Mean Spherical Approximation-Based Partitioned Density Functional Theory

Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.

Quantitative Description of Potential of Mean Force Between Macroparticles in Fluid with Attactive Forces

A statistical mechanics method is proposed for calculation of potential ofmean force (PMF). In the case of solvophobic or solvophilic macroparticles immersed in solvent bathof soft sphere or Lennard-Jones particles, prediction accuracy for the PMF and MF from the simplestimplementation of the proposed method, where hypernetted chain approximation is adopted forcorrelation of the macroparticle-macroparticle at infinitely dilute limit, is comparable to that ofa recent more sophisticated approach based on mixture Ornstein—Zernike integral equation / bridgefunction from fundamental measure functional. Adaptation of the present method for general complexQuids is discussed, and method for improving the accuracy is suggested. Differences and relativemerits of the present recipe compared with that based on potential distribution theory is discussed.

A Global Investigation About Hard Core Attractive Yukawa Approximation and Adhesive Hard Sphere Approximation for Structure of Colloidal Dispersion Systems

The accuracy of hard core attractive Yukawa (HCAY) potential and adhesivehard sphere (AH) potential in representing the structure factor of short range square well potentialand Asakura and Oosawa (AO) depletion potential is examined by comparing theoretical predictionswith the existing simulation data and the present numerical results from the non-linear optimizedrandom phase approximation closure for Ornstein—Zernike equation. For the case of square-well (SW)potential, it is shown that the structure factor of HCAY potential based on a recently proposedsemi-analytical expression for the radial distribution function can describe the structure factor ofSW potential with reduced well width λ ≤ 2 only if the reduced contact potential βε_(sw) ≤0.25, while the analytical expression for the structure factor of AH potential under Percus-Yevick(PY) approximation completely fails for the case of λ 】 1.2. For the case of AO depletionpotential, the domain of validity of both HCAY potential and AH potential is complementary. With theabove analysis and considering the solid-liquid transition of the AH potential with an adhesiveparameter τ below 1.31 cannot be predicted by modified weighted density approximation, the roleplayed by the HCAY potential about the mapping manipulation should not be ignored.