Double layer capacitance, determination

Crossover Current and Double Layer Capacitance Determination... 

Measurements based on the Gouy-Chapman-Stem theory to determine the diffuse double-layer capacitance 10, 24,72, 74... 

This does not imply that this double layer is at its point of zero charge (pzc). On the contrary, as with every other double layer in electrochemistry, there exists for every metal/solid electrolyte combination one and only one UWr value for which this metal/gas double layer is at its point of zero charge. These critical Uwr values can be determined by measuring the dependency onUWR of the double layer capacitance, Cd, of the effective double layer at the metal/gas interface via AC Impedance Spectroscopy as discussed in Chapter 5.7. 

Nonfaradaic components associated with the uncompensated resistance between reference electrodes (7 ) and the double layer capacitance (Qi) can be accurately determined by AC impedance measurements. In this technique, a small AC potential perturbation is superimposed to the DC bias, and the resulting AC current is measured as a function of the frequency of modulation. The simplest circuit considered for a polarizable... 

Kinetic parameters can also be obtained by using the zero-point method as described earlier.40 The advantage of this method is that the values of a and k° can be deduced independent of the determination of values of the double-layer capacitance, electrode impedance, and potential difference across the electrode/solution... 

We have used voltammetric measurements in the absence of the electroactive species to quantitatively evaluate this heat-sealing procedure. The magnitude of the double layer charging current can be obtained from these voltammograms [25,68-70], which allows for a determination of the fractional electrode area (Table 1). This experimental fractional electrode area can then be compared to the fractional pore area calculated from the known pore diameter and density of the membrane (Table 1). In order to use this method, the double layer capacitance of the metal must be known. The double layer capacitance of Au was determined from measurements of charging currents at Au macro-disk electrodes of known area (Fig. 6, curve A). A value of 21 pF cm was obtained. 

As expected, the impedance responses obtained in practice do not fully match that of the model of Fig. 9.13. However, as shown by the typical case of Fig. 9.14 which illustrates the response obtained for a 5 mol% ClO -doped polypyrrole electrode in contact with a LiC104-propylene carbonate solution (Panero et al, 1989), the trend is still reasonably close enough to the idealised one to allow (possibly with the help of fitting programmes) the determination of the relevant kinetics parameters, such as the charge transfer resistance, the double-layer capacitance and the diffusion coefficient. 

AC Impedance measurements enable the determination of charge transfer resistance and double layer capacitance and other parameters related to coated systems. 

Galvanostatic Transient Technique Double-Layer Capacitance Measurements. The value of the fractional surface coverage 9 may be inferred by means of doublelayer capacitance data. As discussed in Section 6.9, the double-layer capacitance C may, in turn, be determined by means of a transient technique. In the galvanostatic transient technique (as in Fig. 6.18), the duration of the constant-current (density) pulse is on the order of microseconds. In the microsecond time range the only process taking place at the electrode is charging of the double layer. Flence, in this case, Eq. (6.96) reduces to... 

The derivative drj/dt can be determined experimentally from the slope of the galvanostatic transient r] = fit). Using Eq. (10.24) and experimental values of and drjldt, one is able to calculate the double-layer capacitance C. 

Electrodeposition of lead-tin alloy films is usually performed in the presence of peptone as an additive. Peptone is adsorbed on the metal surface during the electrodeposition process. The fractional surface coverage Q of the lead-tin electrode may be determined from the double-layer capacitance C measurements, and/or chronopotentiometric measurements. For a solution containing 9.0 g/L of tin and 13.0 g/L of lead, the following relationship between the concentration of peptone, the double-layer capacitance C, and the transition time At is observed (8). 

Fig. 2 Differential double-layer capacitances of Ag(l 11), Ag(lOO), and Ag(l 10) in 10 mM NaF determined applying an ac technique / = (o/2jt = 20 Hz, scan rate = 5 mV s / The calculated curve corresponds to the model polycrystalline Ag electrode [24],...

Rational optimization of performance should be the main goal in development of any chemical sensor. In order to do that, we must have some quantitative tools of determination of key performance parameters. As we have seen already, for electrochemical sensors those parameters are the charge-transfer resistance and the double-layer capacitance. Particularly the former plays a critical role. Here we outline two approaches the Tafel plots, which are simple, inexpensive, but with limited applicability, and the Electrochemical Impedance Spectroscopy (EIS), based on the equivalent electrical circuit model, which is more universal, more accurate, and has a greater didactic value. 

From their calculations of the surface excess entropy and volume of the electric double layer at a mercury-aqueous electrolyte interface, Hill and Payne (HP) [147] postulated an increase in the number of water molecules in the Stern inner region as the surface charge a of about 30 piC/m2, which is consistent with the results of TC on a silver surface obtained some 30 years later. HP used an indirect method to determine the excess entropy and volume by measuring the dependence on temperature and pressure of the double layer capacitance at the mercury-solution interface. 

Finally, the basic equivalence of the two measuring techniques should be appreciated. Although there are many ways to approach such a comparison, the following simplified explanation will, we hope, give a more intuitive feeling for the relationship between EIS and PR measurements. As stated above, both techniques rely on the frequency dependence of the impedance of the double-layer capacitance in order to determine the polarization resistance. EIS uses low frequencies to force the capacitor to act like an open circuit. PR measurements use a slow scan rate to do the same thing. To make comparisons, the idea of equivalent scan rate is useful. Suppose that a particular electrochemical system requires EIS measurements to be made down to 1 mHz in order to force 99% of the current through Rp. What would the equivalent scan rate be for PR measurements A frequency of 1 mHz corresponds to a period of 1000 s. If the sine wave is... 

For processes involving strongly adsorbing reactants, Tp is often sufficiently large to be measured by surface electroanalytical methods (e.g. chronocoulometry, double-layer capacitance), enabling Kt to be evaluated. This allows ket to be determined from kob using eqn. (10). Alternatively, kel can often be evaluated directly in such circumstances by using electrochemi-... 

First, assume that the surface charge on the membrane particles does not interact with the mobile protons (no proton release or uptake). An ion step will result in an increase in the double-layer capacitances of the particles and consequently in a decrease of the surface potentials fr, because the charge densities remain constant. The ISFET will measure a transient change in the mean pore potential. As a result of the potential changes, an ion redistribution will take place and the equilibrium situation is re-established. The theoretical maximum ion step response is the change in the mean pore potential. This is comparable with the Donnan model where the theoretical maximum is determined by the change in the Donnan potential at the membrane solution interface. 

There are two reports that determined the double-layer capacitance of ionic liquids [31, 40]. By an electrocapillary curve measurement using dropping mercury electrode (DME), the integral double-layer capacitances of ionic liquids were shown to be smaller than those of aqueous solutions and larger than those of non-aqueous solutions, as summarized in Table 17.2 [31]. This behavior can be explained by the thinner double-layer being due to the higher ionic concentration than that of nonaqueous solutions. However, the correlation between the doublelayer capacitance and anion size [41] observed in PC solutions [8] is not clear. It was further shown that the double-layer capacitance of the ionic liquid was not dependent on the choice of electrode from among DME, GC, and activated carbon fiber [31]. 

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