Elastic moduli of covalently functionalized single layer graphene sheets

Abstract

Due to their flexibility, large surface area and high specific mechanical properties, single layer graphene sheets (SLGSs) are potential candidates as filler materials for improving mechanical properties of polymers. Their effective utilization as reinforcements requires strong interfacial binding with the matrix surrounding them. The covalent functionalization of SLGSs is an effective technique to enhance this binding. However, covalent bonds introduced by a functional group usually alter the pristine structure of the SLGS that may affect its mechanical properties. Thus it is important to delineate effects of covalent functionalization on elastic moduli of an SLGS. We consider five groups of different polarities, namely, hydrogen (H), hydroxyl (OH), carboxyl (COOH), amine (NH2), and fluorine (F) as model functional groups and investigate their effects on values of Young’s modulus and the shear modulus of the SLGS. We use molecular mechanics (MM) simulations with the MM3 potential and the software TINKER to conduct the study. The pristine and the functionalized SLGSs are deformed in simple tension and simple shear, and from curves of the strain energy density of deformation vs. the axial strain and the shear strain, values of Young’s modulus and the shear modulus, respectively, are derived. These values are based on the hypothesis that the response of an SLGS is the same as that of an energetically and geometrically equivalent continuum structure of wall thickness 3.4Å. It is found that functionalization reduces the elastic moduli of the SLGSs which could be due to nearly 120% local strains induced at the functionalized sites of relaxed but unloaded SLGS, and the change in hybridization from sp2 to sp3. The decrease in the value of the modulus increases with an increase in the amount of functionalization but is essentially independent of the functionalizing agent. For 10% functionalization, Young’s modulus and the shear modulus of the SLGS are found to decrease by about 73% and 42%, respectively. However, the moduli of a fully functionalized SLGS are about the same as those of a 4% functionalized sheet. Even though the moduli of the pristine armchair and zigzag SLGSs are the same, the moduli of functionalized armchair SLGSs are about 20% less than those of the corresponding zigzag SLGSs. The work will help material scientists interested in designing graphene sheet reinforced polymeric composites.