Wetting controlled phase transitions in two-dimensional systems of colloids

The phase behavior of disk colloids, embedded in a two-dimensional fluid matrix that undergoes a first-order phase transition, is studied in the complete wetting regime where the thermodynamically metastable fluid phase is stabilized at the surface of the disks. In dilute collections of disks, the tendency to minimize the extent of the fluid-fluid interface and the extent of the unfavorable wetting phase in the system gives rise to aggregation phenomena and to separation of large domains of disks that have the characteristics of bulk colloidal phases. The conditions for phase transitions among cluster gas, liquid, and solid phases of the disk colloids are determined from the corresponding values of the disk chemical potential within an analytic representation of the grand partition function for the excess energy associated with a gas of disk clusters in the low-disk-density limit. The wetting effective-interface potential is combined with the disk interaction potential in associating an internal energy with each one of the clusters. The theory can thus be applied to any type of interaction potential among disks, provided that the free energy associated with the corresponding bulk colloidal phases is available. A phase diagram is calculated explicitly for the case of hard disks on the basis of an analytical approximation for the free energy of the hard disk fluid phase and the generalized effective liquid approximation for the free energy of the hard disk solid phase.