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# Revisiting the combined photon echo and single-molecule studies of low-temperature dynamics in a dye-doped polymer

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## Abstract

The photon echo (PE) spectroscopy and single-molecule spectroscopy (SMS) may be combined to give a very powerful tool for comprehensive study of low-temperature dynamics in dye-doped disordered solids (polymers, glasses). At the same time, this type of studies are likely to reveal discrepancies when comparing characteristic times of optical dephasing T2 and single-molecule zero-phonon spectral lines (ZPL) broadening obtained from PE and SMS, correspondingly, for tetra-tert-butylterrylene in polyisobutylene in the temperature range of a few–dozen of Kelvins [see Phys. Status Solidi B 241, 3480 and 3487 (2004)]. Inexplicably, PE-experiments demonstrated T2-times to be much shorter than it is sufficient to cause the corresponding ZPL broadening. Here we experimentally solve this problem and show that at T = 4.5–15 K the incoherent PE gives T2-times which correspond to the narrowest SM ZPL. On the SM-level there is a pronounced additional ZPL-broadening due to spectral diffusion processes which are strongly dependent on the characteristics time of the measurement (tens of nanoseconds for PE and seconds for SMS). There is also a broad distribution of ZPL spectral widths for different SMs due to different local environments, that contribute differently to both the optical dephasing and the spectral diffusion processes, but always in addition to the value of inverse optical dephasing times measured using a PE technique.

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It is shown that many center excitations are responsible for the universal low energy spectral properties in an arbitrary ensemble of defect centers with an internal degree of freedom. Universality means a quasiuniform distribution of the energy and the logarithm of the tunneling amplitude together with a disappearance of the dependence on the primary defect parameters.
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Linewidth distributions for single terrylene molecules in polyethylene have been measured in the temperature range from 30 mK to 1.83 K. The temperature dependence of the average linewidth is best described by a linear relationship over the full temperature range. At 30 mK, the linewidth distribution has a full-width at half-maximum of &18.6 MHz and an average linewidth of 42.8(6) MHz. 2000 Elsevier Science B.V. All rights reserved.
Article
By means of single molecule (SM) spectroscopy we investigated elementary matrix excitations in a disordered solid, i.e., quasi-localized low-frequency vibrational modes (LFMs). To this end we recorded the spectra of single tetra-tert-butylterrylene molecules embedded in an amorphous polyisobutylene matrix in a temperature region, where the LFM contribution to line broadening dominates. The individual parameters of LFM in a polymer glass can be determined from the temperature-dependent linewidths of single molecules. The magnitude of the LFM contribution to SM spectra was obtained by the statistical analysis,of the distribution of linewidths of SMs. Pronounced distributions of LFM frequencies and SM-LFM coupling constants were found. This result can be regarded as the first direct experimental proof of the localized nature of LFMs. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weimheim.
Article
Spectra of single tetra-tert-butylterrylene molecules incorporated in purely amorphous polyisobutylene matrix have been measured at 2, 4.5 and 7 K (244, 381 and 187 molecules, correspondingly). This is a temperature region, where the main assumptions of the standard two-level system (TLS) model of low-temperature glasses begin to be not valid. At T = 2 K the main parameters of most of the registered spectra were found to be consistent with the standard TLS model. At T = 4.5 and 7 K some deviations from predictions of this model were observed. The detailed analysis reveals that increasing of temperature leads to additional, in comparison with the predictions of the standard TLS model, line broadening of spectral peaks. This additional line broadening was attributed to the influence of quasi-local low-frequency modes (LFMs) of the amorphous matrix in system under study at T = 4.5 and 7 K. Distributions of single spectral peak widths of the detected spectra (the line width distributions) have been calculated and compared with the line width distributions simulated for the same system. Comparative analysis of experimental and simulated distributions allows to evaluate the value of LFM contribution at 4.5 and 7 K. The single molecule spectroscopy data were compared with the literature values of inverse optical dephasing times, 1/piT(2), as measured for the same system by photon echo (S.J. Zilker et al., J. Chem. Phys. 109 (1998) 6780). (C) 2003 Elsevier B.V. All rights reserved.
Article
According to the modern conception, the dynamics of amorphous solids in the intermediate interval of low temperatures (from a few up to dozens of Kelvins) is determined mainly by quasi-localized low-frequency vibrational modes (LFMs). Up to now, it is known very little about a nature and properties of these excitations in disordered solids. High-selective laser spectroscopy of impurity centres, embedded to transparent disordered matrix as a probe, is a very powerful method for deriving information about LFMs. In the two presented papers the results of our photon echo (PE) and single molecule spectroscopy (SMS) studies of LFMs in organic amorphous solids are discussed. In the first part we review the recent results of our PE-studies. Two cases are analyzed: (a) a coupling of chromophores with a continuous broad spectrum of LFMs, which shape was taken from light scattering experiments, and (b) a coupling of chromophores with continuous LFMs spectra, calculated on the base of the soft potentials model. In the second part we consider the results of our studies of LFMs in a glassy polymer on microscopic level using SMS. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Article
Laser spectroscopic techniques at low temperature, such as fluorescence line-narrowing and hole burning, enable an increase of spectral resolution by a factor of 103–105 compared to conventional spectroscopy at room temperature. With these methods, it is possible to retrieve a fingerprint of the species involved and to measure the rates of dynamic processes that normally remain hidden in the broad absorption bands. A few applications carried out in our laboratory will be discussed: (1) the determination of energy transfer rates in the peripheral LH2 complex of purple bacteria; (2) the study of spectral diffusion and its implications in three types of systems: (a) the B820 and B777 subunits of the LH1 complex of purple bacteria, (b) the photosystem II reaction center (PSII RC) and CP47 antenna complex of green plants, and (c) an organic glass doped with bacteriochlorophyll a; (3) the unraveling of 0-0 transitions and the pathways of photoconversion between a number of conformations of the green fluorescent protein mutant S65T; (4) the measuring of electron-phonon coupling strengths in PSII RC and the red fluorescent protein DsRed; and (5) the determination and comparison of the homogeneous linewidths and optical dephasing in photosynthetic chromoprotein complexes and autofluorescent proteins.
Article
A linear temperature dependence of the specific heat in amorphous solids at very low temperatures is shown to follow from an ionic tunneling model. Moreover, this model predicts both the observed temperature dependence and the magnitude of the thermal conductivity and also explains the anomalous results obtained for the phonon free path by means of stimulated Brillouin scattering.
Article
The concept of “homogeneous” spectral linewidths in doped amorphous solids and some possibilities to separate the linewidth parts related to the optical dephasing and spectral diffusion (SD) are discussed. The results of the model calculations of the photon echo (PE) decay under conditions of a large dispersion of homogeneous linewidths are presented. The deviations of the PE decay from an exponential due to this dispersion are discussed. The experimental data on incoherent PE in the terrylene/polyethylene system are presented and compared with literature single molecule spectroscopy (SMS) data. It is shown that in this case the dephasing time dispersion plays an important role for the linewidth distribution in SMS. A simple method for separation of the dephasing and SD linewidths in the SMS, based on intensity saturation effects, is considered. The facilities of this method using some SMS data are demonstrated.
Article
The study of a new dye-matrix system-quickly frozen ortho-dichlorobenzene weakly doped with terrylene--via single-molecule (SM) spectroscopy is presented. The spectral and photo-physical properties, dynamics, and temperature broadening of SM spectra at low temperatures are discussed. The data reveal a broad inhomogeneous distribution, which indicates a high degree of matrix inhomogeneities, but at the same time, huge fluorescence emission rates and extraordinary SM spectral and photochemical stability with almost complete absence of blinking and bleaching. These unusual properties render the new system a promising candidate for applications in photonics, for example, for delivering single photons on demand.
Article
Measurements of the elastic and inelastic neutron scattering from vitreous silica in the frequency range 0.3 to 4 THz and with scattering vectors in the range 0.2 to 5.3 A&#778-1 are analyzed in conjunction with heat-capacity measurements on the same samples to provide a microscopic description of low-frequency vibrational modes. The results show that additional harmonic excitations coexist with sound waves below 1 THz, and that these excitations correspond to relative rotation of SiO4 tetrahedra.
Article
The Pb(Zr,Ti)O3 (PZT) disordered solid solution is widely used in piezoelectric applications owing to its excellent electromechanical properties. Six different structural phases have been observed for PZT at ambient pressure, each with different lattice parameters and average electric polarization. It is of significant interest to understand the microscopic origin of the complicated phase diagram and local structure of PZT. Here, using density functional theory calculations, we show that the distortions of the material away from the parent perovskite structure can be predicted from the local arrangement of the Zr and Ti cations. We use the chemical rules obtained from density functional theory to create a phenomenological model to simulate PZT structures. We demonstrate how changes in the Zr/Ti composition give rise to phase transitions in PZT through changes in the populations of various local Pb atom environments.
Article
We present a single molecule fluorescence study that allows one to probe the nanoscale segmental dynamics in amorphous polymer matrices. By recording single molecular lifetime trajectories of embedded fluorophores, peculiar excursions towards longer lifetimes are observed. The asymmetric response is shown to reflect variations in the photonic mode density as a result of the local density fluctuations of the surrounding polymer. We determine the number of polymer segments involved in a local segmental rearrangement volume around the probe. A common decrease of the number of segments with temperature is found for both investigated polymers, poly(styrene) and poly(isobutylmethacrylate). Our novel approach will prove powerful for the understanding of the nanoscale rearrangements in functional polymers.