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The degree of randomness, or partial order, present in two-dimensionalsupramolecular arrays of isophthalate tetracarboxylic acids is shown to varydue to subtle chemical changes such as the choice of solvent or smalldifferences in molecular dimensions. This variation may be quantified using anorder parameter and reveals a novel phase behaviour including random tilingwith varying critical properties as well as ordered phases dominated by eitherparallel or non-parallel alignment of neighbouring molecules, consistent withlong-standing theoretical studies. The balance between order and randomness isdriven by small differences in the intermolecular interaction energies, whichwe show, using numerical simulations, can be related to the measured orderparameter. Significant variations occur even when the energy difference is muchless than the thermal energy highlighting the delicate balance between entropicand energetic effects in complex self-assembly processes.

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