The Tiling Structure of Simple Liquids Squares and Triangles in Two Dimensions

Abstract

It has long been appreciated that dense liquids exhibit some degree of transient local structural order. Local triangular lattice-like order has been observed in dense two-dimensional (2D) liquids by a number of workers [1–6]. In this paper, we present results of a molecular dynamics (MD) simulation study that explores the geometrical structure of 2D liquids in more detail. In particular, we show that solid-like fluctuations in the dense 2D liquid are a manifestation of a more general local structural organization resembling plane tilings composed of squares and equilateral triangles (ST tilings), and that the 2D liquid can be characterized as an ST tiling containing numerous low-strength tiling faults. A similar geometrical structure is seen in 2D colloidal liquids [5] and in analog simulation studies of 2D liquids [6]. Our results indicate that square-triangle fluctuations should be a feature of realistic models of dense liquid structure and the melting transition in 2D.