Chronopotentiometry boundary conditions

This last general equation is implemented in the function COFUNC, described in Appendix C. The formula is applied in the seven-point form in the example program CHR0N0EX described in Appendix C, simulating chronopotentiometry. It must be applied before every new iteration, in order for the Co value to be in line with the other C values. In this program, the current is constant and it is the value of Co which is displayed and this should go to zero at T = 1 (Sect. 2.4.2). A more appropriate display might be the electrode potential, which is always the measured quantity, but this will be dealt with together with the more detailed discussion of boundary conditions in Chap. 6. 

This function can be inverted to calculate C0, given G this is useful in the formulation of some boundary conditions. For example, to take a simple case, in chronopotentiometry, one has constant G and computes Co from that and the concentration profile. The function COFUNC does this job. Both G and H are needed, but they appear as the product, so that product is passed to the function. 

A chronopotentiometry program, using CN, is shown here, again, as with the above C0TT CN, with equal intervals. The two programs are in fact very similar, differing only in the boundary conditions in the CN routine, and the initialisation. As before, old known concentrations always include a conforming Co. 

The theoretical treatments for the different voltammetric methods (e.g., polarography, linear sweep voltammetry, and chronopotentiometry) and the various kinetic cases generally follow the procedures described previously. The appropriate partial differential equations (usually the diffusion equations modified to take account of the coupled reactions producing or consuming the species of interest) are solved with the requisite initial and boundary conditions. For example, consider the EfCi reaction scheme ... 

A different boundary condition is the Neumann condition or derivative boundary condition. An example is seen with chronopotentiometry. Equation sets (4 and 10). The procedure here is that a value of Co is computed such that it fits with the concentration profile (set of points C. .. Cn), so as to satisfy the gradient specification. Using the simple two-point approximation (33) and given a G value, this yields an expKcit expression for Co,... 

Integration of equation (1.48) with initial and boundary conditions appropriate to the particular experiment is the basis of the theory of instrumental methods such as chronopotentiometry, chronoamperometry and cyclic voltammetry. The first law applied at the electrode surface, x = 0, is used to relate the current to the chemical... 

Unlike cyclic voltammetry, the solution of Pick s diffusion equations [Eqs. (2.34) and (2.35)] for chronopotentiometry can be obtained as an exact expression by applying appropriate boundary conditions. For a reversible reduction of an electroactive species [Eq. (2.9)], the potential-time relationship has been derived by Delahay for the case where O and R are free to diffuse to and from the electrode surface, including the case where R diffuses into a mercury electrode. 

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