Diffusion controlled electron transfer processes

Tang, J. and Marcus, R. A. (2005) Diffusion-controlled electron transfer processes and power-law statistics of fluorescence intermittency of nanoparticles. Phys. Rev. Lett, 95, 107401-1-107401-4 Tang, J. and Marcus, R. A. (2005) Mechanisms of fluorescence blinking in semiconductor nanocrystal quantum dots./. Chem. Phys., 123,054704-1-054704-12. 

Tang, J. and Marcus, R. A. (2005) Diffusion-controlled electron transfer processes and power-law statistics of fluorescence intermittency of nanoparticles. Phys. Rev. Lett., 95, 107401. 

The variation of the free energy of the FET by stepwise electron transfer using mediator radical cations (benzene, butylbenzene, biphenyl) allows the energetic distinction between the diffusion-controlled (free) and the reaction-controlled electron transfer process. 

It must be noted that the dynamic nature of micelles must especially be borne in mind in dealing with electron transfers which invariably are fast processes. The seminal work of Bruhn and Holzwarth [88], an examination of the kinetics of diffusion-controlled electron transfer reactions in micellar sodium dodecyl sulfate solutions, disclosed that sufficient heed must be paid to the continuous disintegration and reconstitution of the micelles in this time range. 

Similar to those observed with the cysteine-modified electrode in Cu, Zn-SOD solution [98], CVs obtained at the MPA-modified Au electrode in phosphate buffer containing Fe-SOD or Mn-SOD at different potential scan rates (v) clearly show that the peak currents obtained for each SOD are linear with v (not v 1/2) over the potential scan range from 10 to 1000 mVs-1. This observation reveals that the electron transfer of the SODs is a surface-confined process and not a diffusion-controlled one. The previously observed cysteine-promoted surface-confined electron transfer process of Cu, Zn-SOD has been primarily elucidated based on the formation of a cysteine-bridged SOD-electrode complex oriented at an electrode-solution interface, which is expected to sufficiently facilitate a direct electron transfer between the metal active site in SOD and Au electrodes. Such a model appears to be also suitable for the SODs (i.e. Cu, Zn-SOD, Fe-SOD, and Mn-SOD) with MPA promoter. The so-called... 

A general difficulty encountered in kinetic studies of outer-sphere electron-transfer processes concerns the separation of the precursor formation constant (K) and the electron-transfer rate constant (kKT) in the reactions outlined above. In the majority of cases, precursor formation is a diffusion controlled step, followed by rate-determining electron transfer. In the presence of an excess of Red, the rate expression is given by... 

Examination of the behaviour of a dilute solution of the substrate at a small electrode is a preliminary step towards electrochemical transformation of an organic compound. The electrode potential is swept in a linear fashion and the current recorded. This experiment shows the potential range where the substrate is electroactive and information about the mechanism of the electrochemical process can be deduced from the shape of the voltammetric response curve [44]. Substrate concentrations of the order of 10 molar are used with electrodes of area 0.2 cm or less and a supporting electrolyte concentration around 0.1 molar. As the electrode potential is swept through the electroactive region, a current response of the order of microamperes is seen. The response rises and eventually reaches a maximum value. At such low substrate concentration, the rate of the surface electron transfer process eventually becomes limited by the rate of diffusion of substrate towards the electrode. The counter electrode is placed in the same reaction vessel. At these low concentrations, products formed at the counter electrode do not interfere with the working electrode process. The potential of the working electrode is controlled relative to a reference electrode. For most work, even in aprotic solvents, the reference electrode is the aqueous saturated calomel electrode. Quoted reaction potentials then include the liquid junction potential. A reference electrode, which uses the same solvent as the main electrochemical cell, is used when mechanistic conclusions are to be drawn from the experimental results. 

This system can be taken as an example of so-called reversible, diffusion-controlled electrochemical processes. In short, during the initial anodic scan, an electron-transfer process between the ferrocyanide (or hexacyanoferrate(II)) ions, [Fe(CN)6] ", and the working electrode occurs. This can be represented by means of the equation (here, aq denotes species in aqueous solution) ... 

Ru(bpy) +, is diffusion controlled. In the presence of the SiC>2 colloid this back electron transfer process is substantially retarded and ca. 200-fold slower than in the homogeneous phase. The functions of the Si02 colloid in charge separation and retardation of back reactions are attributed to electrostatic interactions of the photoproducts and the charged colloid interface (Figure 3). 

The control of electron transfer is a critical issue in the fabrication of molecular electronic devices from the viewpoint of electronic circuit formation however, electron transfer processes of redox polymer-coated electrodes fabricated using a conventional polymer-coating method usually shows a diffusion-like behavior because the redox sites are randomly distributed in the polymer film (Fig. la) 17-20 consequently, it is difficult to control the electron transfer direction in three dimensions. 

The chronocoulometry and chronoamperometry methods are most useful for the study of adsorption phenomena associated with electroactive species. Although less popular than cyclic voltammetry for the study of chemical reactions that are coupled with electrode reactions, these chrono- methods have merit for some situations. In all cases each step (diffusion, electron transfer, and chemical reactions) must be considered. For the simplification of the data analysis, conditions are chosen such that the electron-transfer process is controlled by the diffusion of an electroactive species. However, to obtain the kinetic parameters of chemical reactions, a reasonable mechanism must be available (often ascertained from cyclic voltammetry). A series of recent monographs provides details of useful applications for these methods.13,37,57... 

Weller 171> has pointed out that the rate constants for electron transfer to fluorescent aromatics are diffusion-controlled when the process is exothermic but are proportional to the free energy change when the process is endothermic. Here (D/D+) is the donor oxidation potential, positive by convention, and E(A jA)... 

The proximity of the diffusion limit also inhibits a detailed discussion of the data in Table 7, but a significant difference to the substituent effects discussed in Section III.D.4 is obvious. Whereas the reactivities of terminal alkenes, dienes, and styrenes toward AnPhCH correlate with the stabilities of the new carbenium ions and not with the ionization potentials of the 7r-nucleophiles [69], the situation is different for the reactions of enol ethers with (p-ClC6H4)2CH+ [136]. In this reaction series, methyl groups at the position of electrophilic attack activate the enol ether double bonds more than methyl groups at the new carbocationic center, i.e., the relative activation free enthalpies are not controlled any longer by the stabilities of the intermediate carbocations but by the ionization potentials of the enol ethers (Fig. 20). An interpretation of the correlation in Fig. 20 has not yet been given, but one can alternatively discuss early transition states which are controlled by frontier orbital interactions or the involvement of outer sphere electron transfer processes [220]. 

When tetrabutylammonium triphenylalkylborate was used as the electron donor, the dye radical anion (DIBF ) was observed as the only transient formed by quenching the dye triplet. The electron transfer rate ealeulated for the electron transfer process is 7.6 x 10 s , i.e., three orders of magnitude below the diffusion-controlled limit. The photobleached products and the transient phenomena observed... 

One of the first reports on the quasireversible electrochemistry of redox proteins appeared in 1977 when Eddowes and Hill demonstrated (10) cyclic voltammetry of horse heart cytochrome c at a gold electrode in the presence of 4,4 -bipyridyl (Bipy) in solution. In the voltammo-grams (Fig. 1), the peak-to-peak separations were close to 60 mV and the faradaic currents varied linearly with (scan rate), indicating a quasireversible one-electron transfer process controlled by linear diffusion of redox species to the electrode surface. The midpoint potential... 

In principle, phenoxyl radicals can react with other molecules also by a hydrogen-abstraction mechanism. The net result of such reactions may be equivalent to that of the electron transfer processes discussed above. It is likely that in aqueous solutions such reactions are much slower than the electron transfer reactions, as indicated by the fact that most reactions between phenoxyl radicals and other phenols are much slower with the neutral phenols than with the phenolate ions. It is possible that even reactions with neutral phenols in aqueous solutions involve an electron transfer mechanism. On the other hand, reactions in organic solvents may well take place by hydrogen abstraction, as discussed before . These reactions take place with much lower rate constants than the electron transfer reactions the most rapid hydrogen abstraction by a phenoxyl radical is probably five orders of magnitude slower than the diffusion-controlled limit and most of them are orders of magnitude slower than that. 

The various examples of photoresponsive supramolecular systems that have been described in this chapter illustrate how these systems can be characterized by steady-state and time-resolved spectroscopic techniques based on either absorption or emission of light. Pertinent use of steady-state methods can provide important information in a simple vay stoichiometry and stability constant(s) of host-guest complexes, evidence for the existence of photoinduced processes such as electron transfer, energy transfer, excimer formation, etc. Investigation of the dynamics of these processes and characterization of reaction intermediates requires in most cases time-resolved techniques. Time-resolved fluorometry and transient absorption spectroscopy are frequently complementary, as illustrated by the study of photoinduced electron transfer processes. Time-resolved fluorometry is restricted to phenomena whose duration is of the same order of magnitude as the lifetime of the excited state of the fluorophores, whereas transient absorption spectroscopy allows one to monitor longer processes such as diffusion-controlled binding. 

In a few systems, quenching rate constants tend toward saturation below the diffusion-controlled limit . This may be observed when the quenching reaction does not involve an electron-transfer process (e.g. , [ RuL3] -[Cr )] ), when the electron transfer is highly nonadiabatic, when the reactive form of the quencher is not the dominant form in solution (e.g. , [ RuL3] -[CU( )] , or when a substitutional or conformational change becomes rate determining. ... 

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