The Pauling model and its solution

The system consists of water molecules at a some temperature T and pressure P. A total of Nl molecules participate in the formation of a regular lattice with a well-defined structure, which for our purposes need not be specified. [It may be an ice If, structure as in the Samoilov (1957) model, or a clathrate type of structure as in the Pauling (1960) model.] The lattice is presumed to contain empty spaces, or holes. We let Nq be the number of holes per lattice molecule, i.e. NqNl is the total number of holes formed by Ni lattice molecules. We assume that the system is macroscopically large, so that surface effects are negligible hence, Nq is considered to be independent of Ni. In the case of ice If, we have Nq = j. Each hole is surrounded by 

12 molecules, but each molecule participates in six holes hence, the number of holes per lattice molecule is j. 

The remaining Nh = Nu, — Ny molecules are assumed to occupy the holes and may be referred to as interstitial molecules.A schematic illustration of such a model in two dimensions is shown in Fig. 2.6. 

To keep the complexity of the model at a minimum, we require the following simplifying assumptions (i) All the holes have the same structure, (ii) A hole can accommodate at most 

Clearly, the condition Nh NqNl must be satisfied. Alternatively, the mole fraction of interstitial molecules is restricted to vary between the limiting values  

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