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Two-dimensional mixtures of dipolar colloidal particles with different dipolemoments exhibit extremely rich self-assembly behaviour and are relevant to awide range of experimental systems, including charged and super-paramagneticcolloids at liquid interfaces. However, there is a gap in our understanding ofthe crystallization of these systems because existing theories such as integralequation theory and lattice sum methods can only be used to study the hightemperature fluid phase and the zero-temperature crystal phase, respectively.In this paper we bridge this gap by developing a density functional theory(DFT), valid at intermediate temperatures, in order to study thecrystallization of one and two-component dipolar colloidal monolayers. Thetheory employs a series expansion of the excess Helmholtz free energyfunctional, truncated at second order in the density, and taking as inputhighly accurate bulk fluid direct correlation functions from simulation.Although truncating the free energy at second order means that we cannotdetermine the freezing point accurately, our approach allows us to calculate abinitio both the density profiles of the different species and the symmetry ofthe final crystal structures. Our DFT predicts hexagonal crystal structures forone-component systems, and a variety of superlattice structures fortwo-component systems, including those with hexagonal and square symmetry, inexcellent agreement with known results for these systems. The theory alsoprovides new insights into the structure of two-component systems in theintermediate temperature regime where the small particles remain molten but thelarge particles are frozen on a regular lattice.

Density functional theory for the crystallization of two-dimensional dipolar colloidal alloys