Charge models

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

In contrast to the point charge model, which needs atom-centered charges from an external source (because of the geometry dependence of the charge distribution they cannot be parameterized and are often pre-calculated by quantum mechanics), the relatively few different bond dipoles are parameterized. An elegant way to calculate charges is by the use of so-called bond increments (Eq. (26)), which are defined as the charge contribution of each atom j bound to atom i. 

VVe therefore return to the point-charge model for calculating electrostatic interactions. If sufficient point charges are used then all of the electric moments can be reproduced and the multipole interaction energy. Equation (4.30), is exactly equal to that calculated from the Coulomb summation. Equation (4.19). 

I is the bond length. The experimental quadrupole moment is consistent with a charge, q, of approximately 0.5e. In fact, a better representation of the electrostatic potential around the nitrogen molecule is obtained using the five-charge model shown in Figure 4.20. 

Given the widespread use of the partial atomic charge model, it is important to consider how the charges are obtained. For simple species the atomic charges required to reproduce the... 

Two charge models for N2 with the electrostatic potentials that they generate. Also shown is the... 

In some cases the atomic charges are chosen to reproduce thermodynamic properties calculated using a molecular dynamics or Monte Carlo simulation. A series of simulations is performed and the charge model is modified until satisfactory agreement with experiment is obtained. This approach can be quite powerful despite its apparent simplicity, but it is only really practical for small molecules or simple models. 

Cox S R and D E Williams 1981. Representation of the Molecular Electrostatic Potential by a New Atomic Charge Model. Journal of Computational Chemistry 2 304-323. 

The ground-state electronic diagrams of some thiazolo dyes have been calculated with the use of theoretical model of fractional core charge model applied to PPP method (659). 

Ground state electronic diagram (Fractional core charge model within PPP framework) 43... 

Reverse osmosis models can be divided into three types irreversible thermodynamics models, such as Kedem-Katchalsky and Spiegler-Kedem models nonporous or homogeneous membrane models, such as the solution—diffusion (SD), solution—diffusion—imperfection, and extended solution—diffusion models and pore models, such as the finely porous, preferential sorption—capillary flow, and surface force—pore flow models. Charged RO membrane theories can be used to describe nanofiltration membranes, which are often negatively charged. Models such as Dorman exclusion and the... 

According to Eq. (13.52), saturation charge is directly proportional to the square of the particle diameter and the external electric field. Particle charging depends also on the composition of the particle, which is taken into account by the relative dielectric constant e,. It is worth noticing that the field charging model should not be applied for small particles (dp < 0.5 pm). 

The traditional unipolar diffusion charging model is based on the kinetic theory of gases i.e., ions are assumed to behave as an ideal gas, the properties of which can described by the kinetic gas theory. According to this theory, the particle-charging rate is a function of the square of the particle size dp, particle charge numbers and mean thermal velocity of tons c,. The relationship between particle charge and time according White s... 

FIGURE 13.14 Particle velocities in an electric field based on different charging models (E 2500 V/cm, nt = 10 s/cm ). 

A. E. Yaroshchuk, S. S. Durkhin. Phenomenological theory of reverse osmosis in macroscopically homogeneous membranes and its specification for the capillary charged model. J Memb Sci 79 133, 1993. 

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