A Case of Fully Diffusion-Controlled Exothermic Triplet Excitation Transfer

Article abstract of DOI:10.1021/ja00542a022

Conventional flash kinetic spectroscopy has been used to determine rate constants (k_obsd) for triplet energy transfer from indeno<2,1-a>indene, a rigid model of trans-stilbene, to azulene as a function of temperature in n-pentane (228 - 290 K), toluene (228 - 309 K), acetonitrile (233 - 308 K), and tert-butyl alcohol (302 - 342 K).In toluene the plot of k_obsd vs.T/η is linear with a slope somewhat smaller than predicted by the Debye equation for a diffusion-controlled process.In n-pentane the plot shows upward curvature, while in tert-butyl alcohol and in acetonitrile the T/η plots show downward curvature.The possibility that the downward curvature is due to deviation from a fully diffusion-controlled process is examined but rejected following a critical comparison of k_obsd with recently reported termination rate constants for coupling and disproportionation of tert-butyl radicals, k_t.The k_obsd/k_t ratios for the entire temperature and solvent range, 3.1 - 4.5, are consistent with the spin-statistical factor φ = 1/4, proposed as the sole deviation of k_t from a fully diffusion-controlled rate constant.Empirically based truncated microfriction factors were used to correct diffusion coefficients in the nonhydroxylic solvents, and calculated values of φ^-1, falling in the 3.5 - 5.0 range, were obtained that were indistinguishable from 4 within the experimental uncertainties of the measurements.It is concluded that excitation transfer is fully diffusion controlled under all conditions employed here and that, following an encounter between donor and acceptor, a probable lower limit for the rate constant of excitation transfer is k_et (*) 2*10¹² s^-1.This result is compared with observations in the literature.Satisfactory adherence to the Arrhenius equation is observed in all four solvents and activation energies are similar to activation energies for viscous flow obtained from the temperature dependence of η using the Andrade equation.Entropies and enthalpies of activation, obtained by applying transition-state theory to k_obsd and 4k_t, obey a common isokinetic relationship, with β = 372 K as the isokinetic temperature.This isokinetic relationship is likely to apply to related diffusion-controlled reactions.Activation entropies, (*), are compared to cratic entropies, ΔS_c, for the reversible formation of an encounter complex.Except for tert-butyl alcohol, where (*) ca. 0, (*) is roughly 4/3ΔS_c reflecting more ordering in the transition state than in the fully formed encounter complex.