Packing Concave Molecules in Crystals and Amorphous Solids: On the Connection between Shape and Local Structure

TL;DR

This study explores how the shape of concave molecules influences their packing in crystals and amorphous solids, revealing relationships between shape, local structure, and contact networks.

Contribution

It introduces the maximum contact number as a new metric for classifying particle shapes and analyzes its role in dense packings of concave molecules.

Findings

Densest crystal packings show a maximum in contacts per particle.

Amorphous structures often include maximum contact pairs.

Over-constrained amorphous structures have many contacts per particle.

Abstract

The structure of the densest crystal packings is determined for a variety of concave shapes in 2D constructed by the overlap of two or three disks. The maximum contact number per particle pair is defined and proposed as a useful means of categorizing particle shape. We demonstrate that the densest packed crystal exhibits a maximum in the number of contacts per particle but does not necessarily include particle pairs with the maximum contact number. In contrast, amorphous structures, generated by energy minimization of high temperature liquids, typically do include maximum contact pairs. The amorphous structures exhibit a large number of contacts per particle corresponding to over-constrained structures. Possible consequences of this over-constraint are discussed.