Electron transfer decay factor

Mainly, three approaches have been used to immobilize the enzyme on transducer or electrode surface, single layer, bilayer, and sandwich configurations [69, 98], In some studies enzymes are covalently linked with sol-gel thin films [99], Sol-gel thin films are highly convenient for fast, large, and homogeneous electron transfer [17]. With an increase in gel thickness the signal decays and diffusion of analytes to biomolecule active site becomes difficult eventually these factors lead to poor response. By employing thin films various biosensors such as optical and electrochemical biosensors have been reported. 

Figure 4 shows the temperature dependence of the decay kinetics measured in PVA films in the 665-nm band (triangles). Some measurements at lower temperatures in the 545-nm band are also shown (circles). The electron transfer rate constant increases by a factor of 2 as the temperature is lowered from 295 K to 100 K, at which point the rate becomes independent of temperature within experimental error. The solid curve through the experimental data in Figure 4 is a theoretical fit that will be discussed below. 

Table II presents the vadues of v, the rate constant for the electron transfer reaction with the donor and acceptor in contact, calculated by deconvolution of the fluorescence decay curves for a number of excited porphyrin-cOkyl halide systems. It appears that the rate parauneter depends strongly on the calculated exothermicity for these reactions. Parauneter i/ contadns information about the Framck-Condon factor of the electron-tramsfer reaction, which is in itself dependent on the reaction exothermicity and reorgauiization energy (22.23). Whether the rate constauit for the electron-transfer reactions depends on the exothermicity in the manner predicted by theory, that is with a simple Gaussian dependence (22), cannot be ainswered at present because of the uncertainties in the energetics of the particular reactions studied here.

From Eq. 14-30 we see that we may divide a one-electron transfer into various steps (maybe somewhat artificially). First, a precursor complex (PR) has to be formed that is, the reactants have to meet and interact. Hence, electronic as well as steric factors determine the rate and extent at which this precursor complex formation occurs. Furthermore, in many cases, redox reactions take place at surfaces, and therefore, the sorption behavior of the compound may also be important for determining the rate of transformation. In the next step, the actual electron transfer between P and R occurs. The activation energy required to allow this electron transfer to happen depends strongly on the willingness of the two reactants to lose and gain, respectively, an electron. Finally, in the last steps of reaction sequence Eq. 14-30, a successor complex may be postulated which decays into the products. 

Some of the fastest photochemical processes occur on the ps time-scale, for instance electron transfer reactions. In the case of intermolecular electron transfers the actual reaction rate constants cannot be obtained when the diffusion of the reactants is the limiting factor. High concentrations must be used to ensure that encounters are faster than the reactions. Figure 8.7 shows the ps transient absorption spectra of the electron transfer between benzo-phenone and DABCO in acetonitrile. The triplet excited state of benzophe-none is seen to decay at 525 nm while the radical anion grows at about 700 nm to reach a maximum concentration after 1 ns. The decay and growth kinetics are shown in (b) of the same Figure. 

Quantitative investigations of the photoinduced electron transfer from excited Ru(II) (bpy)3 to MV2 + were made in Ref. [54], in which the effect of temperature has been studied by steady state and pulse photolysis techniques. The parameters ve and ae were found in Ref. [54] by fitting the experimental data on kinetics of the excited Ru(II) (bpy)3 decay with the kinetic equation of the Eq. (8) type. It was found that ae did not depend on temperature and was equal to 4.2 + 0.2 A. The frequency factor vc decreased about four orders of magnitude with decreasing the temperature down to 77 K, but the Arrhenius plot for W was not linear, as is shown in Fig. 9. 

In the investigations of the systems so far mentioned, only the kinetics of the long-wavelength absorbing radical anions could be monitored spectroscopically. Simultaneous analysis of both transient species was performed using p -chloranil (9) as the acceptor and 2-methoxy-l,l-diphenylethene (10) as the donor [33, 36]. Both the radical anion 9 and the radical cation 10+ decay within the same halflife of ca. 1 ps, as expected for back electron transfer as the major process (Fig. 6). Utilizing the special salt effect (addition of lithium perchlorate) increases the lifetime of both intermediates by a factor of ten. 

Separation of D and A centers by non-conducting media resulted in the strong dependence of the ET rate on distance between D and A and the marked effect of the chemical nature of saturated molecules and bonds between the pair. This dependence can be quantitatively characterized be the decay factor, (3, (Eq. 2.27). The following values of P (in A 1) were found 3-4 (vacuum), 1.6 - 1.75 (water), 1.2 (organic solvents) and 1.08 -1.2 (synthetic D-bridge-A molecules). The effects of distance and the number of intermediate saturated groups (n) on photoinduced electron transfer between a donor and acceptor are discussed in (Verhoeven, 1999). 

The conversion of the initially formed Si np state to the Si ct state by intramolecular electron transfer is very fast and varies in a way that parallels but does not exactly correspond to the dielectric relaxation time for the solvent used. This is because the local environment around the excited-state molecule is different from that surrounding a solvent molecule [120, 340]. That is, the ICT process is to a large extent determined by the dielectric relaxation processes of the solvent surrounding the ANS molecule. Thus, solvent motion seems to be the controlling factor in the formation and decay of the ICT excited state of ANS and other organic fluorophores [120, 340]. A detailed mechanism for fast intramolecular electron-transfer reactions of ANS and 4-(dimethylamino)benzonitrile, using two simplified molecular-microscopic models for the role of the solvent molecules, has been given by Kosower [340] see also reference [116]. 

Rates of Cu+ to Ru + electron transfer also have been measured in modified mutants of spinach plastocyanin, a blue copper protein from the photosynthetic ET chain [79], Ru-bipyridine complexes were introduced at surface sites, with Cu-Ru distances ranging from 13 to 24 A. ET rate constants, measured using laser flash-quench techniques, vary from 10" to 10 s. ET in Ru-modified plastocyanin is not activationless as it is in Ru-modified azurin, suggesting a slightly greater reorganization energy for the photosynthetic protein. The distance dependence of ET in Ru-modified plastocyanin is exponential with a distance decay factor identical with that reported for Ru-modified azurin (1.1 A ). 

The electronic coupling of the reactant state with the product state, F, is a function of the overlap of the donor and acceptor orbitals. This in turn depends on energetic, spatial, geometric, and symmetry factors. At relatively large donor acceptor separations, it can be assumed that the relevant orbitals decay exponentially with distance. In these cases, the electron transfer rate constant will depend on this separation as per Eq. 2, where Rda is the donor-acceptor separation and y is a constant that expresses the sensitivity of the... 

The rate constant for photoinduced electron transfer k4 and the charge recombination rate constant ks are directly observed experimentally. The reciprocal of the 3-ps time constant detected in the transient absorption experiments, equals kn, 3 X 10 s. This assignment is verified by the results for a model P-C6o dyad, where the same value was obtained for the rate constant for photoinduced electron transfer. The charge recombination of (Pzp)3-Pzc-P -C6o is associated with the 1330-ps decay component observed in transient absorption, as demonstrated by the spectral signature of the fullerene radical anion with absorption in the 1000-nm region. This lifetime is within a factor of 2.5 of the lifetime observed for the P" -C6o in a model dyad (480 ps). 

The distance decay constant / (see below) in Miller et al. s original study was 0.9 per CH2, using ferricyanide and iron(IH) hexahydrate [44]. In a later study which accounted more thoroughly for double layer effects, 2 was determined to be 1 eV for kinetically facile redox probes such as ferricyanide, 1.3 eV for Ru-hexamine and 2.1 eV for iron(III) hexahydrate. With a better understanding of the redox probe behavior, f was found to be 1.08 + 0.20 per CH2 and independent of the redox couple and electrode potential [96]. Pre-exponential factors were also extracted from the Tafel plots. The edge-to-edge rate constants (extrapolated) are approximately 10 -10 s for all redox probes, which is reasonable for outer-sphere electron transfer. The pre-exponential factors are 5 x lO s [96]. 

An example of the goodness-of-fit attainable with these equations is given in Figure 8, where the decay kinetics for electron transfer from A,A-dimethylaniline to photoexcited octadecylrhodamine on the surface of CTAB micelles is compared with the theoretical fits for two different concentrations of the donor [82bj. The theoretical decay curves were obtained by numerical integration of Eq. 13, followed by ensemble averaging over the Poisson distribution of donors within the micelles an exponential factor was also added to account for the spontaneous decay of the excited molecules. The parameters AGf and 1 were calculated by assuming that the donor and acceptor molecules are on the surface of a sphere of low dielectric... 

The decay of the parent is biexponential with a short time constant, typically 250 fs, and a longer one, 800 fs. The kinetics appear to be parallel, i.e., correspond to different and competing decay channels. Their pre-exponential factors are different, with the short one dominating. The short decay has been assigned to an ionic to covalent back electron transfer pictured in Figure 17, resulting in iodine dissociation. A back transfer from the iodine n orbital to the half-filled benzene n orbital leaves iodine in a dissociative state. The reaction channel forms (benzene) - -I-1, and corresponds to the minor decay component of the parent. 

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