Solids, charge-transfer kinetics

On the one hand, the thermodynamic realities of the ITIES, e.g., electrocapillarity and standard ion transfer potential, have been well established. On the other hand, our knowledge of charge transfer kinetics is less solid. Although traditional macroscopic concepts appear to be applicable at least as a first approximation, there is still a rift between macroscopic views and microscopic understanding. 

The effects cited above are found when studying electrode kinetics at GDEs, in liquid or solid electrolyte, but in this case, the complexity is related to the evaluation of diffusion and ohmic overpotentials, closely connected to the charge transfer kinetics. However, ehoosing appropiate models, it is possible to calculate different contributions from the simulation of current vs. potential data. 

Accordingly, the exchange current Jq should be small. In an electrochemical cell o depends on the charge transfer kinetics as derived in Chapter 7. Similarly as in pure solid-state devices (Chapter 2), also minority as well as majority processes are possible in electrochemical cells (Sections 7.3.4 and 7.3.5). The lowest Jq values were obtained with minority carrier reactions. Since most electrochemical photovoltaic systems, studied so far are governed by majority carrier processes, relatively low conversion efficiencies were found experimentally. 

Potential differences at the interface between two immiscible electrolyte solutions (ITIES) are typical Galvani potential differences and cannot be measured directly. However, their existence follows from the properties of the electrical double layer at the ITIES (Section 4.5.3) and from the kinetics of charge transfer across the ITIES (Section 5.3.2). By means of potential differences at the ITIES or at the aqueous electrolyte-solid electrolyte phase boundary (Eq. 3.1.23), the phenomena occurring at the membranes of ion-selective electrodes (Section 6.3) can be explained. 

Figure 10. Resistor-network representation of porous-electrode theory. The total current density, i, flows through the electrolyte phase (2) and the solid phase (1) at each respective end. Between, the current is apportioned on the basis of the resistances in each phase and the charge-transfer resistances. The charge-transfer resistances can be nonlinear because they are based on kinetic expressions.

In voltammetric experiments, electroactive species in solution are transported to the surface of the electrodes where they undergo charge transfer processes. In the most simple of cases, electron-transfer processes behave reversibly, and diffusion in solution acts as a rate-determining step. However, in most cases, the voltammetric pattern becomes more complicated. The main reasons for causing deviations from reversible behavior include (i) a slow kinetics of interfacial electron transfer, (ii) the presence of parallel chemical reactions in the solution phase, (iii) and the occurrence of surface effects such as gas evolution and/or adsorption/desorption and/or formation/dissolution of solid deposits. Further, voltammetric curves can be distorted by uncompensated ohmic drops and capacitive effects in the cell [81-83]. 

The symmetry factor P is obviously a central entity in electrodics and a fundamental quantity in the theoretical treatment of charge transfer at surfaces, particularly in relating electrode kinetics to solid-state physics. 

Figure 4 Dark currents in DSSCs with the standard I /I2 redox couple (solid line) and with a kinetically much faster redox couple, ferrocene/ferrocenium, FeCp2 + /0. A = tetrabutylammonium. The charge-transfer resistance, Rct (see Fig. 1), of the 1 2 couple is 106 times greater than that of the FeCp2+/0 couple, leading to what is sometimes mistaken as diode behavior in the dark for the cell containing the 1 2 couple. (Data from Ref. 49.)...

In order to make the comparison between Ep and Ep/2 measurements summarized in Table 9, the two quantities were measured in separate experiments. A recent study by Eliason and Parker has shown that this is not necessary [57]. Analysis of theoretical LSV waves by second-order linear regression showed that data in the region of Ep are very nearly parabolic. The data in Fig. 9 are for the LSV wave for Nernstian charge transfer. The circles are theoretical data and the solid line is that described by a second-order polynomial equation. It was concluded that no detectable error will be invoked in the measurement of LSV Ep and Ip by the assumption that the data fit the equation for a parabola as long as the data is restricted to about 10 mV on either side of the maximum. This was verified by experimental measurements on both a Nernstian and a kinetic system. 

The analysis conducted in this Chapter dealing with different theoretical approaches to the kinetics of accumulation of the Frenkel defects in irradiated solids (the bimolecular A + B —> 0 reaction with a permanent particle source) with account taken of many-particle effects has shown that all the theories confirm the effect of low-temperature radiation-stimulated aggregation of similar neutral defects and its substantial influence on the spatial distribution of defects and their concentration at saturation in the region of large radiation doses. The aggregation effect must be taken into account in a quantitative analysis of the experimental curves of the low-temperature kinetics of accumulation of the Frenkel defects in crystals of the most varied nature - from metals to wide-gap insulators it is universal, and does not depend on the micro-mechanism of recombination of dissimilar defects - whether by annihilation of atom-vacancy pairs (in metals) or tunnelling recombination (charge transfer) in insulators. 

Figure 32. The kinetic data for the intramolecular charge transfer reaction of DMAPS in alcohol solutions, ktra is plotted as a function of the solvent relaxation fceT,. These data span the temperature range from — 50°C to +30°C. The solid line corresponds to the case where t, = t, the expected result for a solvent controlled chemical reaction. The solvents plotted are ethanol ( + ), propanol ( ), butanol(x), pentanol (Ok and hexanol ( ). From Ref. 87 with permission from Chem. Phys. Lett., in press.

Figure 11. Photoion photoelectron coincidence studies of charge-transfer reactions of state-selected ions. Cross sections for nitric oxide symmetric charge-transfer reaction are plotted as function of reactant-ion kinetic energy and reactant-ion vibrational state (o = 0,1,2,3,4,5). Solid lines are linear least-squares fits to experimental data (not shown).86c...

Figure 16. Cross section as function of ion kinetic energy for charge-transfer reaction B+(N20,B)N20+ A, cross section for reaction of B+(IS) produced from BI3 O, cross section for reaction of B+ produced from BF3 (35.3% 3P and 64.5% S ) solid line, cross section for reaction of B+(3/1) obtained by taking difference between two lower curves and correcting for appropriate abundance.7 ...

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