Origin of Kinetic Dispersion in Eosin-Sensitized TiO2: Insights from Single-Molecule Spectroscopy

By removing the effects of ensemble averaging and molecular aggregation, we untangle the factors that govern the dispersive electron transfer kinetics of eosin-sensitized TiO2, focusing on the impact of environmental heterogeneity versus injection from multiple excited states. The blinking dynamics of single eosin Y chromophores on nanocrystalline TiO2 films are analyzed using a change point detection algorithm for binned data. Robust statistical analysis based on maximum likelihood estimation, Kolmogorov–Smirnov tests, and log likelihood ratio tests is used to determine the functional form that best fits the resulting on- and off-time distributions and to distinguish between mechanisms for dispersive electron transfer. Using this approach, we find that the on- and off-time distributions for eosin Y on TiO2 are best fit to lognormal distributions corresponding to μon = −0.64 ± 0.04, σon = 1.52 ± 0.02, μoff = −0.23 ± 0.04, and σoff = 1.96 ± 0.03, respectively. Monte Carlo simulations based on the Albery model for dispersive electron transfer (i.e., where the median rate constant κ is modified by the exponential of a parameter, x, that is normally distributed, k = κ e–γx) successfully reproduce this behavior using a median rate constant for injection and back electron transfer of ∼1010 and ∼104 s–1, respectively, and a corresponding energetic dispersion, γ, of ∼200–350 meV. To examine how injection from both the singlet and triplet excited states contributes to this dispersion, we studied two rhodamine sensitizers, R123 and 5ROX, that inject only from their singlet excited state. Surprisingly, when access to the T1 state is minimized in going from EY to R123 and 5ROX, kinetic dispersion actually increases. Collectively, these observations support the interpretation that static and dynamic inhomogeneities at the EY–TiO2 interface govern kinetic dispersion, with dynamic fluctuations in binding configuration and/or vibrational motion playing a decisive role.