Distribution function w(N)(T) for photons created by three-level nanoparticle in time interval T under cw laser excitation is calculated for various methods of photon counting. It is found that each exponential process exp(-lambda(i)t) in quantum dynamics of three-level nanoparticle manifests itself via Poissonian function P(N)(lambda(i)t)=(lambda(i)t)(N) exp(-lambda(i)t)/N! in the photon distribution function w(N)(T). The distribution function w(N)(T) is expressed via two or three integrals of two or three Poissonian functions P(N)(lambda(i)t). The simple mathematical expression for w(N)(T) enables one to calculate photon distribution in blinking fluorescence with on and off intervals. A scaling between photon distribution function w(N)(T) and photoelectric pulse distribution function w(n)(T) is found. Comparison of the theoretical distribution w(n)(T) and the distribution measured in blinking fluorescence of single polymer molecule dPPV-PPyV and complex organic molecule 1,1(')-didodecyl-3,3,3('),3(')-tetramethylindocarbocyanine perchlorate (DiI) is carried out. The theoretical distributions are able to describe those found in an experiment.
A single complex molecule with conformational changes (conformations 0 and 2) is considered. When such a molecule is irradiated by cw-laser light it can randomly change the intensity or polarization of its fluorescence due to jumps from one conformation to another. In fact, the molecule manifests itself either like the 0-type or the 2-type emitter. An expression for the matrix s αβ (t) called the start-stop correlator (waiting time distribution) in which α = 0,2 and β = 0,2 is derived. An expression for the matrix p αβ (t) called the full correlator is derived as well. It determines the density of the probability of finding an event of α type and an event of β type separated by time interval t. A relation between matrices s αβ (t) and p αβ (t) is found. A mathematical expression for the distribution w N (T ) of events measured in time interval T is derived. It is expressed solely via the matrix s αβ (t). Numerical calculations of the event distribution function for various rates of intra-and interconformational jumps are carried out with the help of the formula for w N (T ) and by the Monte Carlo method. Both methods of the calculation yield identical distributions. Fluctuating fluorescence intensity I(t) for a bin time of 5 ms is calculated for slow and fast interconformational jumps. A relation is found between the autocorrelation function g (2) (t) of fluorescence measurable in experiments and the matrix p αβ (t) calculated theoretically.
CdS colloidal nanocrystals with an average size of 4.5 nm and oleic acid as surfactant were studied using photoluminescence spectroscopy and time-correlated single photon counting technique at different temperatures. Observed spectra revealed three thermally activated luminescence bands at 2.15, 1.76, and 1.37 eV in addition to conventional band edge recombination of the nanocrystals. We present a kinetic model based on concept of single emitters which quantitatively describes the luminescence of the ensemble of the nanocrystals in the temperature range 10–300 K. We determined activation energies (18.2 and 8.6 meV) for transitions responsible for the luminescence. The 1.76 eV band most probably emerges from the intrinsic defects on the surface of CdS, whereas bands at 2.15 and 1.37 eV result from the influence of oleic acid bonded to the surface of the nanocrystals.
A theoretical six-level model for blinking fluorescence of single PPV-PPyV copolymer molecule excited by CW-laser light is proposed. The model has been chosen in accordance with the following facts found in the Paul Barbara group experiment: (i) alternation of two types of fluorescence with moderate and strong levels of emission, (ii) existence of "dark" states with no fluorescence, (iii) linear dependence of inverse on-interval duration on laser intensity, and (iv) existence of laser intensity independent off-intervals. Relations between the distribution function w''(N, T) for photons emitted by a single molecule, the distribution function w'(N, T) for photons arriving at photomultiplier tube (PMT) and photo-electric pulse distribution w(N, T) created in a PMT are discussed. The theory is able to describe pulse distribution function w(N, T) measured experimentally at signal acquisition time T = 0.1 s. Values of all rate constants of the model have been found from comparison of the theory with the experiment. Distributions w(on, off)(t) of on- and off-times and distribution w(N, T) of pulses have been calculated for infrequent and frequent inter-conformational jumps in single copolymer molecule.
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