Broken symmetry and the variation of critical properties in the phase behaviour of supramolecular rhombus tilings

TL;DR

This study investigates how subtle chemical changes influence the degree of order in supramolecular rhombus tilings, revealing a complex phase behavior driven by small energy differences and validated through numerical simulations.

Contribution

It demonstrates the impact of minor chemical variations on the phase behavior of supramolecular arrays and links experimental order parameters to interaction energies via simulations.

Findings

Variation in order correlates with solvent and molecular size changes.

Identifies a novel phase behavior with mixed random and ordered phases.

Small energy differences can significantly alter the system's phase.

Abstract

The degree of randomness, or partial order, present in two-dimensional supramolecular arrays of isophthalate tetracarboxylic acids is shown to vary due to subtle chemical changes such as the choice of solvent or small differences in molecular dimensions. This variation may be quantified using an order parameter and reveals a novel phase behaviour including random tiling with varying critical properties as well as ordered phases dominated by either parallel or non-parallel alignment of neighbouring molecules, consistent with long-standing theoretical studies. The balance between order and randomness is driven by small differences in the intermolecular interaction energies, which we show, using numerical simulations, can be related to the measured order parameter. Significant variations occur even when the energy difference is much less than the thermal energy highlighting the delicate balance between entropic and energetic effects in complex self-assembly processes.