Water Nemethy-Scheraga model

Figure 1.5. (a) Hydrogen-bonded open tetrahedral structure of ice (Gray, 1973). (b) Frank-Wen flickering cluster model of liquid water (Nemethy and Scheraga, 1962). 

Nemethy G, Scheraga HA (1962) A model for the thermodynamic properties of liquid water. J Chem Phys 36 3382-3400... 

G. Nemethy and H. A. Scheraga, /. Chetn. Phys., 36, 3401 (1962). Structure of Water and Hydrophobic Binding in Proteins. 2. Model for Thermodynamic Properties of Aqueous Solutions of Hydrocarbons. 

Nemethy, G., Scheraga, H. A. (1962). Stmcture of water and hydrophobic bonding in proteins. II. Model for the thermodynamic properties of aqueous solutions of hydrocarbons. Journal of Chemical Physics, 36, 3401-3417. 

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. ... 

It is known that the main specific property of pure liquid water as compared to the other solvents consists in its being highly structured. Innumerable models of the water structure, enumeration, and classification of these models are proposed in the literature (see, e.g.,14)). Some of these models such as the one suggested by Samoilov 15) or the one advanced by Nemethy and Scheraga 16) have greatly influenced the concepts of the water structure some of the other models, as Naberukhin 17) wittily puts it, have demonstrated rather inexhaustible imagination of their authors. The basic limitation of all of these models is due to their qualitative character. It means 17) that the main statements and concepts of these models are in requirement of quantitative specification and that their quantification remains basically unsupported by the primary principles of statistical physics. 

G. Nemethy and H, A. Scheraga, J. Chem. Phys., 36, 3382 (1962), The Structure of Water and Hydrophobic Bonds in Proteins. 1. A Model for the Thermodynamic Properties of Liquid Water. G. Nemethy and H. A. Scheraga, ]. Chem. Phys., 36, 3401 (1962). The Structure of Water and Hydrophobic Bonds in Proteins. II. Model for the Thermodynamic Properties of Aqueous Solutions of Hydrocarbons. 

In order to account for some of the differences in thermodynamic properties of H2O and D2O, theoretical studies have been applied. Swain and Bader first calculated the differences in heat content, entropy, and free energy by treating the librational motion of each water molecule as a three-dimensional isotopic harmonic oscillator. Van Hook demonstrated that the vapor pressure of H2O and D2O on liquid water and ice could be understood quantitatively within the framework of the theory of isotope effects in condensed systems. Nemethy and Scheraga showed that in a model based on the flickering cluster concept, the mean number of hydrogen bonds formed by each water molecule is about 5% larger in D2O than in H2O at 25 °C. 

G. Nemethy and G. H. Scheraga, "Structure of Water and Hydrophobic Bonding in Proteins. I. A Model for< the Thermodynamic Properties of Liquid Water," /. Phys, Chem., 36 3382 (1962). 

The theory of Nemethy and Scheraga (1962) was based on the model of Franck and Wen (1957) furthermore, these researchers assumed that liquid water is composed of a mixture of monomers and clusters of uniform size. The size of the clusters, their proportion in the liquid, and the thermodynamic properties of liquid water were computed as a function of temperature by a statistical thermodynamic treatment. In a more recent analysis, Hagler and co-workers (1972,1973), Lentz and co-workers (1974), Owicki and co-workers (1975) used a similar model of liquid water, but they assumed that water consists of a continuous distribution of all possible cluster sizes in equilibrium. They calculated a median cluster size of 11.2 at 0°C and they did not find significant numbers of large clusters. 

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