Limitations of the rate-distribution formalism in describing luminescence quenching in the presence of diffusion

When encountering complex fluorescence decays that deviate from exponentiality, a very appealing approach is to use lifetime or rate constant distributions. These are related by Laplace transform to the sum of exponential functions, stretched exponentials, Becquerel's decay function, and others. However, the limitations of this approach have not been sufficiently discussed in the literature. In particular, the time-independent probability distributions of the rate constants or decay times are occasionally used to describe bimolecular quenching. We show that in such a case, this mathematical formalism has a clear physical interpretation only when the fluorophore and quencher molecules are immobile, as in the solid state. However, such an interpretation is no longer possible once we consider the motion of fluorophores with respect to quenchers. Therefore, for systems in which the relative motion of fluorophores and quenchers cannot be neglected, it is not appropriate to use the time-independent rate or decay time distributions to describe, fit, or rationalize experimental results on fluorescence decay.

Photoinduced bimolecular electron transfer from aromatic amines to pentafluorophenyl porphyrin combined with ultrafast charge recombination persistence with Marcus inverted region

The dynamics of photoinduced bimolecular reductive electron transfer between meso-tetrakis(pentafluorophenyl)porphyrin (H₂F₂₀TPP), an acceptor (A), and five aromatic amines (donor (D)) with varying oxidation potentials (aniline (AN), N-methylaniline (MAN), N-ethylaniline (EAN), N,N-dimethylaniline (DMAN) and N,N-diethylaniline (DEAN)) in dichloromethane (DCM) as a solvent as well as in neat donor solvents were investigated by employing nanosecond to femtosecond time-resolved fluorescence spectroscopy and femtosecond time-resolved transient absorption spectroscopy upon S₂ excitation of H₂F₂₀TPP. Systematic studies of time-resolved fluorescence quenching dependent on the donor concentration in the concentration range of 0.01-2 M and finally in neat donor solvents broadly enabled us to determine the electron transfer dynamics in three regimes of electron transfer: stationary or diffusion-controlled electron transfer, non-stationary electron transfer and intrinsic or ultrafast electron transfer. Depending upon the electron-donating ability of the studied donors, intrinsic electron transfer was found to occur in the time domain of ∼1-9 ps and diffusion-controlled ET dynamics was observed in the time domain of 200-500 ps, whereas the maximum limit of non-stationary electron transfer could be observed in the time domain of 15-50 ps. Femtosecond transient absorption studies together with global and target analysis helped to identify the spectral signature of the (H₂F₂₀TPP˙^-) radical anion as the product of ET. To the best of our knowledge, this is the first ever evidence that shows the spectra of an anion as the product of ET for any porphyrin-based electron transfer dynamics. However, transient absorption measurements confirm that intrinsic ET occurs in the Q_y state, whereas diffusion-controlled ET occurs in the hot Q_x as well as in the thermal equilibrium Q_x state. The most remarkable fact derived from the measurements of transient absorption was that the rate of the forward electron transfer (CS) is exactly the same as the rate of the backward electron transfer (CR) for all three regimes of ET. The thermodynamic driving force for CR was found to lie in the range of the total reorganization energy for the studied systems and hence falls in the Marcus optimal region, and the CR process is barrierless. The dependence on the driving force of the combination of forward and reverse electron transfer exhibited a bell-shaped curve for all three regimes of electron transfer, even though the rate of intrinsic ET is higher by a factor of ∼10² than that of diffusion-controlled ET. These results unambiguously favour the Marcus theory, in particular the controversial Marcus inverted region, of outer-sphere electron transfer.