Dispersive Electron-Transfer Kinetics from Single Molecules on TiO2 Nanoparticle Films

The distributions of electron-transfer dynamics in dye-sensitized TiO2 films are probed using single-molecule microscopy. The time-dependent emission (i.e., blinking dynamics) of rhodamine 6G (R6G) and rhodamine B (RB) sensitized TiO2 films are quantified by constructing cumulative distribution functions of emissive ("on") and nonemissive ("off") events. Maximum likelihood estimation (MLE) methods and quantitative goodness-of-fit tests based on the Kolmogorov Smirnov (KS) statistics are used to establish the best fit to the photophysical data. The on-time distributions for R6G and RB on TiO2 are fit by power laws, but only for emissive durations that last longer than similar to 0.7 s. Furthermore, large variations in the power-law exponents are observed when using least-squares fitting as compared to the combined MLE and KS-test approach. The offtime distributions for molecules on TiO2 and glass are not consistent with power laws and are instead well represented by log-normal distributions. Our observations support the hypothesis that electron-transfer processes are responsible for blinking on TiO2 as well as glass substrates. Furthermore, the on-time and off-time distributions are sensitive to the chromophore as well as the substrate. To understand the origin of these power-law and log-normal distributions, single-molecule blinking dynamics are modeled using Monte Carlo simulations based on a three-level system with the rate constants for population and depopulation of the nonemissive state being log-normally distributed (i.e., Albery model). In this framework, the rate constants for FET and BET are log-normally distributed, consistent with a Gaussian distribution of activation energies.