Phase diagram for an attractive square-well plus a linear tail potential within the van der Waals-like theory

Abstract

The phase equilibrium behavior of a typical colloidal dispersion by the van der Waals-like theory was studied. In this theory, the colloid–colloid potential is split into two parts: a repulsive part modeled by the hard-core potential and an attractive part modeled by the square-well potential corrected by a linear tail. The theory is numerically elegant since the colloidal free energy is analytic and, physically, the model can be used to study the role played by the strength and range of interactions on the formation of coexisting phases. The effect of the strength of the interaction can be accounted for by varying the width of the square-well potential (simulated by γ parameter) while the range of the interaction—by changing the “slope” of the linear potential (simulated by λ parameter). In this work, we consider three separate cases. First, we fixed the threshold values γ_th, being γ^LL_th = 0.221 for liquid–liquid and γ^SS_th = 0.0329 for solid–solid, and increased λ to examine the appearance of the liquid–liquid and solid–solid coexistence curves which were both calculated with respect to their liquid–solid counterparts. Second, we fixed the threshold values λ_th, being λ^LL_th = 0.325 for liquid–liquid and λ^SS_th = 0.0456 for solid–solid, and increased γ (keeping the λ-slope unchanged) to bring in the strength of the interaction. In these two cases, the calculations showed that a switching on of λ or γ has the consequence of inducing stable liquid–liquid or metastable solid–solid coexisting phases. Finally, we maintained a given γ plus λ. Here the calculated liquid–liquid and solid–solid phase diagrams can be analyzed in finer details to exhibit the combined influences of the strength and range of interactions.