Mathematical functions for the analysis of luminescence decays with underlying distributions 1. Kohlrausch decay function (stretched exponential)

Berberan‐Santos, Mário N.; Bodunov, E. N.; Valeur, Bernard

doi:10.1016/j.chemphys.2005.04.006

Cited by 538 publications

(554 citation statements)

References 62 publications

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“…For a quenching process controlled by diffusion contact ) 0.5 and for a single-step RET by the dipole-dipole mechanism will be 0.16, 0.33, and 0.5 respectively for one, two, or three dimensions. 41 Fluorescence decays in fractals are also described by eq 12, 1-dimensional systems with donor decaying only by a random walk to a trapping site will give ∈ [0.5, 1], 1,45 and if a single-step energy transfer is also involved < 0.5 can also be obtained. 1,45 In our case, from the SANS measurements geometry changes were not detected in the copolymer chain upon increasing the fluorenone fraction, but still shows a strong dependence with 9FLO content with values always below 0.5.…”

Section: Discussionmentioning

confidence: 99%

“…Stretched Exponential Function in Decay Data Analysis. The description of fluorescence time decays by a sum of discrete exponentials has the advantage of providing a clear physical meaning for the fitting parameters, 41 decay times, and preexponential amplitudes. Basically, the assumption of a fit with N exponential functions establishes the idea that equal numbers of different kinetic species are present in the system.…”

Section: Discussionmentioning

confidence: 99%

“…Alternatively, the use of a stretched exponential function (eq 12) has been frequently proposed 1,41 to describe the timedependent donor emission in photon-harvesting polymer systems. In this equation, τ 0 is the donor lifetime in the absence of energy acceptors, A is a parameter proportional to the local acceptor concentration, and 0 < e 1 is an empirical parameter directly connected with the physical dimensions where the fluorophores are distributed.…”

Section: Discussionmentioning

confidence: 99%

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Fast and Slow Time Regimes of Fluorescence Quenching in Conjugated Polyfluorene−Fluorenone Random Copolymers: The Role of Exciton Hopping and Dexter Transfer along the Polymer Backbone

et al. 2006

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The luminescence decay kinetics of polyfluorene copolymers containing fluorenone units randomly distributed along the polymer chain have been studied by steady-state and time-resolved fluorescence techniques in toluene solution. The typical green emission from polyfluorenes containing 9-fluorenone moieties is only observed if the 9-fluorenone group is covalently attached to the polymer. Small-angle neutron scattering (SANS) measurements indicate that, independent of the 9-fluorenone fraction, all the studied copolymers adopt an open wormlike conformation. This prevalent 1-dimensional arrangement confirms that the green emission observed with polyfluorenes is not the result of excimer formation in the typical sandwich-like conformation. Analysis of time-resolved fluorescence decays by the maximum entropy method (MEM) collected at the polyfluorene emission (415 nm) and by global analysis of decays collected at 415 and 580 nm (the 9-fluorenone defect emission wavelength) clearly indicates two different time regimes in the population of the fluorenone defect: one occurring in the time interval of 10 to 30 ps and a second one occurring in the time range from 70 to 200 ps. While the slower process shows a linear dependence with the 9-fluorenone fraction, compatible with a hopping migration process along the polymer chain, the faster process does not show such a dependence and instead suggests a short-range Dexter mechanism. These findings are in agreement with our previous work where the presence of a faster component was suggested.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Fast and Slow Time Regimes of Fluorescence Quenching in Conjugated Polyfluorene−Fluorenone Random Copolymers: The Role of Exciton Hopping and Dexter Transfer along the Polymer Backbone

et al. 2006

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“…where R* is the characteristic relaxation rate and β is the stretching parameter [11,22,[29][30][31][32][33][34][35]. If the relaxation is exponential to within experimental uncertainty, β = 1 and R* is labeled R. This occurs in pure compounds like 1 and 2 at temperatures below the maximum in the relaxation rate [2,[8][9][10][22][23][24][25][26][27][28].…”

Section: A Review Of the 1 H Spin-lattice Relaxation Modelmentioning

confidence: 99%

Monitoring a simple hydrolysis process in an organic solid by observing methyl group rotation

Beckmann

Bohen

Ford

et al. 2017

Solid State Nuclear Magnetic Resonance

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experiments allow us to observe the temperature dependence of the parameters that characterize methyl group rotation in both compounds and in mixtures of the two compounds. In the mixtures, both types of methyl groups (that is, molecules of 1 and 2) can be observed independently and simultaneously at low temperatures because the solid state 1 H spin-lattice relaxation is appropriately described by a double exponential. We have followed the conversion 1 → 2 over periods of two years. The solid state 1 H spin-lattice relaxation experiments in pure samples of 1 and 2 indicate that there is a distribution of NMR activation energies for methyl group rotation in 1 but not in 2 and we are able to explain this in terms of the particle sizes seen in the field emission scanning electron microscopy images.

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“…used to describe relaxation effects in disordered materials, as dielectric relaxation [16] or luminescence decays [17]. An overview of broad range of stretchedexponential distributions in nature and economy is given by Laherrere and Sornette [9].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Users Activity on Web-Blogs

Kozioł

2016

Acta Phys. Pol. A

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Activity of users on Internet discussion forums is analyzed. The rank of users is shown to be approximated better by stretched-exponential function than by the Zipf law. Cumulative distribution function is found as an excellent tool in analysis of the dynamics of the collective social phenomena. We are able to approximate the number of blog comments with time by simple sigmoidal functions: probability of posting a comment is given by P (t) = P0(t)/[1 + P0(t)], where P0(t) = (t/t0) β and β is close to 1.

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Mathematical functions for the analysis of luminescence decays with underlying distributions 1. Kohlrausch decay function (stretched exponential)

Cited by 538 publications

References 62 publications

Fast and Slow Time Regimes of Fluorescence Quenching in Conjugated Polyfluorene−Fluorenone Random Copolymers: The Role of Exciton Hopping and Dexter Transfer along the Polymer Backbone

Fast and Slow Time Regimes of Fluorescence Quenching in Conjugated Polyfluorene−Fluorenone Random Copolymers: The Role of Exciton Hopping and Dexter Transfer along the Polymer Backbone

Monitoring a simple hydrolysis process in an organic solid by observing methyl group rotation

Dynamics of Users Activity on Web-Blogs

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