Rates and singlet/triplet ratios from TADF transients

Thermally activated delayed fluorescence has been reported in a number of OLED emitter materials engineered to have low singlet-triplet energy gaps. Here we derive closed solutions for steady state and transient behaviors, and apply these results to obtain the singlet and triplet relaxation, forward and reverse crossing rates and the gap energy and reverse crossing prefactor from delayed and prompt relaxation rates measured over a series of temperatures. The primary rates are then used to calculate the fluorescent/phosphorescent ratio and the singlet/triplet population ratio. The method avoids the need for gated yield measurements. Good fits are obtained using previously published data for 4CzIPN and m-MTDATA:t-Bu-PBD and the results appear to be consistent with reported quantities were available, and with reported behaviors of OLEDS that use these materials.