Diffuse double layer, equation state

Although a family of OgS - Jig8 values are allowed under Equation 7 the actual equilibrium state of the oxide/solution interface will be determined by the dissociation of the surface groups and the properties of the electrolyte or the diffuse double layer near the surface. For surfaces that develop surface charges by different mechanisms such as for semiconductor, there will be an equation of state or charge-potential relationship that is analogous to Equation 7 which characterizes the electrical response of the surface. 

This model is based on the Gouy-Chapman theory (diffuse double-layer theory). The theory states that in the area of the boundary layer between solid and aqueous phase, independently of the surface charge, increased concentrations of cations and anions within a diffuse layer exists because of electrostatic forces. In contrast to the constant-capacitance model, the electrical potential does not change up to a certain distance from the phase boundaries and is not immediately declining in a linear manner (Fig. 14 a). Diffusion counteracts these forces, leading to dilution with increasing distance from the boundary. This relation can be described physically by the Poisson-Boltzmann equation. 

There has been no lack of attempts to correct existing 2D equations of state for the effect of the double layer. Most of these are based on the diffuse double layer model, and therefore remain limited to the low pressure range, i.e. to the least interesting parts of x(A) curves. Henderson-Hasselbalch interpretations, using [II.3.6.53 or 54] cannot be carried out for lack of information on the degree of dissociation a. Basically, the route for incorporation of double layer formation into 2D-equations of state is embodied in (3.4.53] in combination with [3.4.48] and [3.4.16]. Ekjuation [3.4.53] has four parameters, viz. a°,, (or y/, the two are... 

The Debye-Huckel theory was developed to extend the capacitor model and is based on a simplified solution of the Poisson equation. It assumes that the double layer is really a diffuse cloud in which the potential is not a discontinuous function. Again, the interest is in deriving an expression for the electrical potential function. This model states that there is an exponential relationship between the charge and the potential. The distribution of the potential is ... 

We use the Gouy-Chapman theory for the diffuse layer which is based on the Poisson-Boltzmann (P.B.) equation for the potential distribution. Although the different corrections to the P.B. equation in double-layer theory have been investigated (20, 21, 22, 23), it is difficult to state precisely the range of validity of this equation. In the present problem the P.B. equation seems a reasonable approximation at 0.1M of a 1-1 electrolyte to 50mV for the mean electrostatic potential pd at the ohp (24) this upper limit for pd increases with a decrease in electrolyte concentration. All the values for pd calculated in Tables I-IV are less than 50 mV— most of them are well below. If n is the volume density of each ion type of the 1-1 electrolyte in the substrate, c the dielectric constant of the electrolyte medium, and... 

The effect of the double layer on the kinetics is contained within the term xp[(oicn — ZQ)iFA(t>2lRT)], which is known as the Frumkin correction. It is the same for the forward and backward processes in compliance with transition state theory and the importance of the correction depends upon the magnitude and signs of olq, , Zq, and A02- If it is assumed that equilibrium prevails within the diffuse layer even when charge transfer occurs and that the diffusion layer is much thicker than the diffuse layer, then Gouy-Chapman theory can be used to calculate the dependence of 02 on the supporting electrolyte concentration (Equation (5.35)). The combination of these theoretical calculations with experimental o jE data allows the dependence of 02 on potential to be obtained, as shown in Fig. 5.9. The magnitude of A02 depends upon the position of the... 

Thus, the form of the kinetic equation depends substantially on the orientation of the transition state in relation to the electrode and particularly on whether the transition state is adsorbed or is located in the diffusion part of the double layer. In the light of what follows it will become clear that the first case holds in practice, but we will begin with the equation for reduction of unadsorbed particles. Only the case with z = 0 will be examined. 

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