Entropically-stabilised growth of a two-dimensional random tiling

TL;DR

This paper investigates the transition from energetic to entropic stabilization during the growth of two-dimensional molecular tilings, revealing conditions under which equilibrium structures form directly during assembly.

Contribution

It introduces a lattice gas model to distinguish between energetic and entropic growth regimes in molecular tilings, providing a new methodology for analyzing their formation.

Findings

Identification of a transition from energetic to entropic stabilization.

Demonstration that equilibrium configurations can grow directly without relaxation.

Revealed that equilibrium spatial statistics coexist with slow dynamical behavior.

Abstract

The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically-arrested on experimental timescales so the critical regime in their formation is that of initial growth. Here we identify a transition from energetic to entropic stabilisation in the nucleation and growth of a molecular rhombus tiling. Calculations based on a lattice gas model show that clustering of topological defects and the formation of faceted boundaries followed by a slow relaxation to equilibrium occurs under conditions of energetic stabilisation. We also identify an entropically-stabilised regime in which the system grows directly into an equilibrium configuration without the need for further relaxation. Our results provide a methodology for identifying equilibrium and non-equilibrium randomness in the growth of molecular tilings, and we demonstrate that equilibrium spatial statistics are compatible with exponentially slow dynamical behaviour.