Sweep-rate dependence

Thus, when the magnet is sweeping, the field lags the field calculated from the known current. The lag is sweep rate dependent, but may be rather precisely corrected for. 

As expected from the anisotropy of chemical etching of Si in alkaline solutions, the electrochemical dissolution reaction shows a strong dependence on crystal orientation. For all crystal orientations except (111) a sweep rate independent anodic steady-state current density is observed for potentials below PP. For (111) silicon electrodes the passivation peak becomes sweep rate dependent and corresponds to a constant charge of 2.4 0.5 mCcm-2 [Sm6]. OCP and PP show a slight shift to more anodic potentials for (111) silicon if compared to (100) substrates, as shown in Fig. 3.4. 

Figure 15. Dynamic hysteresis-loop effects (a) magnetic viscosity and (b) sweep-rate dependence. The sweep-rate dependence amounts to a fluctuation-field [165] or sweep-rate correction to the static coercivity Hco.

An effect closely related to magnetic viscosity is the dependence of the coercivity on the sweep rate rj = dH/dt Hc is largest for high sweep rates, that is, for fast hysteresis-loop measurements (Fig. 15). Sweep-rate and magnetic-viscosity dynamics have the same origin, but there is a very simple way of deriving a relation for the sweep-rate dependence. Let us assume that the energy barriers exhibit a power-law dependence... 

An experimental approach to analyze the resulting sweep-rate dependence of the coercivity is to exploit the phenomenological relation [159]... 

The manner in which kinetic data are treated in arriving at an electrode mechanism depends primarily upon whether the technique gives a direct measure of the response of the intermediate or an indirect measure, usually the effect of the chemical reaction on the electrode response of the substrate. In the former case, the conventional way of handling the data is to compare the experimental response with theoretical data in the form of a working curve and determine the mechanism from the best fit with theoretical data. The latter case usually involves the calculation of the electrode response to a particular mechanism and then comparing some measurable quantity, for example the sweep rate dependence of the peak potential, with the theoretical value. Which type of analysis is appropriate, direct or indirect, depends upon the... 

The LSV observables, the voltage sweep rate dependence (df /dlogv), the substrate concentration dependence (df /dlogCA), and the dependence of the peak potential upon the concentration of an additional reactant dlogCx) are given by eqns (60), (61) and (62), respectively. The symbols a, b,... 

Figure 68. Sweep rate-dependent micro-SQUID magnetization scans collected for [(triphos) Re (CN)3]4[Mn Cl]4 at 0.5 K showing hysteretic behavior. The outermost curve corresponds to a scan rate of0.560 T/s, and the scan rate decreases for each successive curve by a factor of 2, reaching the value of 0.008 T/s for the innermost curve. [Adapted from (214)].

Schultz and co-workers have used the sweep rate dependence of cyclic voltammograms to determine the rate constants for electron transfer between several coordination complexes and an electrode. When Kei=l, one expects A5 da < llJmol K for the electrochemical reaction (see also Section 7.11.2.7). However, substantial positive values were found for reactions that involve a net change of spin multiplicity. The largest was A5da = 137 J mol K for the [Co([9]aneN3)2] " couple (see also Section 7.11.3.3). 

Electrochemical measurements of the Cu(II/I) potentials with the nS4 ligands (n = 12-16) indicate that the Cu(II) and Cu(I) species each exist in two different conformational states [170]. Conformational rearrangement may either precede or succeed electron transfer. Rorabacher and coworkers interpreted their results in light of a square mechanistic scheme that neatly reconciles the sweep rate dependence of the cyclic voltammograms with the requisite change in coordination geometry at Cu. Kinetic studies on the electron transfer [149, 170, 176-177] support this scheme application of the Marcus cross relationship to reduction of Cu(II) and oxidation of Cu(I) yields widely discrepant values, presumably because of the different conformational states involved. 

CV shares essentially the same working principle with LSV, but the CV scans are repeated in triangular sweeps in both anodic and cathodic directions. Irreversible electrochemical reactions are readily detected in CV. Voltage sweep rate-dependent current features and scan-direction activated hysteresis of voltammograms serve as a useful metric for CV-based evaluations of slurry additives (Emery et al., 2005). The OCP (or oc) of a metal—solution interface has the same physical meaning as Ecorr for that system. While Econ is measured in the potentiodynamic mode, oc is generally determined in the potentiostatic mode as a function of time. The different nomenclatures are commonly used in view of these different methods used to measure the two parameters. 

Thus far this dicussion of cyclic voltammetry has assumed that all the reactants and products are freely soluble in the solution, and that surface processes, such as phase formation and removal, and reactant or product adsorption, need not be considered. If the peaks on an experimental cyclic voltammogram exhibit a shape or sweep rate dependence unlike those discussed so far, it is a good indication that surface processes may be involved. Cyclic voltammetry has proved a very useful technique for the quantitative investigation of reactions involving adsorption processes. It is less well suited to the study of surface reactions such as metal deposition and corrosion, other than as a diagnostic tool. 

Also, the kinetics of the Mo (VI) /Mo (V) electrode reaction become dependent on the composition of the Mo coordination environment Table 4 contains values of the apparent standard heterogeneous rate constant obtained ficmi the sweep rate dependence of the peak potential separation of reactions 10 and 12 [18]. The values of k, h for the catecholate complexes are smaller than that of MoO (Et2dtc)3 and decrease as the electron donating strengths of the catechol substituents increase. 

Figure 4. Sweep rate-dependence of cyclic voltammograms for the reduction of (TCNE)W(CO)5 in CHjClj/O.l M Bu NFF (different peak current scales).

The sweep rate dependence of R was investigated for the same reaction in the interval 15 < V < 160 V/s at 20 Figure 4 shows theoretical (line based on data in Table 1) and experimental (squares) data for vs kCIa assuming k 12.8 x 10 M s Again, the agreement between theoty and experiment is good. 

The diffusion coefficient, using the sweep rate dependence of the peak current by cyclic voltammetry... 

Further data illustrating the electrocatalytic behavior are contained in Figure 7. Figure 7 contrasts the concentration dependence of the first and second wave reduction currents at different voltammetric sweep rates. For (ox) (s-r) reduction, the plots of ip vs FeMoco concentrations are linear and display the sweep rate dependence expected for a diffusion-controlled electrode reaction. Plots of ip vs concentration for (s-r) (red) reduction are likewise linear, but display almost no dependence on sweep rate. Such behavior corresponds to Equations (7) and (8) operating under full catalytic conditions with the sweep-rate in-pendent current depending linearly on catalyst (FeMoco) concentration according to the relationship... 

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