surface. Variety kinds of metal atoms ranging from alkali metals like Li[127], Na[127] and K[128]to transition metals (TMs) such as Au[127], Cu [129]and Fe[130]have been investigated. Basically, there are 3 adsorption sites on the surface of graphene: the hol-low site at the center of a hexagon (H), the bridge site at the midpoint of a carbon—carbon bond (B), and the top site directly above a carbon atom (T). Positions of the 3 sites are recorded inFig. 8. First a detailed and systematic study has been done by K. T. Chan et al. [127], in which 12 different metal adatoms absorbed onto graphene sur-face have been analyzed using DFT theory. They have done a really nice job, since this article has proved to be an useful reference for the theoretical and experimental investiga-tions in analyzing the electronic and magnetic properties of metal adsorbed graphene. The adsorption energy, geome-try, density of states (DOS), dipole moment, charge transfer and work function of each adatom-graphene system are calculated. Different bonding types are discussed and it is suggested that for adatoms picked up from groups I—III of the Periodic Table, the results are consistent with ionic bonding, the adsorption is characterized by minimal changes in the graphene electronic states and large charge trans-fer; While for noble and group IV metals, the calculations are consistent with covalent bonding, and the adsorption is characterized by strong hybridization between adatoms and graphene electronic states [127]. A similar study has been reported by Y. L. Mao, who has analyzed graphene doped by Mn, Fe and Co atoms[130]. Evidences are that the spin-polarized band structures of graphene adsorbed with metal atoms are dissimilar with that of pure graphene (described in Fig. 9). Theoretical studies have conﬁrmed the hypothesis that metal atoms can tune the electronic and magnetic properties of graphene effectively. Addition-ally, metal dimer adsorbed onto the surface of graphene has been discussed by C. Cao[131]. The study proposed by A.V. Krasheninnikov [132] is equally important to that of K. T. Chan et al.[127]since they have provided basic structural,

bonding, and magnetic evidence for the embed TM graphene system. A detailed and supplementary job has been reported by E. J. G. Santos, who has covered most of the 3d transi-tion metal, noble metal and Zn atoms[133]. These detailed and systematic theoretical investigations help us build up a general view of the interaction between graphene and metal atoms. Additionally, instead of putting metal atoms on the surface of graphene, Gorjizadeh et al. have inves-tigated GNRs edges doped by Fe, Mn, and Mg[134]. They report that graphene edge doped by Mg atom turns the semi-conducting armchair ribbon into a metal, while Fe and Mn change it into a ferromagnet with a large magnetic moment [134]. Even though ‘‘edge doping’’ seems to be a fantastic method to tune the electronic and magnetic properties of graphene, more detailed studies of metal atoms edge doped graphene are needed.

In factual experiment, graphene is often deposited onto metal surface and measuring the transport of electrons through a graphene sheet necessarily involves the contact of metal electrodes, moreover the ‘‘substrate effect’’ can tune the electronic properties of graphene to a certain degree, so the bonding mechanics between graphene and metal substrate as well as the evolution in the electronic properties for graphene doped onto metal substrate are of significant importance for evaluating the properties of the fabricated graphene. The process for graphene growth on TM surfaces is studied by S. Saadi[135] and H. Amara [136]. B. Wang has presented a topographical image of an epitaxial graphene sheet on Ru (0001) surface using DFT cal-culations. The results agree well with the scanning tunneling microscopy experiments [137]. Moreover the structure of graphene adsorbed onto metal surface has also been dis-cussed in detail [138—142]. The bonding formation and electronic structure of metal-graphene contacts has been discussed in detail by Q. S. Ran[138]. G. Giovannetti et al. have investigated the adsorption of graphene on a series of metal substrates including (111) surfaces of Al, Co, Ni, Cu, Pd, Ag, Pt, and Au[139]. They summarize that the character-istic electronic structure of graphene is significantly altered by chemisorption on Co, Ni, and Pd but is preserved by weak adsorption on Al, Cu, Ag, Au, and Pt. P. A. Khomyakov further confirms Giovannetti’s conclusion who finds that graphene is chemisorbed on Co, Ni, Pd, and Ti, while the binding to Al, Cu, Ag, Au, and Pt is much weaker[140]. The difference between the two kinds of adsorption is discussed in detail, it is suggested that the electronic structure of graphene is strongly perturbed by chemisorption but is essentially pre-served in the weak binding ‘‘physisorption’’ regime. For physisorbed graphene there is generally electron transfer to (from) the metal substrate, causing the Fermi level to move downward (upward) from the graphene conical points [140].

For the theoretical studies on the application of graphene/metal composites, besides electronic device, the elucidation on the diffusion mechanisms of metal and alkali ions on the graphene surfaces can be helpful for devel-oping higher performance ion batteries [45,143,144]. H. Tachikawa has studied the adsorption and diffusion process of Mg on graphene[45]. Direct molecular orbital—molecular dynamic calculations show that the Mg atom vibrates in the hexagonal site and the diffusion does not occur even at 1000 K. Additionally, E. Durgun et al. has discovered that

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Figure 9 (a) The band structure and corresponding DOS of pure graphene in the 4× 4 supercell. The majority and minority band structures and corresponding DOS of the adatom—graphene systems at the most stable conﬁgurations are shown, (b) for Mn, (c) for Fe and (d) for Co. Solid and dotted lines in the DOS are for majority and minority spin states, respectively. The Fermi level is indicated by the dashed line.

light TM atoms can absorb on both sides of graphene and each adsorbate can hold up to four hydrogen molecules yielding a high-storage capacity [145]. Thus they propose that graphene can be considered as a potential high-capacity H2storage medium, and this ﬁnding opens up a new research

area for the applications of graphene/metal complexes. By ﬁrst-principle plane wave calculation, C. Ataca has reported that the hydrogen storage capacity can be increased to 8.4 wt% by adsorbing Ca to both sides of graphene[49]. More-over, G. Kim has discovered that H2 adsorption behavior,

particularly in Ca-dispersed graphene complexes exhibits a crossover between the multipole Coulomb and Kubas-type (or orbital) interactions as the ionic state of Ca and the num-ber of adsorbed hydrogen molecules change[146]. Hydrogen storage capacity for Al doped graphene[50]and Al-adsorbed graphene[147] has been discussed in detail by Z. M. Ao. A. Bhattacharya[148]and G. Kim[149]have discussed the potential of TM decorated graphene for hydrogen storage. Though the application of metal doped graphene in the ﬁeld

of hydrogen storage has rarely been reported in experiment, we believe that this idea which has been conﬁrmed by a number of DFT simulations will soon be realized in experi-ment.

Graphene interacting with macromolecule

Contrast to numerous theoretical studies on the graphene/metal complexes and the fact that MD method is qualiﬁed to assess the interaction between CNTs and polymer [150—152]. However the study the interaction between macromolecules and graphene are still insufﬁcient. Experimentally, the idea of using graphene to enhance the mechanical properties of graphene has been reported by different researchers [14,153]. T. Ramanathan et al. have reported that adding approximately 1 wt% of graphene into poly(methyl methacrylate) (PMMA) leads to an increase of the elastic modulus by 80% and an improvement in the

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Figure 10 Inﬂuence of chemical functionalization of graphene on the interfacial bonding characteristics of the graphene PE and graphene PMMA systems: (a) interaction energy, (b) interfacial bonding energy, and (c) shear stress. Reprinted ﬁgure with permission from[154]. Copyright 2010 by the American Chemical Society.

ultimate tensile strength by 20% [14]. B. Das et al. has studied the mechanical properties of polyvinyl alcohol (PVA) and PMMA composites reinforced by functionalized few-layer graphene, they suggest that an addition of 0.6 wt% graphene results in a significant increase in both the elastic modulus and hardness [153]. These experimental findings indicate that, graphene as the strongest material known to data, can replace CNTs as the reinforced phase to enhance the mechanical, electrical, and thermal properties of poly-mer composites. Theoretically, the influence of chemical functionalization on the interfacial bonding characteristics between graphene and polymer has been discussed by our group using MD simulation[154,155]. Our study shows that the chemical attachments on graphene can greatly enhance the interfacial bonding characteristics of the graphene-reinforced polymer composites. Simulation results also indicate that the bonding energy and shear stress between graphene and polymer matrixes would increase with the increased concentration of functionalized groups, which is shown inFig. 10 [154]. We have further investigated the role of different functional groups on the bonding energy and shear stress of the graphene—polyethylene (PE) composites. Simulation results show that the interfacial bonding energy of graphene modified by —C6H13 groups with PE matrix

has the strongest enhancement, while the shear force of graphene modiﬁed by —C2H4(C2H5)2groups with PE matrix

is the strongest compared with other investigated systems. The differences in the bonding energy and shear stress are recorded in Fig. 11. We propose that the relatively high shear force of the graphene-C2H4(C2H5)2/PE system is due

to branched structure of —C2H4 (C2H5)2 groups, since they

can more strongly interlock with the polymer molecule and

Figure 11 Inﬂuence of the graphene with different groups randomly chemisorbed to 2.5% of the carbon atoms on the interfacial bonding characteristics for graphene-PE system: (a) phenyl groups, (b) —C6H13and (c) —C2H4(C2H5)2.

contribute to a stronger shear force of the system[155]. This series of articles reported by our group[154,155]severs as a good reference for our fabrication of graphene/polymer composite in the engineering field. Using MD simulation, not only the idea that graphene could enhance the mechanical properties of the polymer matrixes has been confirmed, but also several factors that might influence the mechanical performance of graphene/polymer composites have been quantified and analyzed. Additionally, a recent theoret-ical and experimental study has shown that the unique graphene oxide (GO)—CNT scroll-like structure may be better nano-reinforced fibers compared with that of pure graphene and CNTs [156]. W. Gwizdała has investigated the dynamic behaviors of 4-cyano-4-n-pentylbiphenyl (5CB) mesogen molecules confined between graphene walls. This preliminary study using MD technologies may serve as guidance for the future experiments with various mesogenic layers or clusters covering graphene walls [47]. Similar to metal atoms adsorbed onto the surface of graphene, macromolecules with different polar groups can also adsorbed onto the graphene surface and the interaction between macromolecules and graphene plane appears far more complicated than that with metal atoms, then CMS seems to be an essential tool to analyze the complicated interaction between graphene and macromolecules. Using scanning probemicroscopy combined with first-principles calculations, M. C. Prado suggests that 2D crystals com-posed of long and linear phosphonic acids atop graphene are oriented along the graphene armchair direction only, and ab initio calculations indicate that the presence of molecule crystal atop graphene induces a well-defined shift in the Fermi level; corresponding to hole doping without introducing any defects on its structure which is always the case for metal doping[157]. QC approach is used to explore the electronic properties of the interface between polymer

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Figure 12 (a) Schematic view of single-stranded DNA translocating through a nanopore under the application of a longitudinal electrical ﬁeld Ex, while the transverse tunneling current is recorded for the purpose of sequencing. Wxis the width of the transverse nanoelectrodes. Dy is the inner diameter of the nanopore which characterizes the gap distance between opposing transverse nanoelectrodes. (b) Cross-section visualization (cut along the x—z plane) of the complete atomistic setup employed in the present simulation work, showing the silicon-nitride membrane/nanopore (blue and yellow), a translocating single-stranded DNA molecule, as well as water molecules (red and white) and counter ions (ochre and cyan). (c) Cross-section visualization (cut along the y—z plane) of the setup, showing only the edge-hydrogenated graphene electrodes (cyan and white) and a cartoon-version of the translocating single-stranded DNA molecule with the sugar-phosphate backbone represented as a ribbon and the nucleobases as protruding sticks (colors are used to distinguish between different nucleotides).

molecules and graphene[158—160]. Y. L. Lee et al. have discovered that when ferroelectric polymers for example poly(vinylidene fluorides) (PVDFs) are physisorbed onto the surface of zigzag GNRs, because of the strong dipole moments of PVDFs, and the ground state of zigzag GNRs becomes half-metallic when a critical coverage of PVDFs is achieved on the zigzag GNRs[158]. A theoretical study done by A. Nduwimana has demonstrated that noncovalent polymer functionalization can be used to tailor the band gap of a fixed GNR width[160]. Following these theoretical investigations, the adsorbed macromolecules seems to have a large effect on the electronic properties of graphene, moreover the investigation performed by CMS approach will provide valuable information for further develop-ing graphene-based nanodevices. Besides the electronic properties of graphene, interfacial TR for graphene layers confined in an organic matrix has been analyzed by L. Hu using MD simulation[161]. H. Eslami et al. have conducted a theoretical study on the coefficient of heat conductance of polyamide-6, 6 trimers nanoconfined between graphene surfaces, using the reverse NEMD method coupled with external baths [162]. Though a number of investigations have been done, more detailed investigations of the graphene/polymer nanocomplexes are needed in order to fulfill the full potentials of graphene.

Due to the biocompatibility and adsorption potentials of graphene, recently, there is an increasing attention in the unique biological and medical applications of graphene especially in the ﬁeld of drug delivery systems[163—165] and biomedical devices[166,167]. However, the interaction between biomoleculars and graphene, and the structural morphology for the biomoleculars laid on the graphene surface are still unclear, which hinders the future devel-opment of graphene-based composites as biomaterials. With the help of CMS approach, the adsorption mech-anism and features for biomolecules adsorbed onto the surfaces of graphene have been reported using both MD and DFT methods [168—173]. C. Rajesh et al. have discussed the interaction of phenylalanine (Phe), histidine (His),

tyrosine (Tyr), and tryptophan (Tryp) molecules with graphene and single walled CNTs aiming at understanding the effect of curvature on the non-covalent interaction [169]. The interaction between DNA and graphene has been analyzed in detail by Y. H. He[170], X. C. Zhao[171], S. J. He[172]and so on. In aqueous solution, DNA segments can self-assemble onto graphene surface to form stable hybrid structures and two types of assembly patterns are observed for DNA on graphene surface [171]. This investigation has further emphasis the importance of ␲ stacking forces in determining the morphology for macromoleculars physically adsorbed onto graphene surface. D. Umadevi has studied the physisorption of nucleobases onto graphene and CNTs [173]. It is concluded that graphene not only has higher affinity but also appears to be best suited to differentiate various nucleobases compared with CNTs. This computa-tional study suggest that compared with CNTs, graphene is endowed with better properties for DNA sequencing and this observation should encourage a more focused research on graphene for DNA sequencing. He et al. have proposed the idea of using graphene electrodes with hydrogenated edges for solid-state nanopore-based DNA sequencing and MD simulations in conjunction with electronic transport cal-culations are performed to confirm the potential merits of this idea[170]. Simulation details shows that compared with unhydrogenated system, edge-hydrogenated graphene elec-trodes facilitate the temporary formation of H-bonds with suitable atomic sites in the translocating DNA molecule. As a consequence, the average conductivity is drastically raised by about 3 orders of magnitude while exhibiting significantly reduced statistical variance [170]. Fig. 12 is the schematic view of the graphene-DNA detecting device. Furthermore, DFT calculation helps Y. Li identifies the mechanism of significant improvements on the affinity and selectivity of the molecularly imprinted polyme (MIP)-functionalized graphene materials[174], this confirms the idea that graphene can be used as biological sensors. A. V. Titov has demonstrated that graphene sheets can be hosted into the interior of biological membranes formed

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by amphiphilic phospholipid molecules[175]. MD simulation shows that these hybrid graphene-membrane superstruc-tures can be prepared by forming hydrated micelles of individual graphene flakes covered by phospholipids, which can be then fused with the membrane. According to A. V. Titov, this graphene embedded biological membranes can be made into biological electronic circuits[175]. With the help of CMS, numbers of noble ideas and methods that may hardly be available by the current experimental approach can be confirmed and investigated. With a wider application of graphene-based composite, we believe these ideas con-firmed by the theoretical investigations will soon be realized in factual experiment.

Graphene interacting with water and other solvents

Basically, interfacial water plays a significant role in a variety of fields including biological membrane [176], ion channels [177], reverse osmosis [178]and water purifica-tion [179]. On the other hand, it is also known to all that the presence of a hydrophobic surface, for example, graphene surface can modify the structures and dynamic behaviors of the interfacial water molecules compared with the usual properties of bulk liquid [180]. Therefore, full understandings of the interaction between graphene and water molecules are essential toward a wider application of graphene complexes since most of fabrication process of graphene composites involves the usage of water and organic solvent. C. S. Lin has introduced that when inter-acting with a graphite surface in some specific orientation, the optimized geometry of water hexamer may change its original structure to an isoenergy one, while the smaller water cluster would maintain its cyclic or linear configu-rations[181]. He suggests that the binding energy of water clusters interacting with graphite is dependent on the num-ber of water molecules that form hydrogen bonds, but is independent of the water cluster size[181]. Water droplets on graphite sheets have been conducted to study the effect of water—carbon interaction energy on the contact angle of the droplet[182]. M. C. Gordillo et al. have presented a sys-tematic investigation of water adsorbed on top of a single graphene layer with temperature varying from 25 to 50◦C [183].The difference between graphene and graphite as an adsorbent is presented and discussed in detail. The rela-tionship between the ordering of nanoscale water film on graphene surface and the diffusion of water has also been identified [184]. MD simulations indicate that as the sur-face coverage of water increases, the diffusion coefficient of water increases until a critical surface coverage and a further increase in surface coverage results in a decrease of water diffusion coefficient. They further explain that for thin nanoscale films that form two layers of waters on a hydrophobic surface, the frst layer of water forms a hexag-onal structure, very similar to the ice Ih structure, that is independent of the surface coverage. As the surface cov-erage increases, the ordering of water molecules in the second layer increases and for a critical surface coverage the ordering in the second layer is maximized and the hydrogen bonding between first and second layers is minimal giv-ing rise to fast diffusion. As the surface coverage further

Figure 13 (a) Graphene membrane with a nanopore of diame-ter davg= 0.75 nm (left) and davg= 2.75 nm (right). (b) Simulation setup. Cyan color represents carbon atom, red color and white color represent the oxygen and hydrogen atoms of a water molecule, respectively. Two water reservoirs are attached to each side of the porous graphene membrane. Ly= Lx= 4 nm when the pore diameter is 0.75 nm, and Ly= Lx= 6 nm when the pore diameter is 2.75 nm. In the shaded region (z = 1 nm), external forces are applied on water molecules to create a pressure drop across the membrane.

increases, the hydrogen bonding between the ﬁrst and sec-ond layers increases and the diffusion coefﬁcient of water is reduced[184]. This ‘‘ordering-induced diffusion enhance-ment’’ effect can help us in understanding various nanoscale diffusion processes on the hydrophobic surface. ‘‘Surface roughness’’ effect on the water molecule adsorbed onto a single graphene sheet at room temperature has been pro-posed by M. C. Gordillo by means of MD simulation[185]. It shows that the properties of water adsorbed on graphene depend basically on the average amplitude of the distortions in the Z direction and not of their particular type (ran-dom or periodic). Moreover the binding energies and water structure are scarcely affected by the corrugation, with an average number of 3—3.5 hydrogen bonds per molecule through the distance perpendicular to the surface[185].

Due to the current application of graphene in fuel cells [186—190]and the potential application in molecular siev-ing and water filtration, several researchers have focused in uncovering the ‘‘physical nature’’ of water moleculars and ion transport through ultrathin graphene films. Using MD simulation, M. E. Suk have investigated water trans-port through a porous graphene membrane and compared that with water transport through thin (less than 10 nm in thickness/length) CNT membranes[191]. The configuration of the system is recorded inFig. 13. They suggest that for smaller diameter pores, where a single-file water struc-ture is obtained, CNT membranes provide higher water flux. While for larger diameter pores, where the water struc-ture is not single-file, graphene membranes provide higher water flux compared with CNT membranes[191]. Another studyperformed by J. Goldsmith has focused on pressure-induced flow of water and aqueous salt solutions through

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Figure 14 A snapshot from a nonequilibrium molecular dynamics simulation of pressure-induced ﬂow of a NaCl solu-tion through a model nanopore constructed from a (16, 16) carbon nanotube spanning a membrane formed by two graphene sheets. Carbon atoms are shown in blue, oxygen atoms are red, hydrogens are gray, Na+_{ions are yellow, and Cl}−_{ions are green.} Reprinted ﬁgure with permission from[192]. Copyright 2009 by the American Chemical Society.

nanopores composed of (n, n) CNT that span a membrane constructed of parallel graphene walls as described inFig. 14 [192]. The dependence of the ﬂuxes of water and ions on the nanopore size, nanopore charge pattern, and pressure difference are explored using NEMD [192]. With the help of CMS, we can design graphene membrane structures with considerable size of holes that are more suitable for water transport and puriﬁcation.

In some studies, the ‘‘hydrophobic effect’’ for water molecules confined between two graphene-like plates has been discussed in detail [193,194]. However, by redesign the ‘‘water confined’’ bilayer graphene model, not only the interacting mechanism between graphene and water molecule can be discussed, but also a better understand-ing of the biomolecules interactunderstand-ing with water moleculars can be achieved. This is because when ‘‘dressing’’ up simple graphene plate with physical dipoles, this ‘‘water confined’’ bilayer graphene model can be viewed as a simplified sys-tem for lipid molecules. L. Lu first proposed the idea in 2006 [195,196]. C. Eun further modifies the model by building sys-tems containing phosphatidycholine headgroups attached to graphene plates (PC headgroup plates)[197—199]. A com-parison between MD simulation results and experimental data shows that the force obtained from MD simulation and the measured force from experiments has similar features, this suggests that the simple model can qualitatively repro-duce the interaction between lipid bilayers[197]. Recently, they redesign their initial model by removing the charge from the zwitterionic headgroups. The role of water as a medium is emphasized, and the effect of roughness and flexibility of the headgroups are discussed[199].

In the preparation of graphene sheets, liquid phase exfoliation that involves the use of surfactants has been exploited extensively to produce graphene-like materials with properties comparable to those of graphene [200].

Besides, organic solvent is frequently used in the fabrication of graphene nano-device. So it would also be interest-ing to investigate the interactinterest-ing mechanism between graphene and organic solvent. S. C. Lin et al. have combined MD simulations, theoretical modeling, and experimental measurements to elucidate several important aspects of solution-phase exfoliated graphene dispersed in a sodium cholate (SC) surfactant aqueous solution (Fig. 15) [201]. D. Konatham has conducted a MD simulation containing pristine and functionalized graphene nanosheets dispersed in liquid organic linear alkanes (oils) at room conditions [202]. For the first time, they report that although pristine graphene sheets tend to agglomerate in the oils considered, graphene sheets functionalized at their edges with short branched alkanes yield stable dispersions[202]. C. J. Shih has further developed a theoretical framework that utilizes MD simulations and kinetic theory of colloid aggregation to elucidate the mechanism of stabilization of liquid-phase-exfoliated graphene sheets in N-methylpyrrolidone (NMP), N,N-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), ␥-butyrolactone (GBL), and water [203]. They identify that the dominant barrier hindering the aggre-gation of graphene is the last layer of confined solvent molecules between graphene sheets, which results from the strong affinity of the solvent molecules for graphene. They also ranked the potential solvents according to their ability to disperse pristine, unfunctionalized graphene as follows: NMP≈ DMSO > DMF > GBL > H2O, consistent with the

widespread usage of the ﬁrst three solvents for this pur-pose [203]. The conclusion proposed in this paper is very meaningful for our selection of organic solvent in the liquid-phase-exfoliated graphene sheets process. Lastly, as recent experimental investigations have demonstrated that graphene can be used as high performance batteries [186—190], a number of theoretical researches have focused on the ion transfer on graphene surface[46,204—206]. The characteristic for the electrolytic ions adsorb and aggregate on the surface of graphene has been identiﬁed, and the interaction between graphene plates and the electrolyte has been discussed in detail.

Graphene interacting with other kinds of materials In this section, priority is given to systems containing graphene interacting with CNT and fullerene. In general, the interaction between graphene and other carbon allotrope often result in noble nanostructures that may have poten-tial applications in a variety of ﬁelds, so a great number of theoretical researchers have been fascinated in under-standing the interacting process between them with the aim of designing noble carbon based nanostructures. First, Y. Z. He et al. have reported the formation of ripples on a single layer graphene sheet stroked by a C60 molecule [207]. They suggest that the propagation orientation and amplitude of ripples can be controlled via changing the locally insert slits and the speed of C60. This

interest-ing phenomenon can be used to detect defects on the graphene surface and has potential application in the area of nanomechanics. MD method is used to investi-gate the diffusion process of C60 on a graphene sheet at