The thermodynamic instabilities of a binary mixture of sticky hard spheres

Abstract

The thermodynamic instabilities of a binary mixture of sticky hard spheres (SHS) in the modified Mean Spherical Approximation (mMSA) and the Percus-Yevick (PY) approximation are investigated using an approach devised by X. S. Chen and F. Forstmann [J. Chem. Phys. 97, 3696 (1992)]. This scheme hinges on a diagonalization of the matrix of second functional derivatives of the grand canonical potential with respect to the particle density fluctuations. The zeroes of the smallest eigenvalue and the direction of the relative eigenvector characterize the instability uniquely. We explicitly compute three different classes of examples. For a symmetrical binary mixture, analytical calculations, both for mMSA and for PY, predict that when the strength of adhesiveness between like particles is smaller than the one between unlike particles, only a pure condensation spinodal exists; in the opposite regime, a pure demixing spinodal appears at high densities. We then compare the mMSA and PY results for a mixture where like particles interact as hard spheres (HS) and unlike particles as SHS, and for a mixture of HS in a SHS fluid. In these cases, even though the mMSA and PY spinodals are quantitatively and qualitatively very different from each other, we prove that they have the same kind of instabilities. Finally, we study the mMSA solution for five different mixtures obtained by setting the stickiness parameters equal to five different functions of the hard sphere diameters. We find that four of the five mixtures exhibit very different type of instabilities. Our results are expected to provide a further step toward a more thoughtful application of SHS models to colloidal fluids.

arXiv comment29 pages, 13 figures

References in corpus (6)

• Liquid-vapour phase behaviour of a symmetrical binary fluid mixture
• Analytic solutions for Baxter's model of sticky hard sphere fluids within closures different from the Percus_Yevick approximation
• Structure factors for the simplest solvable model of polydisperse colloidal fluids with surface adhesion
• Stability boundaries, percolation threshold, and two phase coexistence for polydisperse fluids of adhesive colloidal particles
• The density functional theory of classical fluids revisited
• Pathologies in the sticky limit of hard-sphere-Yukawa models for colloidal fluids. A possible correction

Cited by in corpus (14)

• Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions
• Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids
• How `sticky' are short-range square-well fluids?
• Bridging and depletion mechanisms in colloid-colloid effective interactions: A reentrant phase diagram
• The structure of colloidosomes with tunable particle density: simulation vs experiment
• Monte Carlo simulation of the nonadditive restricted primitive model of ionic fluids: Phase diagram and clustering
• Phase behavior of weakly polydisperse sticky hard spheres: Perturbation theory for the Percus-Yevick solution
• Phase diagrams of Janus fluids with up-down constrained orientations
• Monte Carlo simulation of Hard-, Square-Well, and Square-Shoulder Disks in narrow channels
• The moment sum-rules for ionic liquids at criticality
• Effect of quantum dispersion on the radial distribution function of a one-component sticky-hard-sphere fluid
• From the Liouville to the Smoluchowski equation for a colloidal solute particle in a solvent
• Effect of Polydispersity and Anisotropy in Colloidal and Protein Solutions: an Integral Equation Approach
• Andersen-Weeks-Chandler perturbation theory and one-component sticky-hard-spheres