Power law of molecular weight of the nucleation rate of folded chain crystals of polyethylene

The molecular weight (M_n) 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 ∝ M_n^-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 (ΔT) dependence of I fits well with the theoretical I given by classical nucleation theory, I = I₀ exp(-ΔG*/kT) ∝ D exp(-C/ΔT²), where I₀ is proportional to the topological diffusion coefficient of polymer chains (D), ΔG* 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 ΔG* (∝C) does not depend on M_n, while I₀ decreases with increase of M_n, from which it is concluded that formation of a critical nucleus is not controlled by M_n, while only topologic diffusion of polymers is controlled by M_n, i.e., I ∝ D(M_n). Similar power laws of PE were already found by the present authors on I of extended chain single crystals (ECSCs), i.e., I ∝ M_n^-1.0, and on the lateral growth rates (V) of ECSCs and FCSCs, V ∝ M_n^-0.7 and V ∝ M_n^-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(M_n) ∝ M_n^-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.