Potential step methods continued

A related technique is the current-step method The current is zero for t < 0, and then a constant current density j is applied for a certain time, and the transient of the overpotential 77(f) is recorded. The correction for the IRq drop is trivial, since I is constant, but the charging of the double layer takes longer than in the potential step method, and is never complete because 77 increases continuously. The superposition of the charge-transfer reaction and double-layer charging creates rather complex boundary conditions for the diffusion equation only for the case of a simple redox reaction and the range of small overpotentials 77 [Pg.177]

For measurement of R/Rq t, the potential step method is frequendy used the electrode potential is first set at a potential where no adsorption of the sample occurs and then stepped up to the second potential where adsorption does occur. The R/Rq t curve continues to be recorded until no further change in R/Rq takes place. 

As was mentioned in Sects. 2.8.1 and 2.8.2, application of the Laplace transform to the transient potential and current permits determination of the operational impedance. Such a method was initially introduced by Pilla [90-93] and applied to studies using mercury electrodes. Using a fast potentiostat a small potential step was applied, and both voltage and current transients were measured. Of course, because of the nonideal potentiostat response, the potential increase was not a rectangular step but occiured more slowly. Examples of the measured potential and current transients are shown in Fig. 3.6. Such data acquisition was extended to longer times and then extrapolated as the integration had to be continued to inlinity. 

The periodic decreases in the applied potential and current density shown in Fig. 4 are due to the fact that the potential is not applied during the rise in temperature. Several workers have found that the continuous application of potential while temperature is increased continuously at a constant rate to be a more efficient and less complex method of testing [102], The primary reason for preferring the intermittent or step method (the latter is illustrated in Fig. 4) over the continuous method of ECT testing is that the step method better simulates the conditions of the conventional immersion-type test, in which samples are removed from the test solution after exposure at each temperature and inspected, then reimmersed. 

The central step in RG is the selection of a specific polymer trial conformation from an entire tree of possible conformations. The essential difference between the continuous-potential RG method and the earlier schemes is that the selection of the trial conformation involves two stochastic steps the first is the selection of a subset of open branches on the tree, the second is the selection of the trial conformation among the open branches. The crucial new concept in RG is that trial directions can be either open or closed. A trial direction that is closed will never be chosen as a part of the chain. For hard-core potentials, a trial direction is closed if it leads to a configuration that has at least one hard-core overlap - otherwise it is open. Therefore, the selection of the open trial directions is deterministic rather than stochastic. In contrast, for continuous potentials, we use a stochastic rule to decide whether a trial direction is open or closed. The probability that direction i is open depends on its energy ui, hence p = p (rq). It is important to note that, in principle, this stochastic rule is quite arbitrary, the only restriction is 0 < Pi < 1 (for hard-core potentials 0 < pt < 1). However, it is useful to apply the following restrictions [112]... 

There are many variants of the predictor-corrector theme of these, we will only mention the algorithm used by Rahman in the first molecular dynamics simulations with continuous potentials [Rahman 1964]. In this method, the first step is to predict new positions as follows ... 

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. 

Fig. 5.18 Potentiostatic methods (A) single-pulse method, (B), (C) double-pulse methods (B for an electrocrystallization study and C for the study of products of electrolysis during the first pulse), (D) potential-sweep voltammetry, (E) triangular pulse voltammetry, (F) a series of pulses for electrode preparation, (G) cyclic voltammetry (the last pulse is recorded), (H) d.c. polarography (the electrode potential during the drop-time is considered constant this fact is expressed by the step function of time—actually the potential increases continuously), (I) a.c. polarography and (J) pulse polarography...

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