Depletion effects and gelation in a binary hard-sphere fluid

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Abstract
A study of the binary hard-sphere fluid with size ratio [sgrave]B/[sgrave]A = 0.1 is reported. Molecular dynamics and Monte Carlo simulations have been carried out over the mole fraction (x A) range 0.002-0.1 and over the high density range where several recent authors have predicted a thermodynamic demising transition on the basis of integral equations. In this region, there is no evidence of such first-order thermodynamic phase separation, or two fluid phases. The effect of the depletion force, arising from the entropic exclusion of B spheres from between two A spheres, as x B is increased at constant packing fraction y A, is to cause a large increase in the partial pressure of A and the radial distribution function of A at contact, a reduction on the mobility of A, and eventually, at a sufficient x B, the gelation of component A to an open, low coordination, amorphous structure. This gelation transition of A shows discontinuities similar to a glass transition; it can be traced back to the hard sphere glass formation as x B approaches zero. Thermodynamic properties are reported over the range studied, and used to evaluate the predictions of current theories and the accuracy of equations of state. The Boublik—Mansoori—Carnahan—Starling—Leland equation is found to be remarkably accurate in this region, over the whole fluid range, but shows systematic deviations at high packing densities.