P O L Y M E R S 3 / P H / A M
L e c t t u r r e 7 : : L a m e l l l l a e a n d S p h e r r u l l i i t t e s
Perhaps the first model of a semicrystalline polymer was the Fringed
Micelle Model ( diagram after Bunn, 1953 ).
It fitted with many of the observed properties, such as density, mechanical properties, X-ray diffraction, etc.
But some things could not be explained, such as the development of spherulites
(next).
The next two images show polymer spherulites as observed under the polarizing optical microscope.

For the one on the left, a film of a blend of polypropylene with poorly tactic and effectively non-crystallizable polypropylene was melted and cooled to 130 °C, and held at that temperature for about 1 hour. Here the spherulite centres are all in the film

One the right is a section through a pellet of polyethylene. This has a banded appearance. Since this is a section through a 3D object, many of the spherulites are cut off-centre.
Polypropylene blend spherulites observed in polarized light
Polyethylene Banded Spherulites
Lamellae and Spherulites – Page 1

In order to make sense of these patterns, we need to know that polymer crystals take the form of lamellae. Which begs the question:
In the mid 1950’s, people started crystallizing the newly available (Ziegler) high density polyethylene from dilute solutions, and observed crystals like the one on the left. This one takes the form of a truncated lozenge .
In 1957 Keller first reported the nature of these crystals, as revealed in the electron diffraction pattern below right of the crystal below left.
.
In the diffraction pattern there are only hk0 spots, so the Ewald sphere (for electrons of very high radius, almost a plane) must be intersection the ab plane of the crystals.
Therefore, since PE is orthorhombic, the c-axis must lie along the electron beam, and also the normal to the plane of the lamellae.
The thickness of the lamellae is much less than the stretched out length of a molecule, so
Keller worked out that the molecules must be folded back-&-forward inside the crystal as shown left top.
Lamellae and Spherulites – Page 2

The molecular folds are very regularly arranged, dividing the lozenge-like crystal into four sectors which can be detected by careful electron imaging.
What determines the thickness of lamellae? This is a complicated matter, and treated in books, but suffice to say that:
 at lower temperatures: o lamellae grow faster (sideways) but o thinner lamellae are formed.
A stack of lamellar can function as a diffraction grating, so:
We determine the long period of sedimented crystal mats by small-angle X-ray diffraction (SAXS).
Long Period of Poly(4-methyl pentene-1) crystals grown from a 0.1% solution in xylene (Bassett, Dammont & Salovey, 1964)
These lamellae have a very large surface-to-volume ratio. Since the atoms or groups at the surface of a crystal are not totally surrounded by other atoms/groups, they are at a higher energy. The material in the interior of a crystal has a certain specific Gibbs function
(chemical potential), but one must add surface terms, most importantly the fold surface free energy,
 e
, which contributes 2
 e
/   for a lamella of thickness  and crystalline density

.
In consequence melting points are lowered from T m
0 , for infinite thickness, to T m
according to the Hoffman-Weeks equation where
 h v
=
 h.

is the specific enthalpy of melting per unit volume of crystal (as opposed to
 h, the specific enthalpy per unit mass).
Lamellae and Spherulites – Page 3

The diagram shown on the left illustrates the refractive indices of crystalline polyethylene along the three crystallographic axes. In polymer crystals, the c axis is always taken as the axis along the molecular chain direction. Polyethylene is (usually) orthorhombic, so all axes are at right angles.
Those along a and b are so close to being equal that they can be treated as such, while that along c is considerably greater. Where only one R.I. is different, the crystal is said to be uniaxial.
If all the axes are equal, the refractive index in any direction is the same, and its locus (called the indicatrix ) is the surface of a sphere. But if one is different, the indicatrix is a spheroid, in this case a prolate spheroid like a rugger ball.
Now how does this relate to a spherulite?
Taking PE again, lamellae grow rather differently from PE in solution and in molten polyethylene. In their simplest forms (left) the fast growth direction in solution is a and in the melt is b.
The question is: how does this lead to spherulites?
.
Lamellae and Spherulites – Page 4

This is a rough indication how a single lamella branches and then the separate branches splay in 3 dimensions to form a spherulite.
But for most purposes we can treat a spherulite as composed of lamellae radiating from the centre. The slow growth axes all bump into their neighbours, while the fast axis becomes the radial growth direction.
Lamellae and Spherulites – Page 5

This represents a section through the centre of a BS in PE. As the lamellae grow out from the centre along their b-axis (always radial) they keep sprouting little daughter lamellae. However, the c-axis is sometimes facing the observer, so the R.I. ellipsoid appears circular. Then there is zero amplitude birefringence. Daughter lamellae are inclined, so soon the R.I. ellipsoid is sideways-on, giving maximum birefringence.
But along the “Maltese Cross” the ellipsoid is vert. or horiz. So does not split the polarized beam: this is zero extinction birefringence.
Things to note: the banded spherulites in the micrograph so not appear symmetrical.
This is because the film was stretched a bit during the cutting, and so the molecules have been slightly disoriented.
Not all polymer spherulites are banded.
While the radial direction of growth remains the same, the two other (tangential) directions are often jumbled up. So we get the zeroextinction birefringence of the Maltese Cross, but not zero-extinction birefringence associated with banding.
Spherulites GROW!
Lamellae and Spherulites – Page 6

This is a film of PP, grown slowly for 2 hours and similar, for 3 hours
One can monitor crystallization as a function of time and temperature by means of dilatometry , which follows the change in volume as liquid is converted into solid.
Lamellae and Spherulites – Page 7

Crystallization of Polyethylene as a function of time and temperature
Here we plot as a function of time. It is apparent how much more rapid crystallization becomes by even dropping a few degrees y axis = degree of conversion of melt to crystal.
The faster crystallization at lower temperature is due to two factors:
(1) the radial growth rate of spherulites is much faster.
A plot against log (time) is much more informative. Here we can see that the higher temperatures are leading to greater crystallinity. This is partly because the lamellae are thicker (compare solution
crystals on page 3, but also because with
slower crystallization the fold surface can sort themselves better and become thinner.
(2) there are also more nuclei for spherulites available at lower temperature.
This is a polypropylene (PP) spherulite grown for 2 hours at 145°C. The specimen was then quenched into cold water, and formed finely textured material composed of tiny spherulites with much thinner lamellae.
This is a similar PP, but with a nucleating agent, prepared at the same time and temperature. Many more spherulites have formed.
Nucleation allows materials to be crystallized at higher temperatures. Similarly to the PE above, this means greater crystallinity, and so improved stiffness.
Lamellae and Spherulites – Page 8

Plot of spherulitic radial growth rate of PET as a function of temperature. This is based on experimental observations under a microscope. The dotted curve is added to show that the overall crystallization maximum rate is shifted to lower temperatures by increased nucleation.
At T m
= 265°C and T g
= 67°C, the growth rate is theoretically zero.
As we come down from the melting point, thermodynamics ‘helps’ the molecular stems to settle for longer on the growing crystal face, thus allowing the crystal to grow faster. Hoffman and Lauritzen published a theory of this, and you will find it in many books.
As we get nearer to the glass transition, viscosity increases. The rate of diffusion is inversely proportion to the viscosity, so it takes longer for stems to arrive at the growing face.
Lamellae and Spherulites – Page 9

Lamellae and Spherulites – Page 10
Using narrow molecular weight fractions, in this case poly(ethylene adipate), generally gives excellent agreement with the Avrami approach.
Data fits straight line (n = 4) over a wide range of temperatures and conversions. This value is predicted for sporadic nucleation with time. For instantaneous nucleation, n = 3 is predicted.

(a) Data fits portions of an Avrami plot with integer values, but deviates at high conversion.
Type ‘a’ deviations can be explained by having at least two different kinds of crystal growth.
1) different nucleation mechanisms
2) different kinds of spherulite
3) rod to disk to spherulite conversion
(b) Avrami type plots show a linear fit over all conversions but have non-integer values of slope
Type ‘b’ deviations are inconsistent with theory.
‘n’ is never greater than 
4
Difficult to obtain information about the nature of crystal growth in polymers. Deduce from n. A lot of people do this, but it is WRONG WRONG WRONG !!!! The Avrami exponent backs up an observation of spherulitic growth, with instantaneous and/or sporadic nucleation, but it should never be used to determine the kind of growth if other methods, such as direct observation (best) or scattering are available.
This one is right . Need a practical measure of the effect on crystallization rate of various additives. Use ‘t
1/2
’ or ‘induction time’
Lamellae and Spherulites – Page 11

We ‘develop’ the surface like in metallographic etching. We can examine a specimen like this direction in the scanning electron microscope (SEM). But we can’t put this directly under the transmission electron microscope (TEM), so we make a replica. A lot of work, but TEM gives better resolution.
This picture shows a PE specimen crystallized at high temperature for a long time. Here we can see three features of lamellae:
A – here the arrow points to a stack of lamellae, seen sideways on. We can use a view like this to measure lamellae thickness. (Being crystallized slowly at high temperature, the molecules can fold nicely into the lamellae without bits left on the surface to force the lamellae apart).
B – points to a broad flat-on basal surface of a lamella.
C – here the replication has revealed bundles of molecules folding in the crystal. One cannot see individual molecules at this magnification, but the molecular direction is displayed clearly.
Lamellae and Spherulites – Page 12

How do spherulites start? Refer to Schematic of Spherulitic Development on Page 5.
We always like to study specimens grown at high temperatures, because the crystals are well-defined.
This is a crystal of PE grown for 23 hours at 130°C (you cannot crystallize PE much higher than this). The specimen was quenched, and the surrounding material contains small banded spherulites.
Everything is on a smaller scale when crystallized at lower temperatures, and so more difficult to study.
Note that even this ‘single’ crystal is already starting to branch. and at a lower temperature …
And ever more complicated …
Lamellae and Spherulites – Page 13

isotactic -Polystyrene Hedrites
Lamellae and Spherulites – Page 14

Here we see long lamellae (dominant) forming ‘cages’ inside which shorter ones
(subsidiary) are confined. This is the mode of development of structure in all kinds of polymer spherulites.
If you read books, you will find the theory of Keith and Padden, in which the structure of spherulites is formed by diffusion of non-crystallizable material.
This theory is wrong , and should not be followed further.
Lamellae and Spherulites – Page 15

The answer came with study of long chain paraffins. These were synthesized at £10,000 per gram at the University of Durham. They are, in effect, special uniform low molecular weight polyethylenes.
254
At higher temperatures this crystallizes in the extended form (see diagram below) where each molecule goes once through the lamella without any left over to form folds or hanging bits (cilia).
Thus the lamellae can form parallel stacks as seen in the picture..
At lower temperatures this crystallizes in the oncefolded form (see diagram below) where each molecules can either go once through the lamella with hanging bits (cilia), or else can fold into a hairpin.
The presence of cilia gives extra material on the surface which forces the lamellae apart. That is why the material forms dominant and subsidiary lamellae in a pattern similar to the polyethylene on page 15
Lamellae and Spherulites – Page 16