Photonic superdiffusive motion in resonance radiation trapping

In this work we consider the relation between the jump length probability density function and the line shape function in resonance radiation trapping in atomic vapors. The two-sided jump length probability density function suitable for a unidimensional formulation of radiative transfer is also derived. As a side result, a procedure to obtain the Maxwell distribution of velocities from the Maxwell-Boltzmann distribution of speeds was obtained. General relations that give the asymptotic jump length behavior and the Lévy flight parameter niu for any line shape are obtained. The results are applied to generalized Doppler, generalized Lorentz, and Voigt line shape functions. It is concluded that the lighter the tail of the line shape function, the less heavy the tail of the jump length probability density function, although this tail is always heavy, with niu <= 1

Photon trajectories in incoherent atomic radiation trapping as Levy flights

Photon trajectories in incoherent radiation trapping for Doppler, Lorentz, and Voigt line shapes under complete frequency redistribution are shown to be Levy flights. The jump length (r) distributions display characteristic long tails. For the Lorentz line shape, the asymptotic form is a strict power law r ^ (-3/2), while for Doppler the asymptotic is r ^ -2 (ln r)^ (-1/2). For the Voigt profile, the asymptotic form always has a Lorentz character, but the trajectory is a self-affine fractal with two characteristic Hausdorff scaling exponents

Photonic superdiffusive motion in resonance line radiation trapping - partial frequency redistribution effects

The relation between the jump length probability distribution function and the spectral line profile in resonance atomic radiation trapping is considered for Partial Frequency Redistribution (PFR) between absorbed and reemitted radiation. The single line Opacity Distribution Function [M.N. Berberan-Santos et.al. J.Chem.Phys. 125, 174308 (2006)] is generalized for PFR and used to discuss several possible redistribution mechanisms (pure Doppler broadening, combined natural and Doppler broadening and combined Doppler, natural and collisional broadening). It is shown that there are two coexisting scales with a different behavior: the small scale is controlled by the intricate PFR details while the large scale is essentially given by the atom rest frame redistribution asymptotic. The pure Doppler and combined natural, Doppler and collisional broadening are characterized by both small and large scale superdiffusive Levy flight behaviors while the combined natural and Doppler case has an anomalous small scale behavior but a diffusive large scale asymptotic. The common practice of assuming complete redistribution in core radiation and frequency coherence in the wings of the spectral distribution is incompatible with the breakdown of superdiffusion in combined natural and Doppler broadening conditions

Fluorescent homooxacalixarenes: recent applications in supramolecular systems

This review covers recent advances (from 2006 to date) in supramolecular systems based on fluorescent homooxacalixarenes, namely hexahomotrioxacalix[3]arenes, dihomooxacalix[4]arenes and tetrahomodioxacalix[4]arenes, focusing on fluorescence sensing using their intrinsic fluorescence (built-in mesitol-like groups) or the extrinsic fluorescence of organic fluorophores, either covalently linked to the calixarenes or forming supramolecular complexes with them. Sensing applications of ions, ion pairs and neutral molecules are discussed, as well as the potential measurement of temperature based on thermally activated delayed fluorescence

Ditopic Receptors Based on Dihomooxacalix[4]arenes Bearing Phenylurea Moieties With Electron-Withdrawing Groups for Anions and Organic Ion Pairs

Two bidentate dihomooxacalix[4]arene receptors bearing phenylurea moieties substituted with electron-withdrawing groups at the lower rim via a butyl spacer (CF3-Phurea 5b and NO2 Phurea 5c) were obtained in the cone conformation in solution, as shown by NMR. The X-ray crystal structure of 5b is reported. The binding affinity of these receptors toward several relevant anions was investigated by 1H NMR, UV-Vis absorption in different solvents, and fluorescence titrations. Compounds 5b and 5c were also tested as ditopic receptors for organic ion pairs, namely monoamine neurotransmitters and trace amine hydrochlorides by 1H NMR studies. The data showed that both receptors follow the same trend and, in comparison with the unsubstituted phenylurea 5a, they exhibit a significant enhancement on their host-guest properties, owing to the increased acidity of their urea NH protons. NO2-Phurea 5c is the best anion receptor, displaying the strongest complexation for F 12, closely followed by the oxoanions BzO 12, AcO 12, and HSO4-. Concerning ion pair recognition, both ditopic receptors presented an outstanding efficiency for the amine hydrochlorides, mainly 5c, with association constants higher than 109 M 122 in the case of phenylethylamine and tyramine

Conventional vs. Microwave-or mechanically-assisted synthesis of dihomooxacalix[4]arene phthalimides: NMR, X-ray and photophysical analysis

Direct O-alkylation of p-tert-butyldihomooxacalix[4]arene (1) with N-(bromopropyl)-or N-(bromoethyl)phthalimides and K2 CO3 in acetonitrile was conducted under conventional heating (reflux) and using microwave irradiation and ball milling methodologies. The reactions afforded mono-and mainly distal di-substituted derivatives in the cone conformation, in a total of eight compounds. They were isolated by column chromatography, and their conformations and the substitution patterns were established by NMR spectroscopy (1 H,13 C, COSY and NOESY experiments). The X-ray structures of four dihomooxacalix[4]arene phthalimide derivatives (2a, 3a, 3b and 5a) are reported, as well as their photophysical properties. The microwave (MW)-assisted alkylations drastically reduced the reaction times (from days to less than 45 min) and produced higher yields of both 1,3-di-substituted phthalimides (3a and 6a) with higher selectivity. Ball milling did not reveal to be a good method for this kind of reaction