Impurity Quenching of Molecular Excitons. I. Kinetic Comparison of Förster—Dexter and Slowly Quenched Frenkel Excitons in Linear Chains

Abstract

The quenching kinetics of tightly bound excitons for two different one‐dimensional models are compared. The quenching of fully incoherent, or Förster—Dexter, excitons is described by a standard master equation, and that of fully coherent, or Frenkel, excitons by an ad hoc linear differential equation whose eigenvalues are complex. Moments of the chain excitation function (probability that excitation remains at time t) are calculated on each model for finite chains with either localized or uniform initial conditions, free‐end or periodic boundary conditions, one disruptive or one nondisruptive quencher, and various quencher locations, but with only nearest‐neighbor interactions included. The ad hoc equation is treated only in the limit that the quenching is slow enough not to affect the exciton wave functions in first order. In that limit of Frenkel exciton quenching, an analytic expression is given for the mean de‐excitation time in the presence of uniform decay processes such as fluorescence. The master equation is treated for arbitrary relative quencher strength with simple analytic expressions for the zeroth moment obtained by an inverse matrix method. Infinite chains with randomly placed disruptive quenchers are also treated. It is shown that for the Förster—Dexter model the nth moment M_n is proportional to N²ⁿ⁺² for large N (finite chains) or to c^−(2n+2) for small c (infinite chains); for the Frenkel model with an incoherent initial condition, $M_n{\mathrm{\propto \; N}}^{\text{(3n+2)}}$ or c^−(3n+2). This implies that kinetic differences between quenching of Frenkel and Förster—Dexter excitons appear only in higher (than zero) moments and not, e.g., in fluorescence yields. It is also concluded that, because of their ``boundary‐avoiding tendency,'' Frenkel excitons can be quenched much more slowly in some situations than Förster—Dexter excitons. Finally, the intuitive notion that excited‐state energy transfer is a two‐step process—consisting of migration to the quencher neighborhood and subsequent quenching—is substantiated for Förster—Dexter excitons but not for Frenkel excitons.