Diffusion current kinetic effects

The kinetic and polarization equations described in Sections 6.1 and 6.2 have been derived under the assumption that the component concentrations do not change during the reaction. Therefore, the current density appearing in these equations is the kinetic current density 4. Similarly, the current density appearing in the equations of Section 6.3 is the diffusion current density When the two types of polarization are effective simultaneously, the real current density i (Fig. 6.6, curve 3) will be smaller than current densities and ij (Fig. 6.6, curves 1 and 2) for a given value of polarization. 

The forward peak current measured under the effect of the kinetic reaction, ik (kinetic current), is a fraction of the peak current id (diffusive current) that one would record at the same scan rate in the absence of the preceding chemical reaction, according to the relationship ... 

It must be emphasized again that the mid-peak potential is equal to E° for a simple, reversible redox reaction when neither any experimental artifact nor kinetic effect (ohmic drop effect, capacitive current, adsorption side reactions, etc.) occurs, and macroscopic inlaid disc electrodes are used, that is, the thickness of the diffusion layer is much higher than that of the diameter of the electrode. 

Because the kinetic and mass-transport phenomena occur in a thin region adjacent to the electrode surface, this area is treated separately from the bulk solution region. Since kinetic effects are manifested within 100 A of the electrode surface, the resulting overpotential is invariably incorporated in the boundary conditions of the problem. Mass transport in the boundary layer is often treated by a separate solution of the convective diffusion equation in this region. Continuity of the current can then be imposed as a matching condition between the boundary layer solution and the solution in the bulk electrolyte. Frequently, Laplace s equation can be used to describe the potential distribution in the bulk electrolyte and provide the basis for determining the current distribution in the bulk electrolyte. 

The other factor that can show the influence of kinetic, catalytic, and adsorption effects on a diffusion-controlled process is the temperature coefficient.10 The effect of temperature on a diffusion current can be described by differentiating the Ilkovic equation [Eq. (3.11)] with respect to temperature. The resulting coefficient is described as [In (id,2/id,iV(T2 — T,)], which has a value of. +0.013 deg-1. Thus, the diffusion current increases about 1.3% for a one-degree rise in temperature. Values that range from 1.1 to 1.6% °C 1, have been observed experimentally. If the current is controlled by a chemical reaction the values of the temperature coefficient can be much higher (the Arrhenius equation predicts a two- to threefold increase in the reaction rate for a 10-degree rise in temperature). If the temperature coefficient is much larger than 2% °C-1, the current is probably limited by kinetic or catalytic processes. 

Diffusion resistances can occur for Li in the electrode, but also for the salt in the electrolyte (if anion conductivity in the electrolyte is significant). Further effects are due to depletion of carriers at a phase boundary. In such cases, time dependencies of the electrical properties occur (in addition to Rs, effective capacitances Cs also appear). The same is true for impeded nucleation processes. Since any potential step of the electrochemical potential can be connected with current-dependent effective resistances and capacitances, the kinetic description is typically very specific and complex. As the storage processes in Li-based batteries are solid-state processes, the... 

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],... 

Additional deviations from the Nernst law [Eq. (4)] can come from kinetic effects in other words, if the potential scan is too fast to allow the system to reach thermal equilibrium. Two cases should be mentioned (1) ion transport limitation, and (2) electron transfer limitation. In case 1 the redox reaction is limited because the ions do not diffuse across the film fast enough to compensate for the charge at the rate of the electron transfers. This case is characterized by a square-root dependence of the current peak intensity versus scan rate Ik um instead of lk u. Since the time needed to cross the film, tCT, decreases as the square of the film thickness tCT d2, the transport limitation is avoided in thin films (typically, d < 1 xm for u < 100 mV/s). The limitation by the electron transfer kinetics (case 2) is more intrinsic to the polymer properties. It originates from the fact that the redox reaction is not instantaneous in particular, due to the fact that the electron transfer implies a jump over a potential barrier. If the scan... 

As in the case of the conductivity experiments, current-constriction effects can occur in the diffusion experiments, if lateral inhomogeneities are present. In this way resistivities occur that can be easily misinterpreted in terms of sluggish surface steps. A concise treatment of proper surface kinetics will be given now. 

We note that under conditions of diffusion control, the current depends on t . Thus, a small change in drop time, resulting from a change in surface tension with potential, does not produce a large difference in the diffusion current. If the error caused by this effect is considered troublesome, it is possible to knock the drops off at fixed intervals, yielding drops of exactly equal size, irrespective of the surface tension. This mode of operation becomes of particular importance for kinetic studies conducted at the foot of the polaro-graphic wave, since the activation-controlled current is proportional to the surface area, which is itself proportional to (the volume increases linearly with time). 

Electrocatalysts are produced in different ways, on different substrates, and for different purposes,10,64-72 but almost in all cases the electrochemical characterization was performed by using the cyclic voltammetry observations. In this way, it was not possible to analyze the effects of the mass-transfer limitations on the polarization characteristics of electrochemical processes. As shown recently,7,9 the influence of both kinetic parameters and mass-transfer limitations can be taken into account using the exchange current density to the limiting diffusion current density ratio, jo/ju for the process under consideration. Increased value of this ratio leads to the decrease of the overpotential at one and the same current density and, hence, to the energy savings. 

Figure 1 shows several voltammetric techniques applied to this compound. At RT the rate of interconversion of the two isomers is in the slow-reaction limit (1 a for CV studies), and peak currents for both waves are proportional to v i.e., diffusion-controlled behavior is observed. At higher T, where the reaction is in the intermediate-kinetic region, the relative peak currents of the waves vary with scan rate. At slower scans the current for the first peak is enhanced owing to the kinetic effect of conversion of the 1,5-isomer to the 1,3-isomer. At fast scans (> 20 V s ) the kinetic effects could be outrun even at elevated T, returning the system to the slow-reaction (fast-scan) limit. ... 

Fig. 17.2 Tafel plots for the (normalized, dimensionless) current, yjy, that accompanies hydrogen evolution in a solution containing 3.4 mM HCl + 1.0 M KCl, corrected for diffuse-double-layer effects, mass transport controlled kinetics and ohmic potential drop, measured at three temperatures (5, 45, 75°C all results fall on the same line of this reduced plot) at a dropping mercury electrode. The slope obtained from this plot is 0.52, independent of temperature. (Based on data from E. Kirowa-Eisner, M. Schwarz, M. Rosenblum, and E. Gileadi, J. Electroanal. Chem. 381, 29 (1995) and reproduced by the authors.)...

X 10 to 1.4 X 10 cm s , see in all cases the calculated value is always greater by 10-20 times than the experimental one. This is perhaps due to the electrode passivation that cuts off part of the electrode surface from the process. The effect of passivation on the electrode reactions of solvated electrons is discussed in detail in Section 7. Here we shall only mention that passivation does not alter the limiting diffusion current. The different effect of passivation on diffusion and kinetic currents is related to the fact that at the employed rotation rates the thickness of diffusion layer (that determines ij) far exceeds that of the reaction layer (that determines iJ... 

To counteract the (vexing) convection effects on kinetic experiments, Aogaki and co-workers, having developed a special electrode assembly to separate mass transport and kinetic effects, report a marked decrease in the exchange current density (about 25%) in magnetic fields imposed on a copper deposition cell. Virtually no effect on the transfer coefficient (a 0.44) was observed. Experimental results obtained in nickel-phosphorus alloy deposition, cupric ion reduction in ethylenediamine solutions, and the electrolytic reduction of acetophenone " are further demonstrations of the interaction of the magnetic fields with polarization characteristics, and point to the difficulty of fully eliminating the effect of convection and/or diffusion on electrode kinetics. 

When heat flows through a mixture initially of uniform composition, small diffusion currents are set up, with one component transported in the direction of heat flow, and the other in the opposite direction. This is known as the thermal diffusion effect. The existence of thermal diffusion was predicted theoretically in 1911 by Enskog [El, E2] from the kinetic theory of gases and confirmed experimentally by Chapman [Cl, C2] in 1916. It is not surprising that the effect was not discovered sooner, because it is very small. For example, when a mixture of 50 percent hydrogen and 50 percent nitrogen is held in a temperature gradient between 260 and 10°C, the difference in composition at steady state is only 5 percent. In isotopic mixtures the effect is even smaller. 

Equation 5.5.24 is a very compact representation of the way in which the current in a step experiment depends on potential and time, and it holds for all kinetic regimes reversible, quasireversible, and totally irreversible. The function Fi(A) manifests the kinetic effects on the current in terms of the dimensionless parameter A, which can be readily shown to compare the maximum current supportable by the reductive kinetic process at a given step potential FAkfC% vs. the maximum current supportable by diffusion at that potential [/d/(l+ )] Thus a small value of A implies a strong kinetic influence on the current, and a large value of A corresponds to a situation where the kinetics are facile and the response is controlled by diffusion. The function Fi(A) rises monotoni-cally from a value of zero at A = 0 toward an asymptote of unity as A becomes large (Figure 5.5.2). 

Note that k is also the ratio of the largest current supportable by the kinetics divided by the largest current supportable by diffusion thus it is analogous to the parameter A used to characterize kinetic effects on systems based on semi-infinite linear diffusion. 

Bianchini, Serp and cowoikers have also observed a remarkable effect of the MWCNTs on the alcohol diffusion. As shown in Figure 14a, a linear Sap/(V s ) relationship, typical of an electrochemical reaction under diffusion control, features the oxidation of ethanol on PD/MWCNT at scan rates lower than 350 mV s (Sap = specific peak current density). Above this scan rate, the slope decreases tending to a plateau, which has been ascribed to a reaction limited by other factors than substrate diffusion, for example the very low density of catalytic centers due to the extremely low Pd loading (17 pg cm ) as well as the slow desorption of the acetate product. A much narrower window of diffusion-controlled kinetics was observed for the oxidation of glycerol (Fig. 14b), the independence of the peak current density on the voltage scanning frequency being attained already at scan rates above 50 mV s and ascribed to the concomitant action of... 

In the above section, all the equations we derived are based on pure electron transfer kinetics. Unfortunately, in reality, mass transfer (e.g. hydrogen diffusion inside a porous fuel ceU CL) will have an effect on the overall reaction rate, and sometimes can become the rate-determining step. To address this mass transfer effect, we need to introduce another concept, called limiting diffusion current density, which can be expressed as in Eqns (1.35) and (1.36) [9] ... 

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