shapes in real space ––> reciprocal space
DESCRIPTION
Shapes in real space ––> reciprocal space. (see Volkov & Svergun, J. Appl. Cryst. (2003) 36 , 860-864. Uniqueness of ab initio shape determination in small-angle scattering ) Can compute scattering patterns for different shape particles for isotropic dilute monodisperse systems. - PowerPoint PPT PresentationTRANSCRIPT
Shapes in real space ––> reciprocal space(see Volkov & Svergun, J. Appl. Cryst. (2003) 36, 860-864. Uniqueness of ab initio
shape determination in small-angle scattering)
Can compute scattering patterns for different shape particles for isotropic dilute monodisperse systems
Shapes in real space ––> reciprocal space(see Volkov & Svergun, J. Appl. Cryst. (2003) 36, 860-864. 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
Shapes in real space ––> reciprocal space(see Volkov & Svergun, J. Appl. Cryst. (2003) 36, 860-864. 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
Shapes in real space ––> reciprocal spaceApproach 1 (small number of parameters)
Spherical harmonics fcns are angular part of soln to wave eqn
Of the form
Shapes in real space ––> reciprocal space
Approach 2 (large number of parameters)
Represent particle shape by assembly of beads in confinedvolume (sphere)
Beads are either particle (X =1) or 'solvent' (X =0)
To get scattered intensity:
Shapes in real space ––> reciprocal space
bead 'annealing'envelope
Shapes in real space ––> reciprocal space
bead 'annealing'
Shapes in real space ––> reciprocal space
bead 'annealing'envelope
Shapes in real space ––> reciprocal space
bead 'annealing'
Syndiotactic polystyrene(see Barnes, McKenna, Landes, Bubeck, & Bank, Polymer Engineering & Science (1997) 37, 1480. Morphology of syndiotactic polystyrene as examined by small angle scattering)
Semicrystalline PS
Syndiotactic polystyrene(see Barnes, McKenna, Landes, Bubeck, & Bank, Polymer Engineering & Science (1997) 37, 1480. Morphology of syndiotactic polystyrene as examined by small angle scattering)
Semicrystalline PS
Expect peaks in scattering data typical of lamellar structure
Syndiotactic polystyrene(see Barnes, McKenna, Landes, Bubeck, & Bank, Polymer Engineering & Science (1997) 37, 1480. 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 dueto mushy interface
Syndiotactic polystyreneSemicrystalline PS
Propose absence of peaks due to nearly identical scattering densities of amorphous & crystalline regions
High temperature saxs measurements done
Syndiotactic polystyreneSemicrystalline PS
Propose absence of peaks due to nearly identical scattering length densities of amorphous & crystalline regions
High temperature saxs measurements done
Syndiotactic polystyreneSemicrystalline PS
lamellar thickness = 18 nm
averages of intensity data around azimuth
Syndiotactic polystyreneSemicrystalline PS