Theoretical study of the freezing of polystyrene sphere suspensions

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Abstract
We present a theoretical study of the freezing curve of suspensions of charged polystyrene spheres (polyballs) in water. The spheres are assumed to have the same size and charge, and to interact via a modified Debye–Hückel potential. The free energy of the liquid phase is calculated as a function of sphere density and pH of the solution, using a variational procedure in which an effective hard-sphere diameter is the variational parameter. The freezing curve is obtained from a ‘‘Lindemann criterion’’ that the volume fraction occupied by the effective hard spheres should be a constant. The resulting curve is confirmed by analogous Lindemann calculations for the solid phase, and by a calculation of the curve along which liquid and solid phase free energies are equal. For a ‘‘point-like’’ Debye-Hückel interaction for which corrections due to finite polyball radius are neglected, the melting curve is reentrant: For fixed electrolyte concentration, the fluid first crystallizes, then remelts, as the polyball density increases. Reentrance disappears when realistic size corrections are incorporated. The modified melting curve then agrees fairly well with experiment. It is concluded that the freezing of monodisperse polyball suspensions can be understood within the framework of the classical theory of dense fluids with short range repulsive interactions.

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