Cell Time Constants

Figure 4 The effect of the cell time constant on the potential value assumed by the working electrode when a potential step is applied...

The most common rate phenomenon encountered by the experimental electrochemist is mass transport. For example, currents observed in voltammetric experiments are usually governed by the diffusion rate of reactants. Similarly, the cell resistance, which influences the cell time constant, is controlled by the ionic conductivity of the solution, which in turn is governed by the mass transport rates of ions in response to an electric field. 

The lag of potential of the working electrode is directly related to the cell time constant. For a disc macroelectrode (rd = 1 mm, RUC = 50ms), Eq. (5.102) fixes a practical scan rate limit of around 400 V s. This limiting scan rate can be considerably higher in the case of microelectrodes (i.e., kilovolts-per-second or even megavolts-per-second [50]. 

When the electrochemical properties of some materials are analyzed, the timescale of the phenomena involved requires the use of ultrafast voltammetry. Microelectrodes play an essential role for recording voltammograms at scan rates of megavolts-per-seconds, reaching nanoseconds timescales for which the perturbation is short enough, so it propagates only over a very small zone close to the electrode and the diffusion field can be considered almost planar. In these conditions, the current and the interfacial capacitance are proportional to the electrode area, whereas the ohmic drop and the cell time constant decrease linearly with the electrode characteristic dimension. For Cyclic Voltammetry, these can be written in terms of the dimensionless parameters yu and 6 given by... 

The cell time constant, Tceii = RCd expresses the ability of the cell to respond to fast changes in the electrode potential. Part of the current observed initially in a CA experiment in which the potential is changed suddenly is used to charge the doublelayer capacitor and is called the capacitative current, k- Because this charging process passes the resistance in the cell, the current response will be the same as for a RC circuit, that is, an exponential function (Eq. 82). 

Thus, k decreases to zero with time and is diminished by more than 90 % when t > 2.3RCdi. The cell time constant is a very important parameter for evaluation of the time elapsed until k has become insignificant compared to the faradaic current component pertaining to the electrode processes, if. For the LSV or CV techniques, /c has two components, as shown in Eq. 83, since the potential is changed constantly throughout the experiment. 

The introduction of UME to the electroanalytical field has extended the applicability of techniques such as LSV, CV, CA, and DPSC. Because the cell time constant Tceii as well as the iR loss are smaller for UMEs than for the normal-sized electrodes, it... 

Although the DPSC technique with UME has some advantages over fast CV with respect to cell time constant, ohmic drop, and slow heterogeneous kinetics, the technique has rarely been used. The main reason for this is that DPSC is a blind technique, where it is difficult to distinguish between a variation in the real response and experimental artefacts such as adsorption or changes in Cji. 

The effect of the cell time constant on the IMPS response is illustrated in Fig. 14. In this particular case, the time constant for recombination is much longer than iceii and the normalised plot crosses the real axis close to unity. If the two time constants are closer, the IMPS plot crosses the real axis at a point less than unity. 

Even though R rises inversely with rg, Q decreases with the square hence scales with rg. This is an important result indicating that smaller electrodes can provide access to much shorter time domains. Consider, for example, the effect of electrode size in a system with Cd = 20 tF/cm and k = 0.013 Il cm (characteristic of 0.1 M aqueous KCl at ambient temperature). With rg = 1 mm, the cell time constant is about 30 ts and the lower limit of time scale in step experiments (defined as a minimum step width equal to 10/ uCd) is about 0.3 ms. This result is consistent with the general experience that experiments with electrodes of normal size need to be limited to the millisecond time domain... 

The considerations involved in understanding background currents in SWV are exactly those encountered in the treatment of DPV. If is greater than five cell time constants, there is no appreciable charging current contribution, either to the individual current samples or to the differences. Faradaic background processes do contribute and often control the detection limits of SWV. At solid electrodes or near background limits, the effects on the forward and reverse currents can be sizable, but they are often suppressed effectively in the difference currents. 

These considerations show that transient experiments will not be meaningful unless the cell time constant is small compared to the time scale of the measurement, regardless of the high-frequency characteristics of the control circuitry. 

Derive a formula describing current flow in the dummy cell shown in Figure 15.6.1Z upon application of a step in ref froi 0 V to an arbitrary value Derive an equation for the true potential difference between the reference and working electrodes corrected for the drop through R. Is the cell time constant still a factor controlling the rise of true ... 

The response time of an electrode is also a function of the electrode dimension. The cell time constant can be described as [76]... 

How Small a Cell Time Constant Could Be Achieved ... 

In work of this kind, one naturally would like to be able to define the lower bounds of timescale. Equation (1) suggests that one could obtain arbitrarily small cell time constants by relying on sufficiently small electrodes, but eventually there will be a breakdown of equation (1) because of stray capacitance in the cell. In other words, when the interfacial capacitance falls to sufficiently small values, as a consequence of the reduction of area, other components of capacitance will begin to dominate. These will arise from capacitive coupling between leads... 

Fig.7. Plot of cell time constant vs. electrode radius in 1 M acid with a 20 pF stray capacitance.

The above mode implies the possibility of current sampling, in the OFF pulse time of the pulse sequence which generates the drop. If this sampling is done with a delay long enough with respect to the cell time constant of the electrode, the sampled current will be free of the charging component. 

Fig. 3 Relationship between the RC cell time constant and the radius of platinum microdiscs in which the supporting electrolyte is 0.1 M HCl. Cell time constants were measured using chronoamperometry conducted on a microsecond to submicrosecond timescale by stepping the potential from 0.200 to 0.250 V versus Ag/AgCl.

An important cause of nonideal responses is stray capacitance within the electrochemical system that may arise from the electrode itself, the leads, or electrical connections. Stray capacitance will increase the cell time constant as descrihed by Eq. (4). 

There are two major sources of stray capacitance. First, the capacitance of the po-tentiostat and leads. By using high-quality cable of minimum length, for example, by mounting the current-to-voltage converter directly over the electrochemical cell, and by avoiding the use of switches as far as possible, stray capacitance from the electrochemical system can be minimized. Second, the microelectrode itself. For example, if there is a small imperfection in the seal between the insulator and the electrode material, then solution leakage will cause the RC cell time constant to increase massively and the Faradaic response may... 

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