Electron transfer diffusion control limit

Actually the parabolas are truncated at the diffusion-controlled limit because of considerations we met in Chapter 9. We can develop this again here in an abbreviated fashion by writing a two-step scheme, the first being entirely diffusion and the second intramolecular electron transfer ... 

In an EC mechanism the ratio of the forward and backward reaction rates is decisive for k/ d in , the chemical follow-up reaction has no influence here, so that for a sufficiently rapid electron transfer step the limiting current remains diffusion controlled.)... 

An alternative electrochemical method has recently been used to obtain the standard potentials of a series of 31 PhO /PhO- redox couples (13). This method uses conventional cyclic voltammetry, and it is based on the CV s obtained on alkaline solutions of the phenols. The observed CV s are completely irreversible and simply show a wave corresponding to the one-electron oxidation of PhO-. The irreversibility is due to the rapid homogeneous decay of the PhO radicals produced, such that no reverse wave can be detected. It is well known that PhO radicals decay with second-order kinetics and rate constants close to the diffusion-controlled limit. If the mechanism of the electrochemical oxidation of PhO- consists of diffusion-limited transfer of the electron from PhO- to the electrode and the second-order decay of the PhO radicals, the following equation describes the scan-rate dependence of the peak potential ... 

As discussed in later sections, at close contact the contribution to the barrier to electron transfer arising from the solvent is minimized and, more importantly, electronic coupling is maximized. At experimentally accessible ionic strengths, even for like-charged reactants, a significant fraction of the reactants are in close contact as defined by the association constant K = [D, A]/[D][A], where D and A refer to the electron transfer donor and acceptor, respectively. As long as the reaction rate constant, kobs, is well below the diffusion-controlled limit, it is related to the constants in Scheme 1 by fcobs =... 

While the reaction of the solvated electron with hydrogen ions is near the diffusion-controlled limit in aqueous and alcoholic systems (24), the reaction with hydrogen chloride in our system, which presumably gives ethylenediammonium ions, is much slower with k = 1.7 X 106 M l sec."1 Interestingly, the reaction with ammonium ions is at least an order of magnitude faster than this, indicating that appreciable proton transfer from ammonium ion to ethylenediamine does not occur. 

The mechanism shown in Scheme 4.9 has been proposed for the hydrogen atom transfer from phenols (ArOH) to radicals (Y ) in non-aqueous solvents, a kinetic effect ofthe solvent (S) being expected when ArOH is a hydrogen bond donor and the solvent a hydrogen bond acceptor. Steps with mechanistic rate constants k, k-1 and k>, involve proton transfer (the latter two near to the diffusion-controlled limit), and kj involves electron transfer. The step with rate constant fco involves a direct hydrogen atom transfer, and the other path around the cycle involves a stepwise alternative. 

The first-order rate constant can be evaluated from the decay curves of 3C o and the rise curves of Qo and the donor radical cation [125,154], The observed electron transfer rate constants for C6o are usually in the order of 109-1010 dm3 mol-1 s-1 and thus near the diffusion controlled limit which depends on the solvent (e.g., diffusion controlled limit in benzonitrile -5.6 X 109 M-1 s-1) [120,125,127,141,154-156],... 

The electrons are subsequently transferred to the MoFe or VFe protein one at a time. The rate of binding of the Fe protein to the MoFe protein has been estimated to occur with a rate constant, k > 5 X 107 dm3 mol-1 sec-1, which is close to the diffusion-controlled limit (72). The Fe protein-MoFe protein electron transfer is followed, when S2042- is the reductant, by the rate-determining dissociation of the two proteins. 

Fig. 3. Reaction coordinate diagrams for electron transfer, (a) AG° = 0 (f>) AG° negative (c) diffusion-controlled limit, —AG. = X (d) abnormal free-energy region, —AG. > X...

The latter theory of intramolecular electron transfer in nonconjugated polyelectrolytes, which may find support in the behaviour of the ribonuclease-copper(n) system (Levitzky and Anbar, 1967), is in accord with the observed agreement between the specific rates of gelatine, lysozyme and ribonuclease and the sum of specific rates of the constituent amino-acid residues (Braams, 1965, 1967). The latter agreement may, however, be fortuitous, and these proteins, which react at rates approaching the diffusion-controlled limit, may act as overall electron traps according to the first mechanism. 

Hydroxyl radicals ( OH) are powerful oxidants and participate in a number of reactions such as addition to the double bonds forming radical adducts, electron transfer reactions, and H-atom abstraction reaction. The rate constants for the reaction of OH radicals with organic substrates are mostly diffusion controlled (10 -10 ° M" s" ). When OH radical reacts with cellular organic molecules (RH) either by hydrogen abstraction [Eq. (4)] or by addition reaction, it leaves a radical site on the molecule (R ) and sometimes these radicals can add to the oxygen present in the cells, to be converted to peroxyl radicals [ROO, Eqs. (4) and (5)]. Rate constants for these reactions vary between 10 to diffusion-controlled limits depending on the nature and substitution on RH. °... 

The kinetic studies make use of the unequally sized reaction partners (e.g. a large electron donor and a small electron acceptor couple) and benefit from the low viscosity of dichloromethane (DCM), both of which elevate the diffusion-controlled limit. To study the electron transfer, deoxygenated DCM solutions of, for example, w-terphenyl at high concentrations (0.02 m) were irradiated in the presence of different concentrations of fullerene (ca 10 m) [62]. This resulted in accelerated decay of (arene) + UV-Vis absorption, with rates linearly depending on fullerene concentration [62]. Formation of the electron-transfer product, fullerene", was confirmed spectroscopically by measurement of the NIR fingerprint (Amax = 1080 nm) [62, 65]. 

In Pina s work, 2,3-butanedione is trapped inside hemicarcerand 63 to give the corresponding hemicarceplex, and the reactions with several electron donors are investigated in order to elucidate the effect of the encapsulation on the rates of the electron transfer to the triplet excited state of the guest. The determination of phosphorescence quenching lifetimes of free and incarcerated 2,3-butanedione reveals that quenching for uncomplexed 2,3-butanedione occurs at the diffusion-controlled limits for any donor quencher (e.g., amines), whereas in the case of the encapsulated substrate the rate constants are lower (ranging between 3.5 x 10 and 4 X 10 s ) and display an approximately linear dependence upon the oxidation potential of the external quencher. In particular, rate constants decrease with the... 

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... 

In the case of rapid electron transfer reactions, one should take account of diffusion control limiting the utmost feasible reaction rate ... 

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. 

Bimolecular electron transfer proceeds by a number of steps prior and subsequent to the actual electron transfer, any one of which can become rate determining and cause the rate to saturate or plateau below the diffusion-controlled limit. Rate saturation means that the electron-transfer rate no longer increases with increasing driving force in limiting cases the rate also may become independent of the concentration of one of the reactants. 

Ill) Rate Determined by Conversion of Precursor to Successor Compiex. This is the case for the ordinary electron transfer discussed in earlier sections. However, even though all of the preceding steps may be rapid and no unfavorable preequilibria are involved, the rate constants for ordinary electron transfer saturate below the diffusion-controlled limit when the reaction is nonadiabatic (k, << 1). For example, when AG = 0 (the normal condition for a diffusion-controlled reaction), k, for a nonadia-... 

---