Arrhenius plot electron transfer

Fig. 13. Arrhenius plot of k(T) for electron transfer from cytochrome c to the special pair of bacteriochlorophylls in the reaction center of c-vinosum.

As an illustration of these considerations, the Arrhenius plot of the electron-transfer rate constant, observed by DeVault and Chance [1966] (see also DeVault [1984]), is shown in fig. 13. 

Pai Vemeker and Kannan [1273] observe that data for the decomposition of BaN6 single crystals fit the Avrami—Erofe ev equation [eqn. (6), n = 3] for 0.05 < a < 0.90. Arrhenius plots (393—463 K) showed a discontinuous rise in E value from 96 to 154 kJ mole-1 at a temperature that varied with type and concentration of dopant present Na+ and CO2-impurities increased the transition temperature and sensitized the rate, whereas Al3+ caused the opposite effects. It is concluded, on the basis of these and other observations, that the rate-determining step in BaN6 decomposition is diffusion of Ba2+ interstitial ions rather than a process involving electron transfer. 

Figure 23. Arrhenius plot of the electron transfer rate. The electronic coupling strength is TIad = 0.0001 a.u. Solid line-Bixon-Jortner perturbation theory Ref. [109]. FuU-circle present results of Eq. (26 ). Dashed line-results of Marcus s high temperature theory [Eq.(129)]. Taken from Ref. [28].

This factorization of the rate of the elementary process (Eq. 1) leads (with a few approximations) to the compartmentalization of the experimental parameters in the following way the dependence of the rate upon reaction exo-thermicity and upon environmental polarity controls and is reflected in the activation energy and the temperature dependence, whereas the dependence of the rate upon distance, orientation, and electronic interactions between the donor and the acceptor controls and is reflected in Kel- We refer to this eleetronie interaction energy as A rather than the common matrix element symbol H f, since we require that A include contributions from high-order perturbations and in particular superexchange processes. Experimentally, the y-intereept of the Arrhenius plot of the eleetron transfer rate yields the prefactor [KelAcxp)- - AS /kg)], and hence the true activation entropy must be known in order to extract Kel- An interesting example of the extraction of the temperature independent prefaetor has been presented in Isied s polyproline work [35]. 

Figure 8 Modified Arrhenius plots for back electron transfer from colloidal Sn02 to adsorbed Ru(phen)l+ ( ), Os(3,4,7,8-CH3-phen)l+ (0), and Os(3,4,7,8-CH3-phen)2 (m-im)2+ ( ). (Adapted from Ref. 36.)...

As an illustration of these considerations, the Arrhenius plot of the electron transfer rate constant, observed by De Vault and Chance [1966], is shown in Figure 2.11. Note that only Er, which actually is the sum of reorganization energies for all degrees of freedom, enters into the high-temperature rate constant formula (2.66). At low temperature, however, to preserve Er, one has to fit an additional parameter a>, which has no direct physical significance for a real multiphonon problem. 

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. 

The rate constants (kex) of the electron exchange reactions between ZnTPP+ and ZnTPP [Eq. (1)] were determined using Eq. (2), where AHms( and AH°msi are the maximum slope linewidths of the ESR spectra in the presence and absence of ZnTPP+, respectively, and P, is a statistical factor [14]. From the linear plots of (AHmsi - Afi°msl) and [ZnTPP] at various temperatures are obtained the self-exchange electron-transfer rate constant (k ). The Arrhenius plots are shown in Fig. 13.3 together with the observed activation enthalpies (AHols ), where the effect of diffusion (kdiff) is taken into account. The AHol/ values are all positive and decrease in order toluene > MeCN > CH2C12 [16],... 

Fig. 13.3 Arrhenius plots of self-exchange electron transfer between ZnTPP+ and ZnTPP in different solvents [16].

The Arrhenius plot shows an apparent overall activation energy of about 8 kcal/mol, well below the initiation by a hydrogen abstraction [(Eq. (7)] and more consistent with an electron transfer model for initiation reaction [(Eq. (8)]. 

The influence of the temperature was mainly attributed to the distribution function of electrons in the adsorbed states. They also predicted the possibility of a break in the Arrhenius plot corresponding to a transfer probability = 1 but this was not confirmed by the experimental data of Bowden for Pt in 0.1 M H2S04, ° utilized by Schultze and Vetter for comparison with the theoretically expected temperature dependence. 

The steric and electronic effects of the phenol substituents influence the rate of the reaction. The rates of H-atom transfer in various solvents differ slightly, showing an order which follows the ability of the solvent to form hydrogen bonds with phenol. Arrhenius plots were determined over the range 50°C to -60 C, for two of the phenols(2,H,6-tri-t-butyl and 2,6-di-t-butyl), and show positive deviations from linearity which may be attributable to quanturn-mechanical tunnelling of the hydrogen atom. 

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