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Shapes in real space ––> reciprocal space
(see Volkov & Svergun, J. Appl. Cryst. (2003) 36, Uniqueness of ab initio shape determination in small-angle scattering) Can compute scattering patterns for different shape particles for isotropic dilute monodisperse systems
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Shapes in real space ––> reciprocal space
(see Volkov & Svergun, J. Appl. Cryst. (2003) 36, Uniqueness of ab initio shape determination in small-angle scattering) Can compute scattering patterns for different shape particles for isotropic dilute monodisperse systems Approach 1 (small number of parameters) Represent particle shape by an envelope fcn – spherical harmonics
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Shapes in real space ––> reciprocal space
(see Volkov & Svergun, J. Appl. Cryst. (2003) 36, Uniqueness of ab initio shape determination in small-angle scattering) Can compute scattering patterns for different shape particles for isotropic dilute monodisperse systems Approach 1 (small number of parameters) Represent particle shape by an envelope fcn – spherical harmonics Spherical harmonics fcns are angular part of soln to wave eqn Of the form
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Shapes in real space ––> reciprocal space
Approach 1 (small number of parameters) Spherical harmonics fcns are angular part of soln to wave eqn Of the form
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Shapes in real space ––> reciprocal space
Approach 2 (large number of parameters) Represent particle shape by assembly of beads in confined volume (sphere) Beads are either particle (X =1) or 'solvent' (X =0) To get scattered intensity:
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Shapes in real space ––> reciprocal space
envelope bead 'annealing'
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Shapes in real space ––> reciprocal space
bead 'annealing'
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Shapes in real space ––> reciprocal space
envelope bead 'annealing'
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Shapes in real space ––> reciprocal space
bead 'annealing'
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Syndiotactic polystyrene
(see Barnes, McKenna, Landes, Bubeck, & Bank, Polymer Engineering & Science (1997) 37, Morphology of syndiotactic polystyrene as examined by small angle scattering) Semicrystalline PS
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Syndiotactic polystyrene
(see Barnes, McKenna, Landes, Bubeck, & Bank, Polymer Engineering & Science (1997) 37, Morphology of syndiotactic polystyrene as examined by small angle scattering) Semicrystalline PS Expect peaks in scattering data typical of lamellar structure
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Syndiotactic polystyrene
(see Barnes, McKenna, Landes, Bubeck, & Bank, Polymer Engineering & Science (1997) 37, Morphology of syndiotactic polystyrene as examined by small angle scattering) Semicrystalline PS Expect peaks in scattering data typical of lamellar structure non-q–4 slope due to mushy interface
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Syndiotactic polystyrene
Semicrystalline PS Propose absence of peaks due to nearly identical scattering densities of amorphous & crystalline regions High temperature saxs measurements done
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Syndiotactic polystyrene
Semicrystalline PS Propose absence of peaks due to nearly identical scattering length densities of amorphous & crystalline regions High temperature saxs measurements done
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Syndiotactic polystyrene
Semicrystalline PS lamellar thickness = 18 nm averages of intensity data around azimuth
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Syndiotactic polystyrene
Semicrystalline PS
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