A critical edge number revealed for phase stabilities of two-dimensional ball-stick polygons.

Abstract

Phase behaviours of two-dimensional (2D) systems constitute a fundamental topic in condensed matter and statistical physics. Although hard polygons and interactive point-like particles are well studied, the phase behaviours of more realistic molecular systems considering intermolecular interaction and molecular shape remain elusive. Here we investigate by molecular dynamics simulation phase stabilities of 2D ball-stick polygons, serving as simplified models for molecular systems. Below the melting temperature T_m, we identify a critical edge number <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>n</mi></mrow> <mrow><mi>c</mi></mrow> </msub> <mo>=</mo> <mn>4</mn></math> , at which a distorted square lattice emerges; when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi> <mspace></mspace> <mo><</mo> <mspace></mspace> <msub><mrow><mi>n</mi></mrow> <mrow><mi>c</mi></mrow> </msub> </math> , the triangular system stabilizes at a spin-ice-like glassy state; when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi> <mspace></mspace> <mo>></mo> <mspace></mspace> <msub><mrow><mi>n</mi></mrow> <mrow><mi>c</mi></mrow> </msub> </math> , the polygons stabilize at crystalline states. Moreover, in the crystalline state, T_m is higher for polygons with more edges at higher pressures but exhibits a crossover for hexagon and octagon at low pressures. A theoretical framework taking into account the competition between entropy and enthalpy is proposed to provide a comprehensive understanding of our results, which is anticipated to facilitate the design of 2D materials.