An inhomogeneous integral equation for the triplet structure of binary liquids

Abstract

The inhomogeneous integral equation proposed by Attard for the study of triplet correlations ͓J. Chem. Phys. 91, 3072 ͑1989͔͒ has been generalized to multicomponent systems. Defining one of the particles of a triplet as the source of an external field, the three particle distribution functions for the mixture are calculated using the inhomogeneous Ornstein-Zernike equation, an approximate closure relation and the Triezenberg-Zwanzig relation. The proposed theory performs satisfactorily for asymmetric mixtures of Lennard-Jones fluids for which other approximations at the two particle level tend to be rather inaccurate.

Study of the triplet and pair structure of strong electrolytes modeled via truncated Coulomb interactions

“…The improvement of the HNC3 over the HNC is notorious in both cases, and this is in accordance with previous findings for simple fluids 10 and mixtures. 11 Similar results are also found for other cases studied.…”

“…The values of r and s have been chosen to correspond to the position of the relevant peaks of the pair distribution functions. The fact that the BHP approximation yields nonzero g (3) for low angleswhich for the given configuration corresponds to overlapping particles-stems from numerical inaccuracies inherent to the multidimensional Fourier inversion 11 of the OZ3 equation. Aside from this deficiency this approximation qualitatively reproduces the behavior of the like triplet distribution function in agreement with the HNC3 and in marked contrast with the Kirkwood superposition approximation ͑KSA͒.…”

“…A complete description of this method is done elsewhere. 11,14 We have discretized the inhomogeneous functions using 200-250 grid points in r i with a grid size 0.04 ϪϪ ( ϪϪ ϭ2r Ϫ ) and the discrete Legendre transformation is carried out using 60 coefficients. Five search directions did suffice to reach convergence in the GMRESNL algorithm.…”

“…17 However, the fact that the HNC3 must be solved in real space does not allow for a straightforward extension of the renormalization approach, best suited for a Fourier space formalism. One will have then to cope with the integral equation resorting to longer integration ranges than those considered in Lennard-Jones mixtures 11 but subject to computer storage limitations. Consequently we have opted here for a truncated and shifted Coulomb potential to model the electrolyte.…”

“…We will thus use the inhomogeneous Ornstein-Zernike ͑IOZ͒ approach proposed by Attard,10 which has recently been extended by us to describe binary mixtures. 11 In this approach, following Percus source particle method, a given particle is considered as the source of an external potential and hence an IOZ can be constructed to determine a series of inhomogeneous correlation functions which are trivially related to the homogeneous correlation functions of higher order. In addition, the inhomogeneous density is connected with the inhomogeneous pair distribution function by means of a Triezenberg-ZwanzigWertheim-Lovett-Mou-Buff ͑TZWLMB͒ 12,13 integral equation.…”