Molecular Weight Dependence of Crystal Growth Rate

1 Molecular Weight Dependence of Crystal Growth Rate 

Molecular weight dependence of crystal growth rate can be expressed as a function of adsorption of polymer molecules (A ) on to the crystal-growing surface, diffusion of the adsorbed molecules (D ) on the crystal surface and secondary (surface) nucleation based on the adsorbed molecules as schematically illustrated in Fig. 19.22. Accordingly, the growth rate is expressed as follows [29], 

Lauritzen and Hoffmann have introduced the probability parameter of admolecules on the crystal-growing surface prior to surface nucleation but not considered the molecular weight dependence on it [51]. Adsorption of polymer molecules must be a function of molecular conformation on the crystal surface (substrate) as given by the following equation. 

According to reptation mechanism, d equals to -1 for molecules without entanglements and to 2 for entangled molecules [70]. AEj, is the activation energy of molecular diffusion for the adsorbed molecule on the crystal surface. Taking these factors into account, the crystal growth rate is expressed as follows  

The pre-exponential factor of Gq in Eq. (19.2) can be expressed as a function of molecular weight as given by The molecular transport term 

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Umemoto, S., Kobayashi, N., and Okui, N., Molecular weight dependence of crystal growth rate and its degree of supercooling effect, J. Macromol. ScL, Part B Phys. 41, 923-938, 2002. 

S. Umemoto, and N. Okui, Power law and scaling for molecular weight dependence of crystal growth rate in polymeric materials, Pol3rmer 46, 8790 795 (2005). 

S is the thickness of the deposited layer, and CaOe the surface free energy of the lateral and edge faces. Tm is the equilibrium melting point of the polymer and Tc the crystallization temperature. Since chain ends depress the melting point, this, with variations in molecular weight dependence of the growth rates. 

Molecular Weight Dependence of Nucleation and Crystal Growth Rates... 

Molecular weight dependence of overall crystallization rate (k) seems to be very complicated as seen in Fig. 19.2 for PE. The Avrami constant of k is a function of nucleation rate of (1) and crystal growth rate of (G) as expressed by following equation,... 

The molecular weight dependences of many polymers have been presented in order to emphasize the complex behavior and diversity of results. Appropriate theory must explain this behavior. In particular, the increase, decrease and constancy of the overall crystallization kinetics and spherulite growth rates with molecular weight needs to be taken into account. Also to be explained are how the rates are tempered by the crystallization temperatures and the chemical nature of the chain repeating unit. The extensive set of experimental results available allows for a critical and objective examination of this problem and the explanations that have been offered. 

The explanation given for the growth rates of linear polyethylene is highly specific. Based on the successive modifications that have been made, there is a serious question as to whether the reptation concept, as it has been applied, has general applicability to the crystallization kinetics of polymers. If the basic ideas of reptation theory are appropriate, major alterations have to be made so that it explains the molecular weight dependence of all polymers. 

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