Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000))

1. Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000)) semicrystalline poly(3-hydroxybuyrate)

2. Polymers (see Roe: Methods of X-ray and Neutron Scattering in Polymer Science (2000)) semicrystalline poly(3-hydroxybuyrate) note amorphous scattering region

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Polymers B is an adjustable parameter in the procedure Choose B so that x remains constant irrespective of integration limit

11. 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?

12. Polymers Define two sets of coords for pole w z taken as fiber axis (fiber drawing) or MD (blow molding)

13. Polymers In transmission

14. Polymers Probability of finding w in any small range is t() d d t() is orientation distribution function t() normalized such that

15. Polymers Probability of finding w in any small range is t() d d t() is orientation distribution function t() normalized such that

16. Polymers Average pole orientation could be represented by

17. 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

18. Polymers f is the Hermans orientation parameter This f does notcompletely specify crystallite orientation

19. Polymers f is the Hermans orientation parameter This f does notcompletely specify crystallite orientation Need two parameters – fa & fb for two perpendicular poles

20. Polymers f is the Hermans orientation parameter This f does notcompletely 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

21. Polymers If t() is needed, can be expanded as series of spherical harmonics where

22. Polymers

23. Polymers

24. Polymers