Molecular Dynamics Study of the Effect of Chemical Functionalization on the Elastic Properties of Graphene Sheets

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1 Copyright 21 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Nanoscience and Nanotechnology Vol. 1, 1 5, 21 Molecular Dynamics Study of the Effect of Chemical Functionalization on the Elastic Properties of Graphene Sheets Qingbin Zheng, Zhigang Li, Yan Geng, Shujun Wang, and Jang-Kyo Kim Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China In this study, the effects of chemical functionalization on the elastic properties of graphene sheets are investigated by using molecular dynamics (MD) and molecular mechanics (MM) simulations. The influences of the degree of functionalization, which is defined as the ratio of the number of the total sp 3 -hybridized atoms to the number of the total carbon atoms of the graphene sheet, the chirality of graphene sheets, the molecular structure and molecular weight of functional groups on Young s modulus are studied. The dependence of shear modulus and wrinkling properties on the functional groups are also investigated. The simulation results indicate that Young s modulus depends strongly on the degree of functionalization and the molecular structure of the functional groups, while the effects of chirality of the graphene sheets and the molecular weight of the functional groups are negligible. The chemical functionalization also reduces the shear modulus and critical strain, beyond which the wrinkling instability occurs. Keywords: Graphene Sheet, Chemical Functionalization, Young s Modulus, Shear Modulus, Critical Wrinkling Strain. 1. INTRODUCTION Graphene sheets (GS) were officially defined in 1993 but firstly produced in Their unique mechanical, thermal and electrical properties could have numerous potential applications. 2 3 Due to the high flexibility and large interfacial area, graphene can be a good candidate of nanofiller to enhance the mechanical, thermal, and electrical properties of composite materials, such as commonly used polymer matrix. 4 5 Similar to carbon nanotube (CNT) based nanomaterials, the key challenges in the synthesis and processing of GS/polymer composites are the aggregation of GS and poor GS-polymer interactions. 6 7 One effective way to improve the dispersibility of GS and interfacial bonding between GS and the supporting matrix is to functionalize the GS with certain chemical groups before they are dispersed into the matrix. The functional groups, however, may affect the mechanical and physical properties of the GS and composites. Unfortunately, how chemical functionalizatioin affects the mechanical properties of GS is unclear. The elastic properties of pristine graphene have been recently determined by atomic force microscope Author to whom correspondence should be addressed. nanoindentations, which show that the graphene appears to be the strongest material ever. 8 9 The mechanical properties of single GS, however, are not easy to be measured by experiments. As a popular numerical approach, molecular dynamics (MD) simulations can be used to investigate the mechanical properties of GS. The buckling, deformation, Young s and shear moduli of GS have been obtained using atomistic simulations The effects of large defects and cracks on the mechanical properties of CNTs and GS have also been investigated by coupled quantum mechanical/molecular mechanics (QM/MM) calculations. 15 Furthermore, a theoretical framework of nonlinear continuum mechanics for graphene and a new formula of elastic bending modulus for monolayer grapheme have been developed recently as well. 16 However, most of the previous studies have been focused on pristine GS, the effect of chemical functionalization on the elastic properties of GS has not been studied. For practical applications, it is necessary to understand the influence of certain functional groups on the mechanical properties of GS. In this study, we investigate the effects of chemical functionalization on the elastic properties of GS through MD and MM simulations. The force field of the condensedphase optimized molecular potential for atomistic simulation studies (COMPASS) is used to model the interatomic J. Nanosci. Nanotechnol. 21, Vol. 1, No. xx /21/1/1/5 doi:1.1166/jnn

interactions. Speciﬁcally, we study the effects of GS chirality, degree of functionlization, molecular structure and weight of functional groups on Young s modulus of GS.

2 interactions. Speciﬁcally, we study the effects of GS chirality, degree of functionlization, molecular structure and weight of functional groups on Young s modulus of GS. In addition, the shear modulus and wrinkling properties are also examined. 2. EXPERIMENTAL DETAILS In this work, the MD and MM simulations are carried out using Materials Studio developed by Accelrys Inc. The COMPASS module, which has been widely employed for various gas and condensed phase properties of many popular organic and inorganic materials,17 is used to conduct the computations. The electronic structures of all the carbon atoms in the graphene models are sp2 -hybridization. The unsaturated boundary effect is avoided by adding hydrogen atoms on the edges of the GS. A pristine graphene sheet containing 1372 carbon atoms and a graphene sheet functionalized with 88 carboxyl functional groups in the center are shown in Figure 1. The simulations are carried out in the (N, V, T ) ensembles. The temperature of the system is Zheng et al. set to be 1 K such that the thermal effect is avoided. No periodic boundary conditions are used for the pristine and functionalized GS and the time step is 1 fs. All the measurements are made after the systems reach equilibrium, which is achieved through a minimizer processor.18 To obtain Young s modulus, the boundary carbon atoms on the bottom side of GS are constrained and a positive displacement is applied to the boundary carbon atoms on the top side. Young s modulus is given by E= 1 2U V 2 (1) where E is Young s modulus, V is the volume of the GS, U is the strain energy, and is the strain. By changing the displacement of the carbon atoms on the top side, the strain energy and the corresponding strain of the GS are measured and their relationship is obtained by polynomial ﬁttings.19 Young s modulus is then determined through Eq. (1). Using similar approach, we shall also study the shear modulus and wrinkling properties of GS. The shear modulus is estimated by the gradient of stress-strain curve. The critical wrinkling strain is obtained by increasing the displacement of the carbon atoms on the top side until wrinkling occurs. 3. RESULTS AND DISCUSSION 3.1. Effect of Chirality on Young s Modulus The chirality of GS is related to their structure. For example, zigzag GS correspond to zero degree chiral angle and armchair GS correspond to a chiral angle of 3. Figure 2 shows the curves of the strain energy and tensile load for zigzag and armchair GS. The Young s modulus of armchair GS is 1.86 TPa, which is a slightly larger than that of zigzag GS (1.5 TPa). By changing the chiral angle from (zigzag) to 3 (armchair), we study the effect of chirality on Young s modulus, which is depicted in Figure 2. The results conﬁrm that Young s modulus is not sensitive to the chirality of GS. Particularly, the effect of chirality is much weaker for large chiral angles. As shown in Figure 1, the graphene sheet is composed of interconnected hexagons of carbon atoms, which is highly symmetric. The fundamental hexagonal structure makes the GS quite independent of the direction of tensile force. That is why similar Young s modulus is obtained with different axial forces Effect of Degree of Functionalization on Young s Modulus Fig. 1. Molecular models employed in the simulations. A pristine GS (L = nm, L1 = 5 94 nm). A functionalized GS with 88 carboxyl functional groups (top and side views). 2 The chemical functionalization of GS has been performed by attaching different numbers of functional groups on the surfaces of the GS line by line through covalent bonding. The number of functional groups will be equal to that of the sp3 -hybridized carbon atoms on the surface of the GS. J. Nanosci. Nanotechnol. 1, 1 5, 21

Zheng et al. Strain energy (Kcal/mol) Young's modulus (GPa) 12 9 6 3 195 18 165 15 Armchair graphene E=1.86 TPa Zigzag graphene E=1.

3 Zheng et al. Strain energy (Kcal/mol) Young's modulus (GPa) Armchair graphene E=1.86 TPa Zigzag graphene E=1.5 TPa Chiral angel ( ) The degree of functionalization is defined as the ratio of the number of the total sp 3 -hybridized carbon atoms to the number of the total carbon atoms of the GS. Figure 3 shows the strain energy-strain curves for different degrees of functionalization with carboxyl being the functional groups. It is seen that Young s modulus decreases rapidly with increasing degree of functionalization. Young s modulus is reduced by about 42.2% when the GS are functionalized at a degree of functionalization of 16%. The reduction in Young s modulus is caused by the structure change in the GS induced by the functional groups. As shown in the inset of Figure 3, the carbon atoms that are sp 3 -hybridized with functional groups are pulled away from the original plane of GS such that the GS are relatively in a more unstable state compared with the pristine GS. In this case, it becomes easier to deform the functionalized GS than the pristine GS. This is why Young s modulus decreases as the degree of functionalization is increased. The average perpendicular displacements of carbon atoms from the GS plane under different degrees of functionalization are shown in Figure 3, which are consistent with the dependence of Young s modulus on the degree of functionalization shown in Figure 3. Fig. 2. Effect of chirality on the Young s modulus of GS. Strain energy-strain curve of armchair and zigzag GS. Young s modulus of GS as a function of chiral angel. Strain energy (Kcal/mol) Average displacement (angstrom) s = 3.27%, E =.982 TPa s = 6.414%, E =.965 TPa s = 9.621%, E =.727 TPa s = %, E =.678 TPa s = 16.35%, E =.67 TPa Degree of functionalization (%) Fig. 3. Effect of degree of chemical functionalization on Young s modulus of GS. Strain-strain energy curves of functionalized GS with different degrees of functionalization (s is the degree of functionalization), Average perpendicular displacement of the carbon atoms that linked to the functional groups with different degrees of functionalization Effect of Molecular Structure and Weight of Functional Groups on Young s Modulus Different functional groups may affect the Young s modulus of GS in different ways. To understand the effect of Young's modulus (TPa) Young's modulus (TPa) CH 2 O OH C 3 H 7 N(CH 3 ) 2 COOH Degree of functionalization (%) Molecular weight Fig. 4. Effects of molecular structure and molecular weight of functional groups on Young s modulus of GS. J. Nanosci. Nanotechnol. 1, 1 5, 21 3

4 Zheng et al. molecular structure, four functional groups with similar molecular weight, alkyl hydroperoxide ( CH 2 O OH, 43), propyl ( C 3 H 7, 43), dimethylamine ( N(CH 3 2, 44), and carboxyl ( COOH, 45) are identified. Figure 4 shows Young s modulus of functionalized GS. It is found that Young s modulus is increasingly sensitive to the structure of the functional groups as increasing degree of functionalization. Among the four groups, carboxyl affects Young s modulus more than the other three groups, but the qualitative dependence of Young s modulus on the structure of functional group remains the same regardless of the degree of functionalization. We further investigate the effect of molecular weight on Young s modulus. Six alkyl groups with increasing molecular weight ( CH 3, 15; C 2 H 5, 29; C 3 H 7, 43; C 4 H 9, 57; C 5 H 11, 71; C 6 H 13, 85) are chosen as the functional groups. Figure 4 shows that GS functionalized with the six different alkyl groups have similar Young s modulus, which is about.85 TPa. These results indicate that Young s modulus depends strongly on the molecular structure rather than the molecular weight of the functional groups. This is reasonable because the covalent bonding between the carbon atoms and functional groups depends more on the structure of the function group than the molecular weight. It is the covalent bonding that changes the structure of GS (inset of Fig. 3). Therefore, Young s modulus is more sensitive to the structure than the molecular weight of the functional groups. 16 Stress (GPa) Pristine graphene G = 284 GPa 7.5% OH groups G = 166 GPa Shear Modulus and Wrinkling Properties Shear modulus is another important mechanical property of GS. Figure 5 shows the stress-strain curves from the shear displacement of pristine GS and GS functionalized with 7.5% OH groups. The shear modulus of the GS is determined by the slope of the stress-strain curve. It is seen that the functional groups reduce the shear modulus. The critical wrinkling strain, at which the winkling instability takes place, can be obtained by further increasing the shear strain. The critical wrinkling strains for pristine GS and GS functionalized with 7.5% OH groups are about 6% and 4.5% respectively, which shows that chemical functionalization also results in a lower critical wrinkling. The wrinkling mode of a pristine graphene is illustrated in Figure 5. Similar to Young s modulus, this degraded shear stiffness is caused by the attached functional groups, with which the GS are in a relatively less stable state. 4. CONCLUSIONS In this study, the effects of chemical functionalization on the mechanical properties, including Young s modulus, shear modulus, and wrinkling properties, are investigated based on MD and MM simulations. It is found that Young s modulus depends strongly on the degree of functionalization and molecular structure of the functional groups, while the effects of chirality of the GS and molecular weight of the functional groups are unimportant. The chemical functionalization also reduces the shear modulus and the critical wrinkling strain. The simulation results indicate that although chemical functionalization of GS has been considered as an effective way to increase load transfer efficiency in GS/polymer composites, 5 attentions should be paid to the weakened elastic stiffness due to the attachment of functional groups. Acknowledgments: This work was supported by the Research Grant Council of Hong Kong SAR and Henkel International, formerly Imperial Chemical Industries Ltd. (Project No. ICIPLC1.7/8). References and Notes Fig. 5. Stress-strain curve under shear strain (a, G is the shear modulus) and wrinkling structure of pristine GS. 1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 36, 666 (24). 2. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proc. Nat. Acad. Sci. 12, 1451 (25). 3. A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (27). 4. S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, Nature 442, 282 (26). 5. T. Ramanathan, A. A. Abdala, S. Stankovich, D. A. Dikin, M. Herrera-Alonso, R. D. Piner, D. H. Adamson, H. C. Schniepp, X. Chen, R. S. Ruoff, S. T. Nguyen, I. A. Aksay, R. K. Prud Homme, and L. C. Brinson, Nat. Nanotechnol. 3, 327 (28). 4 J. Nanosci. Nanotechnol. 1, 1 5, 21

5 Zheng et al. 6. P. C. Ma, J. K. Kim, and B. Z. Tang, Compos. Sci. Technol. 67, 2965 (27). 7. Q. B. Zheng, Q. Z. Xue, K. Y. Yan, X. L. Gao, Q. Li, and L. Z. Hao, Polymer 49, 8 (28). 8. C. Lee, X. Wei, J. W. Kysar, and J. Hone, Science 321, 385 (28). 9. C. Gomez-Navarro, M. Burghard, and K. Kern, Nano Lett. 8, 245 (28). 1. F. Liu, P. Ming, and J. Li, Phys. Rev. B 76, 6412 (27). 11. Y. Huang, J. Wu, and K. C. Hwang, Phys. Rev. B 74, (26). 12. A. Sakhaee-Pour, Solid State Commun. 149, 91 (29). 13. W. H. Duan and C. M. Wang, Nanotechnology 2, 7572 (29). 14. Y. Gao and P. Hao, Physica E 41, 1561 (29). 15. R. Khare, S. L. Mielke, J. T. Paci, S. Zhang, R. Ballarini, G. C. Schatz, and T. Belytschko, Phys. Rev. B 75, (27). 16. Q. Lu, M. Arroyo, and R. Huang, J. Phys. D: Appl. Phys. 42, 122 (29). 17. H. Sun, J. Phys. Chem. B 12, 7338 (1998). 18. Q. Wang, Carbon 47, 57 (29). 19. Y. D. Kuang, X. D. He, C. Y. Chen, and G. Q. Li, Carbon 47, 279 (29). Received: 4 September 29. Accepted: 3 October 29. J. Nanosci. Nanotechnol. 1, 1 5, 21 5

Effects of functional groups on the mechanical and wrinkling properties of graphene sheets

CARBON 48 (21) 4315 4322 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/carbon Effects of functional groups on the mechanical and wrinkling properties of graphene sheets Qingbin