Kinetics of Crystallization and Melting

In order to characterize the crystallization properties of a given polymer system, experiments have to be carried out with the objective to determine 

As in low molar mass systems crystal formation in a polymer melt starts with a nucleation step. Thermal fluctuations form in the melt embryos, i.e., particles with an enhanced inner order. If the size of an embryo surpasses a critical value it turns into the nucleus of a growing crj tal smaller embryos disappear again. It is possible to directly observe this process with an atomic force microscope, as is shown in Fig. 5.19 for a crystalhzing polyether (short name BA-C8, the material crystallizes slowly at room temperature). The encircled dot in the left-hand picture is a nucleus that subsequently develops into a single lamellar crystallite. 

Data indicate as a further characteristic feature that Tnuc changes exponentially with temperature. This finding demonstrates that the nucleation step is an activated process associated with a free energy barrier to be surmoimted. 

The figures under consideration concern the nucleation out of a homogeneous, pure melt however, this is not the usual case. Under practical conditions, nucleation mostly starts on the surface of low molar mass particles, which come into the sample either uncontrolled, or deliberately as nucleat- 

many lamellar crystallites develop simultaneously, emanating from the surface of the heterogeneity. As a consequence, the growing object shows a quasi-spherical symmetry from the very beginning which differs from the initial anisotropy associated with a homogeneous nucleation. 

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Buchner, S., Wiswe, D. and Zachman, H. G., Kinetics of crystallization and melting behaviour of poly(ethylene naphthalene-2,6-dicarboxylate),... 

Time-Resolved Studies Kinetics of Crystallization and Melting... 

Crystallization is governed by the usual thermodynamic variables of temperature, composition, and pressure. It is common to describe the thermodynamics in terms of dominant chemical species present, vhich in the majority of crystallization processes are the material to be crystallized and a small number of solvents. For all real systems, a further influence has to be taken into account, that is, of impurities. These are present in every system, in varying amounts. These impurities can have an effect on the solubility or melting point of the material to be crystallized, if small. The presence of additional components in the solution is often more noticeable in their effect upon the kinetics of crystallization and more specifically on growth rates of crystals. For the sake of clarity, additive is used as a collective noun for any minor component in a given system, whether this additive is in fact an impurity stemming from the raw materials employed or a by-product from the reaction stages required to manufacture the final product, or a true additive supplied to the system to achieve a specific effect. It is noted that the word impurity is even more widely used, as solvent or solvent mixture can also act as additives. 

The kinetics of crystallization from melts was studied by Avrami and was adapted later on to the case of polymers. Due to the economic repercussions of the crystallization phenomenon and of its kinetics, many smdies were conducted to simplify or refine Avrami s treatment. With respect to nucleation and to its kinetics, the temperature is obviously a parameter of paramount importance. For a sporadic nucleation, it was established that the rate N, which corresponds to the number of nuclei generated per unit time and volume, is given by... 

Moderate chain folding in the amorf ous state solves both the kinetics of crystallization and the measured chain dimensions of amorphous melts and solids, in Lindenmeyefs view. 

Even when the principles of interface reaction and diffusion are thought to be understood, the integrated results may still require major new work. For example, the growth rate of an individual crystal in an infinite melt can be predicted if parameters are known, but the growth rates of many crystals (and different minerals), i.e., the kinetics of crystallization of a magma, is not quantitatively understood. 

Kirkpatrick R.J., Robinson G.R., and Hays J.F. (1976) Kinetics of crystal growth from silicate melts. /. Geophys. Res. 81, 5715-5720. 

Zhang Y. (1988) Kinetics of Crystal Dissolution and Rock Melting a Theoretical and Experimental Study. Thesis, Columbia University, New York. 

Fig. 9. Melting kinetics and crystallization kinetics of polymeric selenium (right) and polyethylene (left). The equilibrium melting temperatures are 494.2 and 414. 6K. The dotted curve indicates that on crystallization of the macromolecule from small molecules Sc2 there is no molecular nucle-ation necessary as in the melt crystallization (see also ref. 43 for a more detailed discussion of Se crystallization and melting). Drawn after Ref. 4,)...

Crystallization from the melt often leads to a distinct (usually lamellar) structure, with a different periodicity from the melt. Crystallization from solution can lead to non-lamellar crystalline structures, although these may often be trapped non-equilibrium morphologies. In addition to the formation of extended or folded chains, crystallization may also lead to gross orientational changes of chains. For example, chain folding with stems parallel to the lamellar interface has been observed for block copolymers containing poly(ethylene), whilst tilted structures may be formed by other crystalline block copolymers. The kinetics of crystallization have been studied in some detail, and appear to be largely similar to the crystallization dynamics of homopolymers. 

There is no comprehensive theory for crystallization in block copolymers that can account for the configuration of the polymer chain, i.e. extent of chain folding, whether tilted or oriented parallel or perpendicular to the lamellar interface. The self-consistent field theory that has been applied in a restricted model seems to be the most promising approach, if it is as successful for crystallizable block copolymers as it has been for block copolymer melts. The structure of crystallizable block copolymers and the kinetics of crystallization are the subject of Chapter 5. 

Attempts have been made with some success to produce other polymers that exhibit this property of natural rubber. Although the melting temperature can be matched by appropriately disrupting the crystallizable structure through controlled introduction of another monomer, an exact match is not possible because the extent of crystallinity and the kinetics of crystallization will differ. 

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