Variational mean spherical scaling approximation for nonspherical molecules: The case of dimers

Abstract

The variational mean spherical scaling approximation (VMSSA) is extended to nonspherical objects in ionic solutions. The mean spherical approximation (MSA) and the binding mean spherical approximation (BIMSA) are extensions of the linearized Poisson–Boltzmann (or Debye–Hückel) approximation that treat the excluded volume of all the ions in the system in a symmetric and consistent way. For systems with Coulomb and screened Coulomb interactions in a variety of mean spherical derived approximations, it has been recently shown that the solution of the Ornstein–Zernike (OZ) equation is given in terms of a screening parameter matrix Γ̳. This includes the “primitive” model of electrolytes, in which the solvent is a continuum dielectric, but also models in which the solvent is a dipolar hard sphere, and much more recently the YUKAGUA model of water that reproduces the known neutron diffraction experiments of water quite well. The MSA can be deduced from a variational principle in which the energy is obtained from simple electrostatic considerations and the entropy is a universal function. For the primitive model it is ΔS=−k(Γ3/3π). For other models this function is more complex, but can always be expressed as an integral of known functions. We propose now a natural extension of this principle to nonspherical objects, such as dumbbells, in which the equivalence to the OZ approach can be explicitly verified.