Polymer Crystal Hierarchy:

We have seen that bio-polymers, specifically proteins, display a structural hierarchy which we describe as an explicit hierarchy since it is composed of close to 0 conformational entropy states with little dispersion in size, while polymer coils structurally display a statistical hierarchy since it is composed of average features generally with many possible conformations so a finite conformational entropy.  The dynamics of long chain molecules (polymers and unfolded proteins) display a statistical hierarchy in time since many conformational paths are available for relaxation of a long chain molecule. 

Polymers can crystallize into chain folded crystals through diffusion following reptation dynamics or Rouse dynamics.  The two routes, associated with concentrated (spherulitic) or dilute (single crystal) conditions lead to different structural hierarchies.  Further, the presence of strain on a concentrated crystallizing solution or melt leads to an identifiable structural hierarchy (polymer fibers).  Several other less well described hierarchies are known for polymer crystals including shish-kebab crystallites, extended chain fibers (gel drawn fibers), axialites, fringed micelles, and lozenge crystals.  All polymer crystals display some common morphological signatures that allow for generalization.  (The majority of the literature in polymer crystalline morphology involves case studies of specifics to some subclasses of polymers.) 

Crystalline polymer morphology has been an intense area of study for about 50 years since it directly impacts industrial production of polyethylene and other polyolefin, polyamide and polyester systems, and because it is a fundamental area for academic contribution.  Major features of polymer crystalline morphology remain ill defined and there are a wide range of fundamental questions remaining unanswered despite the effort that has been invested in this field.  Nonetheless, federal and industrial research funding in polymer crystals has dwindled to non-existence in the US, while significant funding and effort remain in Asia and Europe where the most recent industrial and scientific advances have been made.  Crystalline polymers remain an area where roughly 80% of industrial polymer scientists in the US work with a lack of trained scientists in the US due to the absence of federal or industrial support for education and training.  (For example, UMass Dept. of Polymer Science, Akron, U. Southern Miss. and Case Western have no remaining groups pursuing research in polymer crystals.)

Single Crystal Hierarchy:  Rouse dynamics from good solvent systems leads to nucleation of single chain, tightly folded crystals with no entanglements.  The surface of such crystals have been found to contain adjacent re-entry folds (see AFM below from MIT but this was originally seen at Akron by Giel who is now at Illinois).  The absence of entanglements allows polymers to achieve an ideal condition for crystallization and extremely large aspect ratio sheet-like crystals are formed (an aspect ratio similar to a sheet of notebook paper).  The crystals are based on a hierarchy that begins with  the chain persistence:

Hierarchy of Polymer Single Crystals:
1) Persistence Length
2) Helical Structure
3) Lamellae
     i)  Thickness
     ii&iii)  Width/Length
4')  Epitaxy in some cases
4'')  Buckling/Tent-like structure in some cases

We have already discussed levels 1 and 2.  The lamellar thickness was described first by Keller in Bristol and later by Hoffmann at NBS (now NIST).  The determination of the thermodynamic basis for lamellar thickness is seen as one of the major principles of polymer science.  In terms of hierarchy, the lamellar thickness represents a third type of thermodynamics (Protein Folding, Polymer Chain Scaling and now Crystalline Lamellar Thickness) applicable to hierarchical materials, in this case asymmetric hierarchies. 

The lateral dimensions of polymer single crystals are determined by a balance between transport and growth rates as described by Keith and Padden.