Scaling for Mixtures of Hard Ions and Dipoles in the Mean Spherical Approximation

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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 we get S=-k V/3 π(F[βα])α∈ χ where F is an algebraic functional of the scaling matrices of irreducible representations χ of the closure of the Ornstein-Zernike. 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.