Roughness of growth faces of polymer crystals: Evidence from morphology and implications for growth mechanisms and types of folding

Abstract

It is proposed that the growth faces of lamellar polymer crystals can have an equilibrium roughness (or crenellation). This can explain why some polymer crystals show no evidence of faceting. Support for this idea comes from the extensive theoretical developments on the nature of crystal surfaces. The characteristic habits of polyethylene are analysed in terms of a roughness which, on the {110} faces, increases progressively over a temperature range of about 100°C. At a temperature near 110°C the roughness becomes sufficient for there to be no free energy penalty for arbitrary crystal shapes (e.g. rounded) compared with one bounded by {110} faces. Above this temperature of crystallization most of the habits which are observed are leaf-shaped, with an apex along 〈010〉. Below 110°C{110} facets (or microfacets) are normally seen. There is no positive evidence that faces approximately parallel to (100) planes, observed for crystallization temperatures in the range 80°–110°C, are ever other than rough. The relative rates of growth on the {110} compared with the (100) increase with temperature, since {110} faces predominate at low but not high temperatures of crystallization. These changes are attributed to the increase in roughness with temperature on the {110} faces. The existence of surface disorder (roughness) requires that the binding energy between units in the crystal is comparable with KT. Hence this unit is probably several monomer units of polyethylene (rather than, for example, a complete stem which contains a hundred or more monomers). There is therefore a surface lattice on the growth faces with twenty or more units in the direction perpendicular to the lamellae. Monte Carlo calculations are cited for lattices of 20 by 50 units. These show that a cooperative increase in surface roughness with temperature and a transition between faceted and non-faceted growth can be expected for lattices of such limited extents. No explicit allowance has been made as yet for the consequences of the units being linked into chains and, for that reason, not being able to arrive or leave the surface independently. It is noted that changes in the alkane lattice with temperature indicate a possible evolution in binding energy, and in mobility, and hence may influence surface roughness. Theories of crystallization in polymers have normally assumed a growth surface which is molecularly smooth in equilibrium, and have emphasised nucleation events. Since this paper shows that the equilibrium structure may often be rough, it may be necessary to re-examine the basis of these theories. A brief review is included of the experimental evidence for surface nucleation events: nucleation may be a more important barrier at low temperatures than at high. The type of folding will be influenced by equilibrium roughness just as it will be by kinetic roughness, and some comparisons are made with neutron scattering results on this topic. The degree of adjacent folding is higher in the faceted regime as expected. Brief comments are made on the applicability of this idea to polymers other than polyethylene.