Exciton Bimolecular Annihilation Dynamics in Push-Pull Semiconductor Polymers

Exciton-exciton annihilation is a ubiquitous nonlinear dynamical phenomenon in materials hosting Frenkel excitons, that has been employed to probe exciton diffusion processes in conjugated polymeric materials. In this work, we investigate the nonlinear exciton dynamics of an electron push-pull conjugated polymer by fluence-dependent transient absorption and excitation-correlation photoluminescence spectroscopy, where we can quantitatively show the latter technique to be a more selective probe of the nonlinear dynamics. Simulations based on an exciton annihilation model that implements a simple (\textit{i.e.}\ time-independent) bimolecular rate constant decreasing trend for the extracted annihilation rates with excitation fluence. However, further investigation of the fluence-dependent transients suggests that the exciton-exciton annihilation bimolecular rate parameters are not constant in time, displaying a $t^{-1/2}$ time dependence, which we rationalize as reflective of anisotropic exciton diffusion. At ambient temperature, we estimate the exciton diffusion length to be $9 \pm 2$\,nm. In addition, exciton annihilation gives rise to a long-lived species that recombines on a nanosecond timescale. Our conclusions shed broad light onto nonlinear exciton dynamics in push-pull conjugated polymers.