A critical assessment of unbalanced surface stresses as the mechanical origin of twisting and scrolling of polymer crystals

Twisting of polymer lamellae manifested by e.g. appearance of concentric bands in polymer spherulites examined in a polarized optical microscope remains a topic of research and controversy. It has been interpreted variously as resulting from phenomena that take place during growth or from structural features of individual lamellae, or multilamellar aggregates. Phenomena that take place during growth are of general, or even generic character. They include non-linear diffusion processes leading to rhythmic crystallization, or self-induced compositional or mechanical fields generated near the advancing crystal front. Structural features include cumulative reorientation of lamellae at successive isochiral screw dislocations (possibly linked with surface pressure exerted by cilia) or different surface stresses on opposite fold surfaces of individual lamellae, as a result of different levels of congestion of folds. This contribution reviews evidence that has accumulated in favor of lamellar twist induced by surface stresses that result from differential congestion of fold surfaces, as suggested initially (in 1984) and advocated for many years by Keith and Padden. Such differences in fold surface structure are occasionally amenable to experimental (even if only qualitative) verification, as illustrated by polymer decoration of polyethylene single crystals. Twist is expected when a two-fold symmetry parallel to the growth direction exists in the lamellar structure (crystalline core and fold surface). This symmetry often stems from chirality: most frequently atomic (configurational) or stem (conformational) chirality but chirality (or at least asymmetry) may also be introduced by chain tilt. Possible origins of twisting in chiral polymers are also reviewed. In β sheets of fibrous proteins, the origin of twist stems from the atomic chiral centers in the crystalline core of the lamellae and its transfer to higher structural levels via the strong structural identity of the hydrogen-bonded β sheets. However, in a series of synthetic liquid-crystalline main-chain nonracemic chiral polyesters, the lamellar twist sense depends on the odd or even numbers of atoms in the aliphatic segment. For these and other more flexible chiral polymers, often with helical chain conformation, twisting appears to result from surface stresses associated with different fold structure or conformations at opposite fold surfaces, as suggested by a preliminary analysis of the Form III of isotactic poly(1-butene). Such differences in fold conformations result from, but are not directly related to, the specific helical hand of the polymer since they rest on the details of the chain conformation as it reaches the fold surface. This analysis accounts for the lack of one-to-one correspondence between configurational or conformational chirality of the polymer and lamellar twist sense (the one-to-one correspondence applies however for stereoenantiomers of a given polymer). Twist is not the only known non-planar geometry of polymer lamellae. In a few cases, the lamellae are scrolled. Scrolling of polymer lamellae is also easily accounted for by the existence of surface stresses when the two-fold symmetry parallel to the growth direction is absent. Such surface stresses are again linked to disparities in fold volume, as first suggested for poly(vinylidenefluoride) in its γ Form and later for two long paraffins substituted near their middle carbon atom and that crystallize in hairpin fashion, and for scrolled crystals of polyamide 66. The different nature and structure of polymer crystal fold surfaces, therefore, offer an unusual opportunity to decouple surface and bulk contributions and to analyze the origin of non-planar lamellar geometries at a sub-molecular level. Fold structure disparities and resulting unbalanced surface stresses provide a unified explanation for the formation of non-planar (both twisted and scrolled) lamellar crystals. They account for both the diversity of lamellar morphologies produced under the same crystallization conditions and for the similarity of lamellar morphologies produced under very different crystallization conditions.