Quasi-stationary approximation for analyzing the geminate and bimolecular stages of singlet fission in molecular semiconductors

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Abstract

The work concerns the studying the accuracy of the quasi-static approximation for the calculation of the kinetics of singlet fission (SF) in molecular semiconductors. The SF is known to be accompanied by inverse TT-annihilation (TTA), which essentially controls the specific features of the SF-kinetics. The analysis of the SF-kinetics in the wide time region has been made, which covers both short times usually associated with the stage of geminate TTA and long times typical for the bimolecular TTA. The simple models have been proposed, analysis of which demonstrated good accuracy of formulas, derived within the quasistatic approximation, in the description of SF-kinetics. High accuracy of interpolation formulas, which combine the obtained expressions and allow for describing the kinetics at different stages of the process, is also demonstrated. The proposed formulas are shown to significantly simplify the description of the experimental results.

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About the authors

A. I. Shushin

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Author for correspondence.
Email: shushin@chph.ras.ru
Russian Federation, Moscow

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2. Fig. 1. Comparison of the exact dependence of the kinetic SF function.

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3. Fig. 2. Comparison of the experimental SF kinetics [7] (circles) measured in films containing rubrene nanoparticles with the full kinetic SF function y(t) calculated using the interpolation formula (24). The dashed line also shows the characteristic hemin kinetic function yg(t) calculated in neglecting T-exciton migration, i.e., for the above-mentioned diffusion model parameters, but with see Sects. 2 и 3).

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