Rayleigh Ratio Research Articles

A fast high-resolution method for bearing estimation in shallow ocean

We propose a concise underwater array model based on normal mode theory and put forward a new bearing estimation method using generalized Rayleigh ratio theory to lighten the computation burden of three-dimensional MUSIC method. This method obtains source azimuths by one-dimensional search without prior knowledge of source ranges and depths. So, computational complexity of proposed method decreases exponentially compared with that of maximum likelihood (ML) and three-dimensional MUSIC. Results from simulations and lake experiments turn out to be in close agreement with theoretical analysis.

Determining the simultaneous presence of drug nanocrystals in drug-loaded polymeric nanocapsule aqueous suspensions: A relation between light scattering and drug content

The encapsulation of lipophilic drugs in polymeric nanoparticles can form simultaneously both polymeric nanoparticles and drug nanocrystals. The objective was to detect the presence of nanocrystals in the nanoparticle suspensions using a simple methodology, and to determine if the nanocrystals are formed during preparation or by drug leakage from the particles during storage. Indomethacin was chosen as drug model. Unloaded and drug-loaded (1 mg/mL) nanocapsules showed diameters close to 280 nm and polydispersity lower than 0.20, remaining constant after 120 days. Comparing indomethacin loaded (3 mg/mL) and unloaded formulations, variations in the scattered light depolarization degree indicated the simultaneous presence of nanocrystals and nanocapsules in the suspensions. A relation between the scattered light intensities and the drug precipitation was established. As a function of time, when the decrease in the Rayleigh ratios occurred, the drug contents decreased due to precipitation. On the other hand, when the Rayleigh ratios slightly increase, the drug contents are constant. The nanocrystals formed in the oversaturated formulations, agglomerate and precipitate during storage. When the drug is adsorbed on the nanocapsules, but the system is not oversaturated, no nanocrystal was formed and the formulation is physico-chemically stable at least for 150 days of storage.

Measurement of the effective atomic number of composite materials using Rayleigh to Compton scattering of 279 keV gamma rays

In the present work, to determine the effective atomic number of composite materials of known composition such as brass, bronze, soldering material, perspex and bakelite, the scattering of 279 keV γ-rays is studied using a high-resolution HPGe (high purity germanium) semiconductor detector placed at 50° to the incident beam. The experiment is performed on various elements with atomic number satisfying, 13 ≤Z ≤ 79, for 279 keV incident photons. The intensity ratio of Rayleigh to Compton scattered peaks, corrected for photo-peak efficiency of the γ detector and absorption of photons in the target and air, is plotted as a function of atomic number and constitutes a fit curve. From this fit curve, the respective effective atomic numbers of the composite materials are determined. The agreement of measured values of the effective atomic number with the theoretical calculations is found to be quite satisfactory.

Measurement of effective atomic number of composite materials using scattering of γ-rays

In the present experiment, to determine the effective atomic number of composite materials, the scattering of 145 keV γ-rays is studied using a high-resolution HPGe semiconductor detector placed at 70° to the incident beam. The experiment is performed on various elements of different atomic number, 6⩽ Z⩽64, for 145 keV incident photons. The intensity ratio of Rayleigh to Compton scattered peaks, corrected for photo-peak efficiency of the γ-detector and absorption of photons in the target and air, is plotted as a function of atomic number and constituted a fit curve. From this fit curve, the respective effective atomic numbers of the composite materials are determined. The agreement of measured values of effective atomic number with the theory is found to be quite satisfactory.

Reliability Modeling: Linear Combination and Ratio of Exponential and Rayleigh

The distributions of linear combinations, and ratios of random variables arise explicitly in many reliability problems. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this paper, the exact distributions of alphaX+betaY, and X/Y are derived when X, and Y follow two of the most applied models in reliability. Computer programs for calculating the associated percentage points are also given

Depolarization ratio of Rayleigh scattered radiation by molecules

The depolarization ratios of Rayleigh scattered radiation by molecules has been used to measure the ratio of anisotropic polarizability to isotropic (average) polarizability in the laboratory. The authors have calculated the depolarization ratio for N2, CH3Cl, and H2O from the first principles. It is shown that the depolarization ratio derived from input polarizabilities differs by a factor of about 4 for 1Sigma diatom N2, by a factor of about 2.9 for symmetric top CH3Cl, and by a factor of about 5 for asymmetric top H2O. These large discrepancies arise because in deriving the ratio of anisotropic polarizability to isotropic (average) polarizability from the measured depolarization ratio, the constraints imposed by the conservation of angular momentum have been completely ignored.

Dissipation length scales in turbulent nonpremixed jet flames

Line imaging of Raman/Rayleigh/CO-LIF is used to investigate the energy and dissipation spectra of turbulent fluctuations in temperature and mixture fraction in several flames, including CH 4/H 2/N 2 jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and DLR-B) and piloted CH 4/air jet flames at Reynolds numbers of 13,400, 22,400, and 33,600 (Sandia flames C, D, and E). The high signal-to-noise ratio of the 1D Rayleigh scattering images enables determination of the turbulent cutoff wavenumber from 1D dissipation spectra. The local length scale inferred from this cutoff is analogous to the Batchelor scale in nonreacting flows. The measured thermal dissipation spectra in the turbulent flames are shown to be similar to the model spectrum of Pope for turbulent kinetic energy dissipation. Furthermore, for flames with Lewis number near unity, the 1D dissipation spectra for temperature and mixture fraction are shown to follow nearly the same rolloff in the high-wavenumber range, such that the cutoff length scale for thermal dissipation is equal to or slightly smaller than the cutoff length scale for mixture fraction dissipation. Measurements from the piloted CH 4/air flames are used to demonstrate that a surrogate cutoff scale may be obtained from the dissipation spectrum of the inverse of the Rayleigh signal itself, even when the Rayleigh scattering cross section varies through the flame. This suggests that the cutoff length scale determined from Rayleigh scattering measurements may be used to define the local resolution requirements and optimal data processing procedures for accurate determination of the mean mixture fraction dissipation, based upon Raman scattering measurements or other multiscalar imaging techniques.

Dynamics of Cellulose Whiskers Spatially Trapped in Agarose Hydrogels

The motion of cellulose whiskers trapped in agarose hydrogels is measured by depolarized dynamic light scattering (DDLS) under conditions of optical heterodyning, in which the rigid polymer network provides a static depolarized reference signal. At low concentration in free suspension, the rotational relaxation rate ϑ of the whiskers is decoupled from the osmotic properties of the suspension. When incorporated inside a gel, however, as the agarose concentration increases, ϑ first increases beyond that in the free suspension, reflecting a reduced amplitude of rotational fluctuations of the whiskers due to the repulsive interactions with their surroundings. At the same time, the dynamic light scattering Rayleigh ratio RVH obtained from DDLS decreases with increasing gel concentration. At high gel concentrations, however, ϑ tends to decrease due to the steric hindrance of the network. Except at the lowest whisker concentrations, ϑ is governed by the same fluctuations as those associated with RVH.

A convenient method to determine the Rayleigh ratio with uniform polystyrene oligomers

AbstractThe Rayleigh ratio of toluene at 25°C for a wavelength of 632.8 nm was determined by static light scattering measurement of a certified polystyrene reference material PS 2400 with exactly evaluated or certified mass‐average molecular mass (Mw). At first, static light scattering measurements were carried out for PS 2400 in toluene with a literature value of the Rayleigh ratio of toluene. Then, corrections of degree of depolarization, density fluctuations, and molecular mass dependence of refractive index increment were applied to the observed Mw of PS 2400 to obtain apparent Mw. Finally, from the ratio between the apparent Mw and the certified Mw, the Rayleigh ratio of toluene was reevaluated. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99:1953–1959, 2006

Small-Angle X-ray Scattering and Light Scattering on Lysozyme and Sodium Glycocholate Micelles

Small-angle X-ray scattering (SAXS) together with static (SLS) and dynamic light scattering (DLS) measurements were carried out on aqueous solutions of lysozyme (LY) and of the ionic biological detergent sodium glycocholate (NaGC). Apparent diffusion coefficients (D app), excess Rayleigh ratio, and SAXS spectra were measured for 0.1 M NaGC solutions at different ionic strengths (0.05-0.30 M NaCl). The same data were collected for LY in sodium acetate buffer 50 mM without and with 92 mM NaCl as a function of protein concentration (10-80 g L(-1)). A correlated analysis of SLS data and SAXS spectra was first tested on the LY samples and then extended to the interpretation of the NaGC data to infer information on particle structure and interaction potential. A hard-core (HC) interaction shell of uniform thickness, a screened Coulomb potential of the electric double layer (EDL) or the complete DLVO potential were alternatively used to represent the long-range tail of the interaction potential. Whenever an essentially repulsive tail is expected, all the representations give reasonable results, but the data analysis does not allow the discrimination between the oblate and the prolate symmetries of the NaGC aggregates. The DLVO model allows the interpretation of the data even when the attractive component determines the tail character. With this model an overall fit of the micelle data at all the NaCl concentrations was successfully performed by assuming a simple spherical symmetry of the micelles and invariant values of their ionization degree and Hamaker constant, thus considering just the screening effect of the added electrolyte. Whatever model is used, the results point out that the aggregates are quite hydrated (26-38 water molecules per monomer) and very slightly grow by increasing the NaCl concentration. When spherical symmetry is assumed the aggregate radii for all the samples fall in the range 15-16 A. From the SAXS and SLS, best fitting geometrical parameters, and interparticle structure factor, a D app value was calculated for each sample. An excellent consistence is achieved for LY results. On the contrary, calculated D app values systematically lower than the experimental values are always obtained for the NaGC micelles. Micelle polydispersity and internal dynamics seem to be the most probable reasons of the bad agreement.

Protofibril Formation of Amyloid β-Protein at Low pH via a Non-cooperative Elongation Mechanism

Deposition of the amyloid beta-protein (Abeta) in senile or diffuse plaques is a distinctive feature of Alzheimer's disease. The role of Abeta aggregates in the etiology of the disease is still controversial. The formation of linear aggregates, known as amyloid fibrils, has been proposed as the onset and the cause of pathological deposition. Yet, recent findings suggest that a more crucial role is played by prefibrillar oligomeric assemblies of Abeta that are highly toxic in the extracellular environment. In the present work, the mechanism of protofibril formation is studied at pH 3.1, starting from a solution of oligomeric precursors. By combining static light scattering and photon correlation spectroscopy, the growth of the mass and the size of aggregates are determined at different temperatures. Analysis and scaling of kinetic data reveal that under the studied conditions protofibrils are formed via a single non-cooperative elongation mechanism, not prompted by nucleation. This process is well described as a linear colloidal aggregation due to diffusion and coalescence of growing aggregates. The rate of elongation follows an Arrhenius law with an activation enthalpy of 15 kcal mol(-1). Such a value points to a conformational change of peptides or oligomers being involved in binding to protofibrils or in general to a local reorganization of each aggregate. These results contribute to establishing a clearer relation at the molecular level between the fibrillation mechanism and fibrillar precursors. The observation of a non-cooperative aggregation pathway supports the hypothesis that amyloid formation may represent an escape route from a dangerous condition, induced by the presence of toxic oligomeric species.

Particle Size Distribution in DMPC Vesicles Solutions Undergoing Different Sonication Times

Size distribution of dimyristoylphosphatidylcholine liposome suspensions was investigated by dynamic-light scattering (DLS) as a function of the sonication time (t(s)). Cumulant expansion (second- and third-order) and regularized Laplace inversion (CONTIN) of dynamic single-angle laser light-scattering data were performed. With both methods, the intensity-weighted mean hydrodynamic radius r(I) depended on the investigated lengthscale. The number-weighted mean hydrodynamic radius (r(N)), obtained from CONTIN by modeling dimyristoylphosphatidylcholine vesicles as thin-walled hollow spheres, resulted as independent on the lengthscale. However, the r(N) value obtained from cumulant expansions remained lengthscale-dependent. Therefore, the number-weighted radius distribution function is highly asymmetric. The number-weighted mean radius, the standard deviation, and the number-weighted radius at the peak (r(N)(peak)) all decreased to a plateau when increasing sonication time. At t(s) longer than 1 h, the r(N)(peak) compares well with the radius of unilamellar vesicles in equilibrium with monomers predicted on a thermodynamic basis. The reliability of our analysis is proved by the comparison of experimental Rayleigh ratios with simulated ones, using the normalized number-weighted radius distribution function p(N)(r) determined by DLS data. A perfect agreement was obtained at longer sonication times, and the average aggregation number was determined. At lower t(s) values, simulations did not match experimental data, and this discrepancy was ascribed to the presence of large and floppy unilamellar vesicles with ellipsoidal shapes. Our investigation shows that, from single-angle DLS data, the radius distribution function of the vesicles can only be obtained if p(N)(r) is known.

Amyloid-β Protofibrils Differ from Amyloid-β Aggregates Induced in Dilute Hexafluoroisopropanol in Stability and Morphology

The brains of Alzheimer's disease (AD) patients contain large numbers of amyloid plaques that are rich in fibrils composed of 40- and 42-residue amyloid-beta (Abeta) peptides. Several lines of evidence indicate that fibrillar Abeta and especially soluble Abeta aggregates are important in the etiology of AD. Recent reports also stress that amyloid aggregates are polymorphic and that a single polypeptide can fold into multiple amyloid conformations. Here we demonstrate that Abeta-(1-40) can form soluble aggregates with predominant beta-structures that differ in stability and morphology. One class of aggregates involved soluble Abeta protofibrils, prepared by vigorous overnight agitation of monomeric Abeta-(1-40) at low ionic strength. Dilution of these aggregation reactions induced disaggregation to monomers as measured by size exclusion chromatography. Protofibril concentrations monitored by thioflavin T fluorescence decreased in at least two kinetic phases, with initial disaggregation (rate constant approximately 1 h(-1)) followed by a much slower secondary phase. Incubation of the reactions without agitation resulted in less disaggregation at slower rates, indicating that the protofibrils became progressively more stable over time. In fact, protofibrils isolated by size exclusion chromatography were completely stable and gave no disaggregation. A second class of soluble Abeta aggregates was generated rapidly (<10 min) in buffered 2% hexafluoroisopropanol (HFIP). These aggregates showed increased thioflavin T fluorescence and were rich in beta-structure by circular dichroism. Electron microscopy and atomic force microscopy revealed initial globular clusters that progressed over several days to soluble fibrous aggregates. When diluted out of HFIP, these aggregates initially were very unstable and disaggregated completely within 2 min. However, their stability increased as they progressed to fibers. Relative to Abeta protofibrils, the HFIP-induced aggregates seeded elongation by Abeta monomer deposition very poorly. The techniques used to distinguish these two classes of soluble Abeta aggregates may be useful in characterizing Abeta aggregates formed in vivo.

New methods for measuring macromolecular interactions in solution via static light scattering: basic methodology and application to nonassociating and self-associating proteins

A method for rapid detection and characterization of reversible associations of macromolecules in solution is presented. A programmable dual-syringe infusion pump is used to introduce a solution of time-varying composition into parallel flow cells for concurrent measurement of laser light scattering at multiple angles and ultraviolet–visible absorbance. An experiment lasting less than 15 min produces a large and information-rich set of data, consisting of several thousand values of the Rayleigh ratio as a function of solute concentration(s) and scattering angle. Using a novel treatment of the data, the entire data set may be equally rapidly analyzed in the context of models for self-association. Validation experiments conducted on previously characterized nonassociating and self-associating proteins yielded robust values for molecular weights in the range 10–330 kDa and equilibrium association constants for dimer formation in the range 2 × 10 3–6 × 10 5 M −1.

Thermodynamic models of the system with internal variables: fluctuation and relaxation phenomena

The results on modeling supramolecular ordering in molecular mixtures, selforganized by non-covalent molecular interactions like H-bonding and unified description of their thermodynamic, dielectric, optic, and kinetic properties have been outlined. The interrelations between thermodynamic functions (Gibbs energy, enthalpy, entropy), dielectric (permittivity), optic (refractive index and its fluctuation derivatives, defining Rayleigh light scattering) and kinetic properties of mixtures and microscopic characteristics of supramolecular species are characterised. The main attention is given to formulating of the extended thermodynamic models of the system with internal variables with emphasis for describing the fluctuation and relaxation phenomena in a matter. The general fluctuation theory for mixtures on the basis of the grand canonical ensemble, taking into account the full set of the fluctuating parameters is considered, and the correlation of the density and concentration fluctuations in mixtures was established. The results on the fluctuations of thermodynamic parameters and permittivity (refractive index) in relation with the Rayleigh light scattering are presented. The applications of the non-ideal mixture models (non-ideal mixture of aggregates) for studying Rayleigh light scattering and especially to the concentration one are outlined. The procedure for obtaining thermodynamic potentials of the non-equilibrium states of a matter characterised by the internal parameters of the different tensor dimension from the statistical-mechanical ensembles is developed. The expressions for the fluctuating of Helmgoltz energy F, and Gibbs energy G for the closed systems, as well as the grand thermodynamic potential Ω for the opened systems were derived. Models with discrete number of states, described by the scalar internal parameters such as extents of quasichemical processes and the tensor internal variables, describing the anisotropic states of a system are presented. The tensor affinities of the extended quasichemical processes were introduced. General relationships for the parameters of the fluctuating anisotropic states of liquids were established. Fluctuation of the external and internal thermodynamic parameters in relaxing media, and contributions of the fluctuation of those to thermodynamic functions, Rayleigh ratio, and relaxation properties of the non-ideal mixtures have been established. The unified approach has been developed both for describing and predicting a set of macroscopic properties of mixture, defined by different molecular characteristics on the basis of the extended quasichemical models. Macroscopic manifestations of the internal processes in properties of the liquid mixtures have been outlined.

Depolarization behaviour of dilute polymer solutions: II. Angular dependence and analyzer absorption

AbstractStudy of the depolarization behaviour of dilute polymer solutions leads to determination of the Cabannes factor, necessary for correcting the Rayleigh ratio used in light‐scattering calculations for deviations due to anisotropy. We present here a method to determine the Cabannes factor for polymers as a simultaneous function of both scattering angle and molar mass, accomplished by coupling size‐exclusion chromatography with depolarization multi‐angle light scattering (SEC/D‐MALS). The depolarization behaviour of brominated polystyrene (PSBr), previously studied at a right‐angle geometry, is seen to possess a non‐trivial angular dependence in addition to being a function of molar mass. We also demonstrate initial attempts at correcting SEC/D‐MALS results for absorption of light by the Polaroid filters that act as analyzers in the optical train of the system. Copyright © 2003 Society of Chemical Industry

Phase Transition in Poly(N-isopropylacrylamide) Hydrogels Induced by Phenols

Poly(N-isopropylacrylamide) gels swollen at 20 °C in aqueous solutions of weak aromatic acids (phenol and resorcinol) display a volume transition at aromatic acid concentrations close to 50 mM. Owing to selective solvation, phenol exhibits an excess equilibrium concentration inside the swollen gels that is 7% greater than that in the surrounding bath, while for resorcinol the excess is 20%. The elastic modulus G of the gels at small strains follows the expected behavior of standard network theory, i.e., G ∝ φ1/3, where φ is the polymer volume fraction. Dynamic light scattering measurements, in which light from the thermodynamic fluctuations is heterodyned by that from the large-scale network heterogeneities, show that the collective diffusion coefficient Dc decreases at high aromatic content, while the Rayleigh ratio of the dynamic component of the scattering intensity, Rdyn, increases. No divergence of Rdyn close to the transition is observed, however, in accord with first-order nature of the transition....

Dilute-Solution Properties of Regenerated Silk Fibroin

Viscosity and light-scattering measurements are performed on two dilute aqueous solutions of regenerated silk fibroin (RSF) of Bombyx mori silkworms obtained by dialysis against 6 M LiBr and pure water solutions at ambient temperature. The reduced viscosity of the RSF solutions in 6 M LiBr is found to decrease with decreasing polymer concentration C down to a certain concentration Cc but to increase below Cc. Static light scattering (SLS) for the same system shows that C/Rθ, where Rθ is the Rayleigh ratio, is at its minimum at near Cc. Dynamic light scattering (DLS) has revealed that silk fibroin molecules are present as a mixture of single molecules and aggregates in such a way that the majority of fibroin molecules are present as multichain aggregates above Cc and they start to dissociate below Cc, where most of them become isolated chains. Such a dissociation process of fibroin aggregates is not observed for the RSF solutions in pure water, in which multichain aggregates are dominantly present at higher C and persistently observed even at very low concentration. The aggregation behavior of RSF in both solutions is extensively discussed by combining SLS and DLS data.

Solution Characterization of Monodisperse Atactic Polystyrenes by Static and Dynamic Light Scattering

Anionically polymerized polystyrene standards have been characterized by static and dynamic light scattering in toluene at 25°C. The molecular weights ranged from 3000 to two million g/mol. An appropriate standard for light scattering intensity was developed and the absolute Rayleigh ratio for toluene was determined for the experimental conditions. The molecular weight dependence of the second virial coefficient A 2 could be represented as a power law. The present results are in good agreement with previous measurements of A 2 . For the higher molecular weight polymers, the mean-square radius of gyration was determined. The present results could also be represented as a power law, which was in good agreement with previous results. Dynamic light scattering was analyzed to obtain the mutual-diffusion coefficient as a function of concentration and molecular weight. These results were then used to obtain the self-diffusion coefficient, hydrodynamic radius, and virial coefficient for the mutual-diffusion coefficient. Hydrodynamic radii could be represented as a power law, which was also in good agreement with previous reports. The virial coefficient for the mutual friction was calculated as well. The relationship between molecular weight distribution and the polydispersity index determined from dynamic light scattering was calculated and compared to actual data. The samples used here conformed to the manufacturers' reported weight to number-average molecular weight ratios.

Experimental test of the Rayleigh-Debye-Gans theory for light scattering by fractal aggregates.

Calibrated measurements of optical (lambda = 488-nm) scattering cross sections, in the form of Rayleigh ratios, are presented for two fractal aggregate aerosols. The aggregates have radii of gyration of approximately 280 nm, fractal dimensions of approximately 1.75, and monomer sizes of approximately 20 nm with approximately 150 monomers per cluster. One aerosol was composed of vitreous SiO2 with a refractive index of 1.46, the other of anatase TiO2 with a refractive index of 2.61. We found good agreement with the Rayleigh-Debye-Gans prediction for the scattering cross section of fractal aggregates.