Geminate exciton fusion fluorescence as a probe of triplet exciton transport after singlet fission

The geminate annihilation of two triplet excitons created by singlet exciton fission is affected by the dimensionality of transport as determined by typically anisotropic triplet exciton mobilities in organic molecular crystals. We analyze this process using a random-walk model where the time dynamics of the geminate annihilation probability is determined by the average exciton hopping times along the crystallographic directions. The model is then applied to the geminate fluorescence dynamics in rubrene, where the main channel for triplet-triplet annihilation is via triplet fusion and subsequent photon emission, and we identify the transitions between transport in one, two, and three dimensions.

Figure 1

Geminate reencounter probability after fission, for 2D and 3D transport, for different values of the average annihilation probability per reencounter, $\gamma$. The solid curves are obtained from Eq. (4), while the dots are the result of Monte Carlo simulations. Hopping time ratios are ${\tau }_2/{\tau }_1=1000$, and ${\tau }_3/{\tau }_2=60$ for 3D simulations. Power-law regimes in the data are highlighted with displaced dashed lines labeled with the corresponding power-law exponents. The dashed line labeled “$n=-1.09$” is an extrapolation from the late-time behavior of the 2D $\gamma =0.018$ simulation. The inset gives the behavior, for the 2D case, of the total probability that geminate annihilation occurs before a given time.

Figure 2

Normalized multiscale geminate fluorescence dynamics in rubrene crystals at excitation densities of $\sim 2\times {10}^{19}{\mathrm{m}}^{-3}$ (round data points) and $\sim 12\times {10}^{19}{\mathrm{m}}^{-3}$ (square, orange data points). The higher-density data can be fitted by an exponential decay with a time constant of 60 $\mu \mathrm{s}$ (solid curve). The filled, blue data points highlight the region where we did not see any variability from sample to sample, including those with anomalous fluorescence spectra. Sample-dependent variations at times below 100 ns (dashed lines) correlated with the presence of an anomalous fluorescence emission band near 650 nm. Fluorescence dynamics due only to photons with wavelength less than 600 and more than 650 nm is shown by the solid (samples with normal fluorescence spectra) and dashed (samples with abnormal fluorescence spectra) curves displaced down by three decades, and normalized to the sample-independent fluorescence signal at 100 ns. The inset shows fluorescence dynamics from three different rubrene crystals (vertically offset for clarity) in the time window corresponding to the solid blue dots, where a transition from 2D to 3D transport takes place. Solid curves in the inset are all fits with Eq. (5) for ${\tau }_3=1.3\mu s$ and $p=-0.07$; the dashed lines are power-law extrapolations.