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Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000)) Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
semicrystalline poly(3-hydroxybuyrate)semicrystalline poly(3-hydroxybuyrate)
Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000)) Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
semicrystalline poly(3-hydroxybuyrate)semicrystalline poly(3-hydroxybuyrate)
note amorphous scattering regionnote amorphous scattering region
Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000)) 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
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)) 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 peaksextensive amounts of crystal imperfectionsthermal motion
Degree of crystallinity
Pattern consists of relatively sharp crystalline peaks +amorphous scattering
Comparing intensities of the two ––> % crystallinity
Problems:
small crystallite size broadens peaksextensive amounts of crystal imperfectionsthermal motion
Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000)) 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:
guessmeasure 100% amorphous specimen
Degree of crystallinity
Pattern consists of relatively sharp crystalline peaks +amorphous scattering
Comparing intensities of the two ––> % crystallinity
Methods for separation:
guessmeasure 100% amorphous specimen
Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000)) 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
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)) 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
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)) 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 phaseb = scattering length (like scattering factor)D(s) = distortion factor
Ruland's method
Addresses problems of crystalline imperfections &data truncation
Ncr = no. atoms in crystalline phaseb = scattering length (like scattering factor)D(s) = distortion factor
Polymers Polymers
Ncr = no. atoms in crystalline phaseb = scattering length (like scattering factor)D(s) = distortion factor
D(s) accounts for "imperfections of the first kind"
Ncr = no. atoms in crystalline phaseb = scattering length (like scattering factor)D(s) = distortion factor
D(s) accounts for "imperfections of the first kind"
average lattice no average latticeaverage lattice no average lattice
Polymers Polymers
B is an adjustable parameter in the procedure
Choose B so that x remains constant irrespective of integration limit
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)) Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))
semicrystalline polydimethylpropiolactonesemicrystalline polydimethylpropiolactone
How was this photo taken?
Why does it look like this?
How was this photo taken?
Why does it look like this?
Polymers Polymers
Define two sets of coords for pole wz taken as fiber axis (fiber drawing) or MD (blow molding)
Define two sets of coords for pole wz taken as fiber axis (fiber drawing) or MD (blow molding)
Polymers Polymers
In transmission In transmission
Polymers Polymers
Probability of finding w in any small range is t() d d
t() is orientation distribution function
t() normalized such that
Probability of finding w in any small range is t() d d
t() is orientation distribution function
t() normalized such that
Polymers Polymers
Probability of finding w in any small range is t() d d
t() is orientation distribution function
t() normalized such that
Probability of finding w in any small range is t() d d
t() is orientation distribution function
t() normalized such that
Polymers Polymers
Average pole orientation could be represented byAverage pole orientation could be represented by
Polymers Polymers
Average pole orientation could be represented byAverage 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
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 Polymers
f is the Hermans orientation parameter
This f does not completely specify crystallite orientation
f is the Hermans orientation parameter
This f does not completely specify crystallite orientation
Polymers 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 is the Hermans orientation parameter
This f does not completely specify crystallite orientation
Need two parameters – fa & fb for two perpendicular poles
Polymers 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 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 || zf = 0 if randomf = –1/2 if perpendicular to z
f = 1 if || zf = 0 if randomf = –1/2 if perpendicular to z
Polymers Polymers
If t() is needed, can be expanded as series of spherical harmonics If t() is needed, can be expanded as series of spherical harmonics
wherewhere
Polymers Polymers
Polymers Polymers
Polymers Polymers
