Simulations of energy transfer and trapping in two-dimensional disordered systems

Abstract

A stochastic master equation is solved numerically to study energy transfer via dipole-dipole interactions and trapping in a two-dimensional random array of nonoverlapping donor pigments with dilute traps in the situation where the Förster transfer radii R _D0 and R _T0 (characterizing respectively the interactions among donors and between donor and trap) are equal (R _D0 = R _T0 = R ₀). In the quasi-exponential, long-time regime of the calculated trapping decay , the trapping rate [Wbar] is given by the smallest eigenvalue of the associated master equation matrix and is found to vary linearly with the trap concentration C _T and quadratically with the donor concentration C _D in accordance with phenomenological theories of migration-accelerated quenching in the hopping approximation (i.e. R _D0 ≫ R _T0). At short times, is not exponential and can be conveniently characterized by _e and τ, respectively the 1/e lifetime and the average lifetime of the decay. Quantitative dependences of and [Wbar] on C _D, C _T, R ₀ and τ₀ (the natural lifetime) are given and may be used to describe fluorescence quenching experiments in monolayers of pigments. For the sake of comparing the short time behaviour of our decays to the one observed in the photosynthetic unit (PSU), we have calculated fluorescence decays with parameters appropriate to chlorophyll a in vivo and found they could be easily fitted to a law of the form, exp [- At - Bt ^p] with p close to 1/2. The degree of nonexponentiality is found to be smaller than the one observed in the PSU, where the structure of the medium is believed to be inhomogeneous (rather than homogeneous, as assumed in the present study). Finally, we give the concentration dependence of [nbar] and _h, respectively the walklength of the excitation to the trap and an effective hopping time derived from [nbar] and . The very different behaviour found for relative to other hopping times reported in the literature is explained in terms of the connectivity of the network and local concentration of the clusters visited by the excitation.