Pertubation theory for systems with strong short-ranged interactions

On the critical non-additivity driving segregation of asymmetric binary hard sphere fluids

“…We have reached this conclusion, or rather conjecture, by an indirect approach, starting from binary mixtures of hard spheres with non-additive diameters, as defined in eqs. (6) or (8), and using a version of thermodynamic perturbation theory adapted to singular (hard core) perturbations [13,14]. A modest degree of non-additivity (∆ < 0.1) will drive phase separation for any size ratio ξ.…”

“…[13]; it involves, in particular, a fluctuation term, which would require a knowledge of the three and four-body distribution functions of the reference system, and is hence rather intractable. However it was shown in the same paper that the first order expansion (8) gives very accurate results (compared to simulation data) in the case where ξ = 1 and ∆ = 0.2, as well as for a one component hard sphere fluid, when the diameter is swollen from σ to σ(1 + ∆), with ∆ 0.1.…”

“…even for fairly symmetric mixtures [3]. For a systematic exploration of the dependence of critical non-additivity as a function of size ratio, over the full range 0 ≤ ξ ≤ 1, we have calculated the free energy of a fluid of non-additive hard spheres, using additive hard spheres with the same diameters σ A and σ B as a reference system, and the recently developed Mayer f-function thermodynamic perturbation theory [13,14]. Dividing the pair potential between particles into a reference part and a perturbation,…”

“…We apply a recently developed thermodynamic perturbation theory adapted to singular interactions [13,14] to calculate the free energy of the nonadditive binary hard sphere fluid as a function of packing fraction and concentration. The predictions for the onset of spinodal instability presented in the following sections indeed suggest that a non-zero non-additivity (∆ C > 0) is required to trigger fluid-fluid demixing for extremely asymmetric mixtures (0 ≤ ξ ≤ ξ l 0.01) as well as for size ratios ξ ≥ ξ u 0.1.…”

Mayer function perturbation theory of effective interaction of charged colloids

“…However, the * Corresponding author. Email: wuzh@ihep.ac.cn Mayer function remains finite for any repulsive interaction [3]. Thus, it is more appropriate to expand the grand potential in power series of the Mayer function instead of the interaction potential.…”