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

Abstract

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.

Photoluminescence Intermittency from Single Quantum Dots to Organic Molecules: Emerging Themes

“…Our group recently analyzed the blinking of CdSe/CdS QDs with a total size of 4 nm and found deviations from linearity after the first decade in time, inconsistent with power-law statistics (Figure 3b). Together these studies suggest that for CdSe/CdS QDs of any size power-law statistics may not hold, calling into question the universality of power-law for QDs [56]. Further analysis on giant CdSe/CdS QDs with 1.9 nm cores and 3.5 monolayer shells have revealed that single exponential distributions are more appropriate for describing the durations of bright, gray and dark states [52].…”

“…In this study, the PI exhibited by VR in KAP and DKAP was analyzed using new statistical methods [56] to determine if the underling probability distribution functions describing the on - and off -durations were modified with isotopic substitution. This analysis involved the statistical comparison of complimentary cumulative distribution functions (CDFs) derived from the PI data obtained for VR in KAP and DKAP at three temperatures (23 °C, 45 °C, and 60 °C) [116].…”

“…Cumulative distribution function for the off -event durations for ( a ) CdSe/CdS nanocrystals with 13 nm diameter core/shell (circles) and CdSe/ZnS (triangles) and corresponding linear fits overlaid [51] ( b ) 4 nm diameter CdSe/CdS quantum dots showing longer durations of off -durations (black) and on -durations (gray), fits to power-law performed by MLE method [56]. ( a ) Adapted with permission from: B. Mahler et al Nature Materials 2008, 7 , 659.…”

Cooperation in neural systems: Bridging complexity and periodicity

“…According to a widely shared theoretical interdisciplinary perspective, ranging from neurophysiology to sociology, from geophysics to economics, heavy tails and inverse power law distributions [2,3] are thought to be the signature of complexity. Of special interest are the scale-free distributions in time, for instance, the waiting time distributions of the "light on" and "light off" states of intermittent fluorescence in quantum dots [4][5][6][7], which has been proved [8,9] to be a renewal non-Poisson process. These scale-free waiting time distribution densities have the time-asymptotic form…”

Linear response at criticality

“…The physics of blinking quantum dots (BQDs) [1][2][3][4] has generated a big interest but it is still a not yet fully understood phenomenon [2]. Analysis of the luminescence fluctuations led to the discovery [5,6] that these fluctuations are non-Poisson renewal processes.…”