Water, theories three dimensional models

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. 

It must be realized that a state must be reached where experiments and theory go hand in hand, leading to the development of better (more realistic) models, and acquisition of critical tracer data. In the absence of a knowledge of the processes involved, models employed often yield very erroneous results. Thus, whereas even a few tracer data are quite informative (since a few data points can be treated only with zero order models), any attempts to understand oceanic processes in detail pose a serious challenge. A few examples are considered here, where tracer data have contributed to the development of realistic models. As mentioned earlier, simple one-dimensional models were developed earlier on using two parameters K and w, to consider vertical transfer of tracers through an oceanic column. Even today these are used, in the absence of better alternatives, and in reality, because of a lack of tracer data in the three-dimensional space. The result is that as yet the general validity of the K-w models in space is not known or their dependence on climate. The latter arises because there are experimental tracer data for ocean waters only during the Holocene. 

To start, we consider one-dimensional diffusion model. This is not only because water diffusion into polymer matrix is the first step but the mathematics of two- and three-dimensional diffusion is more complicated. In fact, the results obtained from one-dimensional diffusion model has been practically used whenever diffusion kinetics under investigation. The kinetic models obtained from one-dimensional theory are enough to cover the kinetic models often used by most researchers in the world. Two- or three-dimensional diffusion follows the same principle. 

A. Kovalenko and F. Hirata. Self-consistent description of a metal-water interface by the Kohn-Sham density functional theory and the three-dimensional reference interaction site model. J. Chem. Phys. 110,1999, 10095-10112. 

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