Convolution linear sweep voltammetr

An answer to this lies in the transformation of the linear sweep response into a form which is readily analysable, i.e. the form of a steady-state voltammetric wave. Two independent methods of achieving this goal have been described the convolution technique by Saveant and co-workers11,12, and semi-integration by Oldham13. In this section we describe the convolution technique, and demonstrate the equivalence of the two approaches at the end. 

The convolution technique offers a number of advantages in the treatment of linear sweep data (and perhaps also in other electrochemical techniques). For a reversible reaction in a cyclic voltammetric experiment, the curves of l(t) vs. E for the forward and backward scans superimpose, with l(t) returning to zero at sufficiently positive potentials [where Cr(0, 0 = 0]. This behavior has been verified experimentally (20, 25, 28) (Figure 6.13a). 

In this section we use the well established theory of simple electron processes to re-emphasise the advantages obtained by implementing convolution techniques as opposed to the more conventional linear sweep diffusion controlled chronoamperometric criteria based directly on the current. The brief review also serves to stress the feature that such expressions obtained need not depend on any particular experimental voltammetric technique indeed one can combine data from say cyclic chronoamperometric experiments as a composite test of adherence to the proposed mechanistic scheme. 

By proper treatment of the linear potential sweep data, the voltammetric i-E (or i-t) curves can be transformed into forms, closely resembling the steady-state voltammetric curves, which are frequently more convenient for further data processing. This transformation makes use of the convolution principle, (A.1.21), and has been facilitated by the availability of digital computers for the processing and acquisition of data. The solution of the diffusion equation for semi-infinite linear diffusion conditions and for species O initially present at a concentration Cq yields, for any electrochemical technique, the following expression (see equations 6.2.4 to 6.2.6) ... 

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