Shapes in real space

1
Shapes in real space gt 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
2
Shapes in real space gt 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
3
Shapes in real space gt 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
4
Shapes in real space gt reciprocal space
Approach 1 (small number of parameters) Spheric
al harmonics fcns are angular part of soln to
wave eqn Of the form
5
Shapes in real space gt reciprocal space
Approach 2 (large number of parameters) Represe
nt 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 gt reciprocal space
bead 'annealing'
envelope
7
Shapes in real space gt reciprocal space
bead 'annealing'
8
Shapes in real space gt reciprocal space
bead 'annealing'
envelope
9
Shapes in real space gt reciprocal space
bead 'annealing'
10
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
11
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
12
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-q4 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