Critical points between five microscopic and macroscopic two-dimensional materials

Abstract

The boundary between microscopic and macroscopic worlds has long attracted significant attention. In this study, the growth of five two-dimensional materials, graphene, h-BN, siligraphene, quadrilateral MgO and LiF, from their smallest structural units is simulated at the B3LYP/6-31G(d) level. At each growth step, the average areas of the inner and outermost structural units are calculated. If the total areas of these materials at various growth stages are considered equivalently as the areas of circles, the corresponding radii of circles are then calculated and are denoted as R. It is found for these materials that the variation in the average area difference between inner and outermost units gradually decreases as R increases. This implies the presence of inflection points on curves of the average area difference versus R, which may be the critical points between the microscopic and macroscopic materials. Five critical points of these materials are determined. The corresponding radii R range from 0.731 nm for planar LiF to 1.907 nm for graphene. They are comparable to the critical sizes of pure liquid compounds reported in the literature. It is expected that the critical point data presented in this study will provide guidance for future related experiments.