The statistical mechanics of ion-dipole-tetrahedral quadrupole mixtures

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Abstract
We examine the solution of the Ornstein-Zernike equations for the correlation functions of a fluid mixture in which the molecular interactions consist of a hard sphere plus a multipolar potential that contains coulombic, dipolar as well as quadrupolar terms. In particular we consider the case in which the molecule has a dipole moment in the z direction of the molecular axis system and a non-linear tetrahedral quadrupole tensor of the form Θ xx = - Θ yy , Θ zz = 0 = Θαβ, α ≠ β in the molecular frame. This model is a good representation of the dipolar and quadrupolar properties of water and our analysis will form the basis for constructing a Civilized Model electrolyte in which ions are dissolved in a solvent whose molecules possess water-like multipole moments. One of our main results is that for any theory which retains only the subset of rotational invariants that either appear in the interaction potentials or are generated by angular convolution from those appearing in the interaction potentials, e.g. the linearized hypernetted chain (LHNC) or mean spherical approximations (MSA), the equations for an ion-dipole-tetrahedral quadrupolar mixture only differ from those for an ion-dipole-linear quadrupole mixture (Θ xx = Θ yy = - 1/2Θ zz , Θαβ = 0, α ≠ β) in minor details. We have investigated the thermodynamic properties of a fluid of hard spheres with the dipole and tetrahedral moments of water using thermodynamic perturbation theory. We find that contributions to the thermodynamic properties from dipole-quadrupole interaction are very important. For a pure hard sphere tetrahedral quadrupolar fluid there is considerable difference between the results from perturbation theory and from the MSA, for which we have obtained an analytic solution.