Molecular Dynamics Study on 2D Hard-sphere Dimensional Transition

Abstract

Hard-core particles (i.e. hard-rod, hard-disc, hard-sphere) have been extensively studied as a fundamental model to describe numerous physical phenomena occurring in systems of purely repulsive nature. 3D hard-sphere has been used to explain colloidal system behavior including melting and freezing phenomena. 2D hard-disc was mainly investigated on its correlation with theoretical equations. In this study, we are interested to extend hard-sphere model to describe two-dimensional systems (e.g. graphene, h-BN) behavior through molecular dynamics study. As opposed to common approach in investigating 2D hard-sphere, where monolayer hard-spheres are confined between rigid walls, we employed periodic boundary condition across all directions. We examined thermodynamic properties of the system in 3D tensor form. The distribution of transversal and lateral pressure can be used to observe the dimensional transition of the system. We found that the dimensional transition occurs when the height of the model system is about 10% of the hard-sphere diameter. Below this point, the system behaves comparably to 2D hard-disc system, while higher height allows the system to behave as 3D system.