Primitive model for water

In Fig. 2.26b we show the pair correlation function for the primitive model for water (see Fig. 2.10d). Here, we see a strong peak at R = 2 corresponding to the HBing distance. The height of this peak diminishes as we increase the density while a new peak at R = 1 develops. At p = 0.6, the peak at R = 1 is even higher than the one at R = 2. Clearly, at this density the average intermolecular distance is smaller than R = 2, and hence the particles are more closely packed. 

The first comment refers to the work of Cho et al. (1996), who used an earlier version of the primitive model for water (the one referred to as the BNID potential in Fig. 2.10c). In their conclusion, the authors wrote It might be necessary, in order to reproduce the known temperature and pressure effects, to insert empirically the appropriate double-well feature into the water potential. (italics added)... 

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. 

Solvation of hard rods in the primitive model for water... 

In this approximation we find that most of the water molecules are in the = 4 state. The value of is probably too high. It should be noted that within the primitive model for water, the distribution of species depends only on the solvation Helmholtz energy of the arms and not on the solvation Helmholtz energy of the LJ, or the neon part. 

Clearly, the quantity A [xfi(v/R ) — a (v)] is the change in the average number of the V components induced by the addition of s. Therefore, the second term on the rhs of (7.11.9) may be interpreted as the contribution to AEf due to structural changes in the solvent. For liquid water, we may further identify this general concept of structural change with the particular concept of structural changes as defined in section 7.6. We simply use the definition of the primitive model for water molecules and obtain, for this special case,... 

The 1-D model for water described in this section is referred to as the primitive model. It has almost no other features but the principle of correlation between low local density and strong binding energy. This feature is built-in in the pair potential described in Sec. 2.5.2. A more complicated potential was published earlier as a textbook example and was shown to... 

The second model is a simplified version of a model by Lovett and Ben-Naim published in 1969. It is referred to as the primitive cluster model for water. This model produces the same results for water as the primitive model. However, it has two advantages. First, one can follow the molecular mechanism underlying the characteristic behavior of liquid water. Second, it... 

Fig. 2.9 (a) The primitive model and (b) the primitive cluster model for water-like particles in one dimension. In the latter, each sequence of bonded molecules is viewed as a different component. ... 

The primitive cluster model for water and its partition function... 

These two different points of view were explained in Sec. 2.5 in connection with the primitive and cluster-primitive onedimensional models for water. In the primitive model single water molecules are defined through their pair potential. The structure formed by these water molecules — clusters of HBed molecules — is a result of the specific pair potential. On the other hand, in the cluster primitive model, the structures — clusters of HBed molecules — are assumed to be a part of the description of the model, and the HBs are now part of the internal description of the clusters. 

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. 

We begin with some results on the effect of the solute on the distribution of cluster size. In all of the following discussions, the HB solvent refers to the primitive cluster model for water. 

Despite the simplifying assumptions in the derivation, such as assuming that the medium, water, is a continuum with no structure, and that the only work is electrostatic, and even more assumptions in calculating the properties of individual ions from the measured properties of electrolytes, as estimated by the Born function comes reasonably close to the measured Gibbs energy of ion solvation, as shown in Figure 6.7. Other thermodynamic properties such as the volume, entropy and enthalpy of solvation can also be obtained by appropriate differentiation of Equation (6.5). As a result, ever since its inception the Born equation has been used as a primitive model for the electrostatic contribution to the properties of an ion in a dielectric solvent. 

Another method of calculation developed by Adelman and applied by him to a model for a 1-1 electrolyte in water eives much smaller deviations from the primitive model. (19)... 

Issue is taken here, not with the mathematical treatment of the Debye-Hiickel model but rather with the underlying assumptions on which it is based. Friedman (58) has been concerned with extending the primitive model of electrolytes, and recently Wu and Friedman (159) have shown that not only are there theoretical objections to the Debye-Hiickel theory, but present experimental evidence also points to shortcomings in the theory. Thus, Wu and Friedman emphasize that since the dielectric constant and relative temperature coefficient of the dielectric constant differ by only 0.4 and 0.8% respectively for D O and H20, the thermodynamic results based on the Debye-Hiickel theory should be similar for salt solutions in these two solvents. Experimentally, the excess entropies in D >0 are far greater than in ordinary water and indeed are approximately linearly proportional to the aquamolality of the salts. In this connection, see also Ref. 129. 

There have been considerable efforts to move beyond the simplified Gouy-Chapman description of double layers at the electrode-electrolyte interface, which are based on the solution of the Poisson-Boltzmann equation for point charges. So-called modified Poisson-Boltzmann (MPB) models have been developed to incorporate finite ion size effects into double layer theory [61]. An early attempt to apply such restricted primitive models of the double layer to the ITIES was made by Cui et al. [62], who treated the problem via the MPB4 approach and compared their results with experimental data for the more problematic water-DCE interface. This work allowed for the presence of the compact layer, although the potential drop across this layer was imposed, rather than emerging as a self-consistent result of the theory. The expression used to describe the potential distribution across this layer was... 

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