Scan Rate Dependencies

An alternative electrochemical method has recently been used to obtain the standard potentials of a series of 31 PhO /PhO- redox couples (13). This method uses conventional cyclic voltammetry, and it is based on the CV s obtained on alkaline solutions of the phenols. The observed CV s are completely irreversible and simply show a wave corresponding to the one-electron oxidation of PhO-. The irreversibility is due to the rapid homogeneous decay of the PhO radicals produced, such that no reverse wave can be detected. It is well known that PhO radicals decay with second-order kinetics and rate constants close to the diffusion-controlled limit. If the mechanism of the electrochemical oxidation of PhO- consists of diffusion-limited transfer of the electron from PhO- to the electrode and the second-order decay of the PhO radicals, the following equation describes the scan-rate dependence of the peak potential ... 

It is also possible to use microcalorimetry to obtain useful information about the kinetic processes of the instability (i.e., aggregation, proteolysis) when thermal irreversibility prevails. Scan rates will often distort the onset behavior of the melting transition that can necessarily impose a shift in the Tm, as discussed further in the following text. The scan rate dependence of the Tm may then be used to determine the activation energy of the instability, provided an Arrhenius kinetic model describes the behavior. 

Remmele, R.L., Jr., J. Zhang, V. Dharmavaram, D. Balaban, M. Durst, A. Shoshi-taiskvili, and H. Rand. 2004. Scan-rate dependent melting transitions of interleukin-1 receptor (type II) elucidation of meaningful thermodynamic and kinetic parameters of aggregation acquired from DSC simulations (submitted for publication). 

Figure 6. Cyclic voltammograms of a platinum disk-electrode modified with a film of the octanuclear dendrimer 2, measured in 0.1 M Bu NPFj/CHjClj. The surface coverage of electroactive ferrocenyl sites in the film is determined to be T = 2.01 x 10" mol cm . inset, scan rate dependence of the anodic peak current.

The two-electron reduction of both 3 and 4+ resulted in the elimination of a dtc ligand [23]. For these compounds, the two-electron reduction could be resolved in two separate one-electron steps. The first electron transfer for both 3 and 4+ led to partial dissociation of a dtc ligand nevertheless this step was quasi-reversible, as evidenced by the scan rate dependence of the peak-to-peak separation (AEp) [24] (Sch. 4). This was assigned to the fact that the decoordinated sulfur atom... 

When a ferrocene derivative loaded Pt/Nafion-GOD electrode is transferred to a phosphate buffer solution containing no ferrocene derivatives, the observed redox waves reflect their electrochemical behavior in the film. The scan rate dependence of the cyclic voltammetry for the Pt/Nafion-GOD incorporated with different ferrocene derivatives was studied. A linear plot of the anodic peak current against the square root of the scan rate was obtained in all cases, which is indicative of diffusion controlled redox process. Typical chronoamperometric... 

In these equations a = Rs + Rp,b = RSRPC, t is time, v = sweep rate, and x = 1/RSC + 1 IRVC. Time in Eq. (19) can be equated to the sweep rate since t = A pP/v. All three equations include a term that is independent of voltage scan rate and a second term that depends on voltage scan rate. The scan-rate-dependent term becomes negligible at low scan rates. Macdonald (31) and Townley (33) separately derived the current response of the standard three-element electrical equivalent circuit (Fig. 3a) to a small-amplitude triangular voltage excitation... 

The kinetics of the fac lmer isomerization step can be determined quantitatively from the scan-rate dependence of the oxidation process. Both theory and experiment show that the peak potential corresponding to the oxidation of the /ac° species ( p ) shifts to less positive potentials as the scan rate is increased. This occurs because the oxidation charge-transfer process is electrochemically reversible. Under these circumstances, the isomerization step following the charge transfer removes the product and causes the equilibrium position to move to the right in (41), which effectively facilitates the oxidation step. Consequently, at low scan rates, when the isomerization step is important, the oxidation process requires a lower thermodynamic driving force in order to occur and hence a less positive potential is observed. If the electron-transfer (E) step had been irreversible, the isomerization reaction would have no effect on the voltammetric response since the C step would not be rate determining and no kinetic data could be obtained. 

Similarly, phenothiazine may be oxidized to the cation radical species which then dimerizes forming the 3,10 -diphenothiazinyl species (Tsujino, 1969). The product of the electron-transfer step may react, via a second-order process, with a species in solution to form a new product. An example of this type of mechanism involves the reduction of anthraquinone and its derivatives in the presence of oxygen (Jeziorek etal., 1997). To understand quantitatively an EC and EC2 process, the concentration and scan-rate dependence of the associated cyclic voltammograms is matched with theory deriving from the mass transport/kinetic equations for each species. 

Plot the scan rate dependence of the peak currents and peak potentials (a) iv vs (scan rate)1/2 and (b) AEv vs scan rate. 

What does your scan rate dependence (for L = CN ) tell you ... 

Figure 3. Scan rate dependence of the Os(HI)/Os(II) surface couple for a typical Os(llXMe,PhP)(PyP)Cl, glassy carbon electrode (top) and ip versus v% and i, versus v plots for the anodic wave of this couple (bottom). Cyclic voltammograms were recorded with 0.1 M TEAP as supporting electrolyte.

If the former mechanism were correct (low k ), E would be given by Ep, + Ep /2. A similar procedure would give an incorrect number for the latter mechanism. Therefore, a redox mechanism must be understood if meaningful E values are to be obtained. In the above case in which a followup reaction (to produce Z) occurs, this could be diagnosed by bulk coulometric reduction of the molecule, followed by voltammetric measurements on the reduced solution. Then only the oxidation wave for Z would be observed in the electrolyzed solution. Another method of distinguishing these two mechanisms is from the scan-rate dependence of the AE value, which must follow that of a quasireversible system if Eq. (d) describes the mechanism. 

Electrochemical simulations of the concentration and scan-rate dependence of the voltammetry potentially provide the composition of the intermediates formed during the reaction cycle together with estimates of the rate and equilibrium constants. As shown in the preceding section spectroscopic information can greatly assist the elucidation of the molecular details of these reactions, however, reliable deduction of the structure is greatly enhanced by the incorporation of structural and computational information (Section 1.6). The rapid advance in computer power and implementation of density-functional theory allows a more quantitative approach for evaluation of proposed structures based on spectroscopic information and estimation of the relative energies of the proposed spe-cies. The recent computational study of the electrocatalytic reaction cycle proposed for illustrates the opportunities presented by the approach. 

The scan rate dependence is shown for two regular arrays of 1 pm microdisks, respectively, but with different values of Rq (or center-to-center distance d). 

The scan rate dependence on peak potential makes it dear that, at high microscopic coverage, a near-linear dependence of p on ln(v) applies, with the slope approaching RT/2F. At low 6, however, a hemispherical diffusion becomes predominant. With higher scan rates, the diffusion layer will become thinner and the diffusion regime more planar. Adjacent diffusion domains will then overlap with each other. 

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