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A density functional theory of one- and two-layer freezing in a confined colloid system

We report an analysis of the change in character of the fluid-to-solid transition in a quasi-two-dimensional hard-sphere colloid system as the confining wall separation changes from one to two hard-sphere diameters. Our analysis is based on a study of the bifurcation of solutions of the integral equation for the singlet density, using both direct and pair correlation function representations. Two approximations used in previous bifurcation analyses of freezing are improved in the work reported in this paper. The results of the analysis correctly predict the qualitative change in freezing as a function of the confining wall separation and density, specifically the change from a fluid-to-one-layer hexagonal solid transition to a fluid-to-two-layer square solid transition at a wall separation of 1.6 hard-sphere diameters. The numerical predictions of the theory are in semi-quantitative agreement with simulation data for the density dependence of the liquid–solid transition line for wall separations up to 1.6 hard-sphere diameters.