Substrate Effect on the Thermal Expansion of 2D Materials: An Investigation by Machine Learning Interatomic Potentials

The thermal expansion coefficient (TEC) of suspended two-dimensional (2D) nanomaterials is usually negative due to their ability for large out-of-plane deflection as the temperature increases. The presence of a substrate can nonetheless restrict the flexibility of 2D materials and significantly change their dimensional change by temperature. In this short communication, the thermal expansion coefficients of suspended and supported four popular 2D structures of graphene, phagraphene, C3N and BC3 monolayers is systematically investigated. For this purpose, we conduct molecular dynamics simulation, in which the atomic interactions are defined by highly accurate machine learning interatomic potentials. The obtained results show that by increasing the strength of the van der Waals interactions between the monolayer and the substrate, from 2 meV to 8 meV, the TEC for graphene and phagraphene increases from a negative value to a positive one; while the negative value for the C3N and BC3 structures is still retained. Analysis of molecular dynamics trajectories reveals that the substrate can significantly reduce the formation of out-of-plane wrinkles and consequently affect the value of TEC. The obtained results provide useful vision on the role of substrate on the complex thermal expansion responses of 2D materials.