Nonpolarizable spheres

The conventional viewpoint, which assumes that the ionic atmosphere is spherically symmetric, does not take account of the inevitable effects of ionic polarization. From an analysis of the general solution (19), however, it is evident that the ionic atmosphere must be spherically symmetric for nonpolarizable ions, and the DH model is therefore adequate. (Moreover, in very dilute solution polarization effects are negligibly small, and it does not matter whether we choose a polarizable or unpolarizable sphere for our model.) But once we have made the realistic step of conferring a real size on an ion, the ion becomes to some extent polarizable, and the ionic cloud is expected to be nonspherical in any solution of appreciable concentration. Accordingly, we base our treatment on this central hypothesis, that the time-average picture of the ionic solution is best represented with a polarizable ion surrounded by a nonspherical atmosphere. In order to obtain a value for the potential from the general solution of the LPBE we must first consider the boundary conditions at the surface of the central ion. 

The energy of interaction of an ion with a solvent may be represented by three parts its electrostatic interaction, a solvophobic component, and a specific interaction due to the donor-acceptor interactions. In recent considerations of the electrostatic interaction energy, the basic ideas of the Born model [21] are accepted, though its shortcomings and limitations are evident and the original equation has been modified. The ion, M", in this model is represented by a nonpolarizable metallic sphere with a radius r. 

Wertheim s formulation of his SSC approximation, which we have already discussed in the context of nonpolarizable fluids in Sections II and III, applies to the more general case of polar-polarizable fluids. In describing this case we use his notation. For polarizable dipolar hard spheres, the approximation is defined by the integral equations ... 

For dipolar molecules in which the quantity is appreciably greater than 3a, the whole problem concerning the sensitivity of the anomaly magnitude on the precise forms of a ij) and a ijk) is absent, since the anomaly magnitude will depend entirely on the dipole moment magnitude in the absence of polarizability. Let us take the special case of nonpolarizable dipolar spheres for simplicity. Then the virial theorem yields... 

Simplified Form. Consider first a nonpolarizable point dipole px (solute molecule) located at the center of a sphere of radius a and dielectric constant one which is immersed in a medium of bulk dielectric constant (b. The electrostatic contribution to the chemical potential Pchem of the dipole is given by Kirkwood s (8) Equation 14. 

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