Excitation transfer in disordered two-dimensional and anisotropic three-dimensional systems: Effects of spatial geometry on time-resolved observables

Abstract

A unified treatment of dipole–dipole excitation transfer in disordered systems is presented for the cases of direct trapping (DT) in two-component systems and donor–donor transfer (DD) in one-component systems. Using the two-particle model proposed by Huber we calculate the configurational average of Gs(t), the probability of finding an initially excited molecule still excited at time t. For the isotropic three-dimensional case treated by Huber excellent correspondence is found with the previously reported infinite diagrammatic approximation. The anisotropy of the dipole–dipole interaction is included in the averaging procedure. Two regimes of orientational mobility are considered: the dynamic and static limit, rotations being much faster or slower, respectively, than the energy transfer. The following geometrical distributions are investigated: (a) Infinite systems of one, two, and three dimensions which lead to Förster-like decays. Two orientational distributions are considered for monolayers: dipoles confined to the plane or oriented isotropically. (b) Bilayers and multilayers. The averaging procedure for transfer from one layer to another is outlined in detail. The main parameters determining the decay of Gs(t) are the surface concentration and the ratio of the layer separation and the Förster radius. In a stack with a small number of layers, which is a finite system in one of the dimensions, an average over positions of the initially excited donor is included. At low surface concentration the decay gradually changes from two- to three-dimensional character as one increases the number of layers. This fractal-like behavior is solely due to the presence of excluded volumes and the finite nature of the system. Experimental observables are considered in detail. An analysis including a general formalism is presented to determine the loss of polarization memory if an excitation is transferred to a random distribution within the given geometrical constraints. It follows that after one transfer step, in the worst case, less than 10% of the initial anisotropy is conserved if the appropriate observation geometry is chosen. The anisotropy decay, which is manifested in a transient grating or fluorescence depolarization experiment, is thus a useful observable for Gs(t) in DD transfer.

Wavelength and Temperature Dependence of the Femtosecond Pump−Probe Anisotropies in the Conjugated Polymer MEH-PPV: Implications for Energy-Transfer Dynamics

“…This can be seen by extracting an effective R 0 from our data using eq 2. By use of a number density F ) 10 21 cm -3 , 33 a fluorescence lifetime τ fl of 200 ps at 298 K and 350 ps at 4 K (exponential fits to decays measured in our lab), λ ) 1, γ ) 0.8452, 31 and our experimental values for T pol , we obtain the Förster radii for various excitation wavelengths given in Table 1. The R 0 's calculated from the steady-state spectra at these temperatures are also given.…”

“…We measure both parallel and perpendicular probe signals at several wavelengths in the absorption band. In spin-cast MEH-PPV, the polymer chains lie preferentially in the plane of the film, and in this case of a planar film, the correct definition of the anisotropy is 31 Working up the data according to the definition of the anisotropy for a three-dimensional system does not change the data fits in any important way. We find that in solid MEH-PPV, the anisotropy decay is very rapid, on the order of 1 ps, and nonexponential.…”

“…This offset is too large to be the result of residual back transfer, which is predicted to give an offset of at most a few percent. 31 Its origin is unclear, and it does not vary systematically enough with wavelength to extract a definite trend. More straightforward to analyze is the decay time T pol , which can be directly related to the decay time of G S (t) in eq 2.…”

“…The R 0 's calculated from the steady-state spectra at these temperatures are also given. To calculate these values, eq 1b was used with the parameters n ) 1.7, 34 κ 2 ) 0.6901 (static, randomly oriented molecules), 31 a peak ) 36 000 at 500 nm, 35 and a quantum yield of 0.15. 36 The steady-state R 0 's do not agree with those obtained from the dynamic measurements, being a factor of 1.4-2.3 larger at both 298 and 4 K. As will be discussed below, the actual emission spectrum that determines the initial anisotropy decay is probably the vibrationally Stokesshifted emission prior to further relaxation.…”

Resonance Energy Transfer: Theoretical Foundations and Developing Applications

“…14.7), represent another important facet of the energy transfer. [37][38][39] Certain orientations reduce the rate of transfer to zero; for others, they effect an 'enhancement' of the energy transfer to its maximum possible rate. It is worth noting (since it is a fact that is not infrequently misreported), that energy transfer may be permissible even when the relevant donor and acceptor transition moments are at right angles to each other, if the second term in Eq.…”