Water clustering concept

Recently we have proposed a decomposition scheme of inter-molecular interaction energy in polyhedral water clusters. Central to the scheme is the concept of effective pair interaction energy (effective H-bond energy). In additive approximation, the interaction energy of any molecular system is equal to the sum of all pair interactions. The effective energy of pair interaction (effective energy of H-bond) is... 

Water absorbed in polymers is important for mechanical, electrical and other physical properties. For proteins water is by far the most important solvent. It interacts so strongly with proteins that this water is commonly referred to as bound water. These concepts must, however, be critically examined in order that the molecular properties can be understood. Such questions as what the order is in these water clusters and how far they extend, need to be answered. 

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. 

We refer the interested reader to the literature [51, 73, 80-86] for the use of Kriging in the construction of QCTFF. Here we can only afford three general remarks. Firstly, we know that three of the four types of energy contributions described above can be Kriged successfully for aU 20 amino acids, cholesterol, small carbohydrates and small water clusters (also in the presence of a cation) and a few pilot systems (NMA, ethanol, water, etc.). Proof-of-concept of successful Kriging of the dynamic correlation energy contribution still needs to be obtained but we do not expect any fundamental problems. 

Mauritz et al., motivated by these experimental results, developed a statistical mechanical, water content and cation-dependent model for the counterion dissociation equilibrium as pictured in Figure 12. This model was then utilized in a molecular based theory of thermodynamic water activity, aw, for the hydrated clusters, which were treated as microsolutions. determines osmotic pressure, which, in turn, controls membrane swelling subject to the counteractive forces posed by the deformed polymer chains. The reader is directed to the original paper for the concepts and theoretical ingredients. 

One of the limitations of this model is that the confinement of water molecules within clusters precludes its use within the context of water transport simulation because cluster-connective hydration structure is absent. Furthermore, water activity and contractile modulus are macroscopic based concepts whose application at the nanoscopic level is dubious. P is represented by a function borrowed from macroscopic elastic theory that contains E, and there is no microstructure-specific model for the resistance to deformation that can be applied to Nation so that one is forced to use experimental tensile moduli by default. 

It was also observed, in 1973, that the fast reduction of Cu ions by solvated electrons in liquid ammonia did not yield the metal and that, instead, molecular hydrogen was evolved [11]. These results were explained by assigning to the quasi-atomic state of the nascent metal, specific thermodynamical properties distinct from those of the bulk metal, which is stable under the same conditions. This concept implied that, as soon as formed, atoms and small clusters of a metal, even a noble metal, may exhibit much stronger reducing properties than the bulk metal, and may be spontaneously corroded by the solvent with simultaneous hydrogen evolution. It also implied that for a given metal the thermodynamics depended on the particle nuclearity (number of atoms reduced per particle), and it therefore provided a rationalized interpretation of other previous data [7,9,10]. Furthermore, experiments on the photoionization of silver atoms in solution demonstrated that their ionization potential was much lower than that of the bulk metal [12]. Moreover, it was shown that the redox potential of isolated silver atoms in water must... 

Cluster Theories. Historically, the most important study of water structure based on the existence of clusters was Stewart s x-ray diffraction work (142). In his theory, clusters ( cybotactic swarms ) were postulated to exist, each containing on the order of 10,000 water molecules. Although this constituted an apparently reasonable theory at the time, this view has now yielded to the concept of clusters of considerably smaller sizes. It is interesting to note that without much critical analysis, Frenkel (57) viewed Stewart s theory of water as essentially correct. In fact, Frenkel apparently expected that further work on liquid structures in general would be along the lines Stewart advocated. Luck has discussed this in some detail (100). Subsequent to Stewart s papers, Nomoto (113) discussed a water model, based on ultrasonic studies, involving clusters of several thousand water molecules. 

A theory of water structure involving clusters somewhat similar to the original Nemethy-Scheraga concept has been advocated recently by Luck (101). In his theory, the number of water molecules in the clusters near the freezing point may exceed 100 and, in fact, may approach 700. 

Makogon (1974) was the first to incorporate the above concepts into a hydrate nucleation mechanism, indicating that water molecules cluster with a decrease in temperature. 

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