Hardness, partial charge model

Because of its many approximations, and mostly because it contains no concentration or structural considerations, the model is unable to provide quantitative information and may in no circumstance be a substitute for thermodynamic data. When structural issues such as the presence of multiple bonds are likely to affect the reactivity of a species, the model should be used with extreme care. In addition, the analysis of hydrolysis and condensation reactions with the partial charges model would require modifying the hardness value for each cation. This is also true for the study of complexation, which may only be treated from an extremely qualitative standpoint. However, qualitative information is better than no information at all. 

It is important to realize that the Self-Avoiding MIDCO approach is not a fuzzy set version of a hard surface contact model. If various parts of a macromolecule are placed side by side, then the electronic density charge clouds mutually enhance each other due to their partial overlap, resulting in an actual shape change of these electron density clouds. The various MIDCOs G(K,a) experience significant swelling due to this overlap. The merger of the local parts of the MIDCO actually occurs at a point r that would fall on the outside of each individual MIDCO part without the presence of the other MIDCO part. 

In many physically important cases of localized adsorption, each adatom of the compact monolayer covers effectively n > 1 adsorption sites [3.87-3.89, 3.98, 3.122, 3.191, 3.214, 3.261]. Such a multisite or 1/n adsorption can be caused by a crystallographic Me-S misfit, i.e., the adatom diameter exceeds the distance between two neighboring adsorption sites, and/or by a partial charge of adatoms (A < 1 in eq. (3.2)), i.e., a partly ionic character of the Meads-S bond. The theoretical treatment of a /n adsorption differs from the description of the 1/1 adsorption by a simple Ising model. It implies the so-called hard-core lattice gas models with different approximations [3.214, 3.262-3.266]. Generally, these theoretical approaches can only be applied far away from the critical conditions for a first order phase transition. In addition, Monte Carlo simulations are a reliable tool for obtaining valuable information on both the shape of isotherms and the critical conditions of a 1/n adsorption [3.214, 3.265-3.267]. 

Fig. 6-26. For the hard sphere model on metal electrodes (a) interfacial dipole induced by adsorbed water molecules and (b) interfadal dipole induced by contact adsorption of partially ionized bromine atoms. - 6 = charge number of adsoihed particle (z ). [From Schmickler, 1993.]...

To move beyond the primitive model, we must include a molecular model of the solvent. A simple model of the solvent is the dipolar hard sphere model, Eq. (16). A mixture of dipolar and charged hard spheres has been called the civilized model of an electrolyte. This is, perhaps, an overstatement as dipolar hard spheres are only partially satisfactory as a model of most solvents, especially water still it is an improvement. 

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