Local structure order assisted two-step crystal nucleation in polyethylene

The homogeneous nucleation process of polyethylene (PE) is studied with full-atom molecular dynamic simulation. To account for the complex shape with low symmetry and the peculiar intrachain conformational order of polymer, we introduce a shape descriptor $O_{CB}$ coupling conformational order and interchain rotational symmetry, which is able to differentiate hexagonal and orthorhombic clusters from melt. With the shape descriptor $O_{CB}$, we find that coupling between conformational and interchain rotational orderings results in the formation of hexagonal clusters first, which is dynamic in nature. After the formation of hexagonal clusters, the nucleation of orthorhombic structure occurs inside of them, which proceeds via the coalescence of neighboring hexagonal clusters rather than a standard stepwise growth process. This demonstrates that nucleation of PE crystal is an $O_{CB}$ order assisted two-step process, which is different from previous models for polymer crystallization but similar with that proposed for spherical “atoms” such as colloid and metal.

Figure 1

(a, b) Snapshots of the nucleation process of PE with different types of atoms colored differently. Orange and cyan (red and yellow) correspond the center atom and neighboring atoms of H-$O_{CB}$ (O-$O_{CB}$) clusters, respectively, while the blue ones belong to both. (c) The XRD of the orthorhombic clusters. (d, e, f) The evolutions of the number of $O_{CB}$ structures at 330, 350, and 375 K, respectively.

Figure 2

(a) The $S_2$ evolution of $H-O_{CB}$ at five representative times before 7.5 ns. The black dashed line indicates the formation time of $H-O_{CB}$ clusters, at which $S_2$ shows a local minimum. (b) $O_{CB}$ structures (right column) and their Voronoi volume of carbon atoms (left column) at five representative times, where high Voronoi volume means low density. There seems to be no direct correlation between $H-O_{CB}$ and density observed.

Figure 3

(a) The evolutions of the number of ordered clusters and the size of the largest cluster in a representative region of the system at 375 K. Nucleation of PE is defined by two steps, namely, $O_{CB}$ fluctuation (step I) and orthorhombic nucleation (step II). (b) The evolutions of structural entropy $S_2$ and Voronoi volume of carbon atoms at 375 K.

Figure 4

The evolutions of the number of ordered clusters and the size of the largest cluster in a representative region of systems at 350 K (a) and 330 K (b), respectively.

Figure 5

(a) Ideal orthorhombic (left) and hexagonal (right) lattices of PE. (b) $O_{CB}$ values of orthorhombic and hexagonal lattices. The orthorhombic structure has $O_{CB}$ equal to 0.130, while $O_{CB}$ for the hexagonal lattice equals 0.150 or 0.165, which are well separated from each other.

Figure 6

(a) $O_{CB}$ values of an ideal orthorhombic lattice with five random orientations, which indicate the “mathematic footprint” and do not change with orientation. (b) The distributions of $\phi$ and $\theta$ for orthorhombic and hexagonal lattices of PE, which indicate the connection between these two angles due to the trans conformation and parallel of neighboring segments. (c) The values of $Q_l$ and $\theta$ distributions in the same domain ($-\pi /2, \pi /2$), which indicates that the $Q_l$ keeps most features of $\theta$ distributions. Red and blue dots correspond to orthorhombic and hexagonal structures in (b) and (c), respectively. (d) The structures we found by the $O_{CB}$ parameter.