Inner-surface charge density

Cjnn is the capacitance due to the inner layer, which can be experimentally obtained from the plot of 1/Ld (with Cd being the capacitance measured at a given charge density) for several electrolyte concentrations versus the calculated l/LG-ch at a constant surface charge density (Parsons and Zobel plot) [2]. If this plot is not linear, this is an indication that specific adsorption occurs. 

Artificial asymmetric membranes composed of outer membranes of various species of Gram-negative bacteria and an inner leaflet of various phospholipids have been prepared using the Montal-Mueller technique [65]. Such planar bilayers have been used, for example, to study the molecular mechanism of polymyxin B-mem-brane interactions. A direct correlation between surface charge density and self-promoted transport has been found [66]. 

The Poisson-Boltzman (P-B) equation commonly serves as the basis from which electrostatic interactions between suspended clay particles in solution are described ([23], see Sec.II. A. 2). In aqueous environments, both inner and outer-sphere complexes may form, and these complexes along with the intrinsic surface charge density are included in the net particle surface charge density (crp, 4). When clay mineral particles are suspended in water, a diffuse double layer (DDL) of ion charge is structured with an associated volumetric charge density (p ) if av 0. Given that the entire system must remain electrically neutral, ap then must equal — f p dx. In its simplest form, the DDL may be described, with the help of the P-B equation, by the traditional Gouy-Chapman [23-27] model, which describes the inner potential variation as a function of distance from the particle surface [23]. 

All other inner surfaces have uniform surface charge densities Z, as... 

The chemical interpretation of o-in measured by the Schofield method depends sensitively on the type and concentration of probe electrolyte used. If these properties are chosen so that the cation in the reacting electrolyte neutralizes precisely the exposed functional group charge associated with isomorphic substitutions and dissociated hydroxyls and so that the anion neutralizes only the exposed protonated functional groups, then q+ and q. will have optimal magnitude for the chosen pH value and CTjn will be truly an intrinsic surface charge density. On the other hand, if the cation in the probe electrolyte is not able to displace all of the native adsorbed cations in, e.g., inner-sphere surface complexes, or if the anion cannot displace all of the native anions bound to protonated functional groups, or if either ion does not form only neutral surface complexes in the soil clay, then Ojn will differ from its optimal value. 

A sufficient theoretical basis for the use of electrophoresis to measure the PZC, as discussed in Sec. 3.2, can be developed with Eq. 3.37 and the single assumption that the plane of shear coincides with the periphery of the surface complexes on a soil particle. Under this assumption, the vanishing of ctd at the PZC (Table 3.1) implies that the surface charge density on the plane of shear vanishes as well. This condition and its consequence, p x) = 0, then must also obtain on any plane beyond the plane of shear out into the mobile liquid phase, but Eqs. 1.13 and 3.26 applied to these planes lead to the conclusion that the inner potential, iif x), is equal to a constant everywhere in the mobile liquid phase. This constant may be set equal to zero, from which it follows that = 0 and that u in Eq. 3.37 vanishes at the PZC, as illustrated in Fig. 3.1, Thus it is not... 

A detailed model of the interfacial region requires the specification of the position of the plane where the diffuse ion swarm begins, A popular choice in the literature of soil chemistry has been jc = 0, which means that outer-sphere surface complexes are neglected entirely and inner-sphere surface complexes are ignored if they would protrude beyond the plane to which (Tin, the intrinsic surface charge density, refers. (See Secs. 1.5 and 3.1 for a discussion of trjn ) That this choice is not reasonable physically, however, can be seen from a simple calculation involving Eq. 5.16. Consider a 1 1 electrolyte at the concentration Cq == 100 mol m" and suppose that /r(0) = SRT/F, a value that is not unrealistic for a smectite siloxane surface. Then k = = 1.04 x 10 m" at 298 K, a =... 

Moreover, the charge-balance condition, Eq. 5.59, is imposed explicitly and the full DDL theory expression for cr = aj) is used. Note that Eqs. 5.58 and.5.59 are not consistent for arbitrary values of the surface charge densities and inner potentials unless ions are present in the plane under all circumstances. 

The relationships between surface charge density and inner potential are specified by expressions similar to Eq. 5.58 ... 

If E, and 2 are assumed to be constant. Eqs. [32[ and [33] predict a linear potential drop within each part of the inner double layer, as shown in Fig. (10b). The dependence of the electric potential with distance, in the region from x = d to the bulk solution, i.e, in the diffuse part of the double layer, will be exponential if the surface potential is moderate, as predicted by Eq. 124). In the case of higher surface potentials, the dependence is that shown in Eq. [26], substituting tpn by yj at X = ti. Similarly, the surface charge density, O is related to y by an equation of the type [28]. 

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