POLYMERS 3/PH/AM
Lecture 6: Crystal and Glass
Much of our understanding of the crystalline state comes from the
work of these three at Munich.
Wilhelm Konrad Röntgen (1845 – 1923)
Max von Laue (1879 – 1960)
Paul Peter Ewald (1888 – 1985)
Why do things crystallize?
One of the requirements for things to
crystallize is the ability to pack regularly.
In doing so, the system moves to a less
energetic state.
The enthalpy of crystallization (yes, there is an
accompanying volume change, so PV terms
enter) gets dumped into the universe.
This process is thermodynamically permitted
only if the loss of multiplicity of the system in
crystallizing is less than the gain of multiplicity
in the universe.
Why do Polymers Crystallize ?
Many polymers are able to pack regularly,
like polyethylene.
The polyethylene orthorhombic cell (Bunn,
1953). Note: this comes before the
availability of linear Ziegler PE. But even
the old-fashioned low density PE has only
about 3 branches per 100 carbon atoms.
Even on purely random statistics, that would
give a number average of 33 carbons-in-arow, and a weight average of 66. And
LDPE is far from random. So there is still
quite a lot of material that can crystallize.
Helical Chains and their
Packing
The isotactic polymers discovered by Natta ‘like to’ wind
their chains in helices. These also can pack incrystals,
like the I-polypropylene lattice above. Notice that they
pack in rows (reading from the left) with helices in each
row going the other way from those in the next row.
How do we know polymers are (semi)-crystalline?
Polymer crystallization as observed by X-rays
Rings
Layer Lines
POM (after
E.S.Clark, in
Billmeyer)
X-ray scattering of
X-ray scattering of chemically cross-linked
polycyclooctene (PCO)
http://www.ims.uconn.edu/~mather/Mather_Pubs_files/
Liu%20PCO%20SMP%20in%20Macromolecules.pdf
Ewald Sphere Construction
top – for X-rays —— below – for electrons
Crystallization and Melting: Observation by Thermal Analysis
To understand this, we briefly have to look in real space at what happens. In a bulk
polymer melt, as in a solution, crystallization starts from points called nuclei, but in the
bulk the crystals grow out approximately equally in all three dimensions to give spherulites
which eventually impinge and take up all the volume. Details of this will be the topic of
the next set of notes, but the picture below will suffice for what we are about to say here.
DSC (above) and thermogram of PET (below)
Go to http://www.pslc.ws/mactest/level5.htm, click on “Differential Scanning Calorimetry”
Why don’t polymers always crystallize ?
The chains may be irregular in configuration
They may be copolymers
The chains may be too stiff
They may be blended with other polymers
The Glass Transition (Tg)
Changes in volume (V), enthalpy (H) and
entropy (S) are continuous, but have a
change in slope at Tg.
This means their derivatives such as Cp (
dS/dT) and  ( dV/DT) are discontinuous.
It resembles a 2nd order transition — However the glass transition is not a true
thermodynamic (2nd order) phase transition.
 The temperature Tg is not fixed but depends on experimental conditions, particularly
the cooling rate.
 Glass 1 cooled faster than glass 2, and deviates from equilibrium supercooled line at
higher temperature.
 Cool more slowly and Tg (temperature at which discontinuity in V seen) drops to
lower temperature for glass 2.
The Kauzmann paradox is that apparently if you cool slowly enough it ought to be possible
to achieve an entropy in the glass which is the same, or even lower, than the crystal.
This is still a hotly debated topic amongst theoreticians in this area.
Can you Change the Structure of a Glass?
Yes – although it is a non-equilibrium structure, it is possible to ‘anneal’ the glass, to
encourage it to move towards equilibrium.
Structural Characterization of Amorphous Materials
(These methods will also apply to liquids)
Just as diffraction is very useful for crystals, so it is (strictly speaking scattering) for
amorphous materials. X-ray and neutron scattering most commonly used.
Principles similar, but no longer have sharp Bragg peaks, so have to think carefully about
what information can be extracted from an experiment.
The radial distribution function (RDF) g(r) is defined as the number of atoms lying between
r and r+dr of the centre of any given atom.
g(r) = 4πr2(r)
where (r) is the atomic pair correlation function:
These nearest neighbour positions similar to those in a crystalline solid.
Thermogram of PET