Single Turnover Measurements of Nanoparticle Catalysis Analyzed with Dwell Time Correlation Functions and Constrained Mean Dwell Times

Single turnover measurements of a fluorogenic reaction at the surface of a nanoparticle provide a detailed view of reaction dynamics at a catalyst with multiple heterogeneous active sites. This picture must be extracted from a fluorescence trajectory of one particle, which records individual reaction and desorption events. We have previously proposed analyzing fluorescence trajectories with constrained mean dwell times in either light or dark states, which are averaged over a subensemble of events in which the dwell time in the previous state satisfies a criterion of being less than or greater than a specified time. We have shown that these quantities can be used to distinguish between correlated and independent fluctuations at multiple active sites. Here we show that this analysis is complementary to calculating dwell time correlation functions, whose decay with turnover index quantifies dynamical disorder in the underlying kinetics. We analyze a measured fluorescence trajectory from a gold nanoparticle in terms of both constrained mean dwell times and dwell time correlation functions. The analysis demonstrates that the minimal kinetic model with discrete states that is qualitatively consistent with the data allows active sites to fluctuate among at least three substates with distinct adsorption and reaction rates.