L. Blum

Mean spherical model for asymmetric electrolytes

The mean spherical approximation for the primitive model of electrolytic solutions is solved for the most general case of an arbitrary charge and size. It is found that the excess thermodynamic properties are scaled to the charge and the size by means of a rational expression involving a single parameter. This parameter is found by solving an algebraic equation. The explicit form of this equation is obtained for the cases of a binary mixture and in the limit of low concentrations.

Invariant Expansion for Two‐Body Correlations: Thermodynamic Functions, Scattering, and the Ornstein—Zernike Equation

An invariant expansion of the two‐body statistical correlation function of a fluid is proposed. This expansion does not depend on any particular reference frame used to define the orientation of the molecules, and therefore can be reduced to the expansions of the literature in a simple way. The new expansion permits a rather convenient way of including the effects of molecular symmetry into it. The expressions for a few thermodynamic properties in terms of this expansion are obtained. The equations for x‐ray, neutron, and light scattering are somewhat simpler using this expansion. The Ornstein—Zernike equation has a very convenient form, and is given in Fourier transformed form in terms of 6j angular recoupling coefficients.

Some exact results and the application of the mean spherical approximation to charged hard spheres near a charged hard wall

An inconsistency within one of the Henderson–Abraham–Barker equations which fails to conserve local charge neutrality when applied to ionic mixtures near charged walls is discussed and is resolved by a careful analysis of the limit in which the wall particle is allowed to grow to infinite radius and zero curvature. This gives rise to a correction term which is needed only for the case of electrostatic interactions. The resulting equation is used to obtain exact asymptotic forms for the wall–fluid correlation functions at large positive and negative distances from the interface. Also, an exact relation for the contact value of the density profile is given. By means of a simple argument, results for both the total and direct wall–fluid correlation functions are given in the mean spherical approximation for charged hard spheres near a charged wall. These results are used to determine the capacitance of the interface in the mean spherical and exponential approximations. A modified form of the exponential appr...

Mixtures of hard ions and dipoles against a charged wall: The Ornstein–Zernike equation, some exact results, and the mean spherical approximation

The Ornstein–Zernike equation for a mixture of ions and dipoles near a hard charged wall is obtained. It is shown that the same exact contact and monotonicity theorems, previously derived for the primitive (continuum dielectric) case, also are valid for this model. Rather simple expressions for the contact density, potential difference, capacitance, and distribution functions are obtained in the mean spherical approximation (MSA). These expressions reduce to previously known results in the limits of low and high concentrations of ions. It is found that cooperative alignment of the dipoles near the wall results in an increased potential difference and reduced capacitance of the double layer compared to that calculated when the solvent is represented by a continuum dielectric.

An exact formula for the contact value of the density profile of a system of charged hard spheres near a charged wall

An exact formula for the contact value of the density of a system of charged hard spheres near a charged hard wall is obtained by means of a general statistical mechanical argument. In addition, a formula for the contact value of the charge profile in the limit of large field is obtained. Comparison with the corresponding expressions in the Poisson-Boltzmann theory of Gouy and Chapman shows that these latter expressions become exact for large fields, independent of the density of the hard spheres.

Invariant expansion III: The general solution of the mean spherical model for neutral spheres with electostatic interactions

The partial solution for the mean spherical model of neutral spheres with electrostatic interactions obtained in a previous communication [L. Blum, J. Chem. Phys. 57, 1862 (1972).] is extended to the general case, in which the electrostatic interactions of odd parity, like the dipole‐quadrupole interaction, are included. The solution is given in terms of a linear transform of the direct correlation function, which is shown to be a polynomial in r inside the hard core diameter. The coefficients of this polynomial are determined from a sufficient number of boundary conditions. The method of solution employs the so‐called second Baxter form of the Ornstein‐Zernike equation [Australian J. Phys. 21, 563 (1968).] which is derived for this particular case. Also, alternative forms of the Ornstein‐Zernike equation in coordinate space are obtained. The case of molecules with linear dipole and quadrupole moments is summarily illustrated.

Solution of the Ornstein-Zernike equation with Yukawa closure for a mixture

AbstractThe Ornstein-Zernike equation with Yukawa closure

A microscopic model for the liquid metal-ionic solution interface

[c_{ij} (r) = K_{ij} e^{ - z(r - \sigma _{ij} )} /r