Convolutive techniques, potential sweep

Linear sweep voltammetry Ep measurements have not been applied extensively for the study of heterogeneous charge transfer kinetics. A serious problem with the use of this method is that Ep in itself is not significant in this respect but rather Ep — Etev is the quantity of interest. While AEP in CV is readily measured, this cannot be said for Etev using only LSV as a measurement technique. Therefore, there does not appear to be any advantage in LSV for the study of electrode kinetics. A more detailed analysis of the LSV wave, by convolution potential sweep or normalized potential sweep voltammetry (both to be discussed later) can provide both a and k°. 

Convolution potential sweep voltammetry (CPSV) refers to the mathematical transformation of LSV current—potential data resulting in curves with shapes like conventional polarograms which are suitable for logarithmic analysis. The method was first proposed for the study of electrode kinetics by Imbeaux and Saveant [74] but is equivalent in all respects to a semi-integral technique reported earlier by Oldham [75— 77]. A very readable description of the method has been presented by Bard and Faulkner [21]. 

Basically, experimental approaches to ion transfer kinetics rely on classical galvanostatic [152] or potentiostatic [146] techniques, such as chronopotentiometry [118, 138], chronocoulometry [124], cyclic voltammetry [146], convolution potential sweep voltammetry [147], phase selective ac voltammetry [142], or equilibrium impedance measurements [148]. These techniques were applied mostly to liquid-liquid interfaces with a macroscopic area (typically around 0.1 cm ). However, microelectrode methodology has been successfully introduced into liquid-liquid electrochemistry as a novel electroanalytical tool by Senda and coworkers [153] and... 

In the more advanced kinetic measurements, which were carried out by using chronopotentiometry [118], chronocoulometry [124, 139], linear [146] and convolution [18, 147] potential sweep voltammetry, or phase-sensitive ac polarography [142, 143], the ohmic drop was either numerically subtracted [118], or compensated [124, 139, 142, 143, 146, 147] with the help of the positive feedback. The feedback adjustment was based either on the assumption that the separation of the current peaks measured by the slow potential sweep voltammetry should reach the value of (59/z)mV [124, 139, 146, 147], or on the value of the solution resistance obtained by an ac bridge technique [142, 143]. However, the former adjustment is not very sensitive, whereas the estimated accuracy of 10 Q [142] in the latter case may not be... 

Most of the more advanced techniques have only rarely been used outside the laboratories where they have been developed, and for that reason it is not easy to give recommendations. Examples include normalized sweep voltammetry [34,35,157,158], linear current-potential analysis [33], and the so-called global analysis and related techniques [159-161]. However, one such technique, convolution potential sweep voltammetry, has gained some popularity, and is introduced briefly here. 

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) ... 

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). 

The convolution or semi-integral technique offers advantages in the processing of data obtained by CV for diffusion controlled systems. For a reversible redox couple, in an experiment of CV, the convoluted current curves, l(t) vs. E for forward and reverse sweeps are superimposed, returning to zero at a E sufficiently positive fixrm the formal potential of the redox couple 0/R, where Cr(0, t) = 0, as shown in Figure lb. 

The systematic application of modern electrochemical methodology proved in a first instance to be a very useful tool to gather thermodynamic information, as Gibbs energies of transfer from half-wave potential measurements. Then, in 1981, Samec et al used convolution linear sweep voltammetry to address experimentally the fundamental aspects of ion transfer reactions. The main advantage of this technique when studying charge trans-... 

In 1990, Shao and Girault started a series of investigations based on the kinetic study of the transfer of acetylcholine Ac = CH3C02CH2CH2N (CH3)3 in which the physical properties of one of the solvents were varied. The experimental approach for the measurement of the kinetic parameters was chronocoulometry, a technique which, like convolution linear sweep voltammetry, does not impose any prerequisites on the potential dependence of the rate constants. To verify the suitability of the experimental method, they studied the potential dependence of the rate constant for Ac transfer from water to oil and from oil to water. As illustrated in Fig. 7, the results obtained show that the apparent rate constants obey the Butler-Volmer relationship, expressed by Eq. 10. Note that Fig. 7 has been obtained from two independent experiments. In the first experiment, acetylcholine was only present in the aqueous phase as a chloride salt and forced to cross to the organic phase, whereas in the second, acetylcholine was only present in the organic phase as a tetraphenylborate salt and forced to transfer to the aqueous phase. 

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