Beyond power laws: a new approach for analyzing single molecule photoluminescence intermittency.

The photoluminescence intermittency (PI) exhibited by single emitters has been studied for over a decade. To date, the vast majority of PI analyses involve parsing the data into emissive and non-emissive events, constructing histograms of event durations, and fitting these histograms to either exponential or power law probability distributions functions (PDFs). Here, a new method for analyzing PI data is presented where the data are used directly to construct a cumulative distribution function (CDF), and maximum-likelihood estimation techniques are used to determine the best fit of a model PDF to the CDF. Statistical tests are then employed to quantitatively evaluate the hypothesis that the CDF (data) is represented by the model PDF. The analysis method is outlined and applied to PI exhibited by single CdSe∕CdS core-shell nanocrystals and the organic chromophore violamine R isolated in single crystals of potassium-acid phthalate. Contrary to previous studies, the analysis presented here demonstrates that the PI exhibited by these systems is not described by a power law. The analysis developed here is also used to quantify heterogeneity within PI data obtained from a collection of CdSe/CdS nanocrytals, and for the determination of statistically significant changes in PI accompanying perturbation of the emitter. In summary, the analysis methodology presented here provides a more statistically robust approach for analyzing PI data.