Layer Potential Difference and Capacitance

The dashed lines in Fig. 11 show the capacitance of the diffuse double-layer calculated using the Gouy-Chapman theory from Eq. (35) for A cpi = const=0. As it has been noticed [21], two trends are apparent on comparing the experimental capacitances with those calculated using the GC theory. First, at low surface charge 

The dashed lines in Fig. 13 show the inner-layer potential difference A cpi as a function of the surface charge density. It is apparent that at a constant value of q, A cpi is not independent of the electrolyte concentration and the same is true for the inner-layer capacitance C - [21]. The second trend is obvious at higher surface charge densities, where the experimental capacitance tends to rise above the Gouy-Chapman value, which would correspond to the negative inner-layer capacitance C, 

A recent theoretical analysis of the electrical double layer [39] has implied that the Gouy-Chapman theory overestimates the potential drop across the space charge region and underestimates the corresponding capacitance. This error becomes more pronounced as the ionic diameter and the charge number increase or the solvent dielectric permittivity decreases [39]. Since this may be the case for the ITIES, potential 

Close to the zero-charge potential difference the effect of the ion penetration on the interfacial capacitance can be estimated by solving the linearized Poisson-Boltzmann equations in all three regions of the MVN model [41]. For the sake of simplicity, it was assumed [32] that only the ions from the organic solvent phase enter the inner layer, so that their concentrations differ from zero at X2 x oo, while they turn to zero at x X2, the x-axis being oriented towards the organic solvent phase. In that case, the double-layer capacitance C is [32]  

In the above equations, the superscript i refers to the inner-layer region. Apparently, without the ionic penetration =0, s=0, A=0 and C = Q H- Q For x 4= 0, the parameter A is negative and the inverse capacitance is reduced. 

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