Homogeneous nucleation process of polyethylene (PE) is studied with full-atom molecular dynamic simulation. To account the complex shape with low symmetry and the peculiar intra-chain conformational order of polymer, we introduce a shape descriptor OCB coupling conformational order and inter-chain rotational symmetry, which is able to differentiate hexagonal and orthorhombic clusters from melt. With the shape descriptor OCB, we find that coupling between conformational and inter-chain rotational orderings results in the formation of hexagonal clusters first, which is dynamic in nature. Whilst nucleation of orthorhombic structure occurs inside of hexagonal clusters later, which proceeds via the coalescence of neighboring hexagonal clusters rather than standard stepwise growth process. This demonstrates that nucleation of PE crystal is a two-step process with the assistance of OCB order, which is different from early models for polymer crystallization but similar with that proposed for spherical 'atoms' like colloid and metal. 3 Significance StatementBy introducing a shape descriptor OCB that couples intra-chain conformational order and inter-chain rotational order, we successfully differentiate local structures with hexagonal and orthorhombic symmetries and observe OCB order assisted two-step nucleation process in polyethylene crystallization. OCB order is demonstrated to promote the transformation from flexible chains to conformational ordered segments, which is the most peculiar and critical step in polymer crystallization. The shape descriptor OCB may be universal on differentiating local orders in polymer or systems with connectivity.

Molecular dynamics (MD) simulations are employed to study biaxial stretch-induced crystallization of polymers, during which the individual roles of chain conformation and orientation on crystal nucleation and growth are clarified. Systems with different stiffness and orientations are constructed by changing the stretch ratios of the x-and y-axis, which allow us to figure out the individual contributions of chain conformation and orientation to flowenhanced nucleation. The results show that nucleation occurs in areas with high segment orientation, and the higher orientation corresponds to the shorter nucleation induction period. The relationship between the nucleation induction period and orientation is quantitatively expressed, which indicates that orientation plays a dominant role in flow-enhanced nucleation. On the other hand, the results show that chain stiffness exhibits a negative correlation with nucleation in biaxial stretch, supporting that conformational entropy reduction is not the main driving force in flow-induced crystallization of polymers. With the secondary nucleation model, the crystal growth rates in different directions correlate well with the orientation at the growth front of the clusters, further confirming the decisive role of orientation in crystal nucleation and growth. Finally, crystal cluster merging is proposed to be a way to form shish structures in highly oriented melts.

The nucleation process of polyethylene under quiescent and shear flow conditions are comparatively studied with all-atom molecular dynamical simulations. At both conditions, nucleation are demonstrated to be two-step processes, which, however, proceed via different intermediate orders. Quiescent nucleation is assisted by local structure order coupling conformational and local rotational symmetric orderings, while flow-induced nucleation is promoted by density fluctuation, which is a coupling effect of conformational and orientation orderings. Flow drives the transformation from flexible chains to rigid conformational ordered segments and circumvents the entropic penalty, which is the most peculiar and rate-limited step in polymer crystallization. Current work suggests that flow accelerates nucleation in orders of magnitude is not simply due to flow-induced entropic reduction of melt as early models proposed, which is mainly attributed to the different kinetic pathway via conformational/orientational orderingdensity fluctuationnucleation.

Summary The phase‐field approach has unique advantages in describing fracture phenomena, which has received extensive attention in the past decade. Nevertheless, the phase‐field modeling of fracture is computationally demanding, due to the high temporal‐spatial resolution required for crack tracking. In this contribution, a novel hybrid adaptive finite element phase‐field method (ha‐PFM) is developed to solve brittle fracture problems under quasi‐static and dynamic loading. ha‐PFM can dynamically track the propagation of the cracks and adaptively refine the meshes based on a novel crack tip identification strategy. Afterward, the refined meshes in the noncrack progression region are reconverted into coarse meshes. This scheme prominently reduces the computational cost, eg, CPU time and memory usage. Unlike the previous adaptive phase‐field method, multilevel hybrid triangular and quadrilateral elements were developed to discretize the computational domain, which eliminates hanging nodes and ensures that the meshes in the vicinity of the crack tip are highly isotropic. Several representative benchmarks containing quasi‐static and dynamic fracture were reinvestigated with ha‐PFM, and its excellent performance is substantiated by comparison with the standard phase‐field method and literature results.

The stretch-induced coil–helix transition (CHT) of isotactic polypropylene (iPP) was studied with full-atom molecular dynamics (MD) simulations during the uniaxial stretch process. The results show that imposing stretch induces CHT, which increases both the content and the average length of helices. As strain exceeding a certain value, long helices initially not presented in melt start to emerge, which mainly follow a kinetic pathway of merging adjacent short helices, while overstretch at large strain leads to the helix-extended coil transition. Based on statistics on the distribution of helical length and theoretical calculation, stretch is found to reduce free energy gap for CHT. At small strain, the single-chain model is sufficient to account stretch-induced CHT for the formation of short helices, but the gap reduction is mainly contributed by intrachain energy rather than entropy, which is different from current theories for stretch-induced CHT. While the formation of long helices at large strain requires interchain cooperative interactions, which is accompanied by the formation of helix-rich clusters. Additionally, we found that the content of helices with odd atoms in backbone is higher than their even counterparts, which exhibits an odd–even effect due to their corresponding helical lengths.

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Non-equilibrium molecular dynamics simulations have been performed to study the molecular mechanism of flow-induced crystallization (FIC) of polyethylene (PE). The end-to-end distance of chain R and the content of trans conformation C are extracted out to represent intra-chain conformation ordering at whole chain and segment levels, respectively, while orientation correlation function P, density ρ, and bond orientational order parameter Q are taken to depict inter-chain orders. Imposing the extension induces the intra-chain conformational ordering to occur first, which further couples with the inter-chain order and results in the formation of hexagonal packing. Further increasing strain leads to the appearance of orthorhombic order. The results demonstrate that the FIC of PE proceeds via a multi-stage ordering process, during which coupling occurs among stress, intra-chain conformation, and inter-chain orientation and density orderings. Analyzing the flow-induced energy evolution unveils that not only entropy but also energy plays an important role in the FIC.

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