Donald A. McQuarrie

On the interaction of spherical double layers

The mean spherical approximation of the primitive model of electrolyte solutions is analyzed for the case of two large, charged spherical ions separated by a distance r in a supporting medium of small ions of arbitrary size and concentration. It turns out that the case in which the radii of the small ions is zero (Debye–Huckel approximation) yields a simple analytic solution in agreement with the Verwey–Overbeek asymptotic results for this system. Simple analytic results are employed to illustrate the more general case.

The electrical double layer in the Born-Green-Yvon equation

The first member of the Born-Green-Yvon hierarchy of integral equations is solved numerically for a system of charged hard spheres near a charged wall under two alternative closures. The first is analogous to the superposition approximation and yields results resembling those obtained from other integral equations. The second closure employs electroneutrality to approximate the dependence of the pair correlation function upon distances from the wall. This improved theory gives qualitatively different results which are in general agreement with the modified Gouy-Chapman theory over a wide range of charge densities on the wall.

A theory of cylindrical polyelectrolyte solutions

Structural and thermodynamic properties of a solution of cylindrical polyelectrolyte are calculated in the cell model using the HNC/MSA equation. The electrostatic potential and distribution functions are more sensitive to interionic correlations than are the thermodynamic properties. Satisfactory agreement with recent simulation data is found.

A theory of the electrical double layer through the Born—Green—Yvon equation

Abstract An approximate theory of the electrical double layer is presented based upon the first member of the Born—Green—Yvon hierarchy. A modification of the superposition approximation which is appropriate for an inhomogeneous system involving image potentials is used to derive a closed system of integral equations for the singlet density functions, ϱ i (1) ( z ).

The third virial coefficient of hard discs of different sizes

Explicit calculations are made of the third virial coefficient and of the corresponding term in the expansion of the pair distribution function for three discs or three square-well molecules of different sizes confined to a plane.

Calculation of the force between planar electrical double layers containing counterion mixtures

The distribution of ions about a planar surface of fixed charge density can be solved within the hypernetted chain (HNC)/mean spherical approximation (MSA) by a simplest yet very accurate method based on the calculus of variations. Here we present an application of that work, the calculation of the potential of mean force and the net pressure for two charged planar surfaces immersed in a salt solution. The expression for the potential of mean force is derived from the Ornstein-Zernike relation for a homogenous fluid by taking the planar geometry limit and employing the conventional HNC approximation. This method requires as input only the distribution of ions about an isolated planar double layer. Though this simple method of pressure calculation is more approximate than some other schemes utilizing the HNC approximation, under many circumstances the agreement among the different theories is excellent. We present results for 1:1 and 1:2 salts as well as mixtures of monovalent and divalent counterions for ...

An extended mean spherical approximation for Coulombic systems

A systematic series of extensions of the mean spherical approximation is presented and is used to calculate the structural and thermodynamic properties of the restricted primitive model at reduced temperatures and densities comparable to the molten salt region.

A theory of the interaction between electrical double layers.

A generalization of the Poisson-Boltzmann approach to the repulsive electrostatic force between similar electrical double layers is presented. It is based on the integral equation formalism of the statistical mechanical theories of fluids and it is shown that the Poisson-Boltzmann result follows from a well-defined and improvable set of approximations.

The effect of unequal ionic size on the swelling pressure in clays

In this paper, we use the unequal radius modified Gouy-Chapman theory to evaluate the effect of the ionic size of the electrolyte on the swelling pressures (II) in different clay systems immersed in electrolytic solutions. First the model is applied to a 1:1 electrolyte to show that the coion size is only important at surface charge densities much lower than those found in typical clay systems. The swelling pressure is calculated and the results are compared with experimental data. Literature ionic radii values are used to show the dependence of the swelling pressure on the specific counterions present. Next the model is applied to a 1:1 and 2:1 electrolyte mixture with unequal-sized counterions to show the swelling pressure is highly dependent on both counterion sizes. The unequal and same-sized cases are compared.

A VARIATIONAL SOLUTION OF THE NONLINEAR POISSON-BOLTZMANN EQUATION INSIDE A SPHERICAL CAVITY

Abstract The nonlinear Poisson-Boltzmann equation is solved variationally to obtain the electrostatic potential profile in a spherical cavity containing an aqueous electrolyte solution. The variational solution is based on the linear solution to the Poisson-Boltzmann equation. It is found that a three-parameter trial function provides sufficient accuracy to make the variational potential profile indistinguishable from exact numerical results. The variational solution is valid over the concentration, size, and surface potential ranges typical of phospholipid vesicles. It is anticipated that this solution will be useful in determining the stability of membraneous vesicles and reverse micelles.