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A new lattice model of polymer crystallization is described. Results of numerical solutions of rate equations for crystallization of a two-dimensional "crystal" are presented. It is shown that the crystal thickness varies inversely with supercooling and that kinetics similar to secondary nucleation occurs. This is true even though the growth face is intrinsically rough and hence there cannot be any nucleation. The presence of a low-entropy saddle point during growth is explained, and its influence on the crystal thickness and lamellar morphology is discussed.PACS numbers: 61.50.Cj, 61.41, +e, 82.60,Nh Crystals of long-chain molecules invariably grow as lamellae that are usually much thinner than the length of the chains. '2 Molecules traverse the lamellae many times; the geometry is described in detail below. The precise manner of this folding has been the subject of considerable debate, but the emphasis of this paper is instead the origin of the lamellar habit. This phenomenon has been explained by models that invoke secondary nucleation; i.e. , the nucleation of new layers of the crystal on the advancing edge of the lamella. 3 5The kinetics is also consistent with this mechanism, 5 7 yet the crystals do not always have the faceted edges required for the nucleation process. 's In those cases where crystals of a polymer can be grown with either straight or smoothly rounded morphologies, the latter tend to occur at higher temperatures. It has been proposed that this change is associated with surface roughening. 9'o At the higher temperatures the surface is intrinsically rough on a microscopic scale, since steps across the growth faces and other favorable growth sites are generated by thermal fluctuations in equilibrium. Nucleation of a new layer is not required under these conditions. For growth faces of infinite extent, the theory of the roughening transition is now well established, "' and experimental verification has been obtained. " We now develop further a model of polymer crystallization that applies to rough growth faces and which could also be relevant when the faces are straight. The model reproduces the principal trends in experimental measurements of lamellar thickness and growth rates. The growth face can only be sufficiently rough if the stems (the straight sequences of chain which traverse the crystal) are allowed to vary in length and if short stems are allowed. Our model considers the basic unit of crystallization to be a short sequence of chain (e.g. , six CH2 units of polyethylene; cf. Refs. 4 and 9 and Point'6); stems differ in length according to how many units they contain.The geometry of the crystals is described schematically in Fig. 1(a) with each stem corresponding to a prism. The ends of the stems should be imagined as having attached chains emerging from the crystalline region. In many cases (e.g. , to the left of the diagram) the chains will be folded back into the lamella. Partly attached chains with loops are indicated at the growth surface. Effects of polymer chain connectivity and ...

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Folded‐chain crystals of certain polyamides present some novel diffraction effects due to the small number of repeat units within the lamellar thickness. X‐ray diffraction evidence is available in the complete range from low to wide angles. This information is interpreted in terms of the structure factor of an individual lamella together with the lattice factor appropriate for the stacking of lamellae. When due account is taken of the lattice factor, whose effect can be detected even at large angles, three features of the lamellar structure can be deduced. First, the evidence is in favor of the straight‐chain stems traversing almost the total thickness of each lamella, implying sharp folds at the lamellar surfaces. Some consequences of this result on the interpretation of data obtained from annealed mats are mentioned. Second, the detailed determination of the stem structure demands that the majority of the folds in nylon 66 lie in the acid group. Third, there are regions of depleted electron density at the lamellar surfaces, though features of the crystal structure are still retained. This indicates the presence of some folds deeper in the crystal than the majority.

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