Intermolecular potentials cell theories

In view of the failure of the rigid sphere model to yield the correct isochoric temperature coefficient of the viscosity, the investigation of other less approximate models of the liquid state becomes desirable. In particular, a study making use of the Lennard-Jones and Devonshire cell theory of liquids28 would be of interest because it makes use of a realistic intermolecular potential function while retaining the essential simplicity of a single particle theory. The main task is to calculate the probability density of the molecule within its cell as perturbed by the steady-state transport process. 

As already emphasized, theoretical development in the area of aqueous binary mixtures has been comparatively slow and to date no satisfactory molecular theory exists that can describe the complex physical chemistiy of a binaiy solution. The reason is the complexity of the intermolecular potential. While binary mixtures have often been studied by using a cell or lattice theory (as we discussed in the description of a polymer solution in the Hydrophobic effects chapter), even such a description is hard here because of the amphiphilic nature of the solute. It is really hard to develop a quantitative theory that includes the two different types of local heterogeneity at two sides of a given solute molecule. 

The main problem with implementing the cell theory is that it derives the hydrate pressures in terms of quantities that are not well known. In particular, the intermolecular potentials needed to define the cavity potential are not precisely known, and depends on the property of a state that has never been observed (Le, the empty hydrate lattice). Inevitably, this means that a considerable amount of empirical parameterisation is required to implement the theory. 

The discussion in Section 3 highlighted one of the major difficulties in implementing any statistical mechanical theory. Although the statistical mechanics itself is rigorous, it requires as input the intermolecular potential, and that is never known exactly. In practice, it is not possible to treat the complete statistical mechanical problem, and so simplifying assumptions are usually introduced. For the cell theory this yields the following scheme... 

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