Convolutive potential sweep voltammetry

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

The heterogeneous rates of electron transfer in eq 7 were measured by two independent electrochemical methods cyclic voltammetry (CV) and convolutive potential sweep voltammetry (CPSV). The utility of the cyclic voltammetric method stems from its simplicity, while that of the CPSV method derives from its rigor. 

We deemed it necessary to confirm the CV results by the alternate method using convolutive potential sweep voltammetry, which requires no assumptions as to the form of the free energy relationship and is ideally suited for an independent analysis of curvature revealed in Figure 7. In convolutive linear sweep voltammetry, the heterogeneous rate constant ke is obtained from the cur-... 

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]. 

Aalstad and Parker, 1980, 1981 Linear current potential analysis df/df/Z/P) p Normalized potential sweep voltammetry Convolution potential sweep voltammetry... 

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... 

When the transport of reactants is controlled by linear diffusion, the kinetic analysis can be performed using convolution potential sweep voltammetry [182]. Here it is more convenient to choose one of the reactant concentrations to be equal to zero, i.e., the initial conditions are recovered at sufficiently negative or positive potentials as in linear potential sweep voltammetry. By using the Laplace transform and the convolution theorem in solving the second Fick equation for each reactant, the convolution current m. 

Fig. 22. Logarithm of the apparent backward rate constant Ic vs. the potential E (Tafel plot) of electron transfer between ferrocene in nitrobenzene and hexacyanoferrate(III) in water derived from convolution potential sweep voltammetry. Composition of the aqueous phase I mM K3[Fe(CN)5] + LiCl (O, A, V) or NaCl ( ) or KCl (3). Nitrobenzene phase 0.01 M ferrocene and Bu4NPh4B. Concentration of both base electrolytes 0.01 M (O, , 3), 0.05 M (A) or 0.1 M (V). (After [193]).

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. 

Horvath and Horvai [23] also investigated the VITTM using a poly(vinyl chloride) membrane, which contained hydrophobic electrolytes by changing the ionic composition of aqueous phases, and found that the VITTM was characterized by the ion transfer at two aqueous/membrane interfaces. Samec et al. [24] proposed the theory of the cyclic and convolution potential sweep voltammetry of a reversible ion transfer through a liquid... 

Samec, Z., V. Marecek, J. Weber, and D. Homolka (1981). Charge transfer between two immiscible electrolyte solutions. Part Vll. Convolution potential sweep voltammetry of cesium(l-t-) ion transfer and of electron transfer between ferrocene and hexacyanoferrate(ni) ion across the water/nitrobenzene interface. J. Electroanal. Chem. 126, 105-119. 

Imbeaux, J.C. and Saveant, J.M. (1973) Convolutive potential sweep voltammetry. I. Introduction. Journal of Electroanalytical Chemistry, 44,169-187 and following papers in this volume of Journal of Electroanalytical Chemistry. 

In the case of semiinfinite linear diffusion the semiintegration coincides with the simplest case of convolutive potential sweep voltammetry ... 

Pilo, Maria I., Sanna, G. and Seeber, R. (1992) Analysis of cyclic voltammetric responses by Fourier transform-based deconvolution and convolution procedures , J.Electroanal.Chem. 323, 103-115. See references therein for semiintegral and semidifferential electroanalysis, as well as for convolutive potential sweep voltammetry. 

Kinetic data were obtained by electrochemical methods hke cychc voltammetry (CV), convolution potential sweep voltammetry (CPSV), stationary polarisation curves and electrochemical impedance... 

Imbeaux JC, Saveant JM (1973) Convolution potential sweep voltammetry I. Introduction. J Electroanal Chem 44(2) 169-187. doi 10.1016/S0022-0728(73)80244-X... 

Nadjo L, Saveant JM, Tessier D (1974) Convolution potential sweep voltammetry 111. Effect of sweep rate cyclic voltammetry. J Electroanal Chem 52(3) 403 12. doi 10.1016/ S0022-0728(74)80450-X... 

Saveant JM, Tessier D (1975) Convolution potential sweep voltammetry V. Determination of charge transfer kinetics deviating from the Butler-Volmer behaviour. J Electroanal Chem 65(l) 57-66. doi 10.1016/0368-1874(75)85105-7... 

---