Molecular dynamics simulations of thermal expansion properties of single layer graphene sheets

The area coefficients of thermal expansion (CTEs) of perfect single layer graphene sheet (SLGS) and SLGS with vacancy defects of different distributions were calculated in this work through molecular dynamics (MD) simulations. The effects of some parameters such as temperature, SLGS size, sample area size, vacancy fraction and vacancy distribution on CTE were investigated extensively. Numerical results clearly revealed that for both perfect and defective SLGSs, the area CTEs are negative and nonlinear with the temperature variation within a wide temperature range. Moreover, the area CTEs tend to be more insensitive to the temperature when temperature is higher than 600 K. The area CTE of a perfect SLGS converges only when the SLGS size and the ratio of the sample size to the SLGS size is above a critical value. When the SLGS size or the sample size is small, the area CTE shows distinct size-dependence. In addition, a set of empirical formulations is proposed for evaluating the area CTEs of perfect SLGSs within a wide temperature range. For the SLGS with vacancy defects, the area CTE decreases with the increase of vacancy fraction within the temperature range considered. Furthermore, compared with a decentralised distribution of vacancy defects, a concentrated distribution leads to a smaller value of area CTE of SLGS, especially for the case of high vacancy fraction.