Apparent surface charge density

In the previous contributions to this book, it has been shown that by adopting a polarizable continuum description of the solvent, the solute-solvent electrostatic interactions can be described in terms of a solvent reaction potential, Va expressed as the electrostatic interaction between an apparent surface charge (ASC) density a on the cavity surface which describes the solvent polarization in the presence of the solute nuclei and electrons. In the computational practice a boundary-element method (BEM) is applied by partitioning the cavity surface into Nts discrete elements and by replacing the apparent surface charge density cr by a collection of point charges qk, placed at the centre of each element sk. We thus obtain ... 

An immediate consequence of the onset of spontaneous polarization in a body is the appearance of an apparent surface charge density and an accompanying depolarizing field ED as shown in Fig. 2.43(a). The energy associated with the... 

Therefore, the short-range interactions due to ion hydration do not modify qualitatively the double layer interaction, which remains repulsive at distances larger than the range of the interfacial interaction of the ions. The magnitude of the repulsion is, however, modified, since the relation between the true surface charge density a and the "apparent surface charge density a depends on AW, and hence on the specificity of the ions. 

Babic et al. [2] report a CIP of charging curves (25°C, 0.001-0.1 mol dm KNO3) at pH 7, for self synthesized active carbon obtained from carbonized viscose rayon cloth. Seco et al. [3] titrated commercial activated carbon at four different ionic strengths and attempted to determine the equilibrium constants of reactions (5.32) and (5.33) from these titrations. Only results obtained at extreme pH values (<3 or > 11) were used, thus the apparent surface charge densities were obtained as differences of two large and almost equal numbers. On the other hand, at pH 4-10 the titration curve of carbon suspension and the blank curve were practically identical. 

A number of new approximate, but accurate, analytical results are also presented here the most significant ones are (1) the extension of Gouy-Chapman theory to mixed electrolyte solutions whereby an effective counterion valence is introduced, (2) two approximate potential profiles for curved surfaces (one of them new) are generalized to include the presence of mixed electrolytes, (3) the apparent surface charge density for curved surfaces for which the Debye-Hiickel potential asymptotically matches the Poisson-Boltzmann profile, and (4) a unified treatment of two interacting charged surfaces. 

Equation [93] gives the Debye-Hiickel potential, based on an apparent surface charge density, which matches the nonlinear Gouy-Chapman solution far from a charged planar surface. The ADH//NLDH potential for a sphere is easily found from Eqs. [188], [187], and [300] ... 

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