Electronic energy transport in substitutionally disordered molecular crystals

Abstract

In this paper we present a theoretical study of incoherent electronic energy transfer (EET) in an impurity band of substitutionally disordered, mixed, molecular crystals. Dispersive diffusion of the electronic excitation was treated by an Average Dyson Equation Approximation (ADEA) to the master equation for EET. The ADEA rests on expressing the Green’s function (GF) for the probability of site-excitations in a single fixed spatial configuration in terms of a Dyson equation with a normalized vertex function and subsequently performing the configurational average of the GF, invoking a decoupling approximation which omits many-site contributions. Explicit expressions were derived for the initial site occupation probability, Po(t), the mean square displacement, Σ2(t), and the time dependent diffusion coefficient D(t). We have explored the relation between the ADEA and the stochastic continuous time random walk (CTRW) model applied by us for EET. We have demonstrated that the ADEA and the CTRW results for Σ2(t) and for D(t) are identical, while Po(t) has a similar structure in both schemes. The ADEA/CTRW scheme was utilized to derive analytical results for Po(t), Σ2(t) and D(t) in an impurity band where the pair-probability of EET is determined by multipolar interactions. From the analysis of asymptotic expansions for D(t) in such cases we conclude that the short time diffusion coefficient has the time dependence D(t)∝t(5−n)/n while the long time diffusion coefficient is independent of t, corresponding to an average superlattice of impurities. Numerical calculations based on the ADEA/CTRW scheme were performed to elucidate the quantitative features of the crossover from dispersive transport to pure diffusive behavior and how it is affected by the impurity concentration and by the range of the multipolar interactions. For short range high order multipolar interactions the effects of dispersive energy transport are expected to prevail over a broad concentration and time domain, being more pronounced than in the conventional case of dipole–dipole coupling.

A self-consistent theory of nonequilibrium excitation transport in energetically disordered systems

“…• The energy-independent version of this approximation has seen considerable use in non-self-consistent theories of energy transport. 17…”

The photophysical properties of chromophores at high (100 mM and above) concentrations in polymers and as neat solids

“…The basic physics of EET is well-studied, especially in the limit of the incoherent dipole-dipole interaction, or Forster resonance energy transfer (FRET). In this limit, Forster and later investigators [8][9][10][11][12][13] have shown how FRET occurring between identical chromophores in a concentrated sample leads to an effective diffusion constant for the excitation,…”

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

“…Various factors may complicate the application of such models to real polymeric systems. Such complications include the small distances between chromophores (on the order of a few Angstroms, small compared to molecular dimensions of tens of Angstroms) which preclude the use of the point dipole model, 6 the amount of local disorder (both energetic and orientational), [7][8][9][10] and the possibility that energy transfer occurs on a time scale faster than intramolecular vibrational relaxation (hot transfer). 11 All these factors may be taken into account to at least some degree by modifications of the standard Förster model.…”