Water Bernal-Fowler model

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 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. ... 

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. 

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]. 

As water is a unique liquid, so is amorphous silica a unique solid. They are much alike, both consisting mainly of oxygen atoms with the smaller hydrogen or silicon atoms in the interstices. As pointed out by Weyl and Marboe (2), Some properties of water and silica are so similar that the transition between hydrated silicic acids and the aqueous matrix is a gradual one. Washburn (3) noted that water and amorphous silica both have a temperature of minimum. volume. Ephraim (4) observed another similarity between silica and water in that water is much less dense than e, pected from close packing of the constituent atoms and from X-ray diffraction studies. Bernal and Fowler (5a) concluded that water molecules are arranged in a rather open structure like quartz, and undcrcooled water has a still ifiore open structure, like tridymite. Another model has been proposed by Weres and Rice (5b). 

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