Charges, excess electrostatic

This can be done when TV = TV which implies that q+ = q. = 0 for an overall neutral system, i.e. TV = TV = 0. But note that even for an overall charged system, i.e. a system where a net charge q has been introduced via, e.g. a van de Graaf machine, the excess electrostatic energy is ... 

The non-zero, in general, value of e Pw-e PR in Equation (7.18) implies that there are net surface charges on the gas exposed electrode surfaces. These charges (q+,q.) have to be opposite and equal as the cell is overall electrically neutral and all other charges are located at the metal-solid electrolyte interfaces to maintain their electroneutrality. The charges q+=-q. are quite small in relation to the charges, Q, stored at the metal-electrolyte interface but nevertheless the system has, due to their presence, an excess electrostatic energy ... 

If these postulates hold, excess electrostatic charges will be created in most cases when metal oxides form chemical bonds with one another. Excess negative charges would produce Br0nsted acids positive charges would produce Lewis acids. 

The structure-reactivity relationship for polyamine derivatives in activated ester hydrolysis was previously established [46]. Polyvinylamine (PVA), linear (LPEI) and branched (41% branching) polyethylene imine (BPEI) as well as their dodecyl- and imidazole-substituted derivatives with an approximate and equal degree of substitution (16-20%) were applied as catalysts. The compoundsp-NPA and 4-acetoxy-3-ni-trobenzoic acid (ANBA) as well as some of their homologues were used as substrates. At an excessive catalyst concentration relative to the substrate concentration, reactions proceeded at pseudo first order. In each series of polymers, the reaction rate constant was increased considerably by substitution of dodecyl (hydrophobic site) by imidazolyl (catalytic center) and when a charged substrate (electrostatic effect) was employed. At an equal degree of substitution, the catalytic activity increased in the following order LPEK PVA < BPEI. 

The titration curve of Figure 4 satisfies the Henderson-Hasselbach equation and our Equation (15). The slopes of the lines representing vs F or vs a are practically equal to the theoretical value of /2.3 kT= 17.8 V predicted by (9) and (15). The conclusion expressed by the second Equation (14) is verified e.g. the excess electrostatic partial free energy of an anionic site may then be taken as equal to ze4>Q where is the potential at the charged sites. It may be related also to the measured surface potential of the monolayer even when the distribution of the counterions is ignored. This is not allowed for polyelectrolytes membranes, solutions or gels for which neither the distribution of the fixed charged sites nor the potential shift be measured. 

An additional method for increasing particle size deserves mention. When a precipitate s particles are electrically neutral, they tend to coagulate into larger particles. Surface adsorption of excess lattice ions, however, provides the precipitate s particles with a net positive or negative surface charge. Electrostatic repulsion between the particles prevents them from coagulating into larger particles. 

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