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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 9733-9740 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Small-angle x-ray and neutron scattering are widely used techniques to study the structure of colloidal particles in the size range up to 100 nm. The indirect Fourier transformation technique is well established to obtain model free real space information, but the interpretation of the results is limited to cases where particle interaction can be neglected. The extended generalized indirect Fourier transform (GIFT) allows one to separate inter- and intraparticle effects, but needs models for the particle interaction. We present the application of three different models for the calculation of interaction effects of charged particles, represented by the structure factor. With this extension, useful real space information can be obtained by the GIFT method for solutions with volume fractions up to about 0.3 without any assumption for the shape of the particles. Only the interaction effects need a model assumption, and the parameters determined from this model can give some additional information. Simulations show that it is impossible to determine charge and ionic strength simultaneously. There exists another ambiguity between the parameter sets for charge, radius, and volume fraction, but we show how this problem can be overcome in most cases. The practical applicability of the method is demonstrated by means of the micellar system CTAB in different concentrations from 1% up to 20% and with varying amounts of added salt to screen the charges and change the particle shape. © 2000 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 1175-1188 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Spherical, cylindrical, and lamellar microstructures were examined by (SANS) in the binary system water (D2O)/pentaethylene glycol mono-perdeutero-n-dodecyl ether (C12D25E5) and in the ternary system (D2O)/pentaethylene glycol mono-n-dodecyl ether (C12E5)/perdeuterated n-octane (C8D18). A model-independent picture of the structures emerges from Fourier transformation of the measured SANS spectra. The data analysis makes no a priori assumptions about the type of structure. Rather, the pair distribution functions obtained are so unique that an unambiguous assignment of the local geometry is possible. The different structures for a given mixture are obtained by changing temperature. For water-rich samples the sequence of spherical, cylindrical, and planar structures is obtained with increasing temperature. For oil-rich samples the same sequence occurs as a function of decreasing temperature. As an important additional result, the scattering length density profile normal to the interface is obtained. The interfacial profile is found to be rather diffuse, apparently because of solvent penetration. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Biochimica et Biophysica Acta (BBA)/Biomembranes 1192 (1994), S. 167-176 
    ISSN: 0005-2736
    Keywords: Antineoplastic ; Ether lipid ; Lipid polymorphism ; Quasi-elastic light scattering ; Small-angle X-ray scattering ; X-ray scattering, small-angle
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Chemistry and Pharmacology , Medicine , Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 1212-1216 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The structure of colloidal particles can be studied with small-angle X-ray and neutron scattering (SAXS and SANS). In the case of randomly oriented systems, the indirect Fourier transformation (IFT) is a well established technique for the calculation of model-free real-space information. Interaction leads to an overlap of inter- and intraparticle scattering effects, preventing most detailed interpretations. The recently developed generalized indirect Fourier transformation (GIFT) technique allows these effects to be separated by assuming various models for the interaction, i.e. the so-called structure factors. The different analytical behaviour of these structure factors from that of the form factors, describing the intraparticle scattering, allows this separation. The mean-deviation surface is defined by the quality of the fit for different parameter sets of the structure factor. Its global minimum represents the solution. The former non-linear least-squares approach has proved to be inefficient and not very reliable. In this paper, the incorporation of the completely different Boltzmann simplex simulated annealing (BSSA) algorithm for finding the global minimum of the hypersurface is presented. This new method increases not only the calculation speed but also the reliability of the evaluation.
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  • 5
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 7 (1974), S. 147-153 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A new iterative procedure for desmearing small-angle scattering data including the three types of resolution errors and arbitrary weighting functions is presented. The statistical errors of the data are taken into account by a `weighted least-squares' approximation, i.e. the accuracy of the data controls the iterative process. The degree of smoothing is dependent on a free smoothing parameter and on the accuracy of the data. The method is not restricted to special types of scattering functions. The termination error is negligible; therefore it is possible to correct parts of scattering distributions. This is of importance for investigations in biological substances where the scattering distribution must be determined in parts with different slit widths. No artificial oscillations are generated in the solution of the integral equation. To ensure the stability of the procedure a criterion for uniform convergence of the iterative process is involved. The results of several numerical tests are shown in the figures. The Fortran program was tested for several months with very satisfactory results.
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  • 6
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 10 (1977), S. 415-421 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A new numerical method is presented for simultaneous smoothing, desmearing and Fourier transformation of X-ray and neutron small-angle scattering data. The method can only be applied to scattering curves from dilute particle systems, i.e. for scattering media whose distance distributions are zero beyond a certain value. The distance distribution of the scattering medium is approximated by a linear combination of about 20 to 30 cubic B-splines. These spline functions have a restricted extension in real space. Their coefficients are adjusted by a weighted least-squares operation so that the series, after being Fourier transformed and smeared according to the geometry and wavelength distribution, represents an optimum smoothed approximation of the experimental data. Tendencies towards oscillations in the least-squares operation are suppressed by a new stabilization routine. The method offers a new possibility for the estimation of the radius of gyration, which is generally superior to the Guinier approximation.
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  • 7
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 7-11 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Small-angle scattering data from polydisperse systems can be evaluated under the assumption that all particles have the same shape and that the size distribution depends only on one linear size parameter R. The shape of the particles is assumed to be known a priori. The corresponding size distribution function for the number of particles Dn(R) or for the volume Dv(R) can be computed from the smeared, unsmoothed scattering data by the indirect transformation method restricting the range of definition of the D(R) functions to a finite range Rmin ≤ Rmax. Rmin may be equal to zero, Rmax is limited by the sampling theorem of the Fourier transformation. The resolution in real space is given by the distance of the knots of the B spline functions approximating the size distribution function. The propagated statistical error band in real space can be computed using the inverted matrix of the normal equations. The method gives satisfactory results even in those cases where the shape of the particles is not known exactly, and is superior to analytical methods if the termination effect is critical.
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  • 8
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 577-584 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The cross-section scattering function and the cross-section distance distribution function are of special interest when lamellar or cylindrical particles are investigated by small-angle scattering techniques with high resolution. These functions can be computed from the unsmoothed, smeared scattering data by the indirect transformation method. This method requires an estimate for the maximum cross-section dimension, which can be found from the distance distribution function of the particle. The influence of finite size, the termination effect and the limits of resolution are discussed using results from simulated experiments.
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  • 9
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 12 (1979), S. 166-175 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The distance distribution function contains all the accessible information about the scattering medium. It is possible to determine the following particle parameters from this function: maximum dimension of the particle, radius of gyration, and zero-angle intensity (molecular weight). The shape of the distance distribution function enables one to distinguish and to recognize directly and rationally the following types of particles: compact globular particles; particles elongated in one dimension, with constant and with variable cross-section; spherical vesicles. The thickness of flat particles as well as the inner and outer diameter of spherical vesicles can be determined from the distance distribution function. Inhomogeneous particles with at least two regions of electron densities differing in their signs show typical features in the distance distribution. These characteristics can be found without further assumptions, independently of the shape of the particle. For concentric shells with different electron densities it is possible to obtain some general information about their structure. Residual concentration effects cannot be overlooked in real space. The formation of dimers can be analyzed with the aid of the distance distribution function.
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  • 10
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 16 (1983), S. 42-46 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The possibilities of obtaining structural information from X-ray small-angle scattering experiments with `white' polychromatic synchrotron radiation using line collimation are investigated by numerical simulation. Theoretical scattering curves of geometrical models were smeared with the appropriate wavelength distributions and slit-length functions, afflicted by statistical noise, and then evaluated by identical methods as normally used for experimental data, as described previously [program ITP; Glatter (1977). J. Appl. Cryst. 10, 415–421]. It is shown that even for a wavelength distribution of 50% half width, the information content is not limited to the parameters derived from the central part of the scattering curves, i.e. the radius of gyration and the zero-angle intensity, but also allows qualitative information on particle shape via the distance distribution function p(r). By a `hinge-bending model' consisting of two cylinders linked together at different angles it is demonstrated that changes in the radius of gyration amounting to less than 5% can be detected and quantified, and the qualitative changes in particle shape be reproduced.
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