2D HS Free Energy Calculation through Free Volume Approach

Abstract

For the free energy calculation, statistical geometry approach has been developed and explored extensively to obtain simple yet accurate free energy value of hard-sphere system. Previous study has shown that free volume combined with Molecular Dynamics (MD) simulation can be used to estimate the free energy of 3D hard-sphere system accurately. The idea was extended to calculate the free energy of 2D hard-sphere system unlike 2D hard-disk system. Because of its close resemblance of realistic 2D material (e.g., graphene), it cannot be treated simply as the conventional disk-like 2D system, rather its 3D characteristics coming from spherical shape of atom, wrinkles, and corrugation must be taken into consideration. Thus, we employed unconfined 2D hard-sphere model. Our result shows that the free energy of 2D hard-sphere system was comparable to 2D hard-disk system only when the system height is below a dimensional transition critical point. The discrepancy can be attributed to the 3D characteristics, which could be quantified into a mathematical formulation.