Nucleation of Polymer Crystallization

Polymer crystallization is a typical first-order phase transition, following the nucleation and growth mechanism. Therefore, when isothermal crystallization happens slowly at high temperatures, one can observe a significantly long incubation period for crystal nucleation, followed by a self-acceleration process for crystal growth. This process is illustrated by the time-evolution curve of volume crystallinity in Pig. 10.21. 

This equation is similar with (9.43). One can derive the critical free energy barrier for the critical size nuclei AG as 

In 1926, Volmer and Weber found that the nucleation rate shows a negative exponential dependence on critical free energy barrier (Volmer and Weber 1926). Becker and Doting further proposed that the activation energy for the short-distance diffusion of molecules molecules to enter the crystalline phase should be considered as well (Becker and Doring 1935). Turnbull and Fisher derived the prefactor for the rate equation of crystal nucleation (Turnbull and Fisher 1949). The rate of polymer crystal nucleation i with the change of critical free energy barrier can be expressed as 

Here ig is the prefactor, AU is the activation energy for short-distance diffusion of molecules at interfaces. According to the VFT relaxation mode (6.10), AUlkT oc 1/(T Ty). With the increase of crystallization temperatures, molecular diffusion will be enhanced, and AU will be decreased. On the other hand, AG is the critical free energy barrier for crystal nucleation. For the primary nucleation, AG oc AT. With increase of the crystallization temperatures, AT will become smaller, and AG will rise, accordingly the nucleation rate will be decreased. Thus, at high temperatures, the nucleation rate is mainly dominated by the critical free energy barrier for crystal nucleation, the higher the temperature, the smaller the nucleation rate at low temperatures, the nucleation rate will be mainly dominated by the 

The linear growth rate acmally reflects a net competition result between the growth and the melting upon thermal fluctuations at the lateral surface of lamellar crystals, as given by (Ren et al. 2010) 

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Heterogeneous nucleation of polymer crystallization resembling a visualized metaphor compare the way meat is prepared in an oriental way shish - kebab. 

Price, F. D. The nucleation of polymer crystals. Symposium iiber Makro-molekule, Wiesbaden 1959. Kurzmitteilung 1/B 2. 

Chatterjee A M, Price F P and Newman S (1975) Heterogeneous nucleation of polymer crystallization from melt - I - Substrate induced morphologies. Bull Amer Phys Soc 20 341-341. 

On the basis of the concept described above, we propose a model for the homogeneous crystallization mechanism of one component polymers, which is schematically shown in Fig. 31. When the crystallization temperature is in the coexistence region above the binodal temperature Tb, crystal nucleation occurs directly from the melt, which is the well-known mechanism of polymer crystal nucleation. However, the rate of crystallization from the coexistence region is considered to be extremely slow, resulting in single crystals in the melt matrix. Crystallization at a greater rate always involves phase separation the quench below Tb causes phase separations. The most popular case... 

Fig. 31 Structural formation model for the initial stage of polymer crystallization [19], N G nucleation and growth of oriented domains, SD spinodal decomposition into oriented and unoriented domains, Tb, Ts, and Tx bimodal, spinodal, and crystallization temperatures, respectively I isotropic, N smectic, and C crystalline...

Among the numerous challenges faced in understanding polymer crystallization, the present review focuses only on the following issues, which are directly pertinent to the phenomenon of nucleation in polymer crystals. 

NUCLEATION IN POLYMER CRYSTALLIZATION The nucleation part of the linear growth rate is... 

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