  We present a theoretical model for the study of exciton dynamics in
J-aggregated monolayers of fluorescent dyes. The excitonic evolution is
described by a Monte-Carlo wave function approach which allows for a unified
description of the quantum (ballistic) and classical (diffusive) propagation of
an exciton on a lattice in different parameter regimes. The transition between
the ballistic and diffusive regime is controlled by static and dynamic
disorder. As an example, the model is applied to three cyanine dye
J-aggregates: TC, TDBC, and U3. Each of the molecule-specific structure and
excitation parameters are estimated using time-dependent density functional
theory. The exciton diffusion coefficients are calculated and analyzed for
different degrees of film disorder and are correlated to the physical
properties and the structural arrangement of molecules in the aggregates.
Further, exciton transport is anisotropic and dependent on the initial exciton
energy. The upper-bound estimation of the exciton diffusion length in the TDBC
thin-film J-aggregate is of the order of hundreds of nanometers, which is in
good qualitative agreement with the diffusion length estimated from
experiments.
