Bernal-Fowler model

More recently there have been some modifications in the model, and the mathematical treatments have been considerably improved. Kirkwood (1111) used the Bernal-Fowler model and devised a statistical method to Eillow for near neighbors. Pople (1659) allowed for bending H bonds of the type shown in Fig. 8-1. Harris and Alder applied to Pople s model a statistical mechanical treatment which attempts a precise evaluation of distortion polarization (877). The calculated results are shown in Table 2-III, and in Fig. 2-1 they are compared with experimental values. These changes correct for failures of the simplest dipole picture, and as more of them are added the principal appeal of the electrostatic model—simplicity—tends to be lost. 

The Bernal-Fowler-Pauling statistical model for the proton arrangements in ice presents a very subtle problem in the actual evaluation of the number of possible configurations in a macroscopic crystal. This is not just an academic exercise for, if we suppose there are configurations, all of which are equally likely, then the entropy of the system due to this cause is k In Further, if these configurations become frozen at some temperature where the disordering is still essentially complete, the measured entropy of the ice crystal will still have the residual value In at o °K, entropy from all other sources having vanished. 

It is a rather surprising fact that the numerical magnitudes quoted in this table are hardly changed from the original estimates of Bernal and Fowler [15], It is true that the physical model has with... 

Figures 2.3a,b show the model of Bernal and Fowler (1933) for the water molecule. The molecular geometry is well known (Benedict et al 1956) from rotational and vibrational spectra. The oxygen atom has eight electrons, and has the electronic configuration ls22s22p4. Each hydrogen atom has a Is1 electron these electrons are shared with two bonding electrons of oxygen, to constitute the water molecule.

In 1954 Weiss32 used Bernal and Fowler s simplified solvation model,16 with an Inner Sphere of ionic coordination, i.e., a small spherical double layer around the ion of charge ze, followed by a sharp discontinuity at radius q, the edge of the Outer Sphere or Dielectric Continuum. He used a simple electrostatic argument to determine the energy to remove an electron at optical frequency from the Inner Sphere ... 

In 1933 Bernal and Fowler showed that many of the properties of water can be explained with the aid of a model containing much local order and structure (199). These pioneering workers did not name the intermolecular linkage in their proposed structure, but it is now recog-... 

The number of models that describe the structure and properties of liquid water is enormous. They can be subdivided into two groups the uniform continuum models and the cluster or mixture models. The main difference between these two classes of models is their treatment of the H-bond network in liquid water whereas the former assumes that a full network of H-bonds exists in liquid water, in the latter the network is considered broken at melting and that the liquid water is a mixture of various aggregates or clusters. The uniform continuum models stemmed from the classical publications of Bernal and Fowler, Pople, and Bernal.Among the cluster or mixture models, reviewed in refs 2—6 and 12, one should mention the models of Samoilov, Pauling, Frank and Quist, and Nemethy and Scheraga. ... 

In electrochemical proton transfer, such as may occur as a primary step in the hydrogen evolution reaction (h.e.r.) or as a secondary, followup step in organic electrode reactions or O2 reduction, the possibility exists that nonclassical transfer of the H particle may occur by quantum-mechanical tunneling. In homogeneous proton transfer reactions, the consequences of this possibility were investigated quantitatively by Bernal and Fowler and Bell, while Bawn and Ogden examined the H/D kinetic isotope effect that would arise, albeit on the basis of a primitive model, in electrochemical proton discharge and transfer in the h.e.r. 

Fast proton mobility in water attracted theoretical attention early, beginning with the works of von Grotthuss [7], at a time when the existence of the proton was not known, the chemical formula of water not settled, the notion of molecules was new, and little was known about the electricity laws. Modern landmarks were set by Bernal and Fowler [85], Eigen and de Mayer [86], Conway et al. [87], and Zundel and Metzger [88]. This was followed by more detailed molecular mechanisms, and analytical and computational models, see [68,77,79,84,89-93] and a conceptual essay by Agmon [ 1 ] which stimulated a new round of activities in this area. 

As we indicated above, the pair potential between two water molecules is a complicated function of the distance R and the five orientation angles. The exact analytical form of this pair potential is not known.Earlier models of water were proposed by Bernal and Fowler (1933), Verwey (1941), Bjerrum (1951), Stockmyer (1941), Rowlinson (1951), and others. All these failed to reproduce the characteristic radial distribution of water (see Sec. 1.4.5). What one usually uses in the theory of water is not the true pair potential but an effective pair potential consisting of essentially three parts, which we write as... 

Perhaps the most extensive use of the idea of a mixture model for water and aqueous solutions was published by Bernal and Fowler (1933). They assumed that water consists of three different intermolecular arrangements, meaning three different structures or different components ice-tridymite-like at low temperatures, quartz-like at higher temperatures, and ammonialike at temperatures higher than 200°C. This was the first mixture model where the structures of the components were explicitly described. 

Finally, Bernal and Fowler calculated the heat of sublimation from the model sketched above and found a value of 11.5 calories per mol, whereas the experimental value is 11.81. The attraction is to b 3 attributed essentially to the interaction of the dipoles. 

Pauling (1960) rejected the idea that liquid water contains a significant number of aggregates with quartzlike structures as proposed previously by Bernal and Fowler (1933). Instead, he proposed to view liquid water as a hydrate of itself. The idea is based on the well-known fact that molecules such as xenon, chlorine, and methane form clathrate compounds with water having a well-defined crystalline structure [for details, see Pauling (1960) and Frank and Quist (1961)]. Why not assume, then, that the same structure could host a water, instead of a nonelectrolyte, molecule Frank and Quist (1961) undertook a quantitative development of Pauling s model [the essential features of their treatment, as well as a similar one by Mikhailov (1967), are discussed in detail in the next section]. 

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