1. 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

2. 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

3. 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

4. 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

5. 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:

6. Shapes in real space ––> reciprocal space
envelope
bead 'annealing'

7. Shapes in real space ––> reciprocal space
bead 'annealing'

8. Shapes in real space ––> reciprocal space
envelope
bead 'annealing'

9. Shapes in real space ––> reciprocal space
bead 'annealing'

10. 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

11. 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

12. 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

13. Syndiotactic polystyrene
Semicrystalline PS
Propose absence of peaks due to nearly identical scattering densities of amorphous & crystalline regions
High temperature saxs measurements done

14. Syndiotactic polystyrene
Semicrystalline PS
Propose absence of peaks due to nearly identical scattering length densities of amorphous & crystalline regions
High temperature saxs measurements done

15. Syndiotactic polystyrene
Semicrystalline PS
lamellar thickness = 18 nm
averages of intensity
data around azimuth

16. Syndiotactic polystyrene
Semicrystalline PS