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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 140-156 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general expression for the scattered intensity by populations of Rayleigh–Debye–Gans (RDG) spheroids has been derived for single and independent scattering from nonabsorbing monodisperse particles. The form factor—which contains information on the particle size, shape, and orientation—and the orientation distribution function are expanded in terms of a complete set of spherical harmonics for the polar and azimuthal angles, θ and φ. These expansions lead to a systematic solution procedure for the inverse problem of determining the orientation distribution function for populations of RDG spheroids from scattered intensities in two dimensions. With Fourier sine and cosine transforms of the form factor with respect to φ, the two-dimensional problem (θ, φ) is reduced to several linear one-dimensional problems at various scattering angles, θ. A quadratic optimization routine is used to solve these problems for obtaining the most pertinent orientation distribution coefficients. As an example, the form factors have been calculated for populations of RDG spheroids undergoing rotary diffusion. The diffusion time, initial orientation, aspect ratio, and particle volume have been examined in these simulations with two-dimensional contour plots. Changing the incident beam polarization changes the scattered intensity contours but not the form factor contours, hence yielding no additional information. The inverse problem has been solved and tested with simulated data from azimuthally symmetric populations of spheroids. The performance of the inverse algorithm has been examined for various particle aspect ratios, sizes, and angles, θ. With error-free simulated data, the orientation distribution functions can be precisely determined over the complete angular range from data obtainable over only a small angular range. These results show the robustness of the new approach. When up to 1% random error is introduced in the simulated intensity data, the solution to the inverse problem becomes less precise but is still reasonable. The implications of the inverse algorithm for analyzing experimental data are discussed.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 3600-3611 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The inverse problem of determining orientation distributions of monodisperse spheroidal particles from single and independent Rayleigh–Debye–Gans (RDG) light scattering was formulated previously [C. S. Buehler, J. M. Caruthers, and E. I. Franses, J. Chem. Phys. 92, 140 (1990)] and solved numerically only for azimuthally symmetric orientation distributions. In this paper, the problem is solved for general orientation distributions and is tested experimentally. A new instrument capable of thousands of simultaneous two-dimensional scattering measurements, over the polar (6°–30°) and the azimuthal scattering angles, is described. Measurements were done on oriented prolate polystyrene spheroidal particles, of volume 0.44 μm3 and aspect ratio 3.5, embedded in a polyvinylalcohol matrix. From the measurements and the solution of the inverse problem, reasonable orientation distribution functions were calculated. Simulations and data support the use of the technique for thoroughly probing orientations in dilute dispersions of RDG-type spheroidal particles in either liquid or solid media.
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  • 3
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Industrial & engineering chemistry research 31 (1992), S. 2647-2651 
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Journal of chemical information and modeling 35 (1995), S. 188-195 
    ISSN: 1520-5142
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 2422-2428 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The general direct and inverse problems of turbidity of spheroids which are monodisperse in size and shape and fall in the Rayleigh–Debye–Gans (RDG) and Rayleigh scattering regimes are solved analytically. The theory applies to single and independent scattering from nonabsorbing optically isotropic particles. From turbidity measurements at one incident direction, one wavelength, and three incident polarizations, it is shown that three functions or moments of the orientation distribution functions can be obtained for both regimes. For RDG particles, use of turbidity spectra (at multiple wavelengths) can recover more information, i.e., more moments. The complete orientation distribution function, with no empirical fits, can in principle be obtained from turbidity spectra at many incident directions for the RDG regime, but not for the Rayleigh regime. The approach used is more general, and should provide potentially much more orientation information than measurements of conservative linear dichroism.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Macromolecules 26 (1993), S. 1841-1847 
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 5929-5944 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A mathematically exact method is presented for sampling conformations of polymer molecules in an external field with fixed energy or energy range in accord with the formulation of statistical mechanics for a microcanonical ensemble. As a consequence, conformations of negligible Boltzmann weight can be selectively eliminated from simulations for efficient calculation of macroscopic polymer properties. The method is applicable for conformations that are described by a stochastic differential equation along the contour length in the field-free situation. It is based on the concept of a stochastic bridge process for which a new stochastic differential equation is derived that has stipulations at both ends of the process. This idea is exploited on a pair of stochastic differential equations in the conformation vector X and an augmented variable Z which represents the running Boltzmann weight in the given field, transforming to a new pair of equations for which the terminal Boltzmann weight can be arbitrarily stipulated. The stochastic equation for the bridge involves solving the Fokker–Planck equation for the original stochastic pair. We demonstrate the method on the conformation of a "Brownian" polymer in a quadratic external field of varying strength. The stochastic differential equations for the bridge process in this case can be derived analytically. Sample conformations are displayed that satisfy exactly energy constraints either at fixed values or within a stipulated range. It is shown that polymer properties can be computed more efficiently and accurately with the bridge process simulations than by unconstrained process simulations. The bridge process approach presented here must be distinguished from other approaches such as umbrella sampling methods because of the former's ability to sample conformations exactly with stipulated energy constraints. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 6371-6384 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The inverse problem of estimating the orientation distribution of monodisperse nonspherical Rayleigh particles via electromagnetic scattering is systematically analyzed. Using all the possible angular and polarization information available in Rayleigh scattering, at most 15 averages or moments of the orientation distribution function can be obtained. For monodisperse axisymmetric Rayleigh particles with a plane of symmetry normal to the axis (spheroids, finite cylinders, etc.), the orientation distribution function is expanded in terms of the complete set of surface harmonics. The first 15 coefficients of the expansion can be determined unambiguously without any assumption about the form of the distribution. No additional coefficients can be determined with all conceivable experiments. For distributions which are azimuthally symmetric around the direction of incident light, only three coefficients are nonzero. Average orientation and structure factors are calculated in terms of these coefficients. Computer simulation of experimental errors reveals certain instrument precision requirements for successful measurements. The procedure is applied to a simulated example of spheroids whose orientation distribution is determined by rotational Brownian diffusion.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 1531-1545 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have determined what orientation and size information can be obtained for colloidal dispersions of Rayleigh particles from light scattering measurements. For noninteracting particles and single scattering, a maximum of 15 moments of the orientation/size distribution can be obtained by using a minimum of (i) three distinct orientations of linearly polarized incident light; (ii) three scattering angles θ in one scattering plane; and (iii) three different polarization orientations of the detector. The information obtainable from less complete experiments has also been determined. Specifically, only six combinations of the above fifteen moments can be determined if unpolarized incident light is used. For polydisperse systems with random orientation, two moments of the size distribution can be determined. For polydisperse particles of the same orientation, (i) the orientation and three moments can be determined for axisymmetric particles and (ii) the orientation and six moments can be determined for nonaxisymmetric particles. The results provide guidance for design of instrumentation and experiments.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 51 (1994), S. 661-668 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The self-diffusion coefficient of dodecane in cross-linked polystyrene was measured using pulsed gradient spin echo nuclear magnetic resonance (PGSE-NMR) spectroscopy. The concentration and temperature dependence of the diffusion coefficient was analyzed by the Fujita and Vrentas-Duda models. Parameters describing the Fujita model were determined from fitting of diffusion data to the PVT behavior of the system. Parameters describing the Vrentas-Duda model were determined from the analysis of the viscosity of dodecane, the viscoelastic relaxation properties, and the glass transition temperature of polystyrene as well as from the diffusion coefficient of the system, measured from independent experiments. Both the Fujita and Vrentas-Duda models described well the concentration and temperature dependence of the diffusion coefficient. Mutual diffusion coefficients were determined from these results. © 1994 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
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