Insights into the auxetic behavior of graphene: A study on the temperature dependence of Poisson's ratio and in-plane moduli

Graphene is a highly versatile material with many potential applications. Accurately measuring its mechanical properties, especially Poisson's ratio, has been a significant challenge. Computational methods such as Molecular Dynamics and Monte Carlo have been used to estimate this parameter for free-standing samples. However, many studies underestimate details of local geometrical changes, leading to inaccurate results. Here, we use a Discrete Differential Geometry approach to compute local strains from atomic locations found using Molecular Dynamics simulations of graphene samples deformed in simple tension up to an axial strain of 3% at temperatures between 10 and 600 K. We find that the Poisson's ratio at zero external stress/strain at T = 100 K (600 K) equals -0.557 (-0.601) that has not been widely reported in the literature. However, at T = 10 K, Poisson's ratio equals 0.221. We also show that this auxetic behavior is accompanied by the condition mu/B > 1 between the in-plane shear (mu) and bulk (B) modulus. Moreover, graphene's in-plane Young's modulus at T = 300 K and zero axial strain, Y-0 similar to 200 N/m, is significantly less than the commonly reported experimental value, Y-0 = 340 N/m. We also delineate the dependence upon the axial strain and the temperature of the Poisson's ratio and the in-plane modulus. These findings have important implications for developing graphene-based materials and devices.