LSV slopes

The effect of substrate concentration on the LSV slope for the reduction of 1,1-diphenylethylenea... 

A comparison of LSV slopes obtained from peak and half-peak potential measurements6... 

It was later shown by Parker, on the basis of an analysis of the extensive theoreticel calculations which had been published, that the LSV slopes could be related directly to reaction orders and hence rate laws without consideration of any particular mechanism [66]. For the general rate law... 

Attempts to conduct an LSV mechanism analysis of the reduction of Fl=Nj in DMF were inconclusive due to the irreproducibility of the response. However, the system was found to be well behaved in CH3CN and quantitative data, reproduced in Table 9, were obtained (Parker and Bethell, 1980). It was necessary to restrict v to 1.0 V or less because of the interference of the rate of heterogeneous charge transfer with the response. Use of analog differentiation of the response resulted in precision of 0.2 mV in the peak potentials and the LSV slopes were observed to be 20.7 1.7 and 19.4 1.4 mV decade-, for d /dlogv and df /dlogCA, respectively. The application of (60) and (61) provides the basis for assigning rate law (97) for the reactions... 

Very thorough theoretical analyses of the theoretical LSV slopes, dE jd log v and dEp/dlogC, for various reaction mechanisms were carried out by Nicholson and Shain [12, 13] and Saveant et al. [14-17]. These slopes are very useful in the elucidation of reaction mechanisms. By adaptation of the approach proposed by Parker [18], it is possible to develop simple general equations that directly relate the LSV slopes to the kinetic rate law of the process of interest. The rate law is assumed to be of the general type... 

In Table 3, the LSV slopes for some of the most common mechanisms are listed. 

Oxidation in the presence of pyridine gave the products in 60-85% yield, whereas the electrolysis without pyridine lowered the yield to 10-20% and the products of hydrolysis, because of the accumulation of the acid in the anodic compartment, were identified. The reaction mechanism was proposed on the basis of LSV and CPSV results. The values of dEp/dlogv = 30 mV and dEp/dlogC = 0 mV point to the occurrence of a first-order rate-determining step. Comparison of the CPSV slope values of 58 mV with the theoretical value... 

The interpretation of the anodic branch of LSV for p-Si is apparently more simple because the current increases following an exponential variation with a Tafel slope of 60-80 mV/decade. In this case, an accumulation layer is generated, and then the current is only controlled by the kinetics of the electrochemical reaction, which involves several successive steps. It is not necessary to account for the various reaction paths proposed by many authors. 

These three relationships provide useful experimental criteria for reversible LSV waves. A plot of Ipjvl/2C0 vs. vx/1 is expected to be linear with zero slope. The peak and half-peak potentials for Nemstian charge transfer are independent of v and Ep — Epa is expected to be equal to 56.5/n mV at 298.1 K. 

Measurements of Epf2 were also compared with Ep obtained by differentiation of the response. The substrate concentration in these experiments was varied from 0.50 to 2.00 mM (Table 9). In this case, the standard deviations in the mean values, 28.92 ( 0.60) for AEp/Alogv and 28.14 ( 0.29) mV decade-1 for AEp/2/A log p, are greater than expected from the other data. This is due to the fact that the values obtained at the lowest substrate concentration are abnormally low and perhaps should not be included in the averaging. It appears that the level of precision is very nearly the same for the two types of measurement. The slopes derived from Ep are somewhat closer to the theoretical value than are those from Ep/2. This suggests some deviation from theory of the shape of the LSV wave for this process. 

The reaction order approach for the LSV response to simple reaction mechanisms, eqns. (49)—(51), has already been described. These equations are applied directly to experimental data and rate laws are derived before a mechanism or a theoretical model is considered. Since RA and RB are separable during LSV analysis, the changes in RB as a function of CA can be observed directly from djf p/d log v [72], When RB is changing with changes in CA, this slope will not be linear over large intervals but will appear to be linear over small intervals of v. For the reaction order analysis, CA was defined as the concentration when RB is half-way between the limiting values, usually 1 and 2, i.e. 1.5. In terms of n, multiples of CA, there are again three distinct cases which must be satisfied by f(n). They are n = 1 (,RB = 1.5), n < 1 (RB = 1) and n> 1 (RB = 2). These requirements are satisfied by eqn. (65) and illustrates how RB varies with n. 

Normalized potential sweep voltammetry (NPSV) involves a three-dimensional analysis of the LSV wave where the normalized current (I/Ip) is taken as the Z axis, theoretical electrode potential data as the X axis, and experimental electrode potential data as the Y axis, with the potential axes defined relative to Ep/2. The method is illustrated by the voltammogram in Fig. 15. The projection of the wave on to the X—Y plane results in a straight line of unit slope and zero intercept if the theoretical and experimental data describe the same process. In practice, NPSV analysis simply involves the linear correlation of experimental vs. theoretical electrode potentials at particular values of the normalized current. 

Reaction (77) was also studied using only the forward LSV scan by NPSV analysis [46]. The data are shown in Table 28. The value of fe° determined over a wide range of conditions was 0.29 0.02, which is somewhat lower than that resulting from the DCV study but close to that reported by BarAnski and Fawcett [83] from a.c. measurements, i.e. 0.30 cm s 1. The term mT — 1 is the NPSV slope, i.e. experimental data vs. that for Nernstian charge transfer, with /N ranging from 0.20 to 0.80. 

A more detailed LSV study [58, 89] resulted in the conclusion that the kinetics, under all conditions, could not be described by the simple eCej, scheme. It was proposed that the reaction order in anthracene anion radical (AN- ) varies between 1 and 2 and the reaction order in phenol is greater than 1. A complex mechanism was also indicated from DCV measurements [89]. At a phenol concentration of 10 mM, values of dEpj d log v were in all cases close to that expected for a reaction second order in An-, i.e. 19.5mV decade-1 under the conditions of the experiments. The process is fast enough under these conditions for it to be expected to fall well within the KP zone. That this is the case was indicated by the fact that d p/dlog v was linear over a reasonably wide range of v (10— 1000 mV s-1). The highest value of the slope, observed at a phenol concentration of 100mM, was still significantly lower than 29.3 mV decade -1 predicted for a pseudo-first-order reaction. 

The term voltammetry refers to measurements of the current as a function of the potential. In linear sweep and cyclic voltammetry, the potential steps used in CA and DPSCA are replaced by linear potential sweeps between the potential values. A triangular potentialtime waveform with equal positive and negative slopes is most often used (Fig. 6.8). If only the first half-cycle of the potential-time program is used, the method is referred to as linear sweep voltammetry (LSV) when both half-cycles are used, it is cyclic voltammetry (CV). The rate by which the potential varies with time is called the voltage sweep (or scan) rate, v, and the potential at which the direction of the voltage sweep is reversed is usually referred to... 

LSV is a powerful tool for the study of processes under purely kinetic control. Theoretical analyses of the response for various mechanisms have been carried out [13,15-26], and a series of papers [36,72,79,93] has been devoted to assimilating the theoretical results in a form useful to the experimentalist. For the general rate law, Eq. (33), the dependence of Ep on changes in log v>, log Ca, and log Cx, respectively, is linear with the slopes given by Eqs. (40)-(42), where a, b, and x are the reaction orders. 

The line slope is -0.4960 The % Conilation factor is 99.9776 GAS CHROMATOGRAPHIC CONDITIONS Instrument Type Varian 6000 TCD Carrier Gas Helium Detector 0 TCD x 0.5 Detector TCD X 0.5 Injection Size CSV 0.5 ml LSV 0.2 uL Operating Conditions Isothermal at 115 C Column Description 30 x 1/8" DC-200/500 on Chrom PAW 80/100 mesh GAS CHROMATOGRAPHIC RETENTION ORDER Time Component Area 2.00 Nitrogen 119879 2.14 Methane 3582650 2.52 Caibon Dioxide 158657 2.80 Ethane 507744 3.78 Propane 325695 4.97 Isobutane 310334 5.83 n-Butane 307670 8. 50 Isopentane 177221 9.63 n-Pentane 183160 16.76 n-Hexane 19084 28.75 Heptanes Plus 20897 support package that it provides can a user have all the information necessary to support their analysis. 

Similar situation arose in the system of HfCl4-NaCl-KCl. Two steps were recorded at higher concentrations of HfCl4. The plot of /r( ) had a positive slope for the first step, and negative for the second step. Only at high current densities (chronopotentiometry) and at high scan rates (LSV) did the plot indicate an uncomplicated diffusion process. It was concluded that the adsorption of either Hf(II) or Hf(I) species caused the inactivation of the intermediates. 

The combination of LSV and RDE methods can be further utilized to obtain several intrinsic parameters of the catalyst. These intrinsic parameters include kinetic parameters of the Tafel slope, mass activity, and specific activity which together defined the activity of catalyst. 

Linear sweep voltammetry (LSV) in combination with a rotating disk electrode (RDE) is a widely used technique to study electrode kinetics. Different methods exist to extract the values of the process parameters from polarization curves. The Koutecky-Levich graphical method is frequently used to determine the mass transfer parameters (Diard et al., 1996) the slope of a plot of the inverse of the limiting current versus the inverse of the square root of the rotation speed of the rotating disk electrode is proportional to the diffusion coefficient. If more than one diffusing species is present, this method provides the mean diffusion coefficient of all species. The charge transfer current density is determined from the inverse of the intercept. In practical situations, however, the experimental observation of a limiting current... 

---