Chapter 6. The Crystalline State

6.1 General Considerations

6.1.1 Historical Aspects

6.1.2 Melting Phenomena

Staudinger Macromolecular HypothesisHerman Mark Father of Polymer ScienceZiegler and Natta stereospecific polymers

6.1.3 Example Calculation of Percent Crystallinity

6.2 Methods of Determining Crystal Structure

6.2.1 A Review of Crystal Structure

6.2.2 X-Ray Methods

6.2.3 Electron Diffraction of Single Crystals

6.2.4 Infrared Absorption

6.2.5 Raman Spectra

6.3 The Unit Cell of Crystalline Polymers

6.3.1 Polyethylene

6.3.2 Other Polyolefin Polymers

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6.3.3 Polar Polymers and Hydrogen Bonding

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.

6.4 Structure of Crystalline Polymers6.4.1 The Fringed Micelle Model

According to the fringed micelle model, the crystallites are about 10 nm long.

crystallineamorphous

The chains are long enough to pass several crystallites, binding them together.

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

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.

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

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.

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.

Spherulites are composed of individual lamellar crystalline plates.

Small-angle light scattering

max is the angle at which the intensity maximum occursis the wavelengthU is radial directionR is the radius of the spherulite

6.5.2 Mechanism of Spherulite Formation6.5.3 Spherulites in Polymer Blends and Block Copolymers

6.5.4 Percent Crystallinity in Polymers

Where Ac and Aa represent the area under the Bragg diffraction line.

6.6 Kinetics of Crystallization6.6.1 Experimental Observations of Crystallization Kinetics

6.6.2 Theories of Crystallization Kinetics

6.6.2.1 The Avrami Equation

6.6.2.2 Keith-Padden Kinetics of Spherulitic Crystallization

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 andG 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

6.6.2.3 Hoffman’s Nucleation Theory

6.6.2.4 Example Clculation of the Fold Surface Free Energy

6.6.2.5 Three Regimes of Crystallization Kinetics

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

6.7.4 Extended Chain Crystals

6.8 Thermodynamics of Fusion

6.8.1 Theory of Melting Point Depression

6.8.2 Example Calculation of Melting Point Depression

6.8.3 Experimental Thermodynamic Parameters

6.8.4 Entropy of Melting

6.8.5 The Hoffman-Weeks Equilibrium Melting Temperature

6.9 Effect of Chemical Structure on the Melting Temperature

6.10 Fiber Formation and Structure

6.10.1 X-Ray Fiber Diagrams

6.10.2 Natural Fibers

6.11 The Hierarchical Structure of Polymeric Materials

6.12 How Do You Know It’s a Polymer?