Study of the demixing transition in model athermal mixtures of colloids and flexible self-excluding polymers using the thermodynamic perturbation theory of Wertheim

Abstract

Fluid phase separation in model athermal mixtures of colloids and polymers is examined by means of the first-order thermodynamic perturbation theory of Wertheim [M. S. Wertheim, J. Chem. Phys. 87, 7323 (1987); W. G. Chapman, G. Jackson, and K. E. Gubbins, Mol. Phys. 65, 1057 (1988)]. The colloidal particles are modeled simply as hard spheres, while the polymers are represented as chains formed from tangent hard-sphere segments. In this study the like (colloid–colloid, polymer–polymer) and unlike (polymer–colloid) repulsive interactions are treated at the same level of microscopic detail; we do not employ the common Asakura–Oosawa (AO) approximations which essentially involve treating the polymer as an ideal (noninteracting) chain. The effect of varying both the chain length and the diameter of the hard-sphere segments of the polymer on the fluid phase behavior of the model polymer–colloid system is investigated. We focus our attention on the stability of the fluid phase relative to a demixing transition into colloid-rich and polymer-rich fluid phases by using a spinodal instability analysis and determine the full coexistence boundaries (binodal). The colloid–polymer system represents the limit where the diameter of the colloid is much larger than the diameter of the segments making up the polymer chain. The precise segment/colloid diameter ratio at which liquid–liquid demixing first occurs is examined in detail as a function of the chain length of the polymer. In the case of moderately short chains the addition of polymer induces the “colloidal vapor–liquid” transition found in polymer–colloid systems, while for long chains a “polymeric vapor–liquid” transition is found. The diameter of the polymeric segments must lie between the AO limit (minimum diameter) and the so-called protein limit (maximum diameter) in order for the system to exhibit fluid–fluid phase separation. The maximum value of the segment diameter which induces phase separation is determined from a simple approximate stability analysis. The critical density of the demixing transitions is not found to tend to be zero for infinitely long polymers, but has a limiting value which depends on the diameter of the segment. An examination of the thermodynamic properties of mixing indicates that the fluid–fluid phase separation in such systems is driven by a large positive enthalpy of mixing which is induced by a large positive volume of mixing due to the unfavorable polymer–colloid excluded volume interactions. The enthalpy of mixing makes an unfavorable contribution to the overall Gibbs free energy (which is seen to counter the favorable entropy of mixing), giving rise to fluid–fluid immiscibility.