Crystallization of polyethylene: A molecular dynamics simulation study of the nucleation and growth mechanisms

Molecular dynamics simulations of single polyethylene chain folding during fast quenching using all-atom and united-atom models

Molecular dynamics simulations have been employed to investigate the folding behavior of a single linear polyethylene (PE) chain containing 1000 backbone carbon atoms under fast quenching based on all-atom and united-atom models. The single-chain folding characteristics were studied in detail for six different force fields by analyzing the evolution of chain conformations, folded structure characterisation, free energy and crystallisation. The results show that the all-trans chain undergoes a similar two-stage chain collapse mechanism during isothermal relaxation at T = 500 K, transitioning from local collapse to global collapse into a molten globule state under different force fields. During fast quenching at 100 K ns-1, the molten globule of all-atom model transitions into a folded, significantly anisotropic ordered structure under AMBER-AA or OPLS-AA force fields, while that of the united-atom model remains unchanged in its globular structure. The chain crystallization evolution indicates that the single chain folds into ordered lamellar structures with higher crystallinity under AMBER-AA and OPLS-AA force fields. In contrast, under the other four force fields, the single chain remains in a stable amorphous state.

Investigating the Hydrogen Bond-Induced Self-Assembly of Polysulfamides Using Molecular Simulations and Experiments

In this paper, we present a synergistic, experimental, and computational study of the self-assembly of N,N'-disubstituted polysulfamides driven by hydrogen bonds (H-bonds) between the H-bonding donor and acceptor groups present in repeating sulfamides as a function of the structural design of the polysulfamide backbone. We developed a coarse-grained (CG) polysulfamide model that captures the directionality of H-bonds between the sulfamide groups and used this model in molecular dynamics (MD) simulations to study the self-assembly of these polymers in implicit solvent. The CGMD approach was validated by reproducing experimentally observed trends in the extent of crystallinity for three polysulfamides synthesized with aliphatic and/or aromatic repeating units. After validation of our CGMD approach, we computationally predicted the effect of repeat unit bulkiness, length, and uniformity of segment lengths in the polymers on the extent of orientational and positional order among the self-assembled polysulfamide chains, providing key design principles for tuning the extent of crystallinity in polysulfamides in experiments. Those computational predictions were then experimentally tested through the synthesis and characterization of polysulfamide architectures.

Rheological and Mechanical Properties of Thermoplastic Crystallizable Polyimide-Based Nanocomposites Filled with Carbon Nanotubes: Computer Simulations and Experiments

Recently, a strong structural ordering of thermoplastic semi-crystalline polyimides near single-walled carbon nanotubes (SWCNTs) was found that can enhance their mechanical properties. In this study, a comparative analysis of the results of microsecond-scale all-atom computer simulations and experimental measurements of thermoplastic semi-crystalline polyimide R-BAPB synthesized on the basis of dianhydride R (1,3-bis-(3′,4-dicarboxyphenoxy) benzene) and diamine BAPB (4,4′-bis-(4″-aminophenoxy) biphenyl) near the SWCNTs on the rheological properties of nanocomposites was performed. We observe the viscosity increase in the SWCNT-filled R-BAPB in the melt state both in computer simulations and experiments. For the first time, it is proven by computer simulation that this viscosity change is related to the structural ordering of the R-BAPB in the vicinity of SWCNT but not to the formation of interchain linkage. Additionally, strong anisotropy of the rheological properties of the R-BAPB near the SWCNT surface was detected due to the polyimide chain orientation. The increase in the viscosity of the polymer in the viscous-flow state and an increase in the values of the mechanical characteristics (Young’s modulus and yield peak) of the SWCNT-R-BAPB nanocomposites in the glassy state are stronger in the directions along the ordering of polymer chains close to the carbon nanofiller surface. Thus, the new experimental data obtained on the R-BAPB-based nanocomposites filled with SWCNT, being extensively compared with simulation results, confirm the idea of the influence of macromolecular ordering near the carbon nanotube on the mechanical characteristics of the composite material.

Chiral selecting crystallization of helical polymers: A molecular dynamics simulation for the POM-like bare helix

Polymer crystallization has long been a fascinating problem and is still attracting many researchers. Most of the previous simulations are concentrated on clarifying the universal aspects of polymer crystallization using model linear polymers such as polyethylene. We are recently focusing on a nearly untouched but very interesting problem of chiral selecting crystallization in helical polymers. We previously proposed a stepwise approach using two kinds of helical polymers, simple "bare" helical polymers made of backbone atoms only such as polyoxymethylene (POM) and "general" helical polymers containing complicated side groups such as isotactic polypropylene (iPP). We have already reported on the crystallization in oligomeric POM-like helix but have observed only weak chiral selectivity during crystallization. In the present paper, we investigate the crystallization of sufficiently long POM-like polymer both from the isotropic melt and from the highly stretched melt. We find in both cases that the polymer shows a clear chiral selecting crystallization. Especially the observation of a single crystal growing from the isotropic melt is very illuminating. It shows that the crystal thickness and the crystal chirality is closely correlated; thicker crystals show definite chirality while thinner ones are mostly mixtures of the R- and the L- handed stems. The single crystal is found to have a marked lenticular shape, where the thinner growth front, since being made of the mixture, shows no chiral selectivity. Final chiral crystal is found to be completed through helix reversal processes within thicker regions.

Semiflexible oligomers crystallize via a cooperative phase transition

Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature-density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt-crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization.

Direct observation of long chain enrichment in flow-induced nuclei from molecular dynamics simulations of bimodal blends

Modelling of flow-induced nucleation in polymers suggest that long chains are enriched in nuclei, relative to their melt concentration. This enrichment has important consequences for the nucleation rate and mechanism, but cannot be directly observed with current experimental techniques. Instead, we ran united atom molecular dynamics simulations of bimodal polyethylene blends, comprising linear chains at a 50 : 50 mix of long (1000 carbon) and short (500-125 carbon) chains, under shear flow. We developed a method to extract the nucleus composition during a transient start-up flow. Our simulations show significant and systematic enrichment of long-chains for all nucleus sizes up to and beyond the critical nucleus. This enrichment is quantitatively predicted by the recent polySTRAND model [Read et al. Phys. Rev. Lett. 2020, 124, 147802]. The same model parameters also correctly capture the nucleus induction time in our simulations. All parameters of the model were fitted to a small subset of our data in which long chain enhancement was absent. We conclude that long-chain enrichment is central to the mechanism of flow-induced nucleation and that this enrichment must be captured to correctly predict the nucleation rate.

Crystallization of semiflexible polymers in melts and solutions

We studied the crystallization of semiflexible polymer chains in melts and poor-solvent solutions with different concentrations using dissipative particle dynamics (DPD) computer simulation techniques. We used the coarse-grained polymer model to reveal the general principles and microscopic scenario of crystallization in such systems at large time and length scales. It covers both primary and secondary nucleation as well as crystallites' merging. The parameters of the DPD model were chosen appropriately to reproduce the entanglements of polymer chains. We started from an initial homogeneous disordered solution of Gaussian chains and observed the initial stages of crystallization process caused in our model by orientational ordering of polymer chains and polymer-solvent phase separation. We found that the overall crystalline fraction at the end of the crystallization process decreases with the increasing polymer volume fraction while the steady-state crystallization speed at later stages does not depend on the polymer volume fraction. The average crystallite size has a maximal value in the systems with a polymer volume fraction from 0.7 to 0.95. In our model, these polymer concentrations represent an optimal value in the sense of balance between the amount of polymer material available to increase the crystallite size and chain entanglements, that prevent crystallites' growth and merging. On large time scales, our model allows us to observe lamellar thickening linear in logarithmic time scale.

Microstructure Characterization of Oceanic Polyethylene Debris

Plastic pollution has become a worldwide concern. It was demonstrated that plastic breaks down to nanoscale particles in the environment, forming so-called nanoplastics. It is important to understand their ecological impact, but their structure is not elucidated. In this original work, we characterize the microstructure of oceanic polyethylene debris and compare it to the nonweathered objects. Cross sections are analyzed by several emergent mapping techniques. We highlight deep modifications of the debris within a layer a few hundred micrometers thick. The most intense modifications are macromolecule oxidation and a considerable decrease in the molecular weight. The adsorption of organic pollutants and trace metals is also confined to this outer layer. Fragmentation of the oxidized layer of the plastic debris is the most likely source of nanoplastics. Consequently the nanoplastic chemical nature differs greatly from plastics.

Room temperature crystallization of amorphous polysiloxane using photodimerization

Bulk crystallization in flexible polymeric systems is difficult to control due to the random orientation of the chains. Here we report a photo cross-linking strategy that results in simultaneous cross-linking and crystallization of polysiloxane chains into millimeter sized leaf-like polycrystalline structures. Polymers containing pendant anthracene groups are prepared and undergo [4+4] photocycloaddition under 365 nm irradiation at room temperature. The growth and morphology of the crystalline structures is studied using polarized optical microscopy (POM) and atomic force microscopy and is found to progress through three unique stages of nucleation, growth, and constriction. The mobility of the individual chains is probed using pulsed-field gradient (PFG) NMR to provide insights into the diffusion processes that may govern chain transport to the growing crystal fronts. The room temperature crystallization of this conventionally amorphous polymer system may allow for a new level of morphological control for silicone materials.

Monodisperse Polymer Melts Crystallize via Structurally Polydisperse Nanoscale Clusters: Insights from Polyethylene

This study demonstrates that monodisperse entangled polymer melts crystallize via the formation of nanoscale nascent polymer crystals (i.e., nuclei) that exhibit substantial variability in terms of their constituent crystalline polymer chain segments (stems). More specifically, large-scale coarse-grain molecular simulations are used to quantify the evolution of stem length distributions and their properties during the formation of polymer nuclei in supercooled prototypical polyethylene melts. Stems can adopt a range of lengths within an individual nucleus (e.g., ∼1-10 nm) while two nuclei of comparable size can have markedly different stem distributions. As such, the attainment of chemically monodisperse polymer specimens is not sufficient to achieve physical uniformity and consistency. Furthermore, stem length distributions and their evolution indicate that polymer crystal nucleation (i.e., the initial emergence of a nascent crystal) is phenomenologically distinct from crystal growth. These results highlight that the tailoring of polymeric materials requires strategies for controlling polymer crystal nucleation and growth at the nanoscale.

Dominant Effects of Short-Chain Branching on the Initial Stage of Nucleation and Formation of Tie Chains for Bimodal Polyethylene as Revealed by Molecular Dynamics Simulation

The molecular mechanism of short-chain branching (SCB), especially the effects of methylene sequence length (MSL) and short-chain branching distribution (SCBD) on the initial stage of nucleation, the crystallization process, and particularly the tie chain formation process of bimodal polyethylene (BPE), were explored using molecular dynamics simulation. This work constructed two kinds of BPE models in accordance with commercial BPE pipe resins: SCB incorporated in the long chain or in the short chains. The initial stage of nucleation was determined by the MSL of the system, as the critical MSL for a branched chain to nucleate is about 60 CH2. SCB incorporated in the long chain led to a delay of the initial stage of nucleation relative to the case of SCB incorporated in the short chains. The increase of branch length could accelerate the delay to nucleation. The location of short chain relative to the long chain depended on the MSL of the short chain. As the MSL of the system decreased, the crystallinity decreased, while the tie chains concentration increased. The tie chains concentration of the BPE model with branches incorporated in the long chain was higher than that with branches incorporated in the short chain.

A coarse-grain model for entangled polyethylene melts and polyethylene crystallization

The Shinoda-DeVane-Klein (SDK) model is herein demonstrated to be a viable coarse-grain model for performing molecular simulations of polyethylene (PE), affording new opportunities to advance molecular-level, scientific understanding of PE materials and processes. Both structural and dynamical properties of entangled PE melts are captured by the SDK model, which also recovers important aspects of PE crystallization phenomenology. Importantly, the SDK model can be used to represent a variety of materials beyond PE and has a simple functional form, making it unique among coarse-grain PE models. This study expands the suite of tools for studying PE in silico and paves the way for future work probing PE and PE-based composites at the molecular level.

Polymer nucleation under high-driving force, long-chain conditions: Heat release and the separation of time scales

This study reveals important features of polymer crystal formation at high-driving forces in entangled polymer melts based on simulations of polyethylene. First and in contrast to small-molecule crystallization, the heat released during polymer crystallization does not appreciably influence structural details of early-stage, crystalline clusters (crystal nuclei). Second, early-stage polymer crystallization (crystal nucleation) can occur without substantial chain-level relaxation and conformational changes. This study's results indicate that local structures and environments guide crystal nucleation in entangled polymer melts under high-driving force conditions. Given that such conditions are often used to process polyethylene, local structures and the separation of time scales associated with crystallization and chain-level processes are anticipated to be of substantial importance to processing strategies. This study highlights new research directions for understanding polymer crystallization.

An accelerated united-atom molecular dynamics simulation on the fast crystallization of ring polyethylene melts

To investigate crystallinities based on trans-structures, we determined the differences in the crystallization properties of ring and linear polymers by performing united-atom-model molecular dynamics (MD) simulations of homogeneous polyethylene melts of equal length, N, which refers to the number of monomers per chain. Modified parameters based on the DREIDING force field for the CH₂ units were used in order to accelerate the crystallization process. To detect polymer crystallization, we introduced some local-order parameters that relate to trans-segments in addition to common crystallinities using neighboring bond orders. Through quenching MD simulations at 5 K/ns, we roughly determined temperature thresholds, T_th, at which crystallization is observed although it was hard to determine the precise T_th as observed in the laboratory time frame with the present computing resources. When N was relatively small (100 and 200), T_th was determined to be 320 and 350 K for the linear- and ring-polyethylene melts, respectively, while T_th was found to be 330 and 350 K, respectively, when N was 1000. Having confirmed that the crystallization of a ring-polyethylene melt occurs faster than that of the analogous linear melt, we conclude that the trans-segment-based crystallinities are effective for the analysis of local crystal behavior.

Folded alkane chains and the emergence of the lamellar crystal

The competition between chain stiffness and chain collapse gives rise to complex low temperature morphologies of single polymer chains, in our case alkanes. These structures are characterized by specific sequences of dihedral angles along the chain, i.e., dihedral angle correlations extending beyond local steric effects. To describe and classify these morphologies, one can transfer concepts from protein science, where this creation of dihedral angle correlations underlies the formation of α-helices and β-sheets. We show here by means of flat-histogram Monte Carlo simulations that, although lacking in primary structure being simple homopolymers, short alkane chains fold into non-trivial ground states (tertiary structure) consisting of chain segments of defined secondary structures. The folded lamellar crystal typical for polyethylene chains requires a minimum chain length to occur as the ground state folded structure, which we identify to be around 150 repeat units.

Structural Ordering in SWCNT-Polyimide Nanocomposites and Its Influence on Their Mechanical Properties

Using fully-atomistic models, tens-microseconds-long molecular-dynamic modelling was carried out for the first time to simulate the kinetics of polyimides ordering induced by the presence of single-walled carbon nanotube (SWCNT) nanofillers. Three polyimides (PI) were considered with different dianhydride fragments, namely 3,3',4,4'-biphenyltetracarboxylic dianhydride (BPDA), 2,3',3,4'-biphenyltetracarboxylic dianhydride (aBPDA), and 3,3',4,4'-oxidiphthalic dianhydride (ODPA) and same diamine 1,4-bis[4-(4-aminophenoxy)phenoxy]benzene (diamine P3). Both crystallizable PI BPDA-P3 and two amorphous polyimides ODPA-P3 and aBPDA-P3 reinforced by SWCNTs were studied. The structural properties of the nanocomposites at temperature close to the bulk polymer melting point were studied. The mechanical properties were determined for the nanocomposites cooled down to the glassy state. It was found that the SWCNT nanofiller initiates' structural ordering not only in the crystallizable BPDA-P3 but also in the amorphous ODPA-P3 samples were in agreement with previously obtained experimental results. Two stages of the structural ordering were detected in the presence of SWCNTs, namely the orientation of the planar moieties followed by the elongation of whole polymer chains. The first type of local ordering was observed on the microsecond time scale and did not lead to the change of the mechanical properties of a polymer binder in considered nanocomposites. At the end of the second stage, both BPDA-P3 and ODPA-P3 PI chains extended completely along the SWCNT surface, which in turn led to enhanced mechanical characteristics in their glassy state.

Crystallization in melts of short, semiflexible hard polymer chains: An interplay of entropies and dimensions

What is the thermodynamic driving force for the crystallization of melts of semiflexible polymers? We try to answer this question by employing stochastic approximation Monte Carlo simulations to obtain the complete thermodynamic equilibrium information for a melt of short, semiflexible polymer chains with purely repulsive nonbonded interactions. The thermodynamics is obtained based on the density of states of our coarse-grained model, which varies by up to 5600 orders of magnitude. We show that our polymer melt undergoes a first-order crystallization transition upon increasing the chain stiffness at fixed density. This crystallization can be understood by the interplay of the maximization of different entropy contributions in different spatial dimensions. At sufficient stiffness and density, the three-dimensional orientational interactions drive the orientational ordering transition, which is accompanied by a two-dimensional translational ordering transition in the plane perpendicular to the chains resulting in a hexagonal crystal structure. While the three-dimensional ordering can be understood in terms of Onsager theory, the two-dimensional transition can be understood in terms of the liquid-hexatic transition of hard disks. Due to the domination of lateral two-dimensional translational entropy over the one-dimensional translational entropy connected with columnar displacements, the chains form a lamellar phase. Based on this physical understanding, orientational ordering and translational ordering should be separable for polymer melts. A phenomenological theory based on this understanding predicts a qualitative phase diagram as a function of volume fraction and stiffness in good agreement with results from the literature.

Prediction of Flow Effect on Crystal Growth of Semi-Crystalline Polymers Using a Multi-Scale Phase-Field Approach

A multi-scale phase-field approach, which couples the mesoscopic crystallization with the microscopic orientation of chain segments and macroscopic viscoelastic melt flow, is proposed to study how the crystal growth of semi-crystalline polymers is affected by flows. To make the simulation feasible, we divide the problem into three parts. In the first part, a finitely extensible nonlinear elastic (FENE) dumbbell model is used to simulate the flow induced molecular structure. In the second part, formulas for estimating the density, orientation and aspect ratio of nuclei upon the oriented molecular structure are derived. Finally, in the third part, a massive mathematical model that couples the phase-field, temperature field, flow field and orientation field is established to model the crystal growth with melt flow. Two-dimensional simulations are carried out for predicting the flow effect on the crystal growth of isotactic polystyrene under a plane Poiseuille flow. In solving the model, a semi-analytical method is adopted to avoid the numerical difficult of a "high Weissenberg number problem" in the first part, and an efficient fractional step method is used to reduce the computing complexity in the third part. The simulation results demonstrate that flow strongly affects the morphology of single crystal but does not bring a significant influence on the holistic morphology of bulk crystallization.

Correlation of Solubility with the Metastable Limit of Nucleation Using Gauge-Cell Monte Carlo Simulations

We present a novel simulation-based investigation of the nucleation of nanodroplets from solution and from vapor. Nucleation is difficult to measure or model accurately, and predicting when nucleation should occur remains an open problem. Of specific interest is the "metastable limit", the observed concentration at which nucleation occurs spontaneously, which cannot currently be estimated a priori. To investigate the nucleation process, we employ gauge-cell Monte Carlo simulations to target spontaneous nucleation and measure thermodynamic properties of the system at nucleation. Our results reveal a widespread correlation over 5 orders of magnitude of solubilities, in which the metastable limit depends exclusively on solubility and the number density of generated nuclei. This three-way correlation is independent of other parameters, including intermolecular interactions, temperature, molecular structure, system composition, and the structure of the formed nuclei. Our results have great potential to further the prediction of nucleation events using easily measurable solute properties alone and to open new doors for further investigation.