History of the Kohlrausch (stretched exponential) function: Pioneering work in luminescence

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

doi:10.1002/andp.20085200705

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…The stretched-exponential function is often used for describing PL decay reflecting the relaxation processes due to excitation energy transfer in material ensembles and diffusion-induced relaxation. , Both relaxation processes are possible in doped polythiophenes. In our samples, owing to the inhomogeneity indicated by the absorption spectra in Figure , a photoexcited polaron (energy donor) finds another polaron (acceptor) with lower transition energy, and excitation energy transfer between them is expected.…”

Section: Resultsmentioning

confidence: 99%

Microscopic Mobility of Polarons in Chemically Doped Polythiophenes Measured by Employing Photoluminescence Spectroscopy

2014

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Doped conjugated polymers show high electrical conductivity due to doping-generated polarons, and understanding their transport properties is key to their practical use as transparent flexible electrodes. The transport properties have been widely studied in the field-effect transistor configuration, where the long-range transport affected by grain boundaries and conjugation breaks dominates. In contrast, spectroscopic measurements are sensitive to microscopic transport properties and have a potential to reveal the characteristic transport within an intrachain conjugation region. In this study, we show the photoluminescence of polarons in chemically doped polythiophenes to estimate microscopic carrier mobility through the relaxation dynamics of the photoexcited state of polarons. The estimated carrier mobility is 2 cm2 V–1 s–1 and larger than the reported highest value on the order of 0.1 cm2 V–1 s–1 in field-effect transistors. This study demonstrates the real-time observation of carrier diffusion and scattering in the conductive state of conjugated polymers.

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Section: Resultsmentioning

confidence: 99%

Microscopic Mobility of Polarons in Chemically Doped Polythiophenes Measured by Employing Photoluminescence Spectroscopy

2014

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“…where k B is the Boltzmann constant, T is the temperature, η is viscosity, and r is the particle radius. Complex fluids often display dynamics which cannot be described by a simple exponential decay and are instead often characterized by a Kohlrausch fit 51,52 g q aq bq ( , ) ( ) ( )exp 2( )…”

Section: ■ Introductionmentioning

confidence: 99%

Hierarchical Structure and Dynamics of a Polymer/Nanoparticle Hybrid Displaying Attractive Polymer–Particle Interaction

et al. 2019

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X-ray photon correlation spectroscopy and small-angle Xray scattering were used to study the thermally driven motion and hierarchical structure of palladium (Pd) nanoparticles (NPs) in the concentrated solutions composed of polymers with different molecular weights. The Pd NPs were formed by in situ reduction of palladium(II) acetylacetonate (Pd(acac) 2 ) in the solution of poly(2-vinylpyridine) (P2VP) and benzyl alcohol which acted as the reduction agent and solvent. Below the entanglement molecular weight (M e ) of P2VP, a diffusion mode was found together with a fractal structure built up by the primary particles spanning over a broad range of length scales. Above M e , a subdiffusive motion was identified along with diffusive motion, and the hybrids formed a fractal structure built by the local clusters assembled by primary particles. The structural differences were attributed to different kinetic pathways of NP organization mediated by attractive interaction between P2VP and Pd NPs as well as the viscosity of the matrix phase, and both are dependent on the polymer molecular weight. The bimodal dynamics was ascribed to overlapping dynamic spectra associated with the diffusion of the fractal entity and the constrained subdiffusion of the collective motion of NP clusters within it.

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where I ( t ) is the luminescence intensity, t is time, y 0 is the background (noise level), A is the intensity at t = 0, β is the stretch factor and τ is a characteristic relaxation time. The decay curve and a fit to the function of Equation (1) are shown as an example for T = 30 K in Figure 3 b.…”

Section: Resultsmentioning

confidence: 99%

“…Independently, on the T, all the obtained PL decay curves do not follow a pure mono-exponential function. Nevertheless, they could be successfully fitted by a stretched exponential function that reflects the multisite environment of the Yb 2+ ions [16,17]: In Figure 3a, we presented the results of the PL decay measurements performed on YAS preform at different temperatures in the range from 2 to 300 K. PL kinetics were recorded at 502 nm under excitation at 355 nm. Independently, on the T, all the obtained PL decay curves do not follow a pure mono-exponential function.…”

Section: Resultsmentioning

confidence: 99%

Yb2+-Doped Silicate Glasses as Optical Sensor Materials for Cryogenic Thermometry

El Hamzaoui,

Razdobreev,

Cieslikiewicz-Bouet

et al. 2023

Sensors

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Optical sensors constitute attractive alternatives to resistive probes for the sensing and monitoring of temperature (T). In this work, we investigated, in the range from 2 to 300 K, the thermal behavior of Yb2+ ion photoluminescence (PL) in glass hosts for cryogenic thermometry. To that end, two kinds of Yb2+-doped preforms, with aluminosilicate and aluminophosphosilicate core glasses, were made using the modified chemical vapor deposition (MCVD) technique. The obtained preforms were then elongated, at about 2000 °C, to canes with an Yb2+-doped core of about 500 µm. Under UV excitation and independently of the core composition, all samples of preforms and their corresponding canes presented a wide visible emission band attributed to Yb2+ ions. Furthermore, PL kinetics measurements, recorded at two emission wavelengths (502 and 582 nm) under 355 nm pulsed excitation, showed an increase, at very low T, followed by a decrease in lifetime until room temperature (RT). A modified two-level model was proposed to interpret such a decay time dependence versus T. Based on the fit of lifetime data with this model, the absolute (Sa) and relative (Sr) sensitivities were determined for each sample. For both the preform and its corresponding cane, the aluminophosphosilicate glass composition featured the highest performances in the cryogenic domain, with values exceeding 28.3 µsK−1 and 94.4% K−1 at 30 K for Sa and Sr, respectively. The aluminophosphosilicate preform also exhibited the wider T operating range of 10–300 K. Our results show that Yb2+-doped silicate glasses are promising sensing materials for optical thermometry applications in the cryogenic domain.

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History of the Kohlrausch (stretched exponential) function: Pioneering work in luminescence

Cited by 7 publications

References 12 publications

Microscopic Mobility of Polarons in Chemically Doped Polythiophenes Measured by Employing Photoluminescence Spectroscopy

Microscopic Mobility of Polarons in Chemically Doped Polythiophenes Measured by Employing Photoluminescence Spectroscopy

Hierarchical Structure and Dynamics of a Polymer/Nanoparticle Hybrid Displaying Attractive Polymer–Particle Interaction

Yb2+-Doped Silicate Glasses as Optical Sensor Materials for Cryogenic Thermometry

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