Inner Helmholtz layer, capacity

Using this model, one cannot forecast the adsorption of the background electrolyte ions because this model do not consider the reactions responsible for such a process. Zeta potential values, calculated on the basis of this model, are usually too high, nevertheless, because of its simplicity the model is applied very often. In a more complicated model of edl, the three plate model (see Fig. 3), besides the mentioned surface plate and the diffusion layer, in Stern layer there are some specifically adsorbed ions. The surface charge is formed by = SOHJ and = SO- groups, also by other groups formed by complexation or pair formation with background electrolyte ions = SOHj An- and = SO Ct+. It is assumed that both, cation (Ct+) and anion (A-), are located in the same distance from the surface of the oxide and form the inner Helmholtz plane (IHP). In this case, beside mentioned parameters for two layer model, the additional parameters should be added, i.e., surface complex formation constants (with cation pKct or anion pKAn) and compact and diffuse layer capacities. 

Parsons and Zobel plot — In several theories for the electric - double layer in the absence of specific adsorption, the interfacial -> capacity C per unit area can formally be decomposed into two capacities in series, one of which is the Gouy-Chapman (- Gouy, - Chapman) capacity CGC 1/C = 1 /CH + 1 /CGC. The capacity Ch is assumed to be independent of the electrolyte concentrations, and has been called the inner-layer, the - Helmholtz, or Stern layer capacity by various authors. In the early work by Stern, Ch was attributed to an inner solvent layer on the electrode surface, into which the ions cannot penetrate more recent theories account for an extended boundary region. In a Parsons and Zobel plot, Ch is determined by plotting experimental values for 1/C vs. 1/Cgc- Specific adsorption results in significant deviations from a straight line, which invalidates this procedure. 

Setting as = 0 we obtain A = 1/Cn, where C is the Helmholtz or inner-layer capacity.72 By definition, this is the first-order correction to the Gouy-Chapman theory. Setting as = -aM with as = zeNs, from Eqs. (71) and (72) we obtain for the dipole moment ... 

Triplelayer Intrinsic stability constants Number of surface sites Capacity of the plane (inner and outer Helmholtz) layers -SOH - H+ <=> -SO ... 

Helmholtz, or Stern layer capacity by various authors. In the early work by Stern, Ch was attributed to an inner solvent layer on the electrode surface, into which the ions cannot penetrate more recent theories accoimt for an extended boundary region. In a Parsons and Zobel plot, Ch is determined by plotting experimental values for 1/C vs. 1/Cgc- Specific adsorption results in significant deviations from a straight line, which invahdates this procedure. 

Despite all particularities, let us now point some basic concepts regarding such double layer as well as its influence over electrochemical measurements. Basically this region is composed by two planes the inner Helmholtz plane (IHP) is the layer that passes through the center of adsorbed ions or is just located behind the layer of adsorbed water, being also called compact layer the second one, the outer Helmholtz plane (OHP), passes through the center of hydrated/solvated ions in contact of electrode surface, both these planes are related to different electric potentials and generate certain capacity. Beyond the OHP the diffuse layer is observed. The concentration of ions in the diffuse layer varies as function not only of such electric potential but also regarding the distance from electrode surface [5, 7-9]. 

Thus, if the semiconductor corresponds essentially to an insulator of the Schottky barrier type, use of Mott-Schottky plots will allow the determination of the capacitance of the inner layer. Utilization of impedance measurements with different frequencies may give rise to the possibility of determining the double layer capacity separate from the inner layer. In this way a map of the double layer, an estimation of the Helmholtz potential difference and the potential difference (pd) in the space charge region may be obtained. The pd in the Helmholtz layer is, however, not only given by the charge on the surface of the polymer, but also by the potential difference due to aggregated layers which form within it, and in particular the solvent dipole layer (70). 

Fig. 5-8. An interfadal double layer model (triple-layer model) SS = solid surface OHP = outer Helmholtz plane inner potential tt z excess charge <2h = distance from the solid surface to the closest approach of hydrated ions (Helmluritz layer thickness) C = electric capacity.

Double layer models — The oldest model for the double layer at metal/solution interfaces was proposed by - Helmholtz. He suggested that an excess charge (- double layer, excess charge density) on the metal attracts an equivalent amount of counter ions to the interface, the two opposing layers are separated by a certain distance, which determines the capacity. His model gave rise to the concepts of the inner and outer Helmholtz planes (layers) (- Double layer). 

The fact that in the absence of specific ion adsorption, variations in practically coincide with those may be explained assuming that, under such conditions, the effective permittivity, hence, the capacity for the layer between the electrode and discharging ion localization plane, are much lower than the corresponding values for the layer between the inner and outer Helmholtz planes. Then, the potential drop is concentrated, mainly, in the layer between the electrode and discharging ions, i.e., ( 1 — ( 0, is a relatively small value. Model-based evaluations of respective permittivity values corroborate this picture. 

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