Fluids inside a pore—an integral-equation approach

Abstract

Integral equations for density profiles of fluids inside a slit pore and a spherical pore are derived using an Ornstein-Zernike system of equations. For a hard-sphere fluid we specialize to a Percus-Yevick (PY) closure and a hypernetted-chain (HNC) closure, and also consider the BBGKY hierarchy with a kind of superposition-approximation (SA) closure. The bulk correlation needed in the OZ system of equations is obtained from the PY approximation. These approximations, which will be referred to as the PY/PY and the HNC/PY approximations and the BBGKY-SA scheme, are applied to a pure hard-sphere fluid. It is shown that the BBGKY-SA equation is the same as the HNC equation used with a simple approximation for bulk direct correlation functions. The density profiles, partition coefficients, and solvation forces for the hard-sphere fluids inside a slit and a spherical pore are calculated and compared with simulation results. It turns out that the PY/PY approximation gives us a better overall agreement with simulations than either the HNC/PY approximation or the BBGKY-SA scheme in the slit-pore system. However, the PY/PY approximation yields some unphysical results for high concentrations and certain values of the ratio of spherical-pore diameter to hard-sphere diameter, while the HNC/PY approximation is the best among the three approximations in the spherical-pore system when compared with simulation results. A non-local density-functional form of closure, introduced by Blum and Stell for the flat-wall problem, is also discussed, but not assessed numerically.

Charge neutrality breakdown in confined aqueous electrolytes: Theory and simulation

“…The ionic correlations were treated altogether at the level of the Mean Spherical Approximation (MSA). It is, however, well known that in situations in which electrolyte is bounded by narrow pores -where violation of electroneutrality is expected to take place -size correlations between the confined ions may strongly influence the structure of the EDLs [63][64][65][66] . Furthermore, electrostatic correlations in electrolytes containing multivalent ions usually require use of more accurate approximations.…”

The Effect of Solute Concentration on Equilibrium Partitioning in Polymeric Gels

“…Substituting Eqs. [8], [10], and [11] into Eq. [9], one finds y 21 (r 1 , r 2 ) = 1 + ρ {g 11 (r 1 , r 3 ) − y 11 (r 1 , r 3 )}h 21 (r 2 , r 3 ) dr 3 .…”

“…[2] and [6], one must find an appropriate expression for g 0 21 . To do this, we use the Ornstein-Zernike equation for a two-component system, given by (8)(9)(10) …”

Distribution functions of a heteronuclear hard dumbbell at a hard wall. Pure fluid and mixtures with hard spheres

“…The problem of determining the density profiles or distribution functions has been tackled by simulation technique [1]- [6] or theoretically by employing the solution of the modified Orstein-Zernike equation [7]- [8] or by applying the density functional theory [9]- [11]. Solution of both types of theoretical expressions have been obtained by different numerical methods; some input data (for the corresponding homogeneous systems) are used.…”