Bound surface charge density

In the static case with no leakage across the membrane, there is no current flow inside or outside the cell. At the inside membrane, a surface charge density of free ions neutralizes the electric field in the membrane plus the double layer charges, so that the eeU interior has E = 0 and no current flow. There is electroneutrality in the bulk, but surface charges at the interphase. The intracellular bulk volume has a potential, but zero electric field strength. The membrane has a bound surface charge density qsb, which wfll reduce the membrane E-field to (qgf — qsb)/eo- Thus, the E-field in the membrane is less than the potential difference divided by the membrane thickness. 

Some of the functional groups (e.g., OH) on the clay surface exhibit electrical charges. The magnitude of the electrical charge, as well as its character, are controlled by the properties of the surfaces to which the functional groups are bound and by the composition of the surrounding hquid. Sposito (1984) classified the surface charge density of soils as follows ... 

Intrinsic surface charge density, defined by the number of Coulombs per square meter bound by surface functional groups, either because of isomorphic substitutions, or because of dissociation/protonation reactions. 

A more realistic calculation is presented in Fig. 5b, which implies that there is a surface charge density generated by the dissociation of surface groups. Assuming that the cations can be bound to N negative sites per unit area, the dissociation equilibrium provides the expression ... 

When a polymer simply contains ionic salts that are not bound covalently to the polymer chains themselves, e.g. tetraalkylammonium toluenesulphonate, the situation is more complicated, because ions of both sign are mobile and are available for transfer. The magnitude of the net charge transferred will then depend on the relative transfer aptitude of the two ions in the salt. Both of the ions tend to transfer in excessive amounts, which contaminates the second surface and produces a relatively low net surface charge density. 

Glosli and Philpott also analyzed the various contributions to the total electrostatic potential. Figure 24 shows, for the 1 m NaCl solution at a surface charge density of —4.6pCcm, the contribution of the free (ionic) charges and of the dipole, quadrupole, and octupole contributions from the bound (water) charges to... 

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. 

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