Detection of the reversibility of an excited-state reaction by phase-modulation fluorometry

We used phase and modulation fluorometry to investigate the excited-state proton transfer from 2-naphthol. Phase-sensitive detection of fluorescence allows determination of the phase angles of the two-excited species, naphthol and naphtholate. If the steady-state spectra of the individual species are known and are not identical, then this general procedure yields the phase angles irrespective of the extent of the spectral overlap. The phase difference (Δφ) between the naphthol and naphtholate emission is given by tan Δφ = ω/(Γ_R + k₂ where ω is the circular modulation frequency, Γ_R the decay rate of naphtholate fluorescence and k₂ the rate of the reverse reaction. Hence, Δφ reflects both the decay rate of the reaction product and the rate of the reverse action. This back reaction was also detected by comparison of phase shift (φ) and demodulation (m) values for the initially excited state. Specifically, the reverse reaction results in a double exponential decay of naphthol fluorescence, which is revealed by m/cosφ < 1. The concepts described herein are generally applicable to determination of the reversibility of excited-state reactions.