Mass transport charge transfer

Figure 2 Evans diagram illustrating the influence of solution velocity on corrosion rate for a cathodic reaction under mixed charge transfer-mass transport control. The anodic reaction shown is charge transfer controlled.

The overall reaction, Eq. (1), may take place in a number of steps or partial reactions. There are four possible partial reactions charge transfer, mass transport, chemical reaction, and crystallization. Charge-transfer reactions involve the transfer of charge carriers (ions or electrons) across the double layer. This is the basic deposition reaction. The charge-transfer reaction is the only partial reaction directly affected by the electrode potential. In mass transport processes, the substances consumed or formed during the electrode reaction are transported from the bulk solution to the interphase (double layer) and from the interphase to the bulk solution. This mass transport takes place by diffusion. Chemical reactions involved in the overall deposition process can be homogeneous reactions in the solution and heterogeneous reactions at the surface. The rate constants of chemical reactions are independent of the potential. In crystallization partial reactions, atoms are either incorporated into or removed from the crystal lattice. 

The authors considered analytical and numerical solutions for the differential equations by using the three main overpotentials charge transfer, mass transport, and ohmic drop. We discuss only the case of a two-dimensional system, where the current distribution varies with the radial and the azimuthal coordinates. 

E2 > E21 > E22 > E, and E2 and E22 correspond to potentials in the rising portion of the voltammogram where mixed charge transfer-mass transport control prevails... 

In principle, the polarization at each electrode may have a contribution from charge transfer, mass transport, nucleation and passivation overpotentials. The major contribution will normally be from the charge transfer overpotential since mass transport control has a catastrophic effect on the battery voltage (see Fig. 10.3) and one would not normally design a battery to operate in such conditions. Examples of nucleation and passivation overpotentials do occur. The former occur when the electrode reaction requires the formation of a new phase although the nucleation overpotential is normally a transitory phenomenon since, once nuclei of the new phase are present in numbers, the overpotential will disappear. The... 

As tapp approaches the concentration overpotential, ti ,> becomes very large. The cathodic reaction may be under mixed charged transfer-mass transport or mass transpK>rt control for many corrosion situations, particularly if the cathodic reaction is O2 reduction [5]. The cathodic polarization behavior associated with mixed charge transfer— mass transfer control can be described mathematically by the algebraic combirration of Eqs 20 and 22. Tafel extrapolation of cathodic data becomes difficult under these conditions because the Tafel region may not be extensive. 

The majority of practical power supplies are (nominally) square wave in form, the technique being applied in a largely empirical fashion. It is clear, however, that periodic current reversal may generally affect charge transfer, mass transport and surface electrocrystallization processes. 

Whether the electrode reactions are under charge transfer, mass transport or mixed control, or if resistance polarization is appreciable (see later) in Fig. 10.8 the linear, Tafel regions on the -log i plot signify activation control, i.e, charge transfer predominates. 

Fig. 11.4.6. Current-time curves for different step magnitudes. Ei is the initial potential where no current flows, while E2 is the potential in the mass transport limited region. E2 > 21 > 22 > 1, and E21 and 22 correspond to potentials in the rising portion of the voltammogram where mixed charge transfer-mass transport control prevails...

Many of the electrochemical techniques described in this book fulfill all of these criteria. By using an external potential to drive a charge transfer process (electron or ion transfer), mass transport (typically by diffusion) is well-defined and calculable, and the current provides a direct measurement of the interfacial reaction rate [8]. However, there is a whole class of spontaneous reactions, which do not involve net interfacial charge transfer, where these criteria are more difficult to implement. For this type of process, hydro-dynamic techniques become important, where mass transport is controlled by convection as well as diffusion. 

Equation (22-66) assumes that all mass transport is caused by an electrical potential difference ac ting only on cations and anions. Assuming the transfer of electrical charges is due to the transfer of... 

For quasi-reversible systems (with 10 1 > k" > 10 5 cm s1) the current is controlled by both the charge transfer and mass transport. The shape of the cyclic voltammogram is a function of k°/ JnaD (where a = nFv/RT). As k"/s/naD increases, the process approaches the reversible case. For small values of k°/+JnaD (i.e., at very fast i>) the system exhibits an irreversible behavior. Overall, the voltaimnograms of a quasi-reversible system are more drawn-out and exhibit a larger separation in peak potentials compared to those of a reversible system (Figure 2-5, curve B). 

For quasi-reversible systems the limiting current is controlled by both mass transport and charge transfer ... 

The RHSE has the same limitation as the rotating disk that it cannot be used to study very fast electrochemical reactions. Since the evaluation of kinetic data with a RHSE requires a potential sweep to gradually change the reaction rate from the state of charge-transfer control to the state of mass transport control, the reaction rate constant thus determined can never exceed the rate of mass transfer to the electrode surface. An upper limit can be estimated by using Eq. (44). If one uses a typical Schmidt number of Sc 1000, a diffusivity D 10 5 cm/s, a nominal hemisphere radius a 0.3 cm, and a practically achievable rotational speed of 10000 rpm (Re 104), the mass transfer coefficient in laminar flow may be estimated to be ... 

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