Power Law of Molecular Weight of the Nucleation Rate of Folded Chain Crystals of Polyethylene

Abstract

The molecular weight (Mn) dependence of the primary nucleation rate (I) of folded chain single crystals (FCSCs) of polyethylene (PE) was studied. A power law for the nucleation rate, I ∝ Mn -2.4 , was found. The FCSCs were formed by isothermal crystallization from the melt into an ordered phase ()orthorhombic phase). A new experimental method was established to obtain reliable I, which has been difficult in the case of heterogeneous nucleation for long years. The degree of supercooling (∆T) dependence of I fits well with the theoretical I given by classical nucleation theory, I ) I0 exp(-∆G*/kT) ∝ D exp(-C/∆T 2 ), where I0 is proportional to the topological diffusion coefficient of polymer chains (D), ∆G* is the free energy for forming a critical nucleus, k is the Boltzmann constant, T is temperature, and C is a constant. It is found that ∆G* (∝C) does not depend on Mn, while I0 decreases with increase of Mn, from which it is concluded that formation of a critical nucleus is not controlled by Mn, while only topological diffusion of polymers is controlled by Mn, i.e., I ∝ D(Mn). Similar power laws of PE were already found by the present authors on I of extended chain single crystals (ECSCs), i.e., I ∝ Mn -1.0 , and on the lateral growth rates (V) of ECSCs and FCSCs, V ∝ Mn -0.7 and V ∝ Mn -1.7 , respectively. ECSCs were formed by isothermal crystallization from the melt into a disordered phase ()hexagonal phase). Therefore, it is concluded that a common power law, I, V ∝ D(Mn) ∝ Mn -H of PE is confirmed, irrespective of nucleation or growth and irrespective of crystalline phases, ordered or disordered phases. It is to be noted that the power H depends on the degree of order of the crystalline phase, from which it is concluded that both nucleation and growth are controlled by the "topological" diffusion of polymer chains within interface between a nucleus (or crystal) and the melt and/or within the nucleus. The "topological" diffusion is related to chain sliding diffusion and disentanglements.

Crystallization/Melting Kinetics and Morphological Analysis of Polyphenylene Sulfide

“…This mechanism was explained by low molecular weight components having a large free volume at chain ends, allowing them to migrate to the high temperature side. Further, it is known that the primary nucleation rate for folded chain single crystals of a linear polymer increases with decreasing molecular weight . Taking into account these results, the partial segregation of molecular weight proceeds in the direction perpendicular to the sensor surface under high supercooling.…”

Direct Evidence of Nucleation During the Induction Period of Polyethylene Crystallization by SAXS

“…[5,6] They concluded that the topological processes, such as chain-sliding diffusion and entanglement, have important role in nucleation mechanisms of polymers, as had been predicted in the chain-sliding diffusion theory by Hikosaka. [7,8] However, an important unsolved problem is how the topological processes affect the mechanism of induction of polymers.…”

“…(13) as a function of t in order to obtain observed radius of gyration, R g , and the t dependence of R g [R g (t)] applying Guinier's law, [6] …”

Influence of α′‐/α‐crystal polymorphism on properties of poly(l‐lactic acid)

“…The effect of the chain length on crystal nucleation was analyzed at 60 °C (∼ T g ) and 100 °C, and it was shown that the nucleation kinetics at around T g is independent of the chain length within the molar mass range from about 60 to 600 kDa. In contrast, at higher temperature crystal nucleation is slower in PLLA of higher molar mass, indicating the need for chain diffusion at a length scale that depends on the macroscopic viscosity and pointing to the different morphology/larger size of the crystal nuclei forming at higher temperatures; such molar mass dependence of nucleation kinetics has also been observed in the case of polyethylene …”