Potential-Step Experiments

Initial and boundary conditions in such an experiment include Co(x,0) = C0(b) [i.e., at / = 0, the concentration is uniform throughout the system and equal to the bulk concentration, C0(b)], Co(0,t) = 0 for / 0 (i.e., at later times the surface concentration is zero) and C0(x,0) - C0(b) as % - °° (i.e., the concentration increases as the distance from the electrode increases). Solution to Fick s laws (for linear diffusion, i.e., a planar electrode) for these conditions results in a time-dependent concentration profile  

the current decreases in proportion to the square root of time, with (nDot)112 corresponding to the diffusion-layer thickness. 

Solving Eq. (1.8) (using Laplace transform techniques) will yield the time evolution of the current of a spherical electrode  

The current response of a spherical electrode following a potential step thus contains both time-dependent and time-independent terms—reflecting the planar and spherical diffusional fields, respectively (Fig. 1.3)—becoming time independent at long timescales. As expected from Eq. (1.12), the change from one regime to another is strongly dependent on the radius of the electrode. 

The unique mass transport properties of ultramicroelectrodes (discussed in Section 4.5.4) are attributed to shrinkage of the electrode radius. 

FIGURE 1-2 Concentration profiles for different times t after the start of a potential-step experiment. 

Instead of cycling the potential, the potential can be changed in one step from one level (El) at which the overpotential (rii) is too low to cause any reaction to another level (E2) at which the overpotential (TI2) is so high that the reaction is controlled by the mass transport rate. The corresponding current versus time accompanying the potential step is recorded and analyzed such an experiment is called chronoamperometry. 

Prior to the potential step from Ej to E2, the concentration of the reactant at the surface of the electrode is the bulk concentration C. After the potential is stepped to E2, the surface concentration of the reactant decreases to zero because it reacts immediately under the high overpotential TI2. As time proceeds, the reaction zone depletes, the diffusion distance from the bulk to the eleetrode surface increases, and thus the concentration gradient deereases. So, the current declines with time. On a planar electrode, the eurrent i(t) at any time t is given by the Cottrell equation  

If a spherical electrode or a micro planar electrode is used in the experiment, the diffusion becomes spherical, and the Cottrell equation becomes 

A potential step experiment is typically carried out for a duration of less than a few minutes for the following reasons. First, the reaction zone depletes quickly, so that a longer time is not needed to obtain a well-developed i-t curve. Second, over a longer time the results are likely to be complicated by convection due to the buildup of density gradients and the environmental vibration. 

A charging current will exist during the short duration of the experiment. The charging current can be significant immediately following the potential step. Data obtained in the absence of the active species under the same condition are often used to correct for the charging current. 

---

Alternately, for potential-step experiments (e.g., chronoamperometry, see Section 3-1), the charging current is die same as that obtained when a potential step is applied to a series RC circuit ... 

The potential-step experiment can also be used to record the charge versus tune dependence. This is accomplished by integrating the current resulting from the... 

Derive the Cottrell equation by combining Fick s first law of diffusion with the tune-dependent change of the concentration gradient during a potential-step experiment. 

As an alternative to potential step experiments, current steps have also been used.163,166,167 Again, small-amplitude experiments are preferable,163 and a migration model should be used for data analysis.167... 

Two types of potential step experiments were carried out in this work those in which the working electrode was electrochemically cycled in acid electrolyte alone (type A) before methanol was admitted with the electrode held at a very low potential, and those in which the electrode was cycled in acid electrolyte in the presence of methanol (type B) before the spectroscopic... 

The initial stages, notably the formation of a monolayer on a foreign substrate at underpotentials, were mainly studied by classical electrochemical techniques, such as cyclic voltammetry [8, 9], potential-step experiments or impedance spectroscopy [10], and by optical spectroscopies, e.g., by differential reflectance [11-13] or electroreflectance [14] spectroscopy, in an attempt to evaluate the optical and electronic properties of thin metal overlayers as function of their thickness. Competently written reviews on the classic approach to metal deposition, which laid the basis of our present understanding and which still is indispensable for a thorough investigation of plating processes, are found in the literature [15-17]. 

Fig. 19. Sampled-current voltammogram constructed from the current-time transients that resulted from a series of potential-step experiments at a stationary Pt electrode in a 35.0 x 10 3 mol L-1 solution of Ni(II) in the 66.7 m/o AlCl3-EtMeImCl melt ( ) total current, ( ) partial current for the electrodeposition of Ni, (O) partial current for the electrodeposition of Al. The total current was sampled at 3 s after the application of each potential pulse. Adapted from Pitner et al. [47] by permission of The Electrochemical Society. 

Cyclic voltammetry (CV) curves were recorded on a Kipp and Zonen BD91 X-Y recorder and the current-time transients resulting from the potential step experiments were recorded digitally. The apparatus used included a PAR Model 173 potentiostat and an IBM XT computer... 

A- Single Step Experiments. Potential step experiments were performed in order to determine the reaction mechanism and the reaction rate. As described above, the platinum surface was initially covered by a monolayer of CO at a controlled potential, Ef = 0.40 V (referred to as the initial potential) and then CO was removed from the bulk of the solution. Next, the electrode potential was suddenly changed to a more positive value, Ef, (referred to as the final potential) where the adsorbed CO was oxidized and the rate of oxidation was followed by recording the resulting current transients. 

Figure 2. Three-dimensional plots of the CO oxidation transients determined in the single potential step experiments on the Pt(100) electrode in 0.10 M HC10., solution. The potential step was applied from E = +0.40 V to Ep displayed on the third axis of the figure.

During the potential step experiment, the initial condition (I.C.) and the boundary condition (B.C.) are given as... 

Figure 48 Chronoamperometric double potential step experiment for the process Ox + ne Red inversion time t = 0.2 s. The top part shows the perturbation of the potential applied to the working electrode with time...

Figure 49 The variation of the current ratio in a double potential step experiment for a simple reduction process (t > t)...

Since the effects of the preceding chemical reaction substantially affect the forward response, the single potential step experiment can be adequately used. 

Let us consider, for example, a single potential step experiment that takes place in the equivalent circuit illustrated in Figure 3 (see Chapter 1, Section 5). 

Potential step experiments were conducted to study the electrocatalytic activities of a dean platinum surface. The appUed potential step sequence included 250-600 mV for the measurement after three pretreatment steps, i. e. 1550 mV for 5 s, 1050 mV for 20 s and 30 mV for 2 s. The last step for the pretreatment, 30 mV for 2 s, was added to the steps described earlier for other measmements in order to reduce Pt-OH,... 

Pulse sequence and resulting data for a potential step experiment... 

Figure 5.14 Pulse sequence and resulting data for a potential step experiment (hydrogen saturated solution, 4S°C, 1,500 rpm and pH 6.94).

Simulation of a Potential-Step Experiment for a Reversible E Reaction [1 ]... 

Several detailed studies of electrochemiluminescence emission under controlled potentials have been conducted.11 13,63"67 These have been double potential step experiments where one of the ion radicals was first generated at a potential slightly more negative (or positive, for cation generation) than its half-wave potential for a short time period, and then the potential at the electrode was switched to some... 

Double potential step experiments have provided useful information on some details of the electrochemiluminescence phenomenon. As expected, they have shown that emission is not generated on potential reversal when the initially generated ion is not sufficiently stable to be detected with cyclic voltammetry. Furthermore, current reversal with... 

---