Transcript polymers
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