Electrode rate constant

The current i in this expression is obtained from the limiting current plateau region in Fig. 2.4. This equation is of quite general validity, and it can also be used to analyze voltammograms obtained for electrocatalysis at multilayered polymer-modified electrodes. Of course the heterogeneous modified electrode rate constant kME takes a different meaning. Thus we note that a plot of versus should produce a straight line, called a Koutecky-Levich plot, whose slope... 

Therefore concentration polarization in the solution poses no problem, and it can readily be calculated. The problem is to evaluate the modified electrode rate constant kME-... 

We note from this expression a clean separation into various rate-limiting processes. The first term on the rhs of Eqn. 55 quantifies the process of electron percolation through the layer. The second term describes competition between the surface reaction represented by the rate constant k and the layer reaction represented by the second-order rate constant k. The larger of these two terms dominates. Equation 55 therefore quantifies the transport and kinetics of mediation in the W 1 limit provided we can neglect the direct electrode reaction. The reciprocal form of this expression for k ME nwans that the slower term, whether transport or kinetic, determines the modified electrode rate constant k E-The LIXe ratio determines the location of the reaction zone in the layer. If Xe L, corresponding to a thick film, then tanh (LIXe) = 1, and substrate S penetrates only a distance Xe into the layer. In this case the layer term for the mediation kinetics reduces to kboxXE. On the other hand when L Xe, tanh (LIXe) J-, Xe, and the mediation kinetics are so slow that the layer term reduces to kboKL and the entire layer is used in the mediation reaction. 

Let us now consider the V 1 limit. In this case the expression for the modified electrode rate constant k E is given by Eqn. 53. Again this expression is rather complex. There are two terms in the numerator on the rhs of Eqn. 53. The first of these describes mediated electron transfer and the second, the kinetics for direct reaction at the electrode surface. The denominator on the rhs of Eqn. 53 describes the concentration polarization of 5 in the layer, where it may be consumed at the electrode surface by direct unmediated reaction represented by the heterogeneous rate constant ks, or in a homogeneous reaction layer of dimension Xq. Let us now assume that the direct unmediated process can be neglected. If this is true, then we simplify Eqn. 53 as follows ... 

If we assume that L/Xo kKXo/k, then the modified electrode rate constant is given by k E k bo- This is the expression for a simple surface reaction. On the other hand if k < kKXo, then as before... 

In this case the modified electrode rate constant is given by... 

We noted that in the south west comer of the case diagram, the reaction is limited by the transport of either electrons or substrate. In this region the larger of the two transport fluxes is rate-limiting because the reaction zone locates itself in the layer in such a way that slower moving species have less distance to travel. The layer reaction zone (LRZ) case is in the middle of the Southwest comer, bounded on either side by the Ie or ts cases. Note that in regions very close to the case boundaries we usually have to use the full expressions for the modified electrode rate constant (Eqn. 52 and Eqn. 53). We can use approximate expressions (such as those in Table 2.1) when we move away from the boundaries. 

FIGURE 2.17. Variation of the modified electrode rate constant Ic e for Fe (aq) ion reduction with layer thickness L for the Os-loaded redox-active metallopolymer described in Fig. 2.16. The least squares linear regression line is drawn through the data. Also included are the computer calculated 98% confidence limits corresponding to experimental data. The supporting electrolyte is 0.1 M H2SO4. 

A recent report on the two-electron reduction of (> -C6Me6)2Ru demonstrated the resolution of two-electron processes even when the second is favored thermodynamically. This is a possibility when the second electron transfer is slower than the first. In this case an increase in the scan rate shifts the peak due to the second electron transfer to more negative potentials, eventually resulting in a peak splitting (Figure 3-6). The values of the reduction potentials and electrode rate constants were estimated by simulation analysis ... 

Electrode reaction rate constant k (varies) = Ij nFAY[c ... 

The exchange current is directiy related to the reaction rate constant, to the activities of reactants and products, and to the potential drop across the double layer. The larger the more reversible the reaction and, hence, the lower the polarization for a given net current flow. Electrode reactions having high exchange currents are favored for use in battery apphcations. 

In the presence of 6-iodo-l-phenyl-l-hexyne, the current increases in the cathodic (negative potential going) direction because the hexyne catalyticaHy regenerates the nickel(II) complex. The absence of the nickel(I) complex precludes an anodic wave upon reversal of the sweep direction there is nothing to reduce. If the catalytic process were slow enough it would be possible to recover the anodic wave by increasing the sweep rate to a value so fast that the reduced species (the nickel(I) complex) would be reoxidized before it could react with the hexyne. A quantitative treatment of the data, collected at several sweep rates, could then be used to calculate the rate constant for the catalytic reaction at the electrode surface. Such rate constants may be substantially different from those measured in the bulk of the solution. The chemical and electrochemical reactions involved are... 

Prepare the solutions and measure the pH at one temperature of the kinetic study. Of course, the pH meter and electrodes must be properly calibrated against standard buffers, all solutions being thermostated at the single temperature of measurement. Carry out the rate constant determinations at three or more tempertures do not measure the pH or change the solution composition at the additional temperatures. Determine from an Arrhenius plot of log against l/T. Then calculate Eqh using Eq. (6-37) or (6-39) and the appropriate values of AH and AH as discussed above. 

It is now well established that in lithium batteries (including lithium-ion batteries) containing either liquid or polymer electrolytes, the anode is always covered by a passivating layer called the SEI. However, the chemical and electrochemical formation reactions and properties of this layer are as yet not well understood. In this section we discuss the electrode surface and SEI characterizations, film formation reactions (chemical and electrochemical), and other phenomena taking place at the lithium or lithium-alloy anode, and at the Li. C6 anode/electrolyte interface in both liquid and polymer-electrolyte batteries. We focus on the lithium anode but the theoretical considerations are common to all alkali-metal anodes. We address also the initial electrochemical formation steps of the SEI, the role of the solvated-electron rate constant in the selection of SEI-building materials (precursors), and the correlation between SEI properties and battery quality and performance. 

According to the Marcus theory [64] for outer-sphere reactions, there is good correlation between the heterogeneous (electrode) and homogeneous (solution) rate constants. This is the theoretical basis for the proposed use of hydrated-electron rate constants (ke) as a criterion for the reactivity of an electrolyte component towards lithium or any electrode at lithium potential. Table 1 shows rate-constant values for selected materials that are relevant to SE1 formation and to lithium batteries. Although many important materials are missing (such as PC, EC, diethyl carbonate (DEC), LiPF6, etc.), much can be learned from a careful study of this table (and its sources). 

Additional information on the rates of these (and other) coupled chemical reactions can be achieved by changing the scan rate (i.e., adjusting the experimental time scale). In particular, the scan rate controls the tune spent between the switching potential and the peak potential (during which the chemical reaction occurs). Hence, as illustrated in Figure 2-6, i is the ratio of the rate constant (of the chemical step) to die scan rate, which controls the peak ratio. Most useful information is obtained when the reaction time lies within the experimental tune scale. For scan rates between 0.02 and 200 V s-1 (common with conventional electrodes), the accessible... 

Sodium-silicate glass, 151 Sol-gel films, 120, 173 Solid electrodes, 110 Solid state devices, 160 Solvents, 102 Speciation, 84 Spectroelectrochenristry, 40 Spherical electrode, 6, 8, 9, 61 Square-wave voltammetry, 72, 92 Staircase voltammetry, 74 Standard potential, 3 Standard rate constant, 12, 18 Stripping analysis, 75, 79, 110 Supporting electrolyte, 102 Surface-active agents, 79... 

Stationary microwave electrochemical measurements can be performed like stationary photoelectrochemical measurements simultaneously with the dynamic plot of photocurrents as a function of the voltage. The reflected photoinduced microwave power is recorded. A simultaneous plot of both photocurrents and microwave conductivity makes sense because the technique allows, as we will see, the determination of interfacial rate constants, flatband potential measurements, and the determination of a variety of interfacial and solid-state parameters. The accuracy increases when the photocurrent and the microwave conductivity are simultaneously determined for the same system. As in ordinary photoelectrochemistry, many parameters (light intensity, concentration of redox systems, temperature, the rotation speed of an electrode, or the pretreatment of an electrode) may be changed to obtain additional information. 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

For an electrode with high interfacial rate constants, for example, relation (28) can be plotted, which yields the flatband potential. It allows determination of the constant C, from which the sensitivity factor S can be calculated when the diffusion constant D, the absorption coefficient a, the diffusion length L, and the incident photon density I0 (corrected for reflection) are known ... 

Equation (40) relates the lifetime of potential-dependent PMC transients to stationary PMC signals and thus interfacial rate constants [compare (18)]. In order to verify such a correlation and see whether the interfacial recombination rates can be controlled in the accumulation region via the applied electrode potentials, experiments with silicon/polymer junctions were performed.38 The selected polymer, poly(epichlorhydrine-co-ethylenoxide-co-allyl-glycylether, or technically (Hydrine-T), to which lithium perchlorate or potassium iodide were added as salt, should not chemically interact with silicon, but can provide a solid electrolyte contact able to polarize the silicon/electrode interface. 

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