Rate constants interfacial electron transfer

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. 

These rate constant forms are completely equivalent to the interfacial electrochemical rate constant forms in eqns. (8-2) and (8-3). F is thus the rate constant for electron transfer from the reduced form of the molecule to the substrate and the rate constant for electron transfer from the tip to the oxidized form of the molecule. 

Interfacial electron-transfer reactions between polymer-bonded metal complexes and the substrates in solution phase were studied to show colloid aspects of polymer catalysis. A polymer-bonded metal complex often shows a specifically catalytic behavior, because the electron-transfer reactivity is strongly affected by the pol)rmer matrix that surrounds the complex. The electron-transfer reaction of the amphiphilic block copol)rmer-bonded Cu(II) complex with Fe(II)(phenanthroline)3 proceeded due to a favorable entropic contribution, which indicated hydrophobic environmental effect of the copolymer. An electrochemical study of the electron-transfer reaction between a poly(xylylviologen) coated electrode and Fe(III) ion gave the diffusion constants of mass-transfer and electron-exchange and the rate constant of electron-transfer in the macromolecular domain. 

Schlichthorl et al. [177] have used light modulated microwave reflectivity to derive the rates of interfacial electron transfer processes at the n-Si/electrolyte interface. In these measurements, the modulation frequency was constant, and the rate constants for charge transfer were derived from the potential dependent ARm response. Schlichthorl et al. [73] have extended the technique considerably by introducing frequency response analysis. The technique is therefore analogous to IMPS, although, as shown below, it provides additional information. 

When the scan rate is sufficiently high to preclude sample equilibration with the electrode potential, then one, or both, of the peak currents will fail to achieve the magnitude predicted from the behavior displayed at lower scan rates for examples, see Fig. 3. In such conditions, the peaks become smeared across the potential axis in a maimer that allows for kinetic resolution of the underlying events. If the oxidative and reductive peaks are displaced equally, but in opposite directions, about the reduction potential, then interfacial electron transfer is the rate-limiting step. Fig. 3a. The variation of peak separation with scan rate, sometimes termed a trumpet plot, allows quantification of the standard heterogeneous rate constant for electron transfer. 

In its initial application, a triple potential step was applied at a submarine UME placed in the aqueous subphase of a Langmuir trough, close (1-2 pm) to the monolayer. The technique involves generating an electroactive species (Ox) at the UME by diffusion-controlled electrolysis of a precursor (Red) in an initial potential step. Ox diffuses to, and reacts with, the redox-active amphiphile at the water-air interface resulting in the conversion of the solution redox species to its initial form (Red), which then undergoes diffusional feedback to the UME. In this first step, the rate constant for electron transfer between the solution mediator and the surface-confined species can be measured from the UME current-time transient. In the second period, the potential step is reversed to convert the electrogenerated species (Ox) to its initial form (Red). Lateral diffusion of electroactive amphiphile into the interfacial zone probed by the UME occurs simultaneously in this recovery period. 

This case is shown in Fig. 10.6c and d where through absorption of light a photohole in the vb and a photoelectron in the cb are formed. The probability that interfacial electron transfer takes place, i.e. that a thermodynamically suitable electron donor is oxidized by the photohole of the vb depends (i) on the rate constant of the interfacial electron transfer, kET, (ii) on the concentration of the adsorbed electron donor, [Rads]. and (iii) on the rate constants of recombination of the electron-hole pair via radiative and radiationless transitions,Ykj. At steady-state of the electronically excited state, the quantum yield, Ox, ofinterfacial electron-transfer can be expressed in terms of rate constants ... 

Fig. 2.12. The apparent rate constant of the interfacial electron transfer from the CdS particles prepared with the excess of Cd2+ ions as a function of the methyl-viologen concentration. [CdS] = 10 4 M, [SDS] = 2-1 O 3 M, [TG] = 5T0 3 M. Illumination at X < 360 nm (UFS-1), Cell length 1 is 10 cm., T = 20°C.

Static electron transfer from photoexcited particles to adsorbed substrates has been observed for a wide range of semiconductor and organic materials respectively. For example, the photoinduced reduction of zwit-terionic viologen (ZV) by CdS conduction band electrons is found by time resolved transient absorption spectra to occur with a risetime for ZV -formation of less than 20 ps [116], consistent with a rate constant for interfacial electron transfer of >5 x 10los-1. Strong adsorption of the... 

Gerischer s distribution curves can be interpreted as representing the energy dependence of the electron transfer rate constants involving the reduced and oxidized species. Only a few electrochemical studies have attempted to evaluate the model and quantify the distributions and reorganizational parameters [17, 18]. Nevertheless, it has become common practice to draw a pictorial representation of the distributions when discussing interfacial electron transfer kinetics relevant to dye sensitization. 

Several reports have addressed how interfacial electron transfer rate constants vary with thermodynamic driving force. The driving force is tuned by manipulating the conduction band edge through adsorption of specific cations, utilizing different semiconductors, or by keeping the semiconductor constant with a series of sensitizers with known formal potentials. A difficulty in these studies is that the position... 

The highest interfacial electron transfer rate constant yet reported (about 14,000 s ) is for a c-type cytochrome from Aquifex aolicus This protein has a 62-amino acid linker domain by which it is usually anchored to the periplasmic side of the inner membrane this linker has a cysteine as the terminal residue before the signal region, and the sulfur atom provides an anchor point. The cytochrome adsorbs strongly onto a Au electrode that is already modified with a hexane-thiol SAM (note this requires that the molecules in the SAM move or vacate to allow this). The results are striking. 

Theory Gerischer has described a theory for excited-state electron transfer to semiconductors.90-92 The rate constant for interfacial electron transfer is proportional to the overlap of occupied donor levels of the excited state, fTdon( ), with unoccupied acceptor states in the semiconductor IXE) (Equation 12.6) ... 

FIGURE 12.13 Gerischer-type diagram for interfacial electron transfer. The rate constants for interfacial electron transfer are dependent on the overlap of the sensitizer and the semiconductor density of states. Note that the density of states of the semiconductor is not a singular parameter and can shift with a change in environment, that is, pH, ionic strength, solvent, and so on. 

We now recognize k as the ratio of kf to the steady-state mass-transfer coefficient niQ = DoIrQ. When k 1, the interfacial rate constant for reduction is very small compared to the effective mass-transfer rate constant, so that diffusion imposes no limitation on the current. At the opposite limit, where k >> 1, the rate constant for interfacial electron transfer greatly exceeds the effective rate constant for mass transfer, but the interpretation of this fact depends on whether k is also large. ... 

There is a significant contrast here with Section 5.4.2(e), where we found that the results for reversible systems observed at spherical electrodes could be extended generally to electrodes of other shapes. This is true for a reversible system because the potential controls the surface concentration of the electroactive species directly and keeps it uniform across the surface. Mass transfer to each point, and hence the current, is consequently driven in a uniform way over the electrode surface. For quasireversible and irreversible systems, the potential controls rate constants, rather than surface concentrations, uniformly across the surface. The concentrations become defined indirectly by the local balance of interfacial electron-transfer rates and mass-transfer rates. When the electrode surface is not uniformly accessible, this balance varies over the surface in a way that is idiosyncratic to the geometry. This is a complicated situation that can be handled in a general way (i.e., for an arbitrary shape) by simulation. For UME disks, however, the geometric problem can be simplified by symmetry, and results exist in the literature to facilitate the quantitative analysis of voltammograms (12). 

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