Potential step methods generally

In potential step voltammetry, a DC potential window is covered by a DC ramp (linearly increasing applied DC potential) with discrete and symmetrical pulses superponated to this ramp. As an alternative, the pulse amplitude can increase with each pulse, superponated on a constant DC offset. Methods where pulses are involved superponated on a DC signal are generally called potential step methods. 

Experimental results obtained at a rotating-disk electrode by Selman and Tobias (S10) indicate that this order-of-magnitude difference in the time of approach to the limiting current, between linear current increases, on the one hand, and the concentration-step method, on the other, is a general feature of forced-convection mass transfer. In these experiments the limiting current of ferricyanide reduction was generated by current ramps, as well as by potential scans. The apparent limiting current was taken to be the current value at the inflection point in the current-potential curve. 

The principle of this method is quite simple The electrode is kept at the equilibrium potential at times t < 0 at t = 0 a potential step of magnitude r) is applied with the aid of a potentiostat (a device that keeps the potential constant at a preset value), and the current transient is recorded. Since the surface concentrations of the reactants change as the reaction proceeds, the current varies with time, and will generally decrease. Transport to and from the electrode is by diffusion. In the case of a simple redox reaction obeying the Butler-Volmer law, the diffusion equation can be solved explicitly, and the transient of the current density j(t) is (see Fig. 13.1) ... 

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 ... 

Usually, the study of the kinetics of quasireversible electrode reactions by constant-current techniques (generally called the galvanostatic or current step method) involves small current perturbations, and the potential change from the equilibrium position is also small. When both O and R are initially present, the linearized current-potential-concentration characteristic, (3.5.33), can be employed. Combination with equations 8.2.13 and 8.2.18 (with the latter modified by an added term, Cr) yields... 

In order to be able to easily compare the properties of different methods in a unified way, we focus in this chapter primarily on a particular class of schemes, generalized one-step methods. Suppose that the system under study has a well defined flow map , defined on the phase space (which is assumed to exclude any singular points of the potential energy function). The solution of the initial value problem, z = /(z), z(0) = may be written z(f,<) (with z(0,( ) = <), and the flow-map satisfies = z(f, 5). A one-step method, starting from a given point, approximates a point on the solution trajectory at a given time h units later. Such a method defines a map % of the phase space as illustrated in Fig. 2.1. 

For the electroactive species, the form of the surface conditions depends on the electrochemical technique employed (see Section 1.2). Thus, in current-controlled techniques, the surface condition establishes the surface flux of the species according to the value of the current imposed (Eq. (1.14)). In potential-controlled methods the applied potential determines the surface concentration and flux of the electroactive species through the kinetics of the electrode reaction. In general, for the one-step process (1.1), this can be expressed according to the following first-order rate law for an interfacial process ... 

The difference from classical force field based simulations where the forces are calculated from pre-defined pair potentials is that the forces are derived from the global potential energy surface of an electronic structure theory. The vastly higher computational costs of an electronic structure calculation restrict the system size and the length of trajectories accessible by ab initio molecular dynamics simulations. However, it becomes clear that CPMD and AIMD are important steps towards general predictive methods, due to their independence from parameterizations. 

Kinetic parameters are obtained fromA-r transients by fitting experimental data to model calculations. Where possible these are made analytically but generally they are the result of computer simulations, usually carried out using the finite difference method (see Appendix). Details of the techniques used are given by Kuwana Winograd [7], whilst Hanafey et al [8] discuss the use of double potential step optical measurements which are very effective at differentiating between reaction mechanisms. 

In summary, there is a difference between the jump diffusirai coefficient, which reflects the random walk of a particle in the available DOS and geometry, and the chemical diffusion coefficient measured by inducing a gradient by a small step method. The difference is expressed in (87) and cmisists of the thermodynamic factor that accounts for the difference between a gradient in concentration, and a gradient in electrochemical potential, thus generalizing Pick s law [12],... 

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