Chapter 6. The Crystalline State
6.1 General Considerations
6.1.1 Historical Aspects
Staudinger
Herman Mark
Ziegler and Natta
Macromolecular Hypothesis
Father of Polymer Science
stereospecific polymers
6.1.2 Melting Phenomena
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
Four different polymorphic forms of crystalline cellulose exist.
6.3.5 Principles of Crystal Structure Determination
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 Polymers
6.4.1 The Fringed Micelle Model
According to the fringed micelle model, the crystallites are about 10
nm long.
The chains are long enough
to pass several crystallites,
binding them together.
amorphous
crystalline
6.4.2 Polymer Single Crystals
1957 Keller prepared single crystals of PE.
6.4.2.1 The Folded-Chain Model
Adjacent reentry
10~20 nm thick
(contour length ~ 200 nm)
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 occurs
is the wavelength
U is radial direction
R is the radius of the spherulite
6.5.2 Mechanism of Spherulite Formation
6.5.3 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 Crystallization
6.6.1 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
d = D/G
Where D is the diffusion coefficient for impurity in the melt and
G reprents the radial growth rate of a spherulite.
The quantity d, whose dimension is that of length, determines the lateral
dimensions of the lamellae. Thus d is a measure of the internal structure
of the spherulite, or its coarseness.
Where DF* is the free energy of formation of a surface nucleus of
critical size,
DE is the free energy of activation for a chain crossing the barrier to
the crystal
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?