  In this work we extend Wertheim's thermodynamic perturbation theory (TPT) to
binary mixtures (species A and species B) of patchy colloids where each species
has a single patch which can bond a maximum of twice (divalent). Colloids are
treated as hard spheres with a directional conical asssociation site. We
restrict the system such that only patches between unlike species share
attractions; meaning there are AB attractions but no AA or BB attractions. The
theory is derived in Wertheim's two density formalism for one site associating
fluids. Since the patches are doubly bondable, associated chains, of all chain
lengths, as well as 4-mer rings consisting of two species A and two species B
colloids are accounted for. With the restriction of only AB attractions,
triatomic rings of doubly bonded colloids, which dominate the corresponding
pure component case, cannot form. The theory is shown to be in good agreement
with Monte Carlo simulaion data for the structure and thermodynamics of these
patchy colloid mixtures as a function of temperature, density, patch size and
composition. It is shown that 4-mer rings dominate at low temperatures,
inhibiting the polymerization of the mixture into long chains. Mixtures of this
type have been recently synthesized by researchers. This work provides the
first theory capable of accurately modelling these mixtures.
