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.     

Markov processes in single molecule fluorescence

This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the first-passage time (FPT) distributions out of those states must be describable by a simple exponential law. The observation of non-exponential FPT distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system.     

Analysis of excitation laser intensity dependence of blinking SERRS of thiacarbocyanine adsorbed on single silver nanoaggregates by using a power law with an exponential function

In blinking SERRS, probability distributions of the dark events against their duration were mostly reproduced by a power-law with the same exponential function under various excitation laser intensities, although they were given by a power-law with the different exponential functions at other excitation wavelengths.     

Single molecule measurements of DNA transport through a nanopore

We examined the voltage-driven movement of single-stranded DNA molecules in a membrane channel or "nanopore". Using single channel recording methods and a statistical analysis of many single molecule events, we determined how voltage influences capture and translocation in the nanopore. We verified that the mean time between capture events follows a simple exponential distribution, whereas the translocation times follow a unique distribution that is partly Gaussian and partly exponential. Measurements of polymer sequence effects demonstrated that translocation duration is heavily influenced by specific or nonspecific purine-channel interactions. The single molecule approach we used revealed molecular interactions that can influence both capture rates and translocation velocities in a manner that enriches naive barrier crossing models.     

Single-molecule spectroscopy of interfacial electron transfer

It is widely appreciated that single-molecule spectroscopy (SMS) can be used to measure properties of individual molecules which would normally be obscured in an ensemble-averaged measurement. In this report we show how SMS can be used to measure photoinduced interfacial electron transfer (IET) and back electron transfer rates in a prototypical chromophore-bridge-electrode nonadiabatic electron transfer system. N-(1-hexylheptyl)-N'-(12-carboxylicdodecyl)perylene-3,4,9,10-tetracarboxylbisimide was synthesized and incorporated into mixed self-assembled monolayers (SAMs) on an ITO (tin-doped indium oxide, a p-type semiconductor) electrode. Single-molecule fluorescence time trajectories from this system reveals "blinks", momentary losses in fluorescence (>20 ms to seconds in duration), which are attributed to discrete electron transfer events: electron injection from the perylene chromophore into the conduction band of the ITO leads to the loss of fluorescence, and charge recombination (back electron transfer) leads to the return of fluorescence. Such blinks are not observed when an electrode is not present. The fluorescence trajectories were analyzed to obtain the forward and back electron rates; the measured rates are found to lie in the millisecond to second regime. Different rates are observed for different molecules, but the lifetime distributions for the forward or back electron transfer for any given molecule are well fit by single exponential kinetics. The methodology used is applicable to a wide variety of systems and can be used to study the effects of distance, orientation, linker, environment, etc. on electron transfer rates. The results and methodology have implications for molecular electronics, where understanding and controlling the range of possible behaviors inherent to molecular systems will likely be as important as understanding the individual behavior of any given molecule.     

Fluorescence of single molecules in polymer films: sensitivity of blinking to local environment

The single-molecule fluorescence blinking behavior of the organic dye Atto647N in various polymer matrixes such as Zeonex, PVK, and PVA as well as aqueous media was investigated. Fluorescence blinking with off-times in the millisecond to second time range is assigned to dye radical ions formed by photoinduced electron transfer reactions from or to the environment. In Zeonex and PVK, the measured off-time distributions show power law dependence, whereas, in PVA, no such dependence is observed. Rather, in this polymer, off-time distributions can be best fitted to monoexponential or stretched exponential functions. Furthermore, treatment of PVA samples to mild heating and low pressure greatly reduces the frequency of blinking events. We tentatively ascribe this to the removal of water pockets within the polymer film itself. Measurements of the dye immobilized in water in the presence of methylviologen, a strongly oxidizing agent, reveal simple exponential on- and off-time distributions. Thus, our data suggest that the blinking behavior of single organic molecules is sensitive to their immediate environment and, moreover, that fluorescence blinking on- and off-time distributions do not inherently and uniquely obey a power law.     

A six-coordinate ytterbium complex exhibiting easy-plane anisotropy and field-induced single-ion magnet behavior

The field-induced blockage of magnetization behavior was first observed in an Yb(III)-based molecule with a trigonally distorted octahedral coordination environment. Ab initio calculations and micro-SQUID measurements were performed to demonstrate the exhibition of easy-plane anisotropy, suggesting the investigated complex is the first pure lanthanide field-induced single-ion magnet (field-induced SIM) of this type. Furthermore, we found the relaxation time obeys a power law instead of an exponential law, indicating that the relaxation process should be involved a direct process rather than an Orbach process.     

Mechano-chemical coupling of molecular motors revealed by single molecule measurements

Single molecule measurements have allowed series of kinetic events of biomolecules to be monitored without interruption. The stepwise movement of molecular motors was measured and analyzed in relation to the hydrolysis reaction of ATP. In the case of kinesin, forward and backward steps occurred stochastically at the same chemical state. The directional movement was explained by the asymmetric potential created by the interaction between kinesin and microtubules. Similarly thermal Brownian movement of myosin during the hydrolysis of single ATP molecules was biased through an asymmetric potential, resulting in directional movement. Thus, single molecule measurements have provided new approaches to analyze the function of molecular motors which often consist of several different events.     

Fitting properties from density functional theory based molecular dynamics simulations to parameterize a rigid water force field

In the quest towards coarse-grained potentials and new water models, we present an extension of the force matching technique to parameterize an all-atom force field for rigid water. The methodology presented here allows to improve the matching procedure by first optimizing the weighting exponents present in the objective function. A new gauge for unambiguously evaluating the quality of the fit has been introduced; it is based on the root mean square difference of the distributions of target properties between reference data and fitted potentials. Four rigid water models have been parameterized; the matching procedure has been used to assess the role of the ghost atom in TIP4P-like models and of electrostatic damping. In the former case, burying the negative charge inside the molecule allows to fit better the torques. In the latter, since short-range interactions are damped, a better fit of the forces is obtained. Overall, the best performing model is the one with a ghost atom and with electrostatic damping. The approach shown in this paper is of general validity and could be applied to any matching algorithm and to any level of coarse graining, also for non-rigid molecules.     

Computer simulation study of rotational diffusion in polar liquids of different types

Rotational diffusion in liquid acetonitrile, dimethylsulphoxide (DMSO), water, and methanol is studied with molecular dynamics simulations. The effects of hydrogen bonding and local dipole-dipole correlations (Kirkwood g-factor) on the relationship between the single molecule and collective relaxation are examined. The first rank single molecule dipole moment autocorrelation functions (ACFs) are constructed in the molecule-fixed coordinate frame and the principal components of rotation diffusion tensor are reported. Higher rank orientational ACFs are computed. These ACFs, as a rule, are strongly nonexponential (at least not single exponential) at longer times and the decomposition of these functions into a series of single exponentials results in broad distributions of relaxation times, with the broadening being particularly prominent in the case of higher rank ACFs. The rank dependence of characteristic times calculated as weighted averages over the relaxation time distributions does not follow the pattern of small angle (Debye) diffusion model for all liquids studied in this work except methanol. In contradiction, the same rank dependence computed by direct integration of ACFs leads to good agreement with the Debye diffusion model in the case of acetonitrile, DMSO, and water (but not methanol). The linear-angular momentum cross correlation functions are also computed and the effect of rototranslational coupling on reorientaional relaxation at longer times (>1.0?ps) is found to be small.     

A Monte Carlo simulation of energy transfer processes in thermal unimolecular reactions. II. An applications to polyatomic dissociation

The Monte Carlo method has been used to provide a numerical solution to the ro-vibrational master equation for the low pressure unimolecular decomposition of a polyatomic molecule. This type of solution is made possible through the use of a simple exponential transition probability function, that represents the efficiency with which energy transfer takes place between the reactant molecule and an unspecified heat bath gas. The Monte Carlo technique is used to generate random variables that are distributed in a manner prescribed by the transition probability function. In the case of the present simulation, these variables correspond to random energy jumps induced in the molecule through single collision events. In order to account for the energy dependence of the vibrational state densities, we have proposed that vibrational relaxation in the polyatomic takes place from a single vibrational mode. Under equilibrium conditions we are able to show that with this assumption, the Monte Carlo model is capable of reproducing molecular quantities, such as the average vibrational energy per molecule and the vibrational specific heat, that compare favourable with the corresponding values calculated from equilibrium statistical mechanics. The model has been applied to a study of the low pressure unimolecular decomposition of a series of polyatomics. For three of the molecules, CH₄, CD₄, and C₂H₆ the agreement between the calculated and the high temperature experimental rate constants is very good. The calculations indicate that a significant proportion of the molecules that dissociate are rotationally as well as vibrationally excited. Very few of the reactive molecules have a vibrational energy content equal to or greater than E₀, the dissociation energy. The extent of rotational excitation is found to be temperature dependent.     

Measurement of the radon exhalation rate from the medium surface by tracing the radon concentration

The paper will present a method based on the accumulation chamber technique for measuring of radon exhalation from the medium surface. A radon monitor traces the change of radon concentration in the accumulation chamber, and then the radon exhalation can be obtained accurately through linear fit. Based on our recent experiments, the radon exhalation rate from the medium surface obtained from this method is in good agreement with the actual exhalation rate of our simulation facility. This method is superior to the competition method which obtains the radon exhalation through the exponential fit by an external PC-system. The calculation for the exponential fit is very easy by computer and related software. However, for portable instruments, the single chip microcomputer can’t calculate the exponential fit rapidly. Thus, this method is usable for developing the new portable instrument to classify building materials, etc.     

Generic schemes for single-molecule kinetics. 1: Self-consistent pathway solutions for renewal processes

In this paper, we discuss a strategy for reducing a complex single molecule kinetic process to a set of generic structures (motifs) that are building blocks for a general kinetic scheme. In general, these motifs have complex kinetics (i.e., waiting time distribution functions) which are composed of fundamental kinetic steps. (1) First, we treat four different experimental single molecule measurements within both the usual kinetic framework (i.e., using the rate matrix) and the waiting time distribution function framework. The two frameworks are then shown to be equivalent and can be formulated on the basis of the first passage time distribution function of monitored single molecule events. (2) Second, to calculate this basic quantity, we decompose a complex kinetic scheme with the help of two kinetic motifs, sequential and branching, and derive self-consistent equations by convoluting waiting time distributions and first passage time distribution(s) along the reaction pathway(s). (3) As examples, two experimental systems, a chain reaction model with a special case of enzymatic reactions and a general kinetic model for fluorescence emission, are analyzed on the basis of a generic scheme composed of a monitored link, controlled link, and unknown link, each representing a possible subscheme associated with a complex waiting time distribution function. As a result, single molecule measurements of the generic scheme retain the same functional form when a kinetic link is altered within a subscheme, and different measurements can be classified and analyzed within the same framework. (4) Finally, to explore the physical reasons for nonexponential waiting time distribution, we use the example of blinking phenomena to discuss several scenarios of dynamic and static disorder and their implications for observed memory effects. The self-consistent pathway formalism is presented in this paper for renewal processes and will be generalized to nonrenewal processes with memory effects in a future publication.     

IMPROVED ANALYSIS OF TIME-RESOLVED SINGLE PHOTON COUNTING FLUORESCENCE DATA OF EXCIMER/EXCIPLEX SYSTEMS USING A DUAL ANALYSIS ITERATED RECONVOLUTION PROGRAM ON A DEDICATED LABORATORY MICROCOMPUTER

Abstract A novel iterative reconvolution program for the simultaneous analysis of two sets of time-resolved single photon counting (TRSPC) fluorescence data is described. Each set of data may be fit to a function containing up to three exponential terms and any of the parameters may be constrained to both sets. This dual analysis approach offers great advantages for the study of a coupled photokinetic scheme such as an excimer or exciplex system, both in terms of the accuracy of the results and in the simplicity and speed of the analysis.     

Conductance of single alkanedithiols: conduction mechanism and effect of molecule-electrode contacts

The conductance of single alkanedithiols covalently bound to gold electrodes has been studied by statistical analysis of repeatedly created molecular junctions. For each molecule, the conductance histogram reveals two sets of well-defined peaks, corresponding to two different conductance values. We have found that (1) both conductance values decrease exponentially with the molecular length with an identical decay constant, beta approximately equal to 0.84 A(-1), but with a factor of 5 difference in the prefactor of the exponential function. (2) The current-voltage curves of the two sets can be fit with the Simmons tunneling model. (3) Both conductance values are independent of temperature (between -5 and 60 degrees C) and the solvent. (4) Despite the difference in the conductance, the forces required to break the molecular junctions are the same, 1.5 nN. These observations lead us to believe that the conduction mechanism in alkanedithiols is due to electron tunneling or superexchange via the bonds along the molecules, and the two sets of conductance peaks are due to two different microscopic configurations of the molecule-electrode contacts.     

Polychronous kinetics with diffusion over the reaction state spectrum

The unsteady- and steady-state kinetics of a polychronous first-order reaction with discrete and continuous state distributions under spectral diffusion conditions are considered. An analysis of the model has demonstrated that a quasi-steady-state regime is established in the course of the reaction. In this regime, the shape of the distribution function stops changing and the reaction kinetics obeys an exponential law and can be characterized by a single, average rate constant. Equations are set up for the reaction state distribution and average rate constant in the quasi-steady-state regime. The limits of the kinetic and quasi-steady-state regimes are determined as a function of the spectral diffusion coefficient. The unsteady-state kinetics and the quasi-steady state time depend strongly on the initial state distribution.     

Extraction of lifetime distributions from fluorescence decays with application to DNA-base analogues

Several important aspects of fluorescence decay analysis are addressed and tested against new experimental measurements. A simulated-annealing method is described for deconvoluting the instrument response function from a measured fluorescence decay to yield the true decay, which is more convenient for subsequent fitting. The method is shown to perform well against the conventional approach, which is to fit a convoluted fitting function to the experimentally measured decay. The simulated annealing approach is also successfully applied to the determination of an instrument response function using a known true fluorescence decay (for rhodamine 6G). The analysis of true fluorescence decays is considered critically, focusing specifically on how a distribution of decay constants can be incorporated in to a fit. Various fitting functions are applied to the true fluorescence decays of 2-aminopurine in water-dioxane mixtures, in a dinucleotide, and in DNA duplexes. It is shown how a suitable combination of exponential decays and non-exponential decays (based on a Γ distribution of decay constants) can provide fits of equal quality to the conventional multi-exponential fits used in the majority of previous studies, but with fewer fitting parameters. Crucially, the new approach yields decay-constant distributions that are physically more meaningful than those corresponding to the conventional multi-exponential fit. The methods presented here should find wider application, for example to the analysis of transient-current or optical decays and in F?rster resonance energy transfer (FRET).     

A theoretical study of molecular conduction. III. A nonequilibrium-Green's-function-based Hartree-Fock approach

Many recent experimental and theoretical studies have paid attention to the conductivity of single molecule transport junctions, both because it is fundamentally important and because of its significance in the development of molecular-based electronics. In this paper, we discuss a nonequilibrium Green's function (NEGF)-based Hartree-Fock (HF) approach; the NEGF method can appropriately accommodate charge distributions in molecules connected to electrodes. In addition, we show that a NEGF-based density matrix can reduce to an ordinary HF density matrix for an isolated molecule if the molecule does not interact with electrodes. This feature of the NEGF-based density matrix also means that NEGF-based Mulliken charges can be reduced to ordinary Mulliken charges in those cases. Therefore, the NEGF-based HF approach can directly compare molecules that are connected to electrodes with isolated ones, and is useful in investigating complicated features of molecular conduction. We also calculated the transmission probability and conduction for benzenedithiol under finite electrode biases. The coupling between the electrodes and molecule causes electron transfer from the molecule to the electrodes, and the applied bias modifies this electron transfer. In addition, we found that the molecule responds capacitively to the applied bias, by shifting the molecular orbital energies.     

Covariate model-based fault tree analysis for risk assessment in chemical process industries: A case study of a chlorine manufacturing facility

Fault tree analysis (FTA) is a promising quantitative technique for risk analysis in chemical process industries (CPIs). In FTA, a certain sequence of basic events (causes) leads to one specific Top event (critical event of interest). However, the conventional fault tree analysis has the limitations of staticity and uncertainty. The staticity in conventional FTA arises due to its inability to accommodate time-dependent characteristics of the process system. Whereas uncertainty primarily lies in the failure probability data of basic events. This paper proposes an innovative methodology that uses a time-dependent covariate model to update the failure probability values of major contributing basic events in FTA. A novel subclass of the family of phase-type distributions is used to model the covariates corresponding to the basic events. The newly developed methodology is applied for a case study in a chlorine manufacturing facility to estimate the chlorine release probability. The blockage in the pipeline was identified as the significant reason for chlorine release from expert opinion and sensitivity analysis. The results of the proposed model of FTA are compared with that of conventional FTA.