Mixed kinetics

Figure 1.52. Uniformly mixed kinetics model. q volume flow rate (m /s), Cj initial concentration (molal), 1 height (m), r radius (m), C concentration (molal), V volume of the system (m ).

In solvolytic reactions like those we have just been considering, where the solvent itself is the nucleophile, such mixed kinetics may not be detectable, irrespective of what is actually happening, as both SN1 and Sn2 pathways are likely to follow a rate equation of the form ... 

Figure 14 shows a schematic representation of a mixed potential diagram for the electroless deposition reaction. Oxidation of the reductant, in this case hypophos-phite, is considered to be under 100% kinetic control. A mixed kinetic-diffusion curve is shown for the reduction of the metal ion, in our case Co2+, in the region close to the mixed potential, Em. Thus, since Co deposition occurs under a condition of mixed kinetic and diffusion control, features small relative to the diffusion layer thickness for Co2+ will experience a higher concentration of the metal ion, and hence... 

This equation was calculated numerically for the different values of coefficients D, a, y/v, and d. The theoretical dependence was found to coincide with Equation (13.17) for the coefficient k 8D/3/2 at v/viDO > 0.5. The numerical calculation gave the following equation for the mixed (kinetic and diffusion) regime of oxidation [87] ... 

Fig. 18b.6. (a) Shape of the voltage pulses for diffusion control, mixed diffusion-kinetic control, and kinetic control, (b) concentration gradient of O showing expansion of the diffusion layer with time for complete diffusion controlled reaction, and (c) current transients show diffusion controlled, mixed kinetics and diffusion control, and complete kinetics controlled reactions corresponding to voltage pulses shown in (a). Note that the equations are derived only for the diffusion controlled case. 

A similar role is played by irreversible follow-up reactions, but the possibility of a mixed kinetic control by the two steps of the EC process should then be taken into account. A simplifying assumption is that the follow-up reaction is so fast that the conditions of zone KP prevail. It corresponds to the maximal influence of the coupled chemical step. The dimensionless expression of the cathodic trace of the irreversible voltam-mogram is then given by (see Section 6.2.1)... 

FIGURE 2.5. EC reaction scheme in cyclic voltammetry. Mixed kinetic control by an electron transfer obeying the Butler-Volmer law (with a = 0.5) and an irreversible follow-up reaction, a Variation of the peak potential with the scan rate, b Variation of the peak width with scan rate. Dots represent examples of experimental data points obtained over a six-order-of-magnitude variation of the scan rate. 

As compared to the Nemstian case, the plateau is the same but the wave is shifted toward more negative potentials, the more so the slower the electrode electron transfer. An illustration is given in Figure 4.13 for a value of the kinetic parameter where the catalytic plateau is under mixed kinetic control, in between catalytic reaction and substrate diffusion control. For the kjet(E) function, rather than the classical Butler-Volmer law [equation (1.26)], we have chosen the nonlinear MHL law [equation (1.37)]. 

One such set of circumstances is when it is possible, upon raising the electron donor concentration, to change the rate law from (62) to (61), indicating that kinetic control passes from forward electron transfer to bond breaking according to (63). The passage across the mixed kinetics region... 

The reductive cleavage of iodobenzene and 3-methyliodobenzene was studied by cyclic voltammetry in both DMF and acetonitrile at 21 and 56 °C at different scan rates and has shown that there is a transition between stepwise and concerted mechanisms at lower scan rates. 1-Iodonaphthalene undergoes a stepwise reductive cleavage with mixed kinetic control by electron transfer and follow-up bond breaking, whatever the scan rate. ... 

C-K. Lai andC.L. Cooney, Application of a fluorescence sensor for miniscale on-line monitoring of powder mixing kinetics, J. Pharm. Sci., 93(1), 60-70 (2004). 

MIXED-EUNCTION OXIDASE CYTOCHROME P450 Mixed kinetic order,... 

Mayer, L.M. (1982) Aggregation of colloidal iron during estuarine mixing Kinetics, mechanism, and seasonality. Geochim. Cosmochim. Acta 46 2527-2535... 

We first consider the case of reversible reactions before going on to discuss the general case of mixed kinetic and transport control. 

Silke, G., Knoch, A., and Lee, G. Continuous wet granulation using uidized-bed techniques I. Examination of powder mixing kinetics and preliminary granulation experiments. J. Pharm. Biopharm., 48 (1999), 189-197. 

The second region is the mixed kinetic transport-controlled region, and the most negative part of it can also be used for kinetic and mechanistic studies of the electron-transfer reaction after the experimental currents have been compensated for transport limitations. Finally, a second wave is observed at potentials higher than 0.5 V vs. AglAgCl, which can be attributed to the oxidation of sulphite to sulphate. However, this wave is not further considered because the oxidation mechanism of sulphite showed poor reproducibility (see section 6.3), and sulphite detection in dyeing processes is not of great importance compared with dithionite detection. 

Very early, Miller and Bruckenstein [6] had felt that for an electrochemical system under mixed kinetic control, HMRDE was able to derive information about the kinetic parameters and give more valuable interpretation than by conventional RDE technique. At that time, they developed a theoretical analysis, restricted to quasi steady state, and which is now presented in a more quantitative way and over a large frequency domain with the formalism of EHD impedance (see Chapter 4). 

Electrodeposition of metals is very often evolving under mixed kinetic conditions which deeply influence the resulting structure and aspect of the surface. The following example shows how the EHD technique gives an in-situ information about some geometrical characteristics of the growing electrodeposit in the case of tellurium. 

Liquid clathrates offer a great advantage over solid-state separations (e.g. by formation of Hoffman-type inclusion compounds, Section 9.4) because of the extremely fast mixing kinetics, the avoidance of the need to wait for crystallisation to occur and the easy separation of the two liquid phases. It should also prove possible to run liquid clathrate separations in a continuous extraction manner. The avalues of a number of liquid clathrate-based separations have been reported and are summarised in Table 13.1. 

Experimentally, the interaction of initial substances is always examined over a certain finite period of time. For solid-solid systems, this period usually varies from a few minutes to a few hours and seldom is longer. This time range is in most cases too narrow to enable the transition from linear to parabolic kinetics to be established, the more so that the number of experimental points is known to rarely exceed 5 or 6. Therefore, one of the two extremes (a straight line or a parabola) is observed, or neither a straight line nor a parabola. The latter case is treated as mixed kinetics. 

FIGURE 1.21 An example of a complex-plane impedance plot (Nyquist plane) for an electrochemical system under mixed kinetic/diffusion control, with the mass transfer and kinetics (charge transfer) control regions, for a finite thickness 8N of the diffusion layer. Assumption was made that Kf Kh at the bias potential of the measurement, and D0I = Dmd = D, leading to RB = RCT (krb8N/ >). 

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