Reaction layer thickness

Fig. 5.37 Steady-state concentration distribution (reaction layer) in the case of a chemical volume reaction preceding an electrode reaction (Eq. (5.6.12)) K = 103, kc >oo, A 1 = 0.04s1, D = 10 5cm s i is the effective reaction layer thickness...

The relative importance of reaction with respect to diffusion can be described in terms of the nondimensional (second) Damkohler number [30-36] (also called Thiele modulus), in terms of the reaction layer thickness [37,38] or in terms of lability criteria [39,40]. 

We note incidentally that the reaction layer thickness is on the same order as that of the double layer for k+ 1010 s-1 (typical values of the diffusion coefficient are of the order of 10 5 cm2 s 1). It is only for such fast reactions that their kinetics may be perturbed by the strong electric field present in the close vicinity of the electrode.3... 

We now start examining how competing follow-up reactions control product distribution. The way in which these reactions interfere depends on their rate relative to the diffusion process, or alternatively, on the relative size of the corresponding reaction and diffusion layers (Figure 2.31). For a follow-up reaction with a first (or pseudo-first-order) rate constant, k, occurring in the framework of an EC reaction scheme (see Section 2.2.1), the reaction layer thickness is y/D/k. 

This is no longer the case when competition involves reactions with different orders, as in Scheme 2.17. Unlike the preceding case, the C and D concentration profiles do not have the same shape. Appropriate dimensionless analysis (see Section 6.2.8), where the space variable is normalized toward the reaction layer thickness, leads to the dimensionless parameter... 

The concentration profile of B is squeezed within the reaction layer. It may be analyzed in dimensionless term so as to obtain the expression of the yields with introduction of a minimal number of parameters. This is arrived at by normalizing the space variable versus the reaction layer thickness as y = xy/k /D(y = 1 corresponds to x = fi) and the concentrations as... 

In an EC mechanism, if the reaction layer thickness is small compared... 

The right hand side is the result of integration. As long as local equilibrium prevails, the average value, LA, of the transport coefficient, taken across the reaction layer, is determined by the thermodynamic parameters at the interfaces A/AB and AB/B, and thus is independent of the reaction layer thickness A . If one inserts Eqn. (1.27) into Eqn. (1.26), a parabolic rate law is found... 

When the kinetics of the chemical reaction in solution is very fast with respect to the diffusion transport, the resolution of the problem can be simplified by noting that the concentrations of species B and C are in equilibrium at any point and time (cb(c, t) = Cg, cc(r, t) = c ) and the reaction layer thickness (<5Plane) tends to zero. Taking into account these considerations, the RPV current for the EC mechanism is given by... 

In these electrode processes, the use of macroelectrodes is recommended when the homogeneous kinetics is slow in order to achieve a commitment between the diffusive and chemical rates. When the chemical kinetics is very fast with respect to the mass transport and macroelectrodes are employed, the electrochemical response is insensitive to the homogeneous kinetics of the chemical reactions—except for first-order catalytic reactions and irreversible chemical reactions follow up the electron transfer—because the reaction layer becomes negligible compared with the diffusion layer. Under the above conditions, the equilibria behave as fully labile and it can be supposed that they are maintained at any point in the solution at any time and at any applied potential pulse. This means an independent of time (stationary) response cannot be obtained at planar electrodes except in the case of a first-order catalytic mechanism. Under these conditions, the use of microelectrodes is recommended to determine large rate constants. However, there is a range of microelectrode radii with which a kinetic-dependent stationary response is obtained beyond the upper limit, a transient response is recorded, whereas beyond the lower limit, the steady-state response is insensitive to the chemical kinetics because the kinetic contribution is masked by the diffusion mass transport. In the case of spherical microelectrodes, the lower limit corresponds to the situation where the reaction layer thickness does not exceed 80 % of the diffusion layer thickness. 

The difference lies in the factor a, which is introduced into the rate expression for heterogeneous electron transfer and represents an equivalent reaction-layer thickness (in cm). 

Equations (2.5)-(2.8) describe four different limiting cases for the behaviour of the system. Before proceeding, it is necessary to define the reaction layer thickness (A ) ... 

Reaction layer thickness — Figure. Concentration gradients at the electrode/solution interface... 

The first term of Eq. 7.11 is related to enzyme kinetics, while the second term gives the flux dependence on substrate transport to the reaction layer. It can be seen that the flux increases with increasing substrate (analyte) concentration, with increasing enzyme concentration in the reaction layer, and with increasing reaction layer thickness. 

For optical transducers, the measured signals are directly proportional to [P], so that, once again, reaction layer thickness and mass-transport kinetics determine the sensitivity of the biosensor, and signals are directly proportional to analyte concentration. For potentiometric transducers, signals are proportional to log[P], and therefore to log[S]. ... 

An important advantage of the RDE is that measurements are made under steady-state (i.e., time-independent) conditions. Thus, the general approaches described in Sections 1.4.2 and 1.5 can be applied, with the appropriate choices of m (the mass-transfer coefficient) and (the reaction layer thickness). Moreover, equations of the same form are found with other steady-state techniques and can be found by replacing m = for the RDE with m for the particular technique. For example,... 

The explicit finite difference simulation methods described here are quite straightforward and have been employed for a variety of electrochemical problems. Nevertheless, there are cases when the computation times required for accurate solutions become excessive, and more efficient numerical methods are appropriate. This is generally the case when very rapid coupled homogeneous reactions occur. As discussed in Section B.3, when is large, the reaction layer thickness may be small compared to the box thickness... 

From the analysis of polarograms for the transfer of procaine in Case 2, Senda et al. concluded that the transfer of procaine is described by the CE mechanism, that is, the transfer of the protonated form of procaine with the preceding protonation reaction in W. The major contribution to was found to be proton donation from the acid form of a buffer component, AH, employed. The values of = kf/[AH] at pH 8.0 are given in Table 1 for three different buffers. In this example, the reaction-layer thickness is much thinner, of the order of 10 cm, than the diffusion-layer thickness, which ensures the applicability of the concept of the reaction layer [22]. 

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