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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

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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 Presentation

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Page 1: Shapes in real space ––> reciprocal space

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

Page 2: Shapes in real space ––> reciprocal space

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

Page 3: Shapes in real space ––> reciprocal space

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

Page 4: Shapes in real space ––> reciprocal space

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

Page 5: Shapes in real space ––> reciprocal space

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:

Page 6: Shapes in real space ––> reciprocal space

Shapes in real space ––> reciprocal space

bead 'annealing'envelope

Page 7: Shapes in real space ––> reciprocal space

Shapes in real space ––> reciprocal space

bead 'annealing'

Page 8: Shapes in real space ––> reciprocal space

Shapes in real space ––> reciprocal space

bead 'annealing'envelope

Page 9: Shapes in real space ––> reciprocal space

Shapes in real space ––> reciprocal space

bead 'annealing'

Page 10: Shapes in real space ––> reciprocal space

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

Page 11: Shapes in real space ––> reciprocal space

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

Page 12: Shapes in real space ––> reciprocal space

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

Page 13: Shapes in real space ––> reciprocal space

Syndiotactic polystyreneSemicrystalline PS

Propose absence of peaks due to nearly identical scattering densities of amorphous & crystalline regions

High temperature saxs measurements done

Page 14: Shapes in real space ––> reciprocal space

Syndiotactic polystyreneSemicrystalline PS

Propose absence of peaks due to nearly identical scattering length densities of amorphous & crystalline regions

High temperature saxs measurements done

Page 15: Shapes in real space ––> reciprocal space

Syndiotactic polystyreneSemicrystalline PS

lamellar thickness = 18 nm

averages of intensity data around azimuth

Page 16: Shapes in real space ––> reciprocal space

Syndiotactic polystyreneSemicrystalline PS