Cyclic voltammetry double-layer capacitance

Calculate the lower limit and the upper limit for the sweep rate in a cyclic voltammetry. The double-layer capacitance is 50 pF/cm2 and the diffusion coefficient is 10-5 cm2/s. The measurable current density is 100 pA/cm2 and the sweep range is 10 V. (Kim)... 

We have seen that the instantaneous faradaic current at an electrode is related to surface concentrations and charge transfer rate constants, and exponentially to the difference of the electrode potential from the E° of the electrochemical couple. This is represented in Figure 5.1c by Zf. With very few exceptions, this leads to intractable nonlinear differential equations. These systems have no closed form solutions and are treatable only by numerical integrations or numerical simulations (e.g., cyclic voltammetry). In addition, the double-layer capacitance itself is also nonlinear with respect to potential. 

Figure 4. Apparent double-layer capacitance as a function of Eh, determined from cyclic voltammetry. Increase above about +0.45 volts is due to oxidation of platinum. Zero values at ends of scans are artifacts of the method and do not represent true capacitance values. Temperature = 298 + 1 K.

Gasteiger and Mathias assume a thin-film structure of the ionomer of 0.5-2 nm covering the entire solid catalyst surface. Experimental support for this electrode structure comes from double-layer capacitance measurements using cyclic voltammetry and AC impedance techniques. Gasteiger and Mathias observed values that are typical of Pt and carbon interfaces with electrolyte and imply that the entire solid surface was in contact with electrolyte for these electrodes. Under several assumptions regarding structure, diffusion, and reactivity, a minimum permeability was derived for a maximum of 20 mV loss. 

The popularity of the cychc voltammetry (CV) technique has led to its extensive study and numerous simple criteria are available for immediate anal-j sis of electrochemical systems from the shape, position and time-behaviour of the experimental voltammograms [1, 2], For example, a quick inspection of the cyclic voltammograms offers information about the diffusive or adsorptive nature of the electrode process, its kinetic and thermodynamic parameters, as well as the existence and characteristics of coupled homogeneous chemical reactions [2]. This electrochemical method is also very useful for the evaluation of the magnitude of imdesirable effects such as those derived from ohmic drop or double-layer capacitance. Accordingly, cyclic voltammetry is frequently used for the analysis of electroactive species and surfaces, and for the determination of reaction mechanisms and rate constants. 

At this point, it is of interest to relate the current responses that arise in modulation of the double-layer capacitance by liner-sweep voltammetry (cyclic voltammetry) at a sweep-rate s = dV/dt comparatively to that by alternating voltage. For voltammetry applied at a capacitance, C, the response current, i, is given by... 

Wang H, Pilon L (2012) Physical interpretation of cyclic voltammetry for measuring electric double layer capacitances. Electrochim Acta 64 130-139... 

Figure 3.2 shows the calculated total capacitance as a function of electrode potential when the potential is scarmed forward from low to high and backward from high to low (as in cyclic voltammetry). Note that the double-layer capacitance is treated as potentially independent with a value of 0.15 F/cm for a carbon porous electrode layer [21]. 

Cyclic voltammetry is commonly used to study fuel cell electrodes and hydrogen crossover. In this technique, a linear sweep potential is applied to one electrode, while the other is held constant. The potential is cycled in a triangular wave pattern, while the current produced is monitored. The shape and magnitude of the current response provides useful quantitative and qualitative information regarding the amount of catalyst that is electro-chemically active, the double layer capacitance, hydrogen crossover, and the presence of oxide layers and contaminants. Wu et al. provide a description of this technique with example voltammograms [29]. 

Keywords— Double layer, Capacitance, Stainless-steel, Cyclic voltammetry. Impedance. 

For several decades cyclic voltammetry (CV) has been the technique of choice in investigating charge-transfer kinetic processes. Simultaneous determination of both EIS and CV parameters is very important, as exclusively CV-based analysis often misses important electrochemical aspects of the system, such as the double-layer capacitance, details of the double-layer structure, monolayer adsorption through functional dependence of on electro-... 

The technique of cyclic voltammetry, to be discussed later (Section 15.1) can also be used to determine the double-layer capacitance. In this case, a relatively slow triangular potential waveform is applied, and the current is determined as a function of potential. If the interface is highly polarizable, the result will be that shown in Figure 8.7(a). If there is a significant Faradaic current, a plot such as shown in Figure 8.7(b) will be observed. 

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