Interstitial model For water

Raman spectra). The lifetime of the clusters is of the order 10"n to 10-12 s, so that by superimposing many representations of the V-structure we obtain the D-structure. The co-operative hydrogen bonding may be one reason for the differences between relaxation times obtained by different techniques (Frank, 1973) so comparison between experiment and theory is not straightforward. However, X-ray scattering data show that water does not exist as distinct patches of dense and bulky water. Consequently considerable interest has been shown in interstitial models for water (Samoilov, 1965). 

Fig. 2.6 A schematic description of a two-dimensional interstitial model for water. The lattice molecule occupies the vertices of the hexagons. The interstitial water molecules occupy the holes in the lattice.

Application of an Interstitial Model for Water to Aqueous Solutions... 

In this section, we extend the application of the interstitial model for water to aqueous solutions of simple solutes. This is the simplest model that contains elements in common with similar models worked out by various authors. This model can be solved exactly, and therefore, various general results of the mixture-model formalism can be obtained explicitly. In this respect, this model has also pedagogical value. 

In Chapters 6 and 7, we discuss some aspects of the interstitial models for water. These may be classified formally as lattice models. However, in our application, we shall stress the mixture-model aspect, rather than the lattice aspect of the model. 

Samoilov (1946, 1957) advocated the idea that liquid water could be viewed essentially as ice 4 j with part of its cavities being filled by water molecules. This model may be referred to as an interstitial model for water. Numerous further developments of this model have taken place, due especially to Russian scientists (Yashkichev and Samoilov, 1962 Samoilov, 1963 Gurikov, 1963, 1965, 1966, 1968a, 1968b Krestov, 1964 Vdovenko et aL, 1966, 1967a, 1967b Mikhailov, 1967, 1968 and Narten et aL, 1967). 

Fig. 6.15. Schematic illustration of an interstitial model for water in two dimensions. L-cules are molecules that build up the lattice, whereas the //-cules hold interstitial sites in the lattice.

In this section, we formulate the general aspect of the application of the simplest mixture-model (MM) approach to water. We shall use an exact two-structure model (TSM), as introduced in Section 6.8. In the next section, we illustrate the application of a prototype of an interstitial model for water to solutions and, in Section 6.7, we discuss the application of a more general MM approach to this problem. 

FIGURE 7.12. Schematic illustration of an interstitial model for water in two dimensions. 

We extend here the application of the interstitial model for water (section 7.9) to aqueous solutions of simple solutes. The merits of this model are essentially the same as those discussed in section 7.9. As before, we only outline the derivation of the various thermodynamic quantities and leave the details to the reader. 

In the Frank-Samoilov model for water, (H20)d describes molecules which are interstitial guests in die (H20)b system, the actual structure of which is not specified. It may be based on, for example, pentagonal dodecahedra (p. 226) or on ice-Ih (p. 224), the latter idea being currently favoured especially for water at low temperatures. Calculations indicate that 20% of the water exists in the interstitial form. 

Lattice models for liquids are rarely used nowadays. The same is true of lattice models for water. Nevertheless, the model presented in this section is of interest for three reasons First, it presents a prototype of an interstitial model having features in common with many models proposed for water and used successfully to explain some of the outstanding properties of water and aqueous solutions. Second, this model demonstrates some general aspects of the mixture model approach to the theory of water, for which explicit expressions for all the thermodynamic quantities in terms of molecular properties may be obtained. Finally, the detailed study of this model has a didactic virtue, being an example of a simple and solvable model. 

Over the years, a large number of models of water structure have been developed in an attempt to reconcile all the known physical properties of water and to arrive at a molecular description of water that accounts correctly for its behavior over a large range of thermodynamic conditions. Early models of water structure have been categorized by Fennema (1996) and Ball (2001) into three general types mixture, uniformist, and interstitial. Mixture models are based on the concept of intermolecular hydrogen bonds... 

The model presented in this section is of interest for three reasons. First, it is the simplest interstitial model having features in common with many models proposed for water and used successfully to explain some of the outstanding properties of water and aqueous solutions. Second, this model may be viewed either... 

We conclude this section with a general comment on interstitial models. The study of such models is useful and quite rewarding in providing us insight into the possible mechanism by which water exhibits its anomalous behavior. One should be careful not to conclude that the numerical results obtained from the model are an indication of the extent of the reality of the model. It is possible, by a judicious choice of the molecular parameters, to obtain thermodynamic results which are in agreement with experimental values measured for real water. Such agreement can be achieved by quite different models. The important point is not the quantitative results of the model but the qualitative explanation that the model offers for the various properties of water. We shall use the same model in Sec. 3.6 to explain some aspects of aqueous solutions of simple solutes. 

---