Interfacial electron transfer, calculated

Fig. 3. Like a photoelectrochemical cell, such a powder includes sites for photo-induced oxidation and reduction, but no external current flow accompanies these transformations. Photoactivity is also maintained as the size of the particle decreases to the colloidal range although the absorption characteristics, the quantum efficiency of charge separation, and the kinetics of interfacial electron transfer may be influenced by the particle size. On sufficiently small particles, for example, the calculated space-charge width necessary for effective band bending may exceed the dimensions of the particle.

Fig. 18. The parameter A as a function of the deepness (in energetic scale) of the level of recombination sites for CdS particles. Parameter A is calculated from Eq. (2.19). A is proportional to the ratio between the rate of interfacial electron transfer to the rate of trapped carriers recombination. The location of energy level of recombination site is measured from the bottom of conductivity band.

Fe(CN)6] , electrochemically contacted at a photoisomerizable command interface (lla/llb). Figure 7.15 shows the impedance features (as Nyquist plots) of the nitrospiropyran (11a) and protonated nitromerocyanine (lib) electrodes in the presence of [Fe(CN)6] as a redox probe. The impedance spectra show a larger resistance to interfacial electron transfer when the monolayer is in the neutral dinitrospiropyran state (Ret = 60 kll) than when it is in the positively charged protonated merocyanine state (Ret = 48 kQ) (Figure 7.15, curves b and a). The heterogeneous rate constants for electron transfer between the electrode and the redox probe were calculated to be 0.82 X 10" and 1.1 x 10" cm s" for the 11a and 1 lb-monolayer modified Au-electrodes, respectively. 

In this equation, AE represents the measured cathodic-to-anodic peak potential separation, and (AEp) , denotes the value determined as the ordinate at the origin in the AE versus plot for different concentrations of electroactive species. That (AEp)yn value can be directly related with kinetic parameters for the interfacial electron transfer reaction (Nicholson, 1965b). The slope of the above representation allows for calculation of the uncompensated ohmic resistance in the cell. Figure 1.6 shows AEp versus plots for the Fe(CN)g 7Fe(CN)6 couple at zeolite Y- and hydrotalcite-modihed glassy carbon electrodes immersed in K4Fe(CN)6 solutions in concentrations between 0.1 and 10.0 mM. 

The pressing need for a detailed description of the semiconductor-electrolyte interface is becoming increasingly apparent Gerischer has given an excellent and timely general account of photoassisted interfacial electron transfer, in which particular attention is paid to the role of surface states at the semiconductor-electrolyte interface. Kowalski et al have used the SCF-A -scattered wave method to calculate the position and character of surface states at various characteristic interfaces, and then used these results to develop a model of photoelectrolysis at Ti02 surfaces. 

Since in this case, electrons could only be excited in a single well the photocurrent was small. On the other hand, the quantum yield, that is, the number of transferred electrons per absorbed photons, reached values of up to = 0.63 [80]. This might appear surprisingly high for a relatively thick outer barrier layer. However, calculations and measurements of the temperature dependence of the photocurrent showed that at room temperature the mechanism of electron transfer out of the well was thermionic emission over the barrier [80]. The rate of thermionic emission at lattice temperatures in the range of 200—300 K was sufficient to keep up with the measured rate of interfacial electron transfer. Studies with very thin outer barriers (20 A) have shown that the mechanism of charge transfer was field-assisted tunneling, and the photocurrent was then independent of temperature. 

Figure 3.6 Molecule-Ti02 interfaces used to investigate ultrafast interfacial electron transfer processes. Increased system interaction complexity is illustrated for periodic surface QM calculations of a binding ligand on a clean rutile (110) surface (left), QM cluster calculations of a complete dye molecule (RuN3) in a nanocrystalline environment (middle) and a multiscale MD simulation (right), highlighting both differences and similarities.

As discussed above, interfacial electron transfer at molecule-semiconductor interfaces may in many cases be limited mainly by the interfacial electronic coupling, rather than requiring structural activation processes. From a multiscale perspective that attempts to split complex materials processes into separable problems, this can be taken advantage of by performing electron dynamics simulations on structures that have been previously determined from either quantum chemical calculations or MD simulations. 

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. 

For interfacial systems, potential functions should ideally be transferrable from the gas-phase to the condensed phase. Aqueous-mineral interfaces are not in the gas phase (although they may be close, see (7)), but both the water molecules and the atoms/ions in the substrate are in contact with an environment that is very different from their bulk environment. The easiest different environment to test, especially when comparing with electronic structure calculations, is a vacuum, so there is likely to be a great deal of information available on either the surface of the solid or the gas-phase polynuclear ion or the gas-phase aquo complex (i.e., Fe(H20)63+, C03(H20)62-). The gas-phase transfer-ability requirements on potential functions are challenging, but it is difficult to imagine constructing effective potential functions for such systems without using gas-phase systems in the construction process. This means that any water molecules used on these complexes must also transfer from the gas phase to the condensed phase. A fundamental aspect of this transferability is polarization. 

Figure 29. Calculated current-potential characteristics for direct (dashed lines, 0/cm ) and surface state mediated electron transfer between an -type semiconductor electrode and a simple redox system. The plots show the transition from ideal diode behavior to metallic behavior with increasing density of surface states at around the Fermi-level of the solid (indicated in the figures). This is also clear from the plots below, which show the change of the interfacial potential drop over the Helmholtz-layer (here denoted as A(Pfj) with respect tot the total change of the interfacial potential drop (here denoted as A(p). Results from D. Vanmaekelbergh, Electrochim. Acta 42, 1121 (1997).

The microwave conductivity is proportional to the number of free electronic charge carriers multiplied by their respective mobilities (the contribution of ions and dipoles can be neglected in a first approximation.). The microwave sensitivity constant S must be obtained by calibration. The potential-dependent photoinduced microwave conductivity (PMC) of a semiconductor resulting from illumination has been calculated analytically as a function of the interfacial charge-transfer and surface recombination rates (Schlichthorl and Tributsch, 1992). The starting point is the general set of equations of the form... 

In Figure 5.11, we described the interplay between electron transfer and mass transfer and how both are required to observe a current from a G. sulfurreducens biofilm. It is difficult to determine the role of mass transfer in biofilms simply from cyclic voltammograms usually, certain electrochemical setups are required to investigate mass transfer via electrochemical methods. In our case, we used a combination of EIS and RDEs to study electron transfer and diffusional processes in G. sulfurreducens biofilms respiring on electrodes [50]. We tested the hypothesis that the RDE can be used as an electrochemical tool that controls diffusional processes when EABs are studied. We determined the film resistance, film capacitance, interfacial resistance, interfacial capacitance, and pseudocapacitance of G. sulfurreducens biofilms as shown in Eigure 5.23. The details of the calculations and experimental procedures are given in the literature [50],... 

The main quantity of interest in electron transfer at the interface is the rate of the reaction. It depends on steric, energetic, and dynamic factors. In addition to assuming spherical symmetry of the donor and acceptor, steric considerations in the model calculations are further simplified by keeping the distance between D and A fixed and restricting the couple to the interfacial region. With these simplifications, the dependence of the reaction rate on the separation between the reaction centers and on for both uncharged and charged forms of D... 

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