Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
semicrystalline poly(3-hydroxybuyrate)
Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
semicrystalline poly(3-hydroxybuyrate)
note amorphous scattering region
Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
Degree of crystallinity
Pattern consists of relatively sharp crystalline peaks +
amorphous scattering
Comparing intensities of the two ––> % crystallinity
Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
Degree of crystallinity
Pattern consists of relatively sharp crystalline peaks +
amorphous scattering
Comparing intensities of the two ––> % crystallinity
Problems:
small crystallite size broadens peaks
extensive amounts of crystal imperfections
thermal motion
Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
Degree of crystallinity
Pattern consists of relatively sharp crystalline peaks +
amorphous scattering
Comparing intensities of the two ––> % crystallinity
Methods for separation:
guess
measure 100% amorphous specimen
Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
Total scattering by amorphous & crystalline phases
Q is called the invariant
s = diffraction vector
Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
Total scattering by amorphous & crystalline phases
Q is called the invariant
(r) is electron density distribution
Degree of crystallinity given by
Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
Ruland's method
Addresses problems of crystalline imperfections &
data truncation
Ncr = no. atoms in crystalline phase
b = scattering length (like scattering factor)
D(s) = distortion factor
Polymers
Ncr = no. atoms in crystalline phase
b = scattering length (like scattering factor)
D(s) = distortion factor
D(s) accounts for "imperfections of the first kind"
average lattice
no average lattice
Polymers
B is an adjustable parameter in the procedure
Choose B so that x remains constant irrespective of integration limit
Polymers
(see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
semicrystalline polydimethylpropiolactone
How was this photo taken?
Why does it look like this?
Polymers
Define two sets of coords for pole w
z taken as fiber axis (fiber drawing) or MD (blow molding)
Polymers
In transmission
Polymers
Probability of finding w in any small  range is t() d d
t() is orientation distribution function
t() normalized such that
Polymers
Probability of finding w in any small  range is t() d d
t() is orientation distribution function
t() normalized such that
Polymers
Average pole orientation could be represented by
Polymers
Average pole orientation could be represented by
However, Hermans proposed
where P2 is the second order Legendre fcn
f is the Hermans orientation parameter
= 1 if || z
= 0 if random
= –1/2 if perpendicular to z
Polymers
f is the Hermans orientation parameter
This f does not completely specify crystallite orientation
Polymers
f is the Hermans orientation parameter
This f does not completely specify crystallite orientation
Need two parameters – fa & fb for two perpendicular poles
Polymers
f is the Hermans orientation parameter
This f does not completely specify crystallite orientation
Need two parameters – fa & fb for two perpendicular poles
f = 1 if || z
f = 0 if random
f = –1/2 if perpendicular to z
Polymers
If t() is needed, can be expanded as series of spherical harmonics
where
Polymers
Polymers
Polymers