Scaling for mixtures of hard ions and dipoles in the mean spherical approximation

Using new scaling parameters βi, we derive simple expressions for the excess thermodynamic properties of the mean spherical approximation (MSA) for the ion-dipole mixture. For the MSA and its extensions we have shown that the thermodynamic excess functions are a function of a reduced set of scaling matrices Γχ. We show now that for factorizable interactions like the hard ion–dipole mixture there is a further reduction to a diagonal matrices βχ. The excess thermodynamic properties are simple functions of these new parameters. For the entropy density we get S=−{k/3π}(F[βα])α∈χ, where F is a simple algebraic functional (such as the cube of the modulus of a vector in function space) of the scaling matrices of irreducible representations χ of the closure of the Ornstein–Zernike equation. The new scaling parameters βi are also simply related to the chemical potentials of the components. The analysis also provides a new definition of the Born solvation energy for arbitrary concentrations of electrolytes.