Water nearest neighbor distribution

In the CHS model only nearest neighbors interact, and the interactions between amphiphiles in the simplest version of the model are neglected. In the case of the oil-water symmetry only two parameters characterize the interactions b is the strength of the water-water (oil-oil) interaction, and c describes the interaction between water (oil) and an amphiphile. The interaction between amphiphiles and ordinary molecules is proportional to a scalar product between the orientation of the amphiphile and the distance between the particles. In Ref. 15 the CHS model is generalized, and M orientations of amphiphiles uniformly distributed over the sphere are considered, with M oo. Every lattice site is occupied either by an oil, water, or surfactant particle in an orientation ujf, there are thus 2 + M microscopic states at every lattice site. The microscopic density of the state i is p.(r) = 1(0) if the site r is (is not) occupied by the state i. We denote the sum and the difference of microscopic oil and water densities by and 2 respectively and the density of surfactant at a point r and an orientation by p (r) = p r,U(). The microscopic densities assume the values = 1,0, = 1,0 and 2 = ill 0- In close-packing case the total density of surfactant ps(r) is related to by p = Ylf Pi = 1 - i i. The Hamiltonian of this model has the following form [15]... 

This function is the integrally normalized probability for each water molecule being oriented such that it makes an angle B between its OH bond vectors and the vector from the water oxygen to the carbon atom. This function is calculated for those molecules within 4.9 A of the carbon atom (nearest neighbors), as this distance marks the first minimum in the pair distribution function for that atom. The curve in Figure 10 is typical for hydrophobic hydration (22). 

When Ru-red was used as a catalyst in the presence of a large excess of Ce(IV) oxidant (Scheme 19.1), the rate of 02 evolution was first order with respect to the catalyst concentration, showing that Ru-red is capable of 4-electron oxidation of water. By the decomposition of the Ru-red, N2 was formed its formation rate was second order with respect to the catalyst concentration, showing that the decomposition is bimolecular. The decomposition distance in a polymer (Nafion) matrix was estimated by assuming the random distribution of the catalyst molecule in the matrix. The probability density P(r) of the distance between the nearest neighbor molecules (r nm) is represented by Eq. (19.5) according to the Poisson statistics... 

Computer simulations (Mmite Carlo method and molecular dynamics calculations have been used to analyze the stmcture of water. According to these studies, water is made up of a continuous distribution of associates. The pair interaction between nearest neighbor molecules should not be thought of as either... 

The correlation volume was not accounted in the Butler s scheme. Butler s scheme for dissolution in water accoimted only for the formation of a cavity, introduction of the solute molecule in that cavity, and its interactions with the nearest-neighbor water molecules. He assumed, however, that the water molecules are distributed around a solute molecule as randomly as in its absence. One more step should be added, namely, the formation of a hydrophobic layer of volume around the cavity, in which the water molecules are reorganized and are no longer randomly distributed (Figure 2). While this layer is similar to that suggested by Frank and Evans in their iceberg ... 

Several structural properties are typically monitored to characterize water in these systems. Some of these are the density distribution of water molecules with respect to the surface, surface area per water molecule, the root-mean-square displacements from the optimal surface positions for corrugated surfaces, angular distributions of the dipolar and O—H bond vectors with respect to the surface normal, and moments of the angular distributions. Most of these characterize the water structure with reference to the metal surface. In contrast, the radial distribution function, number of nearest neighbors per molecule, and number of hydrogen bonds per molecule are used to characterize water-water interactions. 

---