Lamellae
The semicrystalline nature of polymers leads to several important issues concerning their structures. If part of the material is crystalline and part is amorphous, how does a chain distribute itself between these two parts? The answer may depend on whether the material is crystallized from the melt, or from dilute solution.
- In the fringed micelle model, PC Fig. 7.25, each chain traverses many crystalline and amorphous regions, a feature that is important in polymers crystallized from the melt.
- Single crystal lamellae can be grown from dilute solution, as was demonstrated over 40 years ago by cooling hot dilute solutions of polyethylene in xylene.
If the solution is sufficiently dilute, crystallization must be an intramolecular process.
The crystals appear to have a flat diamond type of shape.
Electron diffraction shows that the chain axis is perpendicular to the large flat faces and parallel to the thin faces, the latter being only about 10 nm thick.
Therefore the chains must be folded on themselves (PC Fig. 7.27., reproduced from Flory, P. J. "On the Morphology of the Crystalline State in Polymers" J. Am. Chem. Soc. 1962, 34, 2857-2867).
Structure of the Fold Surface
The structure of the fold surface has been controversial.
At issue is the length of the segment that connects two successive crystalline stems.
The two extremes are represented, PC Fig. 7.27, by models known as
- Adjacent re-entry model
- Switchboard model
The preferred structure may depend on whether the material is crystallized from dilute solution or from the melt (with adjacent re-entry more likely if the crystal is prepared in dilute solution).
A density argument shows that there must be some adjacent, or nearly adjacent, re-entry.
Dilatometry shows that the melt is less dense than the close-packed crystal.
Therefore a nonphysical high density would be predicted for the amorphous region if all stems emanating from the fold surface were to propagate into the amorphous region as disordered chains.
Restoration of the real density to the amorphous region requires that some of these emergent chains must quickly turn around and re-enter the crystal from which they emerged, thereby providing space for disordering of the remaining emergent chains.
Simulation
The structure of the amorphous region of a polymer crystallized from the melt has been simulated on a cubic lattice (three dimensions).
The issues involved can be presented in two dimensions using a square lattice (PC Fig. 7.28, reproduced from Dill, K. A.; Flory, P. J. "Interphase of Chain Molecules: Monolayer and Lipid Bilayer Membranes" Proc. Natl. Acad. Sci. USA 1980, 77, 3115-3119).
A few tight folds are required in order to permit disorder of the chains in the amorphous region. Three distinct types of chains are identifiable in the amorphous region in the figure.
- Adjacent re-entry
- A loop, in which a chain re-enters the crystal from which it emerged, but at a non-adjacent site.
- A tie, in which a chain emerges from one crystal, traverses the amorphous region, and then enters another crystal.
A more subtle effect is revealed by examination of the "structure" of the amorphous region, using an order parameter that reveals whether bonds are oriented in all directions with equal probability, or whether there is some preferred direction.
This type of analysis shows that the "amorphous" region is isotropic only in those parts sufficiently far removed from the nearest crystal.
In the regions closer to a crystal face, there is a residual tendency for the bonds to prefer directions normal to the crystal surface.
This region is often called the anisotropic interfacial region.
It is more disordered than the crystal, but not as completely disordered as the true amorphous region.
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July 1, 1999
Wayne L. Mattice: wlm@polymer.uakron.edu