Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation

Dust particles in space often grow by mutual collisions and appear to be an agglomeration of individual grains, the morphology of which can be described by the concept of fractals. In this paper, we study light scattering by fractal aggregates of identical spheres (monomers) using the superposition technique incorporated into the T-matrix method where the orientationally averaged scattering matrix is analytically obtained. We also apply the discrete-dipole approximation, in which the dipole polarizability of spherical monomers is determined by the first term of the scattering coefficients in the Mie theory. Two cases of the ballistic aggregation process (particle–cluster and cluster–cluster aggregations) are considered to model fractal aggregates consisting of silicate or carbon material. The dependences of light-scattering properties on the monomer sizes, aggregate structures and material compositions are intensively investigated. The light-scattering properties of the fractal aggregates strongly depend on the size parameters of the monomers. The difference in the scattering function between the particle–cluster and cluster–cluster aggregates can be seen in the case of monomers much smaller than the wavelength of incident radiation. When the size parameter of monomers exceeds unity, the material composition of the monomers influences the light-scattering properties of the aggregates, but different morphologies result in similar scattering and polarization patterns. We show that silicate aggregates consisting of submicron-sized monomers, irrespective of the aggregate size and morphology, produce a backscattering enhancement and a negative polarization observed for dust in the solar system.     

Vibronic problem in the higher excited states of F-center in alkali halides

Vibronic problem in the higher excited states of F-center in alkali halidesA new approach to the vibronic problems of bound polaron is proposed, taking advantage of the spherical symmetry of the system. By applying the obtained formula to the analysis of the transient absorption spectra due to the transition from the relaxed excited state to higher excited states of F-center in alkali halides, a good fit between the theory and the experiments is obtained and the final states of the transition are assigned to be 3p state and its phonon side bands perturbed through vibronic coupling.     

Motional averaging in an excited state of ZnS: Cu2+

The single isotropic g factor found in the ²E excited state of ZnS:Cu²⁺ is hard to reconcile with the properties of this state, in particular with the moderate strength of the E ? ? vibronic coupling. A vibronic coupling between this state and the vibronic levels of the ground ²T₂ state due to τ₂ modes can bring about motional averaging between strain split states of ²E through a two phonon non-resonant process. In general, excited state mechanisms will be effective between states of the same spin multiplicity and which have large Stoke shifts.     

Extended calculation of polarization and intensity of fractal aggregates based on rigorous method for light scattering simulations with numerical orientation averaging

The intensity and polarization of fractal aggregates have been investigated using both rigorous and approximate methods for light scattering simulations. However, previous studies using the analytical orientation averaging version of the rigorous method were generally limited to a few hundred monomers when the monomer size parameter was around 1.7. In this study, we propose using numerical orientation averaging instead of analytical orientation averaging. The numerical averaging is performed together with a fixed orientation version of the rigorous T-matrix method for clusters of spheres. This approach enables increasing the number of monomers by a factor of 2-7 or the size of monomers by a factor of 8-10 compared to the analytical orientation averaging version.We investigated the influence of monomer size and the number of monomers on the light scattering of silicate aggregates (refractive index m=1.68+0.03i) for incident light with a wavelength of . We considered ballistic particle-cluster aggregates (BPCA) and ballistic cluster-cluster aggregates (BCCA) composed of 128, 256, 512, and 1024 monomers with radii between 0.11 and .Our results show that the size of monomers plays an important role in reproducing the negative polarization branch for all the BPCA and BCCA. Silicate aggregates with the monomer radius of less than contribute to reproducing the negative polarization branch, while aggregates with monomers larger than do not have the negative polarization branch. Polarization oscillation with scattering angle occurs for larger monomers (i.e., monomer radius ).The maximum polarization decreases for increasing monomer radius between 0.11 and . However, the negative polarization branch is generally enhanced for monomer radii up to around , and reduced for further increase of monomer size.The number of monomers also has a large influence on the negative polarization branch in the case of BPCA. The increase in the number of monomers from 128 to 1024 shifts the scattering angle of minimum polarization to larger angles for BPCA. In addition, the increase in the number of monomers reduces the values of negative polarization for BPCA while the variation with the number of monomers for BCCA is small and is not monotonic.     

Effect of a solid substrate on orientational ordering and the process of associate formation in thin interlayers of solutions of some organic compounds

We have studied the vibronic absorption spectra of thin submicron interlayers of anisole and nitrobenzene solutions as a function of the concentration and thickness of the interlayer. We have observed isosbestic points in a series of spectra obtained for different concentrations and thicknesses. This in turn is due to the existence in the system of two types of absorbing centers, which we connect with monomers and molecular associates (dimers). We discuss the relative contribution of different types of interactions leading to dimer formation. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 443–446, July–August, 2006.     

A study of radiative properties of fractal soot aggregates using the superposition T-matrix method

We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D_f, is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N_S, and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D_f<2 but increases rapidly when D_f>2. However, a systematic reduction in light absorption with D_f is observed for clusters with sufficiently large N_S, m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed.     

Radar polarimetry of Saturn's rings: Modeling ring particles as fractal aggregates built of small ice monomers

We analyze ground-based radar polarimetric observations of Saturn's rings at a wavelength of 12.6 cm by employing the model of a vertically and horizontally plane-parallel homogeneous slab composed of clumpy particles in the form of fractal aggregates of small ice monomers. Our model takes full account of the effects of polarization, multiple scattering, and coherent backscattering. Using efficient superposition T-matrix and vector radiative transfer codes, we perform computations of the backscattering circular polarization ratio for fractal aggregates generated with a cluster–cluster aggregation model and having the following characteristics: monomer refractive index m=1.78+i0.003; monomer packing density p=0.2; fractal dimensions D_f=2.5 and 3; and overall fractal radii R in the range 4?R?10 cm. In order to obtain physically realistic values of single-scattering properties of the aggregates we perform averaging over an ensemble of clusters generated for the same values of fractal parameters but having different geometrical configurations of the monomers. We conclude that in the framework of the above morphological model of Saturn's rings and the specific cluster–cluster aggregation procedure, it may be problematic to obtain a satisfactory and realistic agreement between theoretical computations and the observed values of the radar circular polarization ratio.     

Isotopic effect in the vibronic spectra of europium compounds

The effect of the kinematic factor on vibronic spectra of europium compounds and Eu³⁺-doped lanthanide compounds was examined experimentally. It was demonstrated that isotopic or quasi-isotopic substitution of the ions of the crystal lattice gives rise not only to the changes of the vibration frequencies but also to alteration of the value of electron-phonon interaction. The latter displays in changing the relative integral intensity of vibronic sidebands of electronic transitions of Eu³⁺ ion. Eu³⁺ vibronic spectra of a number of pairs of natural and isotopically or quasi-isotopically substituted compounds: nitrates, halides, formates, acetates, oxalates, β-diketonates, etc., were studied. In most cases the substitution of deuterium for hydrogen was applied. Decrease of the electron-phonon interaction with the increase of the isotopic mass depends on different structural characteristics. It was found that a factor of decreasing the relative intensity of the vibronic sideband of electronic transition of Eu³⁺ ion lies within the range ∼1.2 and ∼7 for pairs of compounds under investigation. The largest change of the intensity of vibronic sidebands was observed in a pair of formates Eu(HCOO)₃ and Eu(DCOO)₃ having the tridentate-bridging coordination of the formate anions and a three-dimensional frame structure. One should take into consideration both decreasing the vibration frequencies and diminishing the value of electron-phonon interaction at introduction of heavy isotope or quasi-isotope in the crystal lattice of lanthanide compounds to reduce the multiphonon quenching of luminescence.     

Radiative deactivation of the lowest triplet state of dibenzo-<Emphasis Type="Italic">p</Emphasis>-dioxine

A theoretical evaluation of the dipole moments of vibronic transitions (which are governed by vibronic spin-orbit interactions) was carried out for dibenzo-p-dioxin molecules. On the basis of the comparison of the obtained results with the data on the distribution of line intensities in a fine-structure phosphorescence spectrum of dibenzo-p-dioxin at 4.2 K, it is inferred that radiative deactivation of the lowest triplet state T ₁ (ππ*) occurs from one of the triplet sublevels. For the molecules of dibenzo-p-dioxin and one of the isomers of tetrachlorodibenzo-p-dioxin, the effect of the form of vibrational modes and individual constants of the spin-orbit coupling in O and Cl atoms on vibronic spin-orbit interactions is discussed.     

Vibronic fluorescence and fluorescence excitation spectra of diphenyl oxazolyl benzene and its oxadiazol analogue

The fine-structure fluorescence and fluorescence excitation spectra of conjugated chain compounds—1,4-di(5-phenyl-2-oxazolyl) benzene and its oxadiazol analogue—are obtained at 4.2 K in an n-octane matrix using the Shpolskii method. The spectra are modeled by representing the band of each of the vibronic transitions as the sum of a zero-phonon line and a phonon wing with certain parameters (half-widths, Debye-Waller factors). The spectra calculated in this fashion coincide with the experimental spectra. This makes it possible to determine the relative intensities of vibronic transitions and refine the frequencies of the normal vibrations in the S ₀ and S*₁ states. The parameters of the Franck-Condon and Herzberg-Teller interactions in the molecules considered are determined. The influence of the replacement of one of the CH groups in the heterocycles with a N atom on the parameters determining the formation of vibronic spectra is considered.     

Modeling vibronic spectra and excited states of polyenes with a parametric method

The structural-dynamic models of excited states and vibronic structure of absorption spectra of linear polyenes (R-(CH=CH)_n-R, R=H, CH₃, n=4, 5, 7) are calculated using the parametric method of the theory of vibronic spectra of such molecules. Good agreement is obtained between the calculated and experimental spectra. It is shown that the system of parameters of the method for the polyenes has a high degree of transferability in the series of related polyenes. The constructed models adequately reflect the real structure of the molecules in excited states and allow one to predict quantitatively the fine vibrational structure of the spectra, including relatively weak effects related to the methyl substitution. The dynamic of structural changes of the molecules upon their excitation is studied in the series of polyenes.     

Numerical simulations of single and multiple scattering by fractal ice clusters

We consider the scattering model in the form of a vertically and horizontally homogeneous particulate slab of an arbitrary optical thickness composed of widely separated fractal aggregates built of small spherical ice monomers. The aggregates are generated by applying three different approaches, including simulated cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) procedures. Having in mind radar remote-sensing applications, we report and analyze the results of computations of the backscattering circular polarization ratio obtained using efficient superposition T-matrix and vector radiative-transfer codes. The computations have been performed at a wavelength of 12.6 cm for fractal aggregates with the following characteristics: monomer refractive index m=1.78+i0.003, monomer radius r=1 cm, monomer packing density p=0.2, overall aggregate radii R in the range 4≤R≤10 cm and fractal dimensions D_f=2.5 and 3.We show that for aggregates generated with simulated CCA and DLA procedures, the respective values of the backscattering circular polarization ratio differ weakly for D_f=2.5, but the differences can increase somewhat for D_f=3, especially in case of an optically semi-infinite medium. For aggregates with a spheroidal overall shape, the dependence of the circular polarization ratio on the cluster morphology can be quite significant and increases with increasing the aspect ratio of the circumscribing spheroid.     

Two-photon absorption of tetraphenylporphin free base

We study two-photon absorption (TPA) spectra for toluene solution of 5,10,15,20-tetraphenyl-21H,23H-porphin (H₂TPP) in B and Q bands regions and find the maximum TPA cross-section values of 25 and 1-6 GM in laser wavelength ranges, 730-790 and 1100-1400 nm, correspondingly. In the 730-790 nm range the spectrum is attributed to parity allowed two-photon transition into g parity state, positioned nearby B state. Much lower TPA cross-section of ∼1 GM is measured for the transition into pure electronic Q state and it is due to the contribution of only those low-symmetry H₂TPP confomers, where mutual orientation of the porphyrin plane and the four phenyl rings lifts the center of inversion. The intermediate values of TPA cross-section of ∼6 GM are observed for the transition into vibronic Q states and are explained by TPA-allowed transition into vibronic states, which can occur even for totally centrosymmetrical molecules. Measurement of two-photon polarization ratio, Ω=σ_circ/σ_lin, shows that for parity allowed g→g transition Ω =1.05±0.05 and for transitions into electronic and vibronic Q-states, Ω=0.62±0.06 and 0.79±0.1 (depending on wavelength), respectively. Quantum-chemical calculations of both u and g parity excited energy levels of H₂TPP molecule are performed by CNDO/S method and the results are in good agreement with the experimental data.     

Influence of energy transfer on the intensity pattern of vibronic excitation studied by reduced density-matrix theory

Intensity pattern of the vibronic transitions of a molecular dimer consisting of two molecules interacting through the Coulombic coupling is theoretically studied using a reduced density-matrix approach. The monomeric molecules are assumed to be electronic two-state systems. A single vibration mode with a high frequency and a continuous distribution of low-frequency phonons represented by the Ohmic spectral density are coupled to the electronic transition of the respective molecules. The spin-Boson model is employed to include the effect of electron-vibration and electron-phonon couplings. The intermolecular Coulombic coupling is assumed to be weak (inducing the Förster type of energy transfer process). It is found that, in addition to the well-known excitonic shifts, the intensity of the vibronic side bands reduces with the intermolecular coupling strength in the J-aggregate type of dimer while it increases in the H-aggregate type. When the vibronic bands are blurred by the broadening resulting from the coupling of the electrons to the continuous distribution of the phonons, the absorption line shape shows a wide range of variation depending on the strength of the intermolecular coupling.     

Experimental study and interpretation of the emission band situated at 1.65 eV in cinnabar

In this paper we analyse the cathodoluminescence of cinnabar powder which emission appears as a broad band peaked at 1.65 eV at liquid helium temperature.In a previous paper we showed by kinetics measurements that this luminescence was due to a donor-acceptor pair emission mechanism.However the donor-acceptor model was not sufficient to explain the Gaussian shape of the emission band as well as its important width.We show here the influence of a strong phonon coupling by measurements in terms of temperature. Application of both donor-acceptor and vibronic models allows us to interpret this luminescence satisfactorily. We calculate the fundamental parameters of the emission (Bohr half-radius R_B, maximum radiative probability W_MAX, emission energy of the pairs at infinite separation hv_∞).At the end a deconvolution method which takes into account the vibronic influence permits us to calculate the time-resolved spectra and to compare them with the experimental ones.     

The Phosphorescence Excitation Spectrum of Jet-Cooled Xanthione in the Region of the T1←S0 and S1←S0 Absorption Transitions

The ³A₂(nπ*)→¹A₁X (T₁→S₀) phosphorescence excitation spectrum of jet-cooled xanthione was investigated in the region 14 920-17 600 cm⁻¹. The structure observed is shown to be due to the T₁←S₀ absorption and an assignment in terms of the vibronic structure of that band is proposed. A previous assignment of the S₁←S₀ origin is considered in detail and the transition involved is shown to be most probably due to absorption of a vibronic triplet state T_1z,ν7. An alternative but tentative assignment of the S_1,0←S_0,0 transition is suggested. Comparison is made with previous spectroscopic and theoretical work on the molecule and its congeners, 4H-pyran-4-thione and 4H-1-benzopyran-4-thione.     

随机分布烟尘团簇粒子辐射特性研究

基于分形理论,采用蒙特卡罗方法对随机分布的烟尘团簇粒子结构进行了仿真模拟,利用离散偶极子近似(discrete dipole approximation, DDA)方法研究了随机分布的烟尘团簇粒子的辐射特性,分析讨论了分形维数、原始微粒粒径和数量以及复折射率对随机分布烟尘团簇粒子辐射特性的影响.研究表明,在给定分形维数的情况下,烟尘团簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率;原始微粒较小的团簇粒子,当分形维数较小时,吸收截面变化不明显,但当分形维数大于2时,吸收截面骤然增大,然而,对于具有比较大的原始微粒粒径、数量及复折射率的烟尘团簇粒子,吸收截面随着分形维数的增大而单调递减;随着分形维数的增大,团簇粒子的散射截面、消光截面及单次散射反照率均单调递增;从整体上来讲,团簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别,并且这种差别随着分形维数的增大而减小.该工作对研究气溶胶粒子的辐射及气候效应具有重要的科学价值. 关键词： 烟尘团簇粒子 辐射特性 离散偶极子近似方法     

New polaronic excitons in ferroelectric oxides: phenomenological theory

It is shown that three types of new polaronic excitons exist in ferroelectric oxides-charge transfer vibronic excitons (CTVEs). The electron-hole bipolaron pairs are common in all these cases, the difference having to do with the origin of charge transfer-lattice instabilities. These are the cases of the charge transfer and lattice distortions and their vibronic interactions induced in the harmonic (i) and anharmonic (ii) regimes both in the electronic excited state on the one hand, and the (iii) case of the CTVE excited vibronic state induced in the anharmonic regime but related with electronic ground state on the other. All these CTVEs are characterized by strong coupling with good self-localization conditions in separate orientation wells of their multi-well potentials. The relevant phenomenological theory is developed. While the (i) type CTVE is confirmed by luminescence experiments, the (iii) type CTVE with low excitation energy and with metastable intrinsic defect behaviour can be a candidate for the explanation of an order-disorder effect in the classical ferroelectric oxides discovered recently [Phys. Rev. Lett. 90 (2003) 037601].     

Calculation and interpretation of the absorption and fluorescence spectra of indole in the isolated state and aqueous solution

We have calculated the vibronic absorption and fluorescence spectra of the first (¹ L _b ) and second (¹ L _a ) electronic transitions of indole in the isolated state and aqueous solution. The vibrational structure of the absorption and fluorescence spectra has been interpreted. The influence of the aqueous solution on the vibronic spectra has been shown.     

类金属卟啉化合物的共振拉曼光谱与分子振动

概述卟啉及其金属配合物不仅对于生命科学研究具有重要意义，而且在技术领域也有着广泛的应用。卟啉所具有的高对称性（近似为Ｄ４ｈ）和独特的电子结构也引起了光谱学家和理论化学家的广泛兴趣。七十年代以来，共振拉曼光谱（ＲＲＳ）广泛地用于研究金属卟啉及其相应的生...