Cyclic voltammetry modeling

One of the most problematic issues, still to be fully resolved, is the dependence of the degree of oxidation on potential, as measured most commonly by cyclic voltammetry at low scan rates. There is currently no accepted model to describe the shape of the curve and the hysteresis between anodic and cathodic scans. The debate over whether the charge has a significant component due to a polymer/solution double layer is still not fully resolved. 

Figure 6.8 S-shaped polarization curve observed in the CO oxidation model (for the exact model parameters, see Koperetal. [2001]). The thin line shows the cyclic voltammetry observed at a low scan rate of 2 mV/ s.

Figure 8.16 (a) Cyclic voltammetry for Pt(lll)-nPd deposited in UHV and in 0.05 M H2SO4 with 50mV/s. (b-e) corresponding LIES spectra after wML Pd deposition (0 < n < 1) He energy = 1 keV. (e) Ball models assessed from the in situ SXS analysis. 

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. 

On the basis of theoretical calculations Chance et al. [203] have interpreted electrochemical measurements using a scheme similar to that of MacDiarmid et al. [181] and Wnek [169] in which the first oxidation peak seen in cyclic voltammetry (at approx. + 0.2 V vs. SCE) represents the oxidation of the leucoemeraldine (1 A)x form of the polymer to produce an increasing number of quinoid repeat units, with the eventual formation of the (1 A-2S")x/2 polyemeraldine form by the end of the first cyclic voltammetric peak. The second peak (attributed by Kobayashi to degradation of the material) is attributed to the conversion of the (1 A-2S")x/2 form to the pernigraniline form (2A)X and the cathodic peaks to the reverse processes. The first process involves only electron transfer, whereas the second also involves the loss of protons and thus might be expected to show pH dependence (whereas the first should not), and this is apparently the case. Thus the second peak would represent the production of the diprotonated (2S )X form at low pH and the (2A)X form at higher pH with these two forms effectively in equilibrium mediated by the H+ concentration. This model is in conflict with the results of Kobayashi et al. [196] who found pH dependence of the position of the first peak. 

Cyclic voltammetry (CV) curves were recorded on a Kipp and Zonen BD91 X-Y recorder and the current-time transients resulting from the potential step experiments were recorded digitally. The apparatus used included a PAR Model 173 potentiostat and an IBM XT computer... 

Cyclic voltammetry experiments were controlled using a Powerlab 4/20 interface and PAR model 362 scanning potentiostat with EChem software (v 1.5.2, ADlnstruments) and were carried out using a 1 mm diameter vitreous carbon working electrode, platinum counter electrode, and 2 mm silver wire reference electrode. The potential of the reference electrode was determined using the ferrocenium/ ferrocene (Fc+/Fc) couple, and all potentials are quoted relative to the SCE reference electrode. Against this reference, the Fc /Fc couple occrus at 0.38 V in acetonitrile and 0.53 V in THF [30, 31]. 

In particular, from the analysis in the very low frequency region, the limiting capacitance Q can be evaluated (via the limiting resistance R ). Practical cases have given values of Cj, of about 20mFcm (Panero et al, 1989), i.e. values of the same order as those obtained by cyclic voltammetry, thus confirming the validity of the charge saturation model. 

Figure 18. Schematic model of the structure of Pt particles on an voltammogram in relation to the electrode potential. The hydrogen, double layer, and oxide regions are based on cyclic voltammetry. The lattice disorder decreases in the order D>A>C>B." (Reproduced with permission from ref 40. Copyright 1993 ElsevierSequoia S.A., Lausanne.)...

Rajca and co-workers have studied star-branched and dendritic high-spin polyradicals which are potential organic magnets. Representative data were obtained for the model tetra-anionic compound 55. Three redox waves were observed by cyclic voltammetry and differential pulse voltammetry for a four-electron process between the potentials of -2.00 and -1.20 V (vs. SCE). Electrochemical experiments with these materials have usually been performed at 200 K. The polyradicals, which are less stable for systems with more unpaired electrons, have been characterized by spectroscopic studies, ESR data, and SQUID magnetometiy. 

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