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

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.