Fig. 2
Reaction mechanisms and expected concentration dependence. a Scheme for the mechanism of oxygen-catalysed singlet fission of TIPS-Pn in solution with rate constants. An identical mechanism is proposed for TDCl4. Owing to the relative energies of S1 and T1 compared to 1O2, the individual steps of sequential singlet fission are exothermic. b Scheme for the mechanism of homogeneous singlet fission in TIPS-Pn with corresponding rate constants. c Upper panel: expected chromophore concentration dependence for the quantum yields of homogeneous (red) and sequential (green) SF. Lower panel: expected chromophore concentration dependence for rate constants of the individual processes. The association of an excited and ground-state chromophores (kSF) is the rate-limiting step of homogeneous SF. SF is outweighed by concentration independent, non-SF relaxation pathways (i.e., fluorescence, internal conversion and, to a minor extent, intersystem crossing) for low chromophore concentrations and in the absence of oxygen (black, \({\boldsymbol{k}}_{{\bf{tot}}} \approx {\boldsymbol{k}}_{\bf{R}}\)). At higher chromophore concentrations, \({\boldsymbol{k}}_{{\bf{tot}}} \approx {\boldsymbol{k}}_{{\bf{SF}}}\left[ {{\boldsymbol{S}}_0} \right]\) (black). In contrast, the rate of the first step in sequential SF, that is, the energy transfer (\({\boldsymbol{k}}_1\left[{{\,}_{\,}^3{\mathbf{O}}_2} \right]\)), is not affected by the chromophore concentration because 3O2 is in excess compared to the excited chromophore. However, the subsequent heterogeneous singlet fission (blue, \({\boldsymbol{k}}_2\left[ {{\boldsymbol{S}}_0} \right]\)) exhibits a pseudo-first-order reaction rate and thus a linear dependence on the chromophore ground-state concentration. Finally, regardless of how the triplet is formed, its relaxation rate remains unaffected by the chromophore concentration (yellow, kT). Source Data are provided as a Source Data file
