Models Extended Electrostatic

Figure 3. The photon as a rotating doublet (a) composite photon model—extended electron-positron pair rotating in x-y plane (b) electrostatic field of doublet—electrostatic force on a test particle at rest.

The PPD and shell models are nearly equivalent in this sense, because they model the electrostatic potential via static point charges and polarizable dipoles (of either zero or very small extent). Accuracy can be improved by extending the expansion to include polarizable quadrupoles or higher order terms.The added computational expense and difficulty in parameterizing these higher order methods has prevented them from being used widely. The accuracy of the ESP for dipole-based methods can also be improved by adding off-atom dipolar sites. 

F. J. Olivares del Valle and -M. A. Aguilar,/. Mol. Struct. (THEOCHEM), 280, 25 (1993). Solute-Solvent Interactions. Part 5. An Extended Polarizable Continuum Model Including Electrostatic and Dispersion Terms and Electronic Correlation in the Solute. 

The Electrolyte NRTL model " and the Extended UNIQUAC model" are examples of activity coefficient models derived by combining a Debye-Hiickel term with a local composition model. Equation of state models with electrostatic terms for... 

Figure 2. A schematic of the partitioning in the extended electrostatics model. The extended electrostatics model approximates the full electrostatic interaction by partitioning the electric potential and the resulting forces at atom i into a "Near" and an "Extended" contribution. The near contribution, arises from the charged...

The data in this table and of similar data sets provided by other authors (see Part II) have been interpreted with several degrees of sophistication in the simple model of electrostatic chemical shift When the data base is, however, extended to wide ranges of silica-to-alumina ratios, to other cations and to other microporous materials, the picture is less clear which is either due to inconsistent data acquisition (no single data source available) and/or to the breakdown of the simple shift analysis. 

The continuum treatment of electrostatics can also model salt effects by generalizing the Poisson equation (12) to the Poisson-Boltzmann equation. The finite difference approach to solving Eq. (12) extends naturally to treating the Poisson-Boltzmann equation [21], and the boundary element method can be extended as well [19]. 

On the assumption that = 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric field around an ion. Combined with the above-mentioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene-water and 1,2-dichloroethane-water interfaces. 

Similar instability is caused by the electrostatic attraction due to the applied voltage [56]. Subsequently the hydrodynamic approach was extended to viscoelastic films apparently designed to imitate membranes (see Refs. 58-60, and references therein). A number of studies [58, 61-64] concluded that the SQM could be unstable in such models at small voltages with low associated thinning, consistent with the experimental results. However, as has been shown [60, 65-67], the viscoelastic models leading to instability of the SQM did not account for the elastic force normal to the membrane plane which opposes thickness... 

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