Excited state relaxation in bichromophoric rotors: Time-resolved fluorescence of 1,3-di(N-carbazolyl) propane: A three-state analysis

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Abstract
The transient fluorescence profiles of 1,3‐di(N‐carbazolyl)‐propane, DCP, were reinvestigated as a function of temperature in toluene as solvent. Typically three‐exponential patterns, both for the low‐energy, red edge fluorescence of the excimer FE(t) and, in part, for the monomer fluorescence FM(t) were observed in the moderate temperature range −15≤t/°C≤55, whereas at temperatures t/ °C>55 profiles were found to be approximately biexponential, within the limitations of time resolution. On the premises given in Sec. IV of this work, data were analyzed in terms of a discrete three‐state model which assumes two monomeric conformers (X1=tt, X2=tg±) and a single excimer‐forming conformation (X3=g∓g±) interconverting in an open, linear scheme. Starting from a generalized treatment of n‐particle interaction, the analytical δ‐pulse solutions to the fluorescence evolutions X1(t), X2(t), and X3(t) were formulated in terms of 18 amplitudes Aij(k) (i, j=1,2,3) and 3 eigenvalues τj =−1/Tj ( j=1,2,3) for two different, initial boundaries (k=1,2). For reasonable choices of fluorescence rate constants, the simulated parameters proved useful (a) to recover satisfactorily the experimental subnanosecond (T1) and nanosecond time constants (T2,T3), (b) to rationalize the biexponential rise of excimer fluorescence at moderate temperatures, and (c) to explain the pseudo‐Birks behavior in the high‐temperature regime. Results from both experiments and computation allow to specify the time scales of rotating carbazole chromophores, and they strongly indicate that the rapid conformational equilibrium hypothesis is not valid in DCP. The limitations of the minimal model have been addressed and the potential problem encountered in analyzing the data by a discrete set of multiexponentials has been discussed.