Solids interfacial potential distributions

Figure 19. The electronic structure of an n-type semiconductor/electrolyte solution interface under conditions of free electron depletion at the surface. Shown are the conduction and valence band edges as a function of the distance from the surface. The interfacial potential drop is distributed over a region in the solid (depletion region, width 4c) and the molecular Helmholtz layer at the liquid side (not shown). The interfacial capacitance is represented by a series connection of the capacitance of the depletion layer (Csc) and the Helmholtz layer (Csoi).

The quantities or elements cpi and unit length (flcm ) corresponding to the whole electrode area A, and is an impedance length (flcm ). The overall impedance is isomorphous to that of a transmission line. Regarding the electrical potential distribution, the simple assumption is made that an ac potential can be defined in each phase and 02 which is, at each frequency, a unique function of position x no radial distribution of potential into the pores or solid particles is considered. It follows that the ac potential difference between the two phases at a point X, i.e., the overvoltage in interfacial reactions, is 02 - 0i ... 

The GCSB models have predicted a variety of interfacial properties, for example, capacitive behavior, charge and potential distributions, and potential dependence of surface tension (the so-called electrocapillary curves), which have been experimentally tested by a variety of electrochemical and physical methods with varying levels of success. For instance, much has been learned over the past 70 years about ion adsorption and solvent orientation at Hg and well-defined solid metal electrodes from capacitance measurements. " Similarly, studies in recent decades using in situ scanned probe microscopy and surface force microbalance method have been used to map the electrical forces (and thus electric field) extending from electrode surfaces. 

When charges preferentially adsorb onto an interface adjacent to an aqueous solution they are balanced by counterions creating an electric double layer. For an aqueous NaCl solution I/kq = 30.4 nm at 10 M, 0.96 nm at 0. IM, and in pure water of pH 7, 1/kd is about one micron (e.g., Israelachvili 1992). With this in mind, the interfacial dynamics at an ice/solution interface can become quite complicated, and our studies of premelting dynamics might require consideration of a continuous variation in the interaction potential depending on the redistribution of ions. Preferential ion incorporation is best demonstrated in this context of solid/liquid solute distribution introducing ionic coefficients . A simple example for a monovalent electrolyte solution is... 

Calculations of the variations expected in the fluorescent-yield (FY) profiles as a function of the distribution model parameters are shown in Figure 7.19. When the species of interest resides predominantly at the solid surface, the FY profile shows a maximum at the critical angle for total external reflection. As the ratio of the surface-bound species to the total number of species in the solution volume adjacent to the surface decreases, the FY distribution broadens at the low angles. A similar effect is noted when a diffuse layer accumulation arises due to an interfacial electrostatic potential. 

Figure 15. Energetics of the charge recombination following electron injection (/ i) from a dye excited state S into the conduction band of a semiconductor. Thermalization and/or trapping of injected electrons (Mh) takes place prior to the interfacial electron back transfer to the dye oxidized state S (/cb). The reaction free energy associated to the latter process depends upon the population of the electronic states in the solid and can be distributed over a broad range of values. Numerical potential data shown are those of the c/s-[Ru (dcbpy)2(NCS)2] Ti02 system.

Development of conditional (or variable) surface charges involves chemical reactions in the interfacial layer. Therefore, the individual material features, (i.e., the chemical properties of both the potentially charged sohd material and the dissolved species) have to be considered. When a chemically reactive surface group is exposed to an aqueous solution, the surface may become charged due to a surface reaction (e.g., dissociation, association, complexation) if the aqueous solution contains the other reactant as a dissolved species. The charging process on variable-charge sites is determined by not only the quality and quantity of active sites but also the composition of aqueous solution. An elechical double layer develops around particles due to the distribution of ionic species between the solid-liquid interfacial layer and the equilibrium Uquid phase. 

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