Recent experiments aimed at probing the dynamics of excitons have revealed
that semiconducting films composed of disordered molecular subunits, unlike
expectations for their perfectly ordered counterparts, can exhibit a
time-dependent diffusivity in which the effective early time diffusion constant
is larger than that of the steady state. This observation has led to
speculation about what role, if any, microscopic disorder may play in enhancing
exciton transport properties. In this article, we present the results of a
model study aimed at addressing this point. Specifically, we present a general
model, based upon F\"orster theory, for incoherent exciton diffusion in a
material composed of independent molecular subunits with static energetic
disorder. Energetic disorder leads to heterogeneity in molecule-to-molecule
transition rates which we demonstrate has two important consequences related to
exciton transport. First, the distribution of local site-specific diffusivity
is broadened in a manner that results in a decrease in average exciton
diffusivity relative to that in a perfectly ordered film. Second, since
excitons prefer to make transitions that are downhill in energy, the steady
state distribution of exciton energies is biased towards low energy molecular
subunits, those that exhibit reduced diffusivity relative to a perfectly
ordered film. These effects combine to reduce the net diffusivity in a manner
that is time dependent and grows more pronounced as disorder is increased.
Notably, however, we demonstrate that the presence of energetic disorder can
give rise to a population of molecular subunits with exciton transfer rates
exceeding that of subunits in an energetically uniform material. Such
enhancements may play an important role in processes that are sensitive to
molecular-scale fluctuations in exciton density field.Comment: 15 pages, 3 figure
