1. Chapter 6. The Crystalline State

2. 6.1 General Considerations

3. 6.1.1 Historical Aspects 6.1.2 Melting Phenomena Staudinger Macromolecular Hypothesis Herman Mark Father of Polymer Science Ziegler and Natta stereospecific polymers

8. 6.1.3 Example Calculation of Percent Crystallinity

9. 6.2 Methods of Determining Crystal Structure 6.2.1 A Review of Crystal Structure 6.2.2 X-Ray Methods

10. 6.2.3 Electron Diffraction of Single Crystals 6.2.4 Infrared Absorption 6.2.5 Raman Spectra

11. 6.3 The Unit Cell of Crystalline Polymers 6.3.1 Polyethylene

12. 6.3.2 Other Polyolefin Polymers 3131 7272 4141

14. 6.3.3 Polar Polymers and Hydrogen Bonding

17. 6.3.4 Polymorphic Forms of Cellulose 6.3.5 Principles of Crystal Structure Determination Four different polymorphic forms of crystalline cellulose exist. Experiments do not yield the crystal structure; only researchers’ imagination and hard work yield that. Natta and Corradini postulated three principles for the determination of crystal structures: 1.The equivalence postulate. 2.The minimum energy postulate. 3.The packing postulate.

18. 6.4 Structure of Crystalline Polymers 6.4.1 The Fringed Micelle Model According to the fringed micelle model, the crystallites are about 10 nm long. crystalline amorphous The chains are long enough to pass several crystallites, binding them together.

19. 6.4.2 Polymer Single Crystals 6.4.2.1 The Folded-Chain Model 1957 Keller prepared single crystals of PE. 10~20 nm thick (contour length ~ 200 nm) Adjacent reentry

20. If the polymer solution is slightly more concentrated, or if the crystallization rate is increased, the polymers will crystallize in the form of various twins, spirals, and dendritic structures, which are multilayered.

22. PEO-b-PS : the crystals reject the amorphous portion (PS), which appears on the surfaces of the crystals.

23. 6.4.2.2 The Switchboard Model In the switchboard model the chains do not have a reentry into the lamellae by regular folding; they rather reenter more or less randomly.

24. 6.5 Crystallization From the Melt 6.5.1 Spherulitic Morphology Maltese cross When the spherulites are nucleated simultaneously, the boundaries between them are straight. However, when the spherulites have been nucleated at different times, their boundaries form hyperbolas.

25. Spherulites are composed of individual lamellar crystalline plates.

26. Small-angle light scattering  max is the angle at which the intensity maximum occurs is the wavelength U is radial direction R is the radius of the spherulite

30. 6.5.2 Mechanism of Spherulite Formation 6.5.3 Spherulites in Polymer Blends and Block Copolymers

32. 6.5.4 Percent Crystallinity in Polymers

35. Where A c and Aa represent the area under the Bragg diffraction line.

36. 6.6 Kinetics of Crystallization 6.6.1 Experimental Observations of Crystallization Kinetics

40. 6.6.2 Theories of Crystallization Kinetics 6.6.2.1 The Avrami Equation

46. 6.6.2.2 Keith-Padden Kinetics of Spherulitic Crystallization

48. Where  F* is the free energy of formation of a surface nucleus of critical size,  E is the free energy of activation for a chain crossing the barrier to the crystal Where  is the diffusion coefficient for impurity in the melt and G reprents the radial growth rate of a spherulite. The quantity , whose dimension is that of length, determines the lateral dimensions of the lamellae. Thus  is a measure of the internal structure of the spherulite, or its coarseness.  = D/G

49. 6.6.2.3 Hoffman’s Nucleation Theory

50. 6.6.2.4 Example Clculation of the Fold Surface Free Energy

51. 6.6.2.5 Three Regimes of Crystallization Kinetics

56. 6.7 The Reentry Problem in Lamellae 6.7.1 Infrared Spectroscopy 6.7.2 Carbon-13 NMR 6.7.3 Smal-Angle Neutron Scattering 6.7.3.1 Single-Crystal Studies 6.7.3.2 Melt-Crystallized Polymers

66. 6.7.4 Extended Chain Crystals

68. 6.8 Thermodynamics of Fusion

70. 6.8.1 Theory of Melting Point Depression

72. 6.8.2 Example Calculation of Melting Point Depression

73. 6.8.3 Experimental Thermodynamic Parameters 6.8.4 Entropy of Melting

75. 6.8.5 The Hoffman-Weeks Equilibrium Melting Temperature

76. 6.9 Effect of Chemical Structure on the Melting Temperature

79. 6.10 Fiber Formation and Structure

82. 6.10.1 X-Ray Fiber Diagrams

83. 6.10.2 Natural Fibers

86. 6.11 The Hierarchical Structure of Polymeric Materials

87. 6.12 How Do You Know It’s a Polymer?