ELECTRONIC-ENERGY TRANSFER IN ANISOTROPIC SYSTEMS .3. MONTE-CARLO SIMULATIONS OF ENERGY MIGRATION IN MEMBRANES

Electronic energy migration in membrane systems has been studied by means of Monte Carlo (MC) simulations according to an algorithm described previously [S. Engstrom, M. Lindberg, and L. B.-A. Johansson, Chem. Phys. 89, 204 (1988)]. In the systems investigated, the interacting donor molecules are randomly localized in mono-, bi-, and multilayers and are either oriented with their transition dipoles isotropically or parallel to the layers. The mean-square displacement [<R(t)2>] of the excitation and experimental observables in terms of different fluorescence depolarizations were determined. All results are relevant for the "slow case," which means that translational and rotational motions of the donors are much slower as compared to the rate of fluorescence. A two-particle approximation for calculating the excitation probability of the initially excited molecule [denoted by G(s)(t)] and the fluorescence depolarizations in two-dimensional systems has been published previously [J. Baumann and M. D. Fayer, J. Chem. Phys. 85, 4087 (1986)]. By using the MC algorithm, we have in this work tested this model extensively. The excitation probability G(s)(t) is found to be in excellent agreement with the MC simulations for all of the systems studied. For isotropically oriented donor molecules in multilamellar systems, the simulations show that G(s)(t) is very well approximated by that of a monolayer at distances of d greater-than-or-equal-to 3 R0 between the layers. At distances of d less-than-or-equal-to 0.5 R0, the function G(s)(t) is equal to that of a three-dimensional solution. For the in-plane oriented dipoles in a multilayer system, G(s)(t) is very well approximated by that for a single bilayer at d > 2 R0. In general, the depolarizations obtained by the two-particle model and MC simulations differ depending on the particular orientational distribution and the experimental geometry. To obtain a physically correct behavior of the fluorescence anisotropy at long times (i.e., the limiting anisotropy) is not possible within a two-particle approach. We instead propose a phenomenological model for calculating the fluorescence anisotropy which is a function of G(s)(t) obtained within the two-particle approximation. This model gives a remarkably good agreement with the MC simulations and has the correct limiting anisotropy. The MC simulations of energy migration show that <R(t)2> is about twice as large for in-plane oriented donors in mono- and bilayers, as compared to the case of isotropically oriented transition dipoles. For multilayer systems consisting of layers separated by d = R0, we find that <R(t)2> is only slightly larger for the in-plane oriented transition dipoles as compared to the isotropic orientational distribution.