Influence of polydispersity on the critical parameters of an effective-potential model for asymmetric hard-sphere mixtures

Abstract

We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential (R. Roth et al, Phys. Rev. E62 5360 (2000)) designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: q ≡ σs/σ b = 0.1 and q = 0.05. We find that inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.

Three-body interactions in complex fluids: Virial coefficients from simulation finite-size effects

“…Considering first the calculation of B 2 for hard spheres, here one has N = 2 and hence r min = r. Fig. 2(a) plots the measured forms of P 2 (r), P ig 2 (r) and their ratio g 2 (r) obtained by a simple Monte Carlo simulation of a pair of particles in a periodic box of volume V = (2.5σ) 3 , with σ the hard sphere diameter. For this simple interaction potential, the limiting value of g 2 (r) pertains for all r > σ.…”

“…This is to be compared with the exact value of B 3 = 5π 2 σ 6 /18 = 2.741557σ 6 . Finally, we consider B 4 , which we have measured for a system of size V = (3.5σ) 3 . The measured value of f 4 together with Eq.…”

Empirical expressions of the pair correlation functions at contact and equation of state of the liquid hard-sphere mixtures at large size ratio

“…We also consider the sticky sphere fluid, the second virial coefficient of which is the same as for the "Götzelmann" fluid (such a sticky representation is here labelled GS). As discussed by Largo and Wilding [11] the critical point of the GS fluid and of the Götzelmann fluid are almost the same (see Table 1). We also consider the HS liquid mixture binodal obtained from the solution of the Orstein-Zernike equations and the fundamental measure theorymean spherical approximation (FMT-MSA) closure of AA [7].…”

“…As a consequence, the work of AA legitimates the use of analytical models to represent the effective interaction in asymmetric hard-sphere mixtures at large size ratio R > 5. Such models are, for instance, the depletion potential of Götzelmann et al [9] or, more drastically, the corresponding effective sticky potential [10,11] for which simulations have been performed by Miller and Frenkel [12]. The latter model reproduces almost quantitatively the phase diagram of the HS fluid mixture and so the (metastable) fluid-fluid equilibrium in the colloidal limit.…”

Effect of Energy Polydispersity on the Nature of Lennard-Jones Liquids

“…Experimental liquids, however, are often dispersed in additional variables besides their size. As an example: Colloidal fluids can have distribution in their size as well as their charge 39 ; polymer fluids need both a size and energy distribution to be described correctly in simulations 40 . In this paper we study energy polydisperse LJ liquids as a first step in understanding how these additional factors affect polydisperse RS liquids.…”