Polymer crystallization, nucleation thickness

Confined crystallization is particularly appealing, since the miaodomain dimensions are comparable to the polymer crystal thickness, and the nucleation and diffusion steps of the crystallization process are influenced by this restriction in space. The development of crystallization studies where the process is somehow controlled is very relevant, mainly because polymer crystallization so far is not a well-understood process. 

Polymer crystallization is usually initiated by nucleation. The rate of primary nucleation depends exponentially on the free-energy barrier for the formation of a critical crystal nucleus [ 110]. If we assume that a polymer crystallite is a cylinder with a thickness l and a radius R, then the free-energy cost associated with the formation of such a crystallite in the liquid phase can be expressed as... 

Once primary nuclei are formed the ensuing spherulites grow radially at a constant rate. Primary crystallization, which occurs initially on the surface of the primary nucleus and then on the surface of the growing lamellar, also involves a nucleation step, secondary nucleation. It is this step that largely governs the ultimate crystal thickness and which forms the focus of most kinetic theories of polymer crystallization. 

Polymer crystal growth is predominantly in the lateral direction, because folds and surface entanglements inhibit crystalliza- 4 don in the thickness direction. Neverthe-1 less, there is a considerable increase in the fold period behind the lamellar front during crystallization from the melt and, as we have j seen, polymers annealed above their crys-tallization temperature but below Tm also irreversibly thicken. Nevertheless, in most theories of secondary nucleation, the most i widely used being the theory of Lauritzen and Hoffman,28 it is assumed that once a part of a chain is added to the growing crystal, its. fold period remains unchanged. 

The major theory [3 7] of polymer crystallization, due primarily to Lauritzen and Hoffman (LH), is a generalization of small-molecule crystallization theory of surface nucleation and growth to incorporate chain folding. In the model of LH theory (Fig. 1.3a), polymer molecules are assumed to attach at the growth front in terms of stems, each of length comparable to the lamellar thickness L. For each polymer molecule, the first step is to place its first stem at the growth surface, whose lateral dimension is taken as Lp. This step is assumed to be associated with a nucleation. The barrier for this step was assumed... 

The nucleation and growth processes, similar to the situation in low molar mass organic crystals, are dependent on the degree of supereooling of the melt or solution phase. The crystal thickness or alternatively the thiekness of eaeh new crystalline layer in a growing crystal is the one that grows fastest rather than the one that is at equilibrium. There is a wealth of information available on the crystallization of many polymers as well as several theories that aim to prediet the crystallization rates, crystal shapes and lamellar thieknesses. 

The changes in the rate are a consequence of the change in balance between free energy of the melt and that of the solid and its influence on the nucleation processes. The LH theory has been used extensively to analyse polymer crystal growth data and is able qualitatively to describe processes that occur in a number of polymer systems. Its success lies in its ability to describe the temperature dependence of both the initial crystal thickness (L ) and the linear growth rate (coj.). A large volume of data has been shown to fit the relationship ... 

Although secondary nucleation theory was, for a period, widely accepted, it is now coming under increasing pressure, from experimental data, from computer simulation, and from new approaches to the fundamental process of crystalhzation. It is not clear at this stage whether all that is required is a few adjustments to the theory, or whether the idea of a nucleation barrier is flawed, or even if the idea that the crystal thickness seen is the fastest growing is correct. With the development of new theoretical tools, and the increased integration of theory with computer simulation, it is hoped that a more complete model for polymer crystallization can be developed. 

According to Hoffman nucleation theory (see Sect. 1.6.1), if chains in a polymer crystal stayed as they were laid down, the crystal would melt almost immediately above its crystallization temperature (solid black line at 45 in Fig. 2.1) however, following subsequent processes the lamellar thickness increases by a thickening factor p (2 in the case of polyethylene) giving a slope with its reciprocal y (here 1/2) in a Hoffman-Weeks plot. The theory of this is quite complicated, and the simple linear plot has been called into question (Marand et al. 1998). Nevertheless, it suffices as a very practical guide to the use of DSC in relating thermal history of a polymer specimen to lamellar morphology. 

A special kind of morphology found in polymers crystallizing in contact with a nucleating surface is the trans-crystalline structure. The nucleating object may be a flat surface or a fibril. The densely appearing nucleations at the surface of the nucleating object result in a one-dimensional (columnar) growth in a direction parallel to the normal of the surface. The thickness of the trans-crystalline layer depends on the outcome of the competition between surface nucleation and bulk nucleation. 

---