Temperature-Dependent Adhesion of Graphene Suspended on a Trench

Graphene deposited over a trench has been studied in the context of nanomechanical resonators, where experiments indicate adhesion of the graphene sheet to the trench boundary and sidewalls leads to self-tensioning; however, this adhesion is not well understood. We use molecular dynamics to simulate graphene deposited on a trench and study how adhesion to the sidewalls depends on substrate interaction, temperature, and curvature of the edge of the trench. Over the range of parameters we study, the depth at the center of the sheet is approximately linear in substrate interaction strength and temperature but not trench width, and we explain this using a one-dimensional model for the sheet configuration.