  Two-dimensional mixtures of dipolar colloidal particles with different dipole
moments exhibit extremely rich self-assembly behaviour and are relevant to a
wide range of experimental systems, including charged and super-paramagnetic
colloids at liquid interfaces. However, there is a gap in our understanding of
the crystallization of these systems because existing theories such as integral
equation theory and lattice sum methods can only be used to study the high
temperature 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 the
crystallization of one and two-component dipolar colloidal monolayers. The
theory employs a series expansion of the excess Helmholtz free energy
functional, truncated at second order in the density, and taking as input
highly accurate bulk fluid direct correlation functions from simulation.
Although truncating the free energy at second order means that we cannot
determine the freezing point accurately, our approach allows us to calculate ab
initio both the density profiles of the different species and the symmetry of
the final crystal structures. Our DFT predicts hexagonal crystal structures for
one-component systems, and a variety of superlattice structures for
two-component systems, including those with hexagonal and square symmetry, in
excellent agreement with known results for these systems. The theory also
provides new insights into the structure of two-component systems in the
intermediate temperature regime where the small particles remain molten but the
large particles are frozen on a regular lattice.
