A realistic statistical-mechanics model is applied to describe the repulsive interaction between charged colloids. The latter, in combination with the long-range van der Waals attraction simulated under excess salt environment, gives rise to a total intercolloidal particle potential showing a clear second potential minimum. Differing from the usual Derjaguin-Landau-Verwey-Overbeek (DLVO) model, the present model is valid at any finite concentration of colloids and is thus an appropriate model for investigating the low- and high-density liquid phase transition. Employing this two-body colloid-colloid potential and in conjunction with the Weeks-Chandler-Andersen [J. D. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys. 54, 5237 (1971)] thermodynamic perturbation theory, we derive analytical expressions for the pressure, chemical potential, and related thermodynamic functions. These thermodynamic quantities were used to calculate the phase diagrams of charged colloidal dispersions in terms of the critical parameters: temperature, volume fraction, and electrolyte concentration parameter k(D). Compared with the DLVO model, we find the areas enclosed within the spinodal decomposition and also the liquid-liquid coexistence curves broader in the present model for an excess salt condition kappa=k(D)sigma(0)< or similar to 200, sigma(0) being the macroion diameter, in addition to exhibiting a shift in the critical point kappa(c) to lower values; for kappa>300, the disparities between the two models reduce. The same thermodynamic perturbation theory has been employed to study also the weak reversible coagulation whose physical origin is attributed to the presence of the second potential minimum. We examine various colloidal parameters that affect the structure of the latter and deduce from our analysis the conditions of colloidal stability. In comparison with the measured flocculation data for a binary mixture of polystyrene lattices and water, we find that our calculated results are generally reasonable, thus lending great credence to the presently used model.
