Double layers, origin capacity

Relaxation methods for the study of fast electrode processes are recent developments but their origin, except in the case of faradaic rectification, can be traced to older work. The other relaxation methods are subject to errors related directly or indirectly to the internal resistance of the cell and the double-layer capacity of the test electrode. These errors tend to increase as the reaction becomes more and more reversible. None of these methods is suitable for the accurate determination of rate constants larger than 1.0 cm/s. Such errors are eliminated with faradaic rectification, because this method takes advantage of complete linearity of cell resistance and the slight nonlinearity of double-layer capacity. The potentialities of the faradaic rectification method for measurement of rate constants of the order of 10 cm/s are well recognized, and it is hoped that by suitably developing the technique for measurement at frequencies above 20 MHz, it should be possible to measure rate constants even of the order of 100 cm/s. 

Experimental investigation of potential distribution across the double layer on semiconductor electrodes is most frequently performed by differential capacity (see the next section) and photocurrent measurement techniques. A survey of experimental results obtained in this field is beyond the scope of the present review. Certain data illustrating the pinning and more detailed discussion of its origins will be presented in Section IV.2. 

The capacity of the double layer depends strongly on the solvent but there is a qualitative similarity in the shape of capacity-potential curves in all solvents including water. Early measurements seemed to indicate qualitative differences between water and such non-aqueous solvents as methanol, ethanol and ammonia which have featureless capacity curves in contrast to the characteristic humped curves found in water. However, more recent studies have shown that capacity humps occur commonly in solvents of widely differing types. They are found in solvents of high and medium dielectric constant and probably have a common origin in field reorientation of solvent dipoles. 

In another report [4], an error in the interpretation of the CPE is pointed out. On the one hand, the double-layer capacity is replaced by the CPE, i.e. the CPE is a property of the double layer itself. On the other, the CPE is discussed as originating from surface inhomogeneities. 

On other hand, in relation to OH adsorption, the results of values agree well with at > 0.75 V, but exhibit clear deviations at lower potentials. This deviation is, as in the case of hydrogen adsorption, originated by the different double-layer correction employed in both mathematical treatments. If one calculates the entropy of adsorbed OH by using Gibbs thermodynamics, but assuming a constant double-layer capacity, then the resulting... 

The double-layer capacity (Cai), which is a simple electrical capacity, is often represented by a nonlinear capacity or a constant-phase element (CPiidi) so as to adjust the difference of the electrochemical system from the ideal behavior of an electrical system. Indeed, the use of a simple capacity does not facilitate a perfect adjustment of the real and simulated spectra. The origin of this deviation from the ideal is essentially attributed to irregularities on the surface of the electrode (roughness, presence of impurities, variation in thickness or surface composition of the electrode). 

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