Polymer crystallization primary nucleation

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... 

Interestingly, this barrier does not depend on chain length. This result coincides with experimental observations on the primary nucleation rate of bulk polymers [128-130]. For secondary nucleation of crystallization on a smooth growth front, a similar free-energy expression can be obtained for 2D nucleation ... 

Polymer crystallization is usually divided into two separate processes primary nucleation and crystal growth [1]. The primary nucleation typically occurs in three-dimensional (3D) homogeneous disordered phases such as the melt or solution. The elementary process involved is a molecular transformation from a random-coil to a compact chain-folded crystallite induced by the changes in ambient temperature, pH, etc. Many uncertainties (the presence of various contaminations) and experimental difficulties have long hindered quantitative investigation of the primary nucleation. However, there are many works in the literature on the early events of crystallization by var-... 

Note Nucleation may be classified as primary or secondary. Primary nucleation can be homogeneous or heterogeneous if heterogeneous nucleation is initiated by entities having the same composition as the crystallizing polymer, it is called self-nucleation. Secondary nucleation is also known as surface nucleation. 

In polymers crystallized from the melt, in most cases spherulitic structures are observed spherical agglomerates of crystals and amorphous regions, grown from a primary nucleus via successive secondary nucleation (Figure 4.18). The dimensions of the spherulites are commonly between 5 pm and 1 mm. When spherulites grow during the crystallization process, they touch each other and are separated by planes. In a microtome slice they show a very attractive coloured appearance in polarized light. 

The primary crystallization process is characterized by three parameters. These are the rate of radial growth of the spherulite, G, the time constant for nucleation, t , and the time constant for the primary crystallization process, Tc, which is determined from the Avrami equation. All three parameters seem to depend on the stereoregularity of the polymer, but the nucleation rate seems to depend most strongly. 

The relationship for primary nucleation (Equation 10-34) only applies to pure polymers. In most practical cases, crystallization... 

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. 

Fig. 10.23 Illustration of three basic situations of crystal nucleation. From left to right are primary nucleation in the bulk polymer phase, secondary nucleation on the smooth growth front, and tertiary nucleation at the terrace of the growth front...

It was often found that, contrary to the theoretical prediction, the value of n is noninteger (Avrami 1939). The Avrami model is based on several assumptions, such as constancy in shape of the growing crystal, constant rate of radial growth, lack of induction time, uniqueness of the nucleation mode, complete crystallinity of the sample, random distribution of nuclei, constant value of radial density, primary nucleation process (no secondary nucleation), and absence of overlap between the growing crystallization fronts. These assumptions are often not met in polymer (blend) crystallization. Also, erroneous determination of the zero time and an overestimation of the enthalpy of fusion of the polymer at a given time can lead to noninteger values for n (Grenier and Prud homme 1980). 

---