Dispersive Electron-Transfer Kinetics of Rhodamines on TiO₂: Impact of Structure and Driving Force on Single-Molecule Photophysics

Abstract

The effects of dye structure, driving force of photoinduced electron transfer, and adsorption affinity on the dispersive electron-transfer dynamics of rhodamines on TiO 2 films are investigated using single-molecule microscopy. The time-dependent emission (i.e., blinking dynamics) of rhodamine-sensitized TiO 2 films are quantified using maximum likelihood estimation (MLE) and quantitative goodness-of-fit tests based on the Kolmogorov–Smirnov (KS) statistic to determine the best fit to the photophysical data. Although the observation of significant p -values (i.e., ranging from 0.16 to 0.53) seems to support the power-law model for the on-time distributions, only a minor subset of the data are actually represented by power laws (i.e., ∼15–20% of events). Instead, the MLE/KS analysis reveals that log-normal distributions, not power laws, most closely represent the entire on-time and off-time distributions for RB, R6G, R123, and 5-ROX on TiO 2 . Monte Carlo simulations based on the Albery model for dispersive electron transfer (i.e., activation barriers to electron transfer are Gaussian distributed) demonstrate that the log-normal fit parameters (i.e., μ on/off and σ on/off ) are dependent on the average rate constants for injection and recombination as well as the extent of energetic dispersion about the mean activation barrier. The single-molecule results for RB, R6G, R123, and 5-ROX on TiO 2 are interpreted in the context of ensemble-averaged spectroscopic and electrochemical characterization and suggest that heterogeneity in electronic coupling and reorganization (i.e., static and dynamic disorder) play a decisive role in the observed dispersive kinetics.