Most of the semicrystalline polymers exhibit fascinating morphological patterns consisting of regular concentric rings overlaid on the conventional spherulitic structure, which is common to both organic and inorganic compounds (cf. Figure 58a). These structural features, the so-called banded spherulites, can be repeatedly formed upon the polymer crystallisation from the melt and are therefore largely independent from the initial processing conditions of the polymer film. The spatial scale pertinent to such structures is undoubtedly the largest that the semicrystalline polymers can ever form: the banded spherulites may be as big as several centimetres in diameter, whereas the height of the band is in the order of micrometres [1]. Although it is now well documented that banded spherulites are due to the formation of nonplanar polymer crystals (see Figure 58b), the exact reasons for the appearance of the curved crystals and the details of their microstructure are not known.

Initially, the idea that the lamella twisting results from the surface stresses was put forward in the early 1960s by Geil [1]. Later on, a qualitative model accounting for the existence of unbalanced surface stresses was introduced by Keith and Padden (KP) [2]. The positive and negative sign of the stresses generated on the surface of a twisted lamella according to the KP-model is shown by different colours in Figure 58b. Since the very introduction of the KP model, its experimental verification has been essentially missing. Also, the factors controlling the chirality of the crystalline lamellae, which are supposedly adopting the form of left- and right-handed helicoids or helices (see Figure 58b) remain unclear.

We used the micro-focus X-ray diffraction facility at beamline ID13 to explore the chirality of the crystalline lamellae of polyethylene, which can be considered as the archetypal semicrystalline polymer with an achiral backbone. In particular, we aimed to identify the added chirality parameter imparted to the polyethylene chain by the crystallisation process.


Fig. 58: a) Polarised optical micrograph of banded polyethylene spherulites melt-crystallised at 105°C. b) Schematic illustration of the banded spherulite structure, which is composed of lamellar helicoids growing from the spherulitic centre outwards. The origin of lamellar twist is supposed to be due to unbalanced surfaces stresses of positive or negative sign (indicated by red and blue colour). c) Averaged X-ray pattern recorded during a radial microfocus scan across the whole polyethylene spherulite.

The structure of banded spherulites grown in free-standing polyethylene films was explored by performing radial scans with a microfocus X-ray beam (see Figure 58c). We observed that the lamellar twist occurs in a strictly regular and uniform way. The exact orientation of the polyethylene unit cell within the lamella was found from the relative shift of the SAXS signal with respect to the WAXS peaks of the crystalline lattice as displayed in Figure 59. The crystalline stems of polyethylene are inclined with respect to the normal to the lamellar surface by 35 degrees, which corresponds to the (201) fold plane. Importantly, the chain direction was found to be unique for the entire stack of the polyethylene lamellae. The latter observation signifies that, on the local scale, the microstructure of bulk polyethylene is single-crystal-like.


Fig. 59: a) Azimuthal position of the meridional 200 reflection and SAXS interference maximum versus radial distance from the spherulite centre. b) Orientation of the polyethylene unit cell with respect to the lamellar basal plane. The crystalline stems are tilted by about 35° about the lamellar normal in the (010) plane perpendicular to the crystal growth direction (b axis). The chain tilt in a lamellar stack has a unique direction in space. c) Model illustrating the rotating unit cell of polyethylene. The k0l reflections rotate in the (010) plane. The curved arrows indicate the rotation direction of the unit cell.

Based on the Ewald sphere construction, we deduced that the polyethylene lamellae with both left and right handed chirality can coexist within the same spherulite. Most importantly, we have shown that the added chiral parameter is the chain tilt direction. Thus, when looking along the crystal growth direction, the lamella having the crystalline stems tilted to the right from the normal to the lamellar basal plane will form a right-handed helicoid, whereas the lamella having the stems tilted to the left will be left-handed (see Figure 59c). The latter finding is in agreement with the qualitative model of Keith and Padden.


Principal publication and authors

M. Rosenthal (a), G. Bar (b), M. Burghammer (c) and D.A. Ivanov (a), Angew. Chem: Int. Ed. 50, 8881–8885 (2011).

(a) Institut de Sciences des Matériaux de Mulhouse, CNRS-Université de Haute Alsace, Mulhouse (France)

(b) Analytical Technology Center, Dow Olefinverbund GmbH, Schkopau (Germany)

(c) ESRF



[1] P.H. Geil, Polymer Single Crystals, John Wiley and Sons Inc., New York (1963).

[2] H.D. Keith and F.J. Padden, Polymer 25, 29–41 (1984).