Depletion effects and gelation in a binary hard-sphere fluid

A study of the binary hard-sphere fluid with size ratio sigma(B)/sigma(A)= 0.1 is reported. Molecular dynamics and Monte Carlo simulations have been carried out over the mole fraction (x(A)) range 0.002-0.1and over the high density range where several recent authors have predicted a thermodynamic demixing 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.