Absorption and propagation of light in quaterthiophene crystals

We examine absorption of light in quaterthiophene crystals for different directions of the ray and wave-normal vector after refraction on the vacuum/crystal interface. Experimental non-normal incidence spectra are reported where different absorption bands show different behaviour as a function of the angle of incidence. This allows to identify those originating from the b_u Frenkel exciton state.     

Absorbance spectra of polycrystalline samples and twinned crystals of oligothiophenes

We propose optical absorption technique at oblique incidence as one of the spectroscopic tools that allow experimentally recognizing the macroscopic order and structural features of molecular solids of conjugated molecules, from single crystals to polycrystalline or twinned samples. We apply this spectroscopy to quaterthiophene as representative of a wide class of materials that usually possess optical transitions of Frenkel exciton origin with strong directional dispersion. The comparison between experimental and simulated data gives evidence of the high sensitivity of this technique for determining quantitatively the polycrystallinity of the measured samples, whose domains may show mirror-like orientation of the unit cell with respect to one of its faces.Frenkel exciton; Oligothiophene, Optical properties     

The Index of a Cyclic Quartic Field

Let K be a cyclic quartic field. Let i(K) denote the index of K. It is known that i(K){1, 2, 3, 4, 6, 12}. In Part 1 of this paper we show that i(K) assumes all of these values and we give necessary and sufficient conditions for each to occur. In Part 2 an asymptotic formula is given for the number of cyclic quartic fields with discriminant x and i(K)=i for each i{1, 2, 3, 4, 6, 12}.     

Polarized Absorption,Spontaneous and Stimulated Blue Light Emission of J‐type Tetraphenylbutadiene Monocrystals

Blue amplified spontaneous emission at room temperature is demonstrated from the exposed face of the strongly emitting organic semiconductor 1,1,4,4‐tetraphenyl‐1,3‐butadiene in single crystal form. The symmetry of the crystal and calculation of lattice sums indicate the J‐type organization of the molecular transition moments. The minimum in the lowest exciton dispersion branch, from which emission takes place, is found at the edge of the Brillouin zone leading to a dominant vibronic emission since the zero‐phonon line is forbidden. The observed gain narrowed line is attributed to the vibronic replica which becomes amplified with increased pumping. The reported emission is along the normal to the exposed crystal face, important for the development of vertical cavity geometry lasers based on organic single crystals. The threshold excitation fluence of 400 μJ cm^?2 is comparable to other organic crystalline systems, even if the amplification path is much reduced as a consequence of the vertical geometry. Considering these relevant aspects, the optical characterization of this material is provided. The polarized absorption spectra are reported and the properties of the lowest‐energy excitonic state investigated. Calculation of the electronic transitions for the isolated molecule, lattice sums for the transition at lowest energy, and the symmetry of the crystal allow attributing the largest face of the samples and the observed optical bands in the spectra. Polarized time‐resolved spectra are also reported allowing to identify the intrinsic excitonic emission.     

Reclassifying exciton-phonon coupling in molecular aggregates: evidence of strong nonadiabatic coupling in oligothiophene crystals

Exciton-phonon (EP) coupling in molecular aggregates is reexamined in cases where extended intermolecular interactions result in low-energy excitons with high effective masses. The analysis is based on a single intramolecular vibrational mode with frequency omega0 and Huang-Rhys factor lambda2. When the curvature Jc at the exciton band bottom is much smaller than the free-exciton Davydov splitting W, the strength of the EP coupling is determined by comparing the nuclear relaxation energy lambda2omega0 with the curvature. In this way, weak (lambda2omega0<4piJc), intermediate I (lambda2omega0 approximately 4piJc), and strong I (lambda2omega0>4piJc) coupling regimes are introduced. The conventional intermediate (lambda2omega0 approximately W) and strong (lambda2omega0>W) EP coupling regimes originally defined by Simpson and Peterson [J. Chem. Phys. 26, 588 (1957)] are based solely on the Davydov splitting and are referred to here as intermediate II and strong II regimes, respectively. Within the intermediate I and strong I regimes the near degeneracy of the low-energy excitons allows efficient nonadiabatic coupling, resulting in a spectral splitting between the b- and ac-polarized first replicas in the vibronic progression characterizing optical absorption. Such spectral signatures are clearly observed in OT4 thin films and crystals, where splittings for the lowest energy mode with omega0=161 cm(-1) are as large as 30 cm(-1) with a small variation due to sample disorder. Numerical calculations using a multiphonon BO basis set and a Hamiltonian including linear EP coupling yield excellent agreement with experiment.     

Measured Davydov splitting in oligothiophene crystals

The polarized absorption spectra of single crystals of oligothiophenes in a wide spectral range are reported. The experimental procedure is discussed, underlying several details which are relevant to obtain reliable spectra particularly for samples of increasing thickness. On the basis of these considerations, it has been possible to fully detect the transition to the upper Davydov exciton originating from the first molecular state. The position and shape of the main exciton peak in these materials are compared and discussed, taking into consideration the molecular arrangement and the longitudinal contribution which depends on the transition moment orientation. The Davydov splitting values as deduced from the experimental data at room temperature are also reported either for the first vibronic replica or for the electronic transition as a whole. The difference between the purely transverse and the measured Davydov splitting is discussed.     

Values of the Euler phi function not divisible by a given odd prime

An asymptotic formula is given for the number of integers n≤x for which φ(n) is not divisible by a given odd prime.     

Dielectric tensor and optical spectra of quaterthiophene crystals

We present an approach to the microscopic calculation of the dielectric tensor near the resonances of mechanical Frenkel excitons in a vibronic coupling regime with one effective mode. The model, applied to the prototypical quaterthiophene crystal, is based on a discrete distribution of charges for the evaluation of the molecular transition moment, whilst the coulombic interactions responsible for the exciton delocalization in the crystal are calculated by the Ewald method. From the calculated tensor we simulate absorbance and reflectance spectra and by a direct comparison with the experimental ones, we identify the origin of some shoulders present in the spectra.     

Effect of static and dynamic disorder on exciton mobility in oligothiophenes

The polarized optical absorption spectra of different quaterthiophene single crystals in the energy region of the exciton bands originating from the first molecular transition are reported as measured in the temperatures ranging from 7 to 140 K. The intrinsic higher mobility of the b-polarized 0-0 a(u) exciton both with respect to its replicas and to the a-polarized structures is demonstrated in high quality crystals at the lowest temperatures. The influence of structural disorder on mobility is discussed considering, for the different samples, the measured lineshape and linewidth of the absorption peaks, and the relative lineshift and intensity ratio between the 0-0 a(u) line and its first replica at the lowest temperature. The influence of dynamic disorder is discussed considering the lineshape and linewidth of the measured peaks as a function of temperature for both polarizations in the framework of the exciton-phonon coupling theory.