Charge Transfer and Mass Transport

The driving force for an electrochemical process is the overpotential. This is, in the case of a reversible redox electrode or a reversible metal/metal ion electrode, the deviation of the potential from the Nemst potential. The overpotential consists of several parts. One part is caused by deviation of the surface concentration from the bulk concentration. The replenishment of the surface concentration can be limited by diffusion. Then one speaks of diffusion overpotential. Another part is the overpotential necessary to drive the charge transfer. 

The ratio rfH for current density approaching zero is the electrode resistance consisting of charge transfer resistance and diffusion resistance. 

For analyzing the charge transfer process, it is necessary to eliminate the contribution from diffusion that means = RTInFii — 0. Many electrochemical methods are only devoted to this goal. 

The principal way to eliminate the diffusion term is reduction of the diffusion layer thickness. Under stationary condition this is achieved by enforced convection. For non-stationary conditions one can describe the increasing diffusion contribution by a time-dependent diffusion layer thickness. 

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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). 

When both the charge transfer and mass transport terms are significant a more complicated relationship is valid ... 

I. Epelboin, C. Gabrielh., M. Keddam, and H. Takenouti, A coupling between charge transfer and mass transport leading to multi-steady states. Application to localized corrosion, Z. Phys. Chem. N.F. 98 215 (1975). 

The phenomena are common to every value of temperature. Moreover, the decrease in temperature emphasizes the behavior in fact, the charge transfer and mass transport mechanisms are reduced at lower temperatures. 

This consideration confirms the crossing effect of the two parameters, which impacts on charge transfer and mass transport electrode processes. 

Four different regimes of the I-V curve for moderately doped silicon electrodes in an HF electrolyte are shown in Fig. 3.2. These regimes will now be discussed in terms of the charge state of the electrode, the dependence on illumination conditions, the charge transfer, the mass transport, and accompanying chemical reactions. Transient effects are indicated in Fig. 3.2 by a symbol with an arrow. 

If UPD and OPD processes of 2D and 3D Me phase formation are investigated under non-equilibrium conditions, then A// and, therefore, t] and A can be influenced by the reaction kinetics. For example, the charge transfer itself, mass transport, and chemical reaction steps which precede or follow the charge transfer can be kinetically hindered. Then, A/i, rj, and E are determined not only by crystallization overvoltage and underpotential as defined in eq. (1.3), but also contain charge transfer, diffusion, and/or chemical reaction contributions. 

Fig. 7.8 Origins of selectivity of amperometric sensors based on charge-transfer resistance and mass transport resistance...

It is useful now to describe the origins of the shape of the anodic and cathodic E-log i behaviors shown in Fig. 2. Note that the anodic reaction is linear on the E-log i plot because it is charge transfer controlled and follows Tafel behavior discussed in Chapter 2. The cathodic reaction is under mixed mass transport control (charge transfer control at low overpotential and mass transport control at high overpotential) and can be described by Eq. (1), which... 

The tertiary current distribution Ohmic factors, charge transfer controlled overpotential effects, and mass transport are considered. Concentration gradients can produce concentration overpotentials. The potential across the electrochemical interface can vary with position on the electrode. 

Two impedance arcs, which correspond to two relaxation times (i.e., charge transfer plus mass transfer) often occur when the cell is operated at high current densities or overpotentials. The medium-frequency feature (kinetic arc) reflects the combination of an effective charge-transfer resistance associated with the ORR and a double-layer capacitance within the catalyst layer, and the low-fiequency arc (mass transfer arc), which mainly reflects the mass-transport limitations in the gas phase within the backing and the catalyst layer. Due to its appearance at low frequencies, it is often attributed to a hindrance by finite diffusion. However, other effects, such as constant dispersion due to inhomogeneities in the electrode surface and the adsorption, can also contribute to this second arc, complicating the analysis. Normally, the lower-frequency loop can be eliminated if the fuel cell cathode is operated on pure oxygen, as stated above [18],... 

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