Dependence of mechanical properties on crystal orientation of semi-crystalline polyethylene structures

Abstract

Molecular dynamics simulations based on a united atom method are employed to study the molecular response of semi-crystalline polyethylene structures with unidirectional and bidirectional molecular orientation. The initial structures are generated from isothermal crystallization at 375 K of pre-oriented melts. Deformation simulations are conducted at a constant strain rate of 1.24 nm/ns at both constant volume (NVT) and constant lateral stress (NL_zσ_xσ_yT) conditions. In order to connect characterization results at various length scales two-point statistics are introduced to capture the morphological changes in semi-crystalline structures during the deformation, based on the density and orientational differences of the amorphous and crystalline regions. In this new approach, molecular conformational changes are well captured in the two-point auto- and cross-correlation spectra, to understand the morphological evolution of different domains consisting of macromolecular chains on a statistical level. The pseudo-laminar semi-crystalline structures are preserved for both structures up to a strain level of 0.5, with the rotation and orientation of chains in the crystalline region facing towards the uniaxial deformation direction. A laminar to fibrillar transition is observed for the bidirectional oriented semi-crystalline structure at higher strain levels. Recovery tests confirm the stability of the laminar and fibrillar structures at certain stages of the deformation.

Introduction

Semi-crystallinity is a unique and important structural characteristic of thermoplastic polymers. Owing to the significant differences in the morphology and orientation between crystalline and amorphous regions, such as in the orientation ordering, tensile modulus and relaxation time, the molecular level mechanisms of semi-crystalline polymer deformation have been studied for decades. Early attempts tried to fit semi-crystalline polymer deformations using a universal rubber elasticity model [1], in which the chain entanglements are concentrated in the amorphous region and the interface between the amorphous and crystalline regions, which are responsible for the inelastic strain. Such models treated the crystallites as rigid bodies without structural details and rotational degrees of freedom during deformation. Bartczak et al. [2], [3] carried out a series of X-ray scattering and transmission electron microscopy experiments on compression and shearing deformation experiments on semi-crystalline polyethylene samples. Direct evidence of interlamellar sliding and intralamellar shearing were found. Peterlin and Meinel [4], [5], [6] investigated the plastic deformation of polyethylene samples by two-dimensional (2D) small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS). By comparing the intensity changes of the meridional and equatorial scattering peaks, a microfibril model was proposed and a lamellar to fibrillar transition was suggested based on scattering data.

To fit the stress–strain relationship of linear polymers into a general visco-elastic model, Strobl and colleagues [7], [8], [9], [10] examined the true stress–strain behavior of polymer samples, with the assistance of a video-controlled stretching device. From extensive deformation and subsequent recovery tests, critical states were identified [11] which occurred at certain strain levels that were independent of temperature, strain rate and degree of crystallinity. In that model, two linear regions in the initial stages terminated with “double yielding points” [11], while the third critical point was associated with the onset of fibrillation. The fourth point was believed to have originated from chain disentanglements, and was associated with initiation of cracking and failure.

Morphological evolution of the deformation process is accessible using in-situ synchrotron X-ray techniques. Pioneering work by Samon, Schultz and Hsiao et al. [12], [13] on structure development in polymer melt spinning, involving both SAXS and WAXS, showed that the melt spinning process was a combination of the crystallization (early stage) and uniaxial deformation (drawing stage). In the case of polyethylene, the amorphous lamellar thickness increased, while the crystal lamellar thickness remained constant at slow or moderate take-up speed, and reduced at higher speed. Different behaviors of the lamellae were attributed to the large difference in their tensile modulus. A later paper also calculated the Hermans' orientation factor [14] of crystal chain axis as a function of strain. Based on results from different diffraction peaks, the general trend showed a drastic rise of the chain orientation along the stretching direction in the early stage of deformation.

Men et al. [15] studied the uniaxial deformation of over-stretched polyethylene samples, and observed decrease in tilt angle and increase in fibril length with increased strain. A later study [16] indicated lamellar to fibrillar transitions in the tensile deformation of high-density polyethylene. The breakdown of the initial laminated crystallites and fibril formation during tensile deformation was identified by the peak shift in the SAXS patterns. Stribeck et al. [17] developed a multidimensional chord distribution function (CDF), based on data analysis of the SAXS pattern, which strongly enhances the sharpness of surfaces and distinguishes the correlation between the surface orientations. The crystallization behavior from a highly oriented melt [18] and the deformation process [19] were characterized by the CDF method, accompanied with wide angle X-ray diffractions patterns and thermal analysis. Highly oriented crystals were found to have crystallized from the highly oriented melt. The lamellar to fibrillar transition and co-existence of lamellar and fibrillar domains were also confirmed.

Due to the structural complexity and long relaxation time, simulations of the crystallization behavior from polymer melt were not frequently reported compared to the attention devoted to metallic and inorganic systems. Early attempts were based on the Monte Carlo (MC) approaches [20] on the high coordination lattice [21]. Molecular dynamics (MD) simulations [22] investigated single chain crystallization behavior in vacuum. Rutledge et al. were able to crystallize n-eicosane (C₂₀H₄₂) [23] and n-octane (C₈₀H₁₆₂) [24] chains from the melt state. Crystal growth kinetics was also studied. The crystallization behavior for longer polyethylene-like chain lengths was also reported [25]. Chains with 400 repeating units from the unidirectional oriented melt were observed to partially crystallize within 30 nanoseconds (ns) into a lamellar semi-crystalline structure. Similar approaches were also applied by Yamamoto [26] in a recent communication to simulate a fiber spinning process. The initial orientation imposed to the melt was believed to reduce the induction period of nucleation substantially, compared to that at the isotropic condition; this work also describes lamellar fibrillar transformation in biaxial deformation.

The mechanical properties of amorphous polymer samples have also been simulated using united atom MD simulations [27], [28], [29]. True stress–strain curves were computed from the uniaxial deformation tests, with a fixed strain rate in the direction of stretching and zero lateral pressure. Although the strain rate is orders of magnitude higher than the experimental values (a general limitation of the MD simulations), the overall characteristics of the response of polymers to deformation were captured, including the initial elastic deformation, the yield point and the strain hardening.

In most experimental studies and applications, polyethylene samples prepared for deformation tests are semi-crystalline. Owing to the structural complexity of the multi-phase nature of the system, almost all the previous studies [30], [31], [32] have adopted an MC approach which fixes the crystalline layers and only relaxes the amorphous part, on the basis of which interfacial structures and deformation mechanisms have been examined. A recent publication on the mechanical property of a semi-crystalline polymer [32] allowed all the united atoms of the initial structure to relax. The initial structure was built using an MC algorithm [30], which consists of two crystalline lamellae with fixed distance, and certain number of “bridge” and “tail” connections of amorphous regions in between the crystals.

In this paper, the mechanical behavior of semi-crystalline polyethylene structures with different crystal orientations is simulated using MD. Focus is placed on semi-crystalline structures that are directly crystallized from pre-oriented melt. Morphological changes of the samples at the molecular level are examined.