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

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 o f the linearized Poisson-Boltzmann (or Debye-Huckel) approximation that tre at the excluded volume of all the ions in the system in a symmetric and con sistent way. For systems with Coulomb and screened Coulomb interactions in a variety of mean spherical derived approximations, it has been recently sh own that the solution of the Ornstein-Zernike (OZ) equation is given in ter ms of a screening parameter matrix <(Gamma)double under bar>. 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 know n neutron diffraction experiments of water quite well. The MSA can be deduc ed 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 Delta S = -k(Gamma(3)/3 pi). For other models thi s function is more complex, but can always be expressed as an integral of k nown functions. We propose now a natural extension of this principle to non spherical objects, such as dumbbells, in which the equivalence to the OZ ap proach can be explicitly verified. (C) 1999 American Institute of Physics. [S0021-9606(99)50922-7].