Double layer capacitance conditions

The origin of the observed correlation was not established, and the relation was not interpreted as causal. It could be argued that a sustained elevated potential due to as-yet unknown microbial processes altered the passive film characteristics, as is known to occur for metals polarized at anodic potentials. If these conditions thickened the oxide film or decreased the dielectric constant to the point where passive film capacitance was on the order of double-layer capacitance (Cji), the series equivalent oxide would have begun to reflect the contribution from the oxide. In this scenario, decreased C would have appeared as a consequence of sustained elevated potential. 

As was discussed in section 2.1.1, electrocapillarity measurements at mercury electrodes, which have well-defined and measurable areas, allow the double-layer capacitance, CDL, to be obtained as Fm-2. Bowden assumed that the overpotential change at the very beginning of the anodic run in H2-saturated solution was a measure of the double-layer capacity. The slope of the E vs. Q plot in this region was taken as giving 1/CDL, and this gave 2 x 10 5 F. He then assumed that, under these same conditions, the double-layer capacity, in Fm-2, of the mercury electrode is the same. This gave the real surface area of the electrode as 3.3cm 2, as opposed to its geometric area of I cm2. 

The preceding derivation has assumed implicitly that the double-layer charging current is negligible in front of the Faradaic current or that it can be eliminated by a simple subtraction procedure. In cases where these conditions are not fulfilled, the following treatment will take care of the problem under the assumption that the double-layer capacitance is not affected appreciably by the Faradaic reaction but may nevertheless vary in the potential range explored. The first step of the treatment then consists of extracting the Faradaic component from the total current according to (see Section 1.3)... 

Under ideal conditions, charge consumed by the double-layer capacitance and adsorbed reactants will follow the same time course as discussed earlier for ordinary chronocoulometry. Since the ratio of electrode area to solution volume is larger for thin-layer experiments, charge thus accounted for may represent a much greater proportion of the total. This fact points to an advantage of restricted diffusion experiments for studying some surface phenomena. 

As can be seen in this figure, the combined effect of ohmic drop and double-layer capacitance is much more serious in the case of CV. The increase of the scan rate (and therefore of the current) causes a shift of the peak potentials which is 50 mV for the direct peak in the case of the CV with v = 100 V s 1 with respect to a situation with Ru = 0 (this shift can be erroneously attributed to a non-reversible character of the charge transfer process see Sect. 5.3.1). Under the same conditions the shift in the peak potential observed in SCV is 25 mV. Concerning the increase of the current observed, in the case of CV the peak current has a value 26 % higher than that in the absence of the charging current for v = 100 Vs 1, whereas in SCV this increase is 11 %. In view of these results, it is evident that these undesirable effects in the current are much less severe in the case of multipulse techniques, due to the discrete nature of the recorded current. The CV response can be greatly distorted by the charging and double-layer contributions (see the CV response for v = 500 V s-1) and their minimization is advisable where possible. 

It is impossible to write an advanced text in any area of physical chemistry without resort to some mathematical derivations, but these have been kept to a minimum consistent with clarity, and used mostly when several steps in the derivation involve approximations, or some other physical assumption, which may not be obvious to the reader. Thus, the theories of the diffuse-double-layer capacitance and of electrocapillary thermodynamics are derived in some detail, while the discussion of the diffusion equation is limited to the translation of the conditions of the experiment to the corresponding initial and boundary conditions and the presentation of the final results, while the sometimes tedious mathematical methods of solving the equations are left out. The mathematical skills needed to comprehend this book are minimal, and it should be easily followed by anybody with an undergraduate degree in science or engineering. An elementary knowledge of thermodynamics and of chemical kinetics is assumed, however. 

One such properly is the capacitance, which is observed whenever a metal-solution interphase is formed. This capacitance, called the double layer capacitance, is a result of the charge separation in the interphase. Since the interphase does not extend more than about 10 nm in a direction perpendicular to the surface (and in concentrated solutions it is limited to 1.0 nm or less), the observed capacitance depends on the structure of this very thin region, called the double layer. If the surface is rough, the double layer will follow its curvature down to atomic dimensions, and the capacitance measured under suitably chosen conditions is proportional to the real surface area of the electrode. 

To probe the microscopie order of SAMs (here we will treat only nonelectroactive SAMs those containing tethered redox probes will be discussed later) under the conditions used during electrochemieal electron-transfer measurements, functional characterization is performed by cyclic voltammetric techniques. In this subsection, electrochemical blocking effect EBE) and double-layer capacitance (Cai) experiments are detailed. When these experiments are carried out using a struetural probe of molecular scale [30, 44, 45], they provide the greatest sensitivity to defects because the effects of defects and disorder dominate the electrochemical response. 

In a SAM-modified electrode, the SAM functions as a dielectric, reducing the permeability of the monolayer by electrolyte and decreasing the charging current [23, 30, 48]. However, a thinner film [30, 49], one with a higher dielectric constant (e.g., containing unsaturated carbons [50]), or one which is more permeable to electrolyte (i.e., a more defective SAM), exhibits increased Cji because the resulting electrical double layer is better organized [23, 30, 48[. The double-layer capacitance is, thus, a convenient check of monolayer quality under the conditions of electrochemical electron-transfer measurements. 

Another characteristic electrochemical property of a semiconductor/electrolyte contact is the double-layer capacitance, which is an approximation of the space-charge capacitance (Chapter 4). The space-charge capacitance can be determined by impedance measurements. If no current flows in the depletion region, the impedance is given by the reciprocal value of the space-charge capacitance. For other conditions the capacitance can be calculated from the complex impedance measurements. How to measure the impedance and to evaluate the data was described in Chapter 4 as well as the influence of diffusion processes in Chapter 5. 

The parallel capacitance calculated from the data of Figure 7.16 is not a pure double-layer capacitance, it is too frequency-dependent. It must be due to redox or sorption processes at the platinum surface, or the fractal surface of black platinum. Under optimum conditions, it is possible to obtain capacitance values of the order of 50 pF/mm at 20 Hz (Schwan, 1963). 

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