Application of an Exact Two-Structure Model TSM

The simplest version of the mixture-model approach and, in fact, the most useful one is the so-called two-structure model (TSM). We studied one specific example of a TSM in the previous section. Many ad hoc models of liquid water fall into the realm of the TSM [notable examples are those of Samoilov (1946), Hall (1948), Grjotheim and Krogh-Moe (1954), Pauling (1960), Wada (1961), Danford and Levy (1962), Krestov (1964), Marchi 

In this section, we lay the general foundation of the idea of the TSM for liquids, and particularly for liquid water. We explore both the usefulness and the limitations of this approach. Of course, because of its generality, we cannot expect to pursue the study to the point where comparison with experimental results is possible. This must be done by invoking a specific ad hoc model for the system. The latter may be viewed as an approximate version of the exact TSM, a topic which will concern us in the next section. 

Xjr may be referred to as the mole fraction of molecules with low (L) local density, and x as that of molecules with relatively high (H) local density. The new vector composed of two components (x, x ) is also a quasicomponent distribution function, and gives the composition of the system when viewed as a mixture of two components, which we may designate as L- and i7-cules. Starting with the same vector = ( c( )j c(1)j ) we may, of course, derive many other TSM s differing from the one in (6.73). A possibility which may be useful for liquid water is 

As a second example, consider the quasicomponent distribution function, based on the concept of binding energy (BE) (Section 5.2). We recall that the vector (or the function) x gives the composition of the system when viewed as a mixture of molecules differing in their BE. Thus, X (v) dv 

The above examples illustrate the general procedure by which we construct a TSM from any quasicomponent distribution function. From now on, we assume that we have made a classification into two components, L and H, without referring to a specific example. The arguments we use will be independent of any specific classification procedure. We will see that in order for such a TSM to be useful in interpreting the properties of water, we must assume that each component in itself behaves normally (in the sense discussed below). The anomalous properties of water are then interpreted in terms of structural changes that take place in the liquid. 

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