Excitation migration and transfer to interstitial traps - Low dimensional transport and conformational motion

An effective medium approximation (EMA) has been used in an attempt to analyze incoherent migrational trapping in a system of 1-D regular and immobile donors, where trapping is a time-dependent stochastic process - due to the dynamic conformational disorder of interstitial accepters, By assuming (I) the time duration of the elementary act of conformational transition to be longer than the time involved in the electronic site-to-site transfer and (II) the transport of excitation during conformational event to be negligible, the hypersurface of the effective trapping rate coefficient K-eff(z) in Laplace space can be formulated on the basis of a stochastic master equation analysis. The computation has been centered on conformational transitions between two relative positions in the donor-acceptor pair connected by flexible carbon-carbon spacer-groups, where the dynamical fluctuation of acceptor positions, due to the conformational motion of spacer segments, dichotomically modulates the trapping rate coefficient. On these premises K-eff(z) can be obtained by numerically solving a third order polynomial equation which allows, after Laplace inversion, the mean-square distance of migrating excitation [r(2)(t)] and the survival probability of donor excitation [P(t)] to be analyzed. The effect of conformational motion on the excitation trapping efficiency has been calculated for a series of conformative and electronic parameters. The non-Markovian character of trapping becomes apparent for slow to moderate conformational motion in the short-to-intermediate time regime and disappears for fast conformational transitions. Furthermore, the asymptotic trapping rate K-eff(z = 0(+)) which represents the Markov approximation of the memory function K-eff(t) has been analyzed for different rates of conformational motion and equilibrium conformational probabilities and, finally, the investigation has been extended to 2-D transport in a preliminary attempt.