Potential step methods diffusion control

A single DBP droplet is positioned in the vicinity of the microelectrode by the laser trapping technique, and the droplet-microelectrode (edge-to-edge) distance (L) is controlled arbitrarily in micrometer dimension. Knowing the oxidation potential of PPD in the water phase to be 30 mV, PPD is oxidized by a potential step method (100 mV) to induce the dye formation reaction. The anodic current relevant to oxidation of PPD reaches a steady-state value within a short electrolytic time (t) because of cylindrical diffusion of PPD to the microelectrode. The dye formation in the droplet can be easily confirmed by the color change from transparent to cyan or yellow. The dye formation reaction in a single microdroplet could be... 

The Cottrell equation is derived from Pick s second law of diffusion (Section 1.5) and predicts the variation of the current in time, when a potential step is applied under conditions of large overpotential. For this equation to be valid the current must be limited by diffusion of the analyte to the electrode surface, and thus the solution has to be unstirred. The overpotential at which the reaction is driven must be large enough to ensure the rapid depletion of the electroactive species (O) at the electrode surface, such that the process would be controlled by the diffusion to the electrode. This equation is most often applied to potential step methods (e.g., chronoamperometry see Chapter 11) ... 

The double potential step method (6) is included in this chapter as it underpins many other reversal techniques designed to study the stability of the product. Its principle is rather simple and it is a good stepping stone before tackling cyclic voltammetry. The potential is stepped to a value E- where species R is formed at a diffusion-controlled rate, and then, after a time t, to a more anodic value 2 where R is oxidised (Figure 11.2a). 

It follows from (10.12) or (10.13) that the photoelectrochemical disintegration of CU2O suggests consumption of H ions at the electrode surface. This process should be accompanied by a comparatively slow, diffusional mass transport in the solution. The sharp potential drop after the illumination is switched on creates the conditions that are similar to those for the potential step method. It can be showed that the quantities presented at t > 0 in Figure 10.13 vary linearly with 1 / that is characteristic of diffusion-controlled processes. 

The characteristic feature of solid—solid reactions which controls, to some extent, the methods which can be applied to the investigation of their kinetics, is that the continuation of product formation requires the transportation of one or both reactants to a zone of interaction, perhaps through a coherent barrier layer of the product phase or as a monomolec-ular layer across surfaces. Since diffusion at phase boundaries may occur at temperatures appreciably below those required for bulk diffusion, the initial step in product formation may be rapidly completed on the attainment of reaction temperature. In such systems, there is no initial delay during nucleation and the initial processes, perhaps involving monomolec-ular films, are not readily identified. The subsequent growth of the product phase, the main reaction, is thereafter controlled by the diffusion of one or more species through the barrier layer. Microscopic observation is of little value where the phases present cannot be unambiguously identified and X-ray diffraction techniques are more fruitful. More recently, the considerable potential of electron microprobe analyses has been developed and exploited. 

However, when one gets down to detailed quantitative equations to represent real, actual reactions with several steps in consecutive sequence, the mathematics become very complex. Thus, the change in the limiting current with time introduces complications that one tries to avoid in other transient methods by working at low times (constant current or constant potential approaches) or at times sufficiently high that the current becomes entirely diffusion controlled. However, taking into account the... 

The important concept in these dynamic electrochemical methods is diffusion-controlled oxidation or reduction. Consider a planar electrode that is immersed in a quiescent solution containing O as the only electroactive species. This situation is illustrated in Figure 3.1 A, where the vertical axis represents concentration and the horizontal axis represents distance from the electrodesolution interface. This interface or boundary between electrode and solution is indicated by the vertical line. The dashed line is the initial concentration of O, which is homogeneous in the solution the initial concentration of R is zero. The excitation function that is impressed across the electrode-solution interface consists of a potential step from an initial value E , at which there is no current due to a redox process, to a second potential Es, as shown in Figure 3.2. The value of this second potential is such that essentially all of O at the electrode surface is instantly reduced to R as in the generalized system of Reaction 3.1 ... 

In aqueous methanol, indomethacin exhibits a half-wave potential (E.,-) at the droning mercury electrode which is dependent upon pH. In 0.1M methanolic lithium chloride, indomethacin has two waves between -1.4v and -1.6v (vs. S.C.E.). The first step height is diffusion controlled and corresponds to a two electron reduction of the amide carbonyl. The second wave is believed to be a kinetic wave. The method as described is specific for nonhydrolyzed indomethacin and is suitable for analysis of capsules, suppositories and suspensions with precision of +1.2%, +0.7% and +1.2% for the respective formulations(43). 

Double-potential step chronoamperometry This method was proposed in 1965 by Schwarz and Shain [18] for the investigation of follow-up reactions especially for the mechanism. During the first potential pulse the product B is produced at a stationary electrode under diffusion-controlled conditions for a timed interval tp. During this interval substance B diffuses into the solution and simultaneously undergoes a chemical reaction. Then, the potential is suddenly switched to a value where B is converted back into A. The backward current indicates the amount of B which has not reacted and can be related to the rate constant kf. The forward current-time dependence is given by the Cottrell equation... 

Equation (96) can be solved analytically for two cases, as characterized by the kinetics of hydrogen transfer across the metal interface (i) pure diffusion control and (ii) diffusion control with a limited rate of entry (see Section III.1). As with the permeation methods, in both cases the layer of adsorbed hydrogen is assumed to adjust very rapidly to a potential step. 

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