Exciton-exciton scattering in disordered linear chains of poly(di-n-hexylsilane)

We have measured the time response of photoluminescence intensity in poly(di-$n$-hexylsilane) films at 2 K with excitation densities from $1.2\times {10}^{17}$ to $1.1\times {10}^{19}$ excitons ${\mathrm{cm}}^{-3}.$ At the highest density, the photoluminescence has a rise time of 1.4 ps, which is ascribed to the exciton-exciton scattering time between initially photogenerated excitons. The inverse of rise times are sublinear to the excitation densities. The decay profiles are explained by the exciton-exciton annihilation with a rate constant of $(1.0\mathrm{}\pm 0.5)\times {10}^{-8}\hspace{0.5em}{\mathrm{cm}}^3\hspace{0.5em}{\mathrm{s}}^{-1}.$ These processes are discussed in terms of exciton wave functions obtained by the one-dimensional Frenkel exciton model with disorder. We propose directional relaxation of excitons toward interacting points between different polymer chains as a mechanism for the efficient exciton-exciton annihilation.