Application of a One-Dimensional Model

In Sec. 2.5, we introduced two 1-D models for water. The two models are almost equivalent in their capacity to unveil the molecular reasons for the outstanding properties of liquid water. Extending the application of these two models for aqueous solutions shows that while the primitive model fails to show large negative anomalous entropy and enthalpy of solvation of inert solutes, the primitive cluster succeeds. The reason is that the entropy and enthalpy of solvation of a solute in water are due to the capability of the solute to induce structural changes in the solute. In the TD primitive model, one could not achieve that effect, not because of any deficiency of the model but because of the assumption of nearest-neighbor interactions only. 

In order to produce large negative entropy and enthalpy of solvation, one needs to find a mechanism by means of which a solute can stabilize or enhance the formation of hydrogen bonds. This could have been achieved in the primitive model by introducing second nearest-neighbor interactions for triplets of water-solute-water in such a way that when the two water molecules are hydrogen bonded, the in-between solute molecule will stabilize the triplet, and hence enhance the formation of hydrogen bonds across the solute. This is shown schematically in Fig. 3.21. 

In Fig. 3.21a, we show the primitive model for water. If we place a solute (dark circle) between two hydrogen-bonded molecules, then the hydrogen bond energy between these two molecules will not be counted in the partition function. This is a result of using only pairwise interactions between pairs of consecutive water molecules. In real liquid water, we assume that a solute can penetrate a hole within the hydrogen-bonded network of water molecules without breaking the hydrogen bonds. 

in order to achieve a stabilization of clusters in the primitive model, we have to introduce three-body potentials. The addition of three-body potentials in the primitive model would have rendered the solution of the 1-D partition function impossible. Instead, the primitive cluster model takes into account all the hydrogen bondings as part of the internal function of the cluster. The very design of the primitive cluster model (Fig. 3.21b) is such that when a solute penetrates in between the hydrogen-bonded molecule it leaves the hydrogen bond intact. Therefore, a solute penetrating a hole within a cluster is expected to stabilize the cluster, i.e. it will shift the equilibrium towards formation of more hydrogen bonds. 

In the next section, we show some results for the solvation of hard rods HRs) in the primitive model. This is important since the primitive model can show the low solubility of HRs 

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