Selected results for the primitive cluster model

In this section, we present some results on the cluster-size distribution and related quantities. The calculations are performed for the following set of parameters  

More detailed temperature dependence for each type of cluster is shown in Fig. 2.30. As expected, the mole fraction of the monomers increases monotonically as a function of T, eventually reaching X(l) = 1 at high temperatures. 

The overall structural changes in this system are captured by the quantity (Xhb). This is the analog of the average number of HBs per particle, as discussed in Sec. 2.5.3, which in real liquid water is also a measure of the overall structure of the system. 

In order to gain insight into the molecular mechanism underlying the anomalous behavior of liquid water (as well as of aqueous solutions, discussed in Chapter 3), we need to examine the temperature and the pressure derivatives of the quantity (Xhb). To see this, it is sufficient to consider a simple two-structure model for water. Let xhb be the HBed component (or the icelike species in the traditional mixture-model theories of water). 

Structural changes induced by the change in the temperature. It is clear that these minima also occur in the ranges of T and P at which we have observed the anomalous temperature dependence of the volume, namely 2 T 3 and 4 P 9. (See Sec. 2.5.3. Note, however, that in Sec. 2.5.3 we studied the primitive model, but as we have pointed out the cluster model exhibits the same behavior as the primitive model). Once we increase the pressure beyond P 10, the system is highly compressed and the quantity 9(Xhb)/9T becomes positive, i.e. increasing the temperature causes an expansion from the close-packed structure into the open, HBed structure. 

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