Transient Response to a Potential Step

Frequency-domain measurements provide an attractive alternative to transient techniques involving steps in potential or current because their capability to make repeated measurements at a single frequency improves the signal-to-noise ratio and extends the range of characteristic frequencies sampled. These measurements are a type of transient measurement in which the input signal is cyclic. 

---

In the case of an anay of band electrodes or interdigitated electrode structures, the width of each single electrode element and the gap between the electrode elements must be considered carefully in the sensor design. Interactions between electrode elements and their effects on the transient response to a potential step perturbation will directly affect the overall sensor output. When an interdigitated electrode structure is used, chemical cross-talk among the reactants and products in both electrode elements (cathode and anode) may occur, which will then influence the sensor output [3], Therefore, the relative location of the sensing elements is also an essential consideration. 

Measurements of the current or charge transient response to a potential step have been made in many in-... 

Potential Step Transients This refers to the current transient in response to a potential step. In solid-state devices a technique known as junction recovery is applied to barrier junctions as a probe of the charge density in localized states, particularly in amorphous materials [104]. A large negative potential step is applied to a forward biased junction and... 

Example 3 Calculation of the I-t transient in response to a potential step from a potential where the rate of the electrode process... 

The response to a potential step is a current transient, a time-dependent current density (Fig. 1). These experiments are classified as chronoamperometiy. Potential transient as a response to current step experiments, formerly also called charging curves [5], is related to chronopotentiometiy. These transients are recorded and interpreted. Step experiments are large signal, time domain experiments and investigate processes far from equilibrium they are... 

The current density of a redox reaction will change, if the potential is changed. Chronoam-perometry usually starts at potentials without far-adaic processes. The response to a potential step, the current transient, cmitains the re-arrangement of the electrode interface, mainly double-layer charging, which is indicated by a current peak and can be reduced to some 10 ps in a suitable potentiostatic setup. Assuming a simple reaction... 

Figure 6.2(b) shows a trace of current against time in response to the potential step. The trace shows a rapid rise in current, with this rise requiring perhaps as long as a few thousands of a second (i.e. milliseconds). The time between the potential step and the maximum is known as the rise time. The current trails off smoothly after the rise time until, eventually, it reaches zero. Such plots are often termed transients to emphasize their pronounced time dependence. 

This last point, which has been ignored until now, in fact imposes limitations on all transient techniques. Essentially, in addition to the faradaic current flowing in response to a potential perturbation, there is also a current due to the charging of the electrochemical double-layer capacitance (for more details see Chapter 5). In chronoamperometry this manifests itself as a sharp spike in the current at short times, which totally masks the faradaic current. The duration of the double layer charging spike depends upon the cell configuration, but might typically by a few hundred microseconds. Since It=o cannot be measured directly it is necessary to resort to an extrapolation procedure to obtain its value, and whilst direct extrapolation of an /Vs t transient is occasionally possible, a linear extrapolation is always preferable. In order to see how this should be done we must first solve Pick s 2nd Law for a potential step experiment under the conditions of mixed control. The differential equations to be solved are... 

Fig. 22. Typical transient response of a La0 9Sr0 (Mn03 electrode to (a) a current step of 400 pA, (b) a potential step of 350 mV, located in region II. From ref. [76].

Figure 5.28 Current response for a 10 pm radius mercury microelectrode immersed in a 5 pM solution of adriamycin, following a potential step from —0.700 to —0.350 V the supporting electrolyte is 1.0 M perchlorate at a pH of 4.5. The inset shows the semi-log plot for data between the marks on the current-time transient, with the time axis being referenced to the leading edge of the potential step. From R. J. Forster, Analyst, 121, 733-741 (1996). Reproduced by permission of The Royal Society of Chemistry...

A calculated transient current response to a 10 mV step in potential, introduced at time to, is presented in Figure 7.1 for the electrical circuit inserted in the figure. The time constants for the circuit tmder the conditions of tiie simulation were Ti = 0.0021 s (76 Hz) and T2 = 0.02 s (8 Hz). The potentiail dependence of parameter l i is consistent with the behavior of the charge-transfer resistance described in Chapter 10. 

In a potential-step experiment, the potential of the working electrode is instantaneously stepped from a value where no reaction occurs to a value where the electrode reaction under investigation takes place and the current versus time (chronoamperometry) or the charge versus time (chronocoulometry) response is recorded. The transient obtained depends upon the potential applied and whether it is stepped into a diffusion control, in an electron transfer control or in a mixed control region. Under diffusion control the transient may be described by the Cottrell equation obtained by solving Tick s second law with the appropriate initial and boimdary conditions [1, 2, 3, 4, 5 and 6] ... 

Measurement of Membrane Resistance. For a given value of Cm, HI is a function of the potential across the semiconductor and insulator (Vt) The equivalent circuit can therefore be simplified as shown in Figure 4. For bias potentials near I pip, HI follows 4 approximately linearly. Because no significant direct current can flow through the insulator, Rm doesn t enter into the DC characteristics of this system, but only affects transient responses to changes in bias potential. Let us consider the case where the bias potential is stepped with time. Immediately after the potential step, the new bias potential will be distributed across the capacitances with the time constant Ti (Equation 5). Ci is the total capcitance of the insulator in contact with electrolyte and Co is the total capacitance of the depletion region under the electrolyte (therefore Ct is calculated for the area of the semiconductor in contact with solution and not just the illuminated area as in Equation 4). Re is due to the resistance of the electrolyte. 

The potential Ei is chosen so that no reaction occurs (7 = 0), then, at time / = 0 a pulse is made to a potential 2, where the reduction of O is diffusion controlled. After time r at this potential it is stepped back to a value 3, where R is reoxidised, usually to 0, again at a diffusion controlled rate. Thus the current that flows in response to the last pulse is used to monitor the amount of R present, the higher the value of k the less R there will be, and hence the lower the current observed. Fig. 2.12 shows the type of / vs r transient that is found, and it is most simply analysed in the following way which eliminates any dependence on the electrode area, solution concentration, or diffusion coefficients. The values of /f and the currents on the forward and back pulses respectively, are determined for a range of values of t, as shown in Fig. 2.12. It can be shown that the ratio —/ bAV is a rather complex function of k, t, and r [19]. However, it is a fairly simple matter to obtain k values by comparison of the experimentally determined value with working curves of this ratio plotted as a function... 

---