Bernal and Fowler

The theory of the structure of ice and water, proposed by Bernal and Fowler, has already been mentioned. They also discussed the solvation of atomic ions, comparing theoretical values of the heats of solvation with the observed values. As a result of these studies they came to the conclusion that at room temperature the situation of any alkali ion or any halide ion in water was very similar to that of a water molecule itself— namely, that the number of water molecules in contact with such an ion was usually four. At any rate the observed energies were consistent with this conclusion. This would mean that each atomic ion in solution occupies a position which, in pure water, would be occupied by a water moldfcule. In other words, each solute particle occupies a position normally occupied by a solvent particle as already mentioned, a solution of this kind is said to be formed by the process of one-for-one substitution (see also Sec. 39). 

More complicated and less known than the structure of pure water is the structure of aqueous solutions. In all cases, the structure of water is changed, more or less, by dissolved substances. A quantitative measure for the influence of solutes on the structure of water was given in 1933 by Bernal and Fowler 23), introducing the terminus structure temperature, Tsl . This is the temperature at which any property of pure water has the same value as the solution at 20 °C. If a solute increases Tst, the number of hydrogen bonded water molecules is decreased and therefore it is called a water structure breaker . Vice versa, a Tsl decreasing solute is called a water structure maker . Concomitantly the mobility of water molecules becomes higher or lower, respectively. 

Table 9 compares ionic enthalpies of hydration from the Bernal and Fowler,164 Latimer et al.165 and Rashin and Honig88 procedures. Given the inherent uncertainty, the latter two sets of data are remarkably similar, considering that they were obtained 46 years apart. A number of tabulations of the thermodynamic solvation properties of ions in various solvents have now appeared. It is important to keep in mind, however, that there is a degree of arbitrariness associated with the experimental AHsoivation and AGSoiVation of individual ions. 

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... 

In this section, the structures of ice, water, and the hydrogen bond are based on the classical works of Bernal and Fowler (1933), Pauling (1935), and Bjerrum (1952), as well as the reviews of Frank (1970), and Stillinger (1980). These subjects are treated in comprehensive detail in the seven volume series edited by Franks (1972-1982), to which any student of water compounds will wish to refer. A second series of monographs on water, also edited by Franks (1985-1990), was published to update the earlier monograph series. Discussion on computer simulation studies of the structure and dynamics of water is largely based on the work of Debenedetti (1996, 2003). 

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 ... 

Since Bernal and Fowler,16 the charging radius r0 in the Born equation has been put equal to the Inner Sphere radius, or approximately the ion to water molecule center distance plus 1.4 A. At least for 1+ ions, this gives a fairly good approximation to the Gibbs energy of interaction of the ion with the outer Dielectric Continuum if aT and s are constant throughout the medium. High-valency ions are discussed in Section IV. 

The preceding description of the solvent surrounding an ion was used as the basis of a structural treatment of ion-solvent interactions initiated by Bernal and Fowler (1933). Their paper is a seminal one for much else in the structural picture of hydration (Section 2.4). 

Bernal and Fowler s calculation remains famous because it grappled for the first time with the structure of water and with ion-solvent interactions on a molecular basis. Better theories have been developed, but most have their roots in the Bernal and Fowler work of 1933. 

It is of interest to note that the lengthy and complex calculation Debye made was published in the same (first) edition of the Journal of Chemical Physics as an article by Bernal and Fowler, who first suggested several seminal concepts about the structure of water that are now commonly accepted in solution theory. The velocity amplitude is measured in cm s". It is the ratio of the pressure of the ultrasonic wave to the characteristic acoustic impedance of the media. 

There are a number of publications in the field of the structure of ionic solutions that are particularly seminal and although published half a century ago have great influence on present concepts. One of them is the paper by Bernal and Fowler in which the associated structure of water was first established (in 1933) from the interpretation of the original X-ray data on liquids. However, another paper of great importance is that by Hasted, Ritson, and Collie in 1948, for it was here that the dielectric properties of solutions were first reeorded on a large seale. In subsequent publications the relation of the dielectric constant of the solution and solvation was first investigated. 

The seminal work in this field was carried out by Kebarle and it is surprising to note the gap of 30 years between the foundation paper hy Bernal and Fowler on solvation in solution and the first examination of the simpler process of hydration in the gas phase. A series of plots showing the concentrations of various hydrate complexes for NafHjO) as a function of the total pressure of water vapor is given in Fig. 2.29. ... 

If one is going to consider protons actually jumping from one quasi-stationary water molecule to the next, the classical view would be to ask what fraction of them would be sufficiently activated to get over the top of the corresponding energy barrier. Another possibility was discussed not long after the introduction of quantum mechanics in 1928 by Bernal and Fowler. In a famous paper of 1933, they applied quantum mechanics to the possibility of tunneling through a barrier. 

A third approach to understanding the anomalous behavior of the nonconforming ion was provided by Bernal and Fowler in the paper mentioned earher. Their suggestion was that when the proton jumped from an... 

---