  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.
