Molecular dynamics simulations of steady-state crystal growth and homogeneous nucleation in polyethylene-like polymer

Investigation of Crystallization and Relaxation Effects in Coarse-Grained Polyethylene Systems after Uniaxial Stretching

In this study, we investigate the thermo-mechanical relaxation and crystallization behavior of polyethylene using mesoscale molecular dynamics simulations. Our models specifically mimic constraints that occur in real-life polymer processing: After strong uniaxial stretching of the melt, we quench and release the polymer chains at different loading conditions. These conditions allow for free or hindered shrinkage, respectively. We present the shrinkage and swelling behavior as well as the crystallization kinetics over up to 600 ns simulation time. We are able to precisely evaluate how the interplay of chain length, temperature, local entanglements and orientation of chain segments influences crystallization and relaxation behavior. From our models, we determine the temperature dependent crystallization rate of polyethylene, including crystallization onset temperature.

Coarse-grained molecular dynamics simulations of void generation and growth processes in the fracture of the lamellar structure of polyethylene

We investigate the void generation and growth process in semicrystalline polymers by large-scale coarse-grained molecular dynamics simulations. Voids are generated in the amorphous layers and grow spherically and then cylindrically, consistent with the results of previous experiments. Interestingly, the fusion of voids is indicated to enlarge the voids in the direction perpendicular to the stretching direction, but not beyond the crystalline layers. The orientational order along the stretching direction increased sharply before void generation, but the increase leveled off afterward. The simulations also clearly reveal that the crystalline layers break but do not bend in the fragmentation process. The dependence of the void growth process on stretching velocity and the stability levels of voids at constant strain are also discussed.

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.

Interaction of high-intensity focused ultrasound with polymers at the atomistic scale

Experiments show that high-intensity focused ultrasound (HIFU) is a promising stimulus with multiple superior and unique capabilities to induce localized heating and achieve temporal and spatial thermal effects in the polymers, noninvasively. When polymers are subjected to HIFU, they heat up differently compared to the case they are subjected to heat sources directly; however, the origins of this difference are still entirely unknown. We hypothesize that the difference in the macroscale response of polymers subjected to HIFU strongly depends on the polymer chains, composition, and structure, i.e. being crystalline or amorphous. In this work, this hypothesis is investigated by molecular dynamics studies at the atomistic level and verified by experiments at the macroscopic scale. The results show that the viscoelasticity, measured by stress-strain phase lag, the reptation motion of the chains, and the vibration-induced local mobility quantified by the root mean square fluctuation contribute to the observed difference in the HIFU-induced thermal effects. This unravels the unknown mechanisms behind stimulating the polymers by HIFU, and paves the way in front of using this method in future applications.

Insight into the Microcosm of the Human Growth Hormone and Its Interactions with Polymers and Copolymers: A Molecular Dynamics Perspective

Therapeutic proteins nowadays have increasingly been applied for their considerable potential in treating a wide variety of diseases. The effectiveness and potency of native therapeutic proteins are limited by various factors (e.g., stability, blood circulation time, specificity). Over the past years, a great deal of effort has been devoted to developing safe and efficient protein delivery systems. Entrapment of protein into polymeric and copolymeric matrices is common among the different types of protein-based drug formulation. However, despite the massive efforts toward developing therapeutic protein delivery in experimental studies and industrial applications, there is relatively little data on the influence of polymers and copolymers on therapeutic proteins at the atomic and molecular levels. Herein, molecular dynamics (MD) simulations are used to study the effects of biocompatible synthetic polymers including methoxy poly(ethylene glycol) (MPEG), poly(lactic acid) (PLA), and poly(lactic acid) copolymers (poly(lactic-co-glycolic acid)) PLGA and MPEG-PLA(PELA)) on the structure and dynamics of the human growth hormone (hGH), and the results are compared with previous experimental findings. Our results indicate that the hGH conformation remains stable both in pure water and in the presence of polymers, and these results are in good agreement with previous experimental data. It is shown that the MPEG chains are self-assembled and folded into a semicrystalline structure; therefore, only a small portion of the protein interacts with the polymer. The other three polymers, however, interact well with the protein and partially cover its surface. Our findings suggest that the use of these polymers for protein encapsulation has the advantage of reducing protein aggregation and thus increasing drug serum half-life. Eventually, we anticipate that the research results will expand the current knowledge about encapsulation mechanisms and the molecular interactions between hGH and the polymers.

Property Decoupling across the Embryonic Nucleus-Melt Interface during Polymer Crystal Nucleation

Spatial distributions are presented that quantitatively capture how polymer properties (e.g., segment alignment, density, and potential energy) vary with distance from nascent polymer crystals (nuclei) in prototypical polyethylene melts. It is revealed that the spatial extent of nuclei and their interfaces is metric-dependent as is the extent to which nucleus interiors are solid-like. As distance from a nucleus increases, some properties, such as density, decay to melt-like behavior more rapidly than polymer segment alignment, indicating that a polymer nucleus resides in a nematic-like droplet. This nematic-like droplet region coincides with enhanced formation of ordered polymer segments that are not part of the nucleus. It is more favorable to find nonconstituent ordered polymer segments near a nucleus than in the surrounding metastable melt, pointing to the possibility of one nucleus inducing the formation of other nuclei. In this vein, there is also a second region of enhanced ordering that lies along the nematic director of a nucleus, but beyond its nematic droplet and fold regions. These results indicate that crystal stacking, a key characteristic of lamellae in semicrystalline polymeric materials, begins to emerge during the earliest stages of polymer crystallization (i.e., crystal nucleation). More generally, the findings of this study provide a conceptual bridge between polymer crystal nucleation under nonflow and flow conditions and are used to rationalize previous results.

Divining the shape of nascent polymer crystal nuclei

We demonstrate that nascent polymer crystals (i.e., nuclei) are anisotropic entities with neither spherical nor cylindrical geometry, in contrast to previous assumptions. In fact, cylindrical, spherical, and other high symmetry geometries are thermodynamically unfavorable. Moreover, postcritical transitions are necessary to achieve the lamellae that ultimately arise during the crystallization of semicrystalline polymers. We also highlight how inaccurate treatments of polymer nucleation can lead to substantial errors (e.g., orders of magnitude discrepancies in predicted nucleation rates). These insights are based on quantitative analysis of over four million crystal clusters from the crystallization of prototypical entangled polyethylene melts. New comprehensive bottom-up models are needed to capture polymer nucleation.

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.

Crystal Growth in Polyethylene by Molecular Dynamics: The Crystal Edge and Lamellar Thickness

We carried out large-scale atomistic molecular dynamics simulations to study the growth of twin lamellar crystals of polyethylene initiated by small crystal seeds. By examining the size distribution of the stems-straight crystalline polymer segments-we show that the crystal edge has a parabolic profile. At the growth front, there is a layer of stems too short to be stable, and new stable stems are formed within this layer, leading to crystal growth. Away from the edge, the lengthening of the stems is limited by a lack of available slack length in the chains. This frustration can be relieved by mobile crystal defects that allow topological relaxation by traversing through the crystal. The results shed light on the process of polymer crystal growth and help explain initial thickness selection and lamellar thickening.

Crystallization of finite-extensible nonlinear elastic Lennard-Jones coarse-grained polymers

The ability of a simple coarse-grained finite-extensible nonlinear elastic (FENE) Lennard-Jones (LJ) polymer model to be crystallized is investigated by molecular dynamics simulations. The optimal FENE Lennard-Jones parameter combinations (ratio between FENE and LJ equilibrium distances) and the optimal lattice parameters are calculated for five different perfect crystallite structures: simple tetragonal, body-centered tetragonal, body-centered orthorhombic, hexagonal primitive, and hexagonal close packed. It was found that the most energetically favorable structure is the body-centered orthorhombic. Starting with an equilibrated polymer liquid and with the optimal parameters found for the body-centered orthorhombic, an isothermal treatment led to the formation of large lamellar crystallites with a typical chain topology: folded, loop, and tie chains, and with a crystallinity of about 60%-70%, similar to real semicrystalline polymers. This simple coarse-grained Lennard-Jones model provides a qualitative tool to study semicrystalline microstructures for polymers.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

Stress-Strain Relationships in Hydroxyl Substituted Polyethylene

Stress-strain relationships in semicrystalline hydroxylated polyethylene are studied using all-atom molecular dynamics simulations. Chain sizes ranging from 50 to 2000 carbons are gradually cooled from melt in order to obtain semicrystalline samples for pure, 4%, and 8% hydroxylated chains. Local orientational order of the polymer backbone and hydrogen bonding behavior is studied. The effects of -OH substitution and chain length on stress-strain relationships are examined at 300 K. The number of hydrogen bonds is found to be independent of the chain length. Stress-strain relationships are generally unaffected by 4% hydroxyl substitution in long chain polyethylene. The presence of 8% -OH tends to increase the elastic limit of the material. A method for comparing semicrystalline samples of substituted and unsubstituted polymeric chains is presented by eliminating differences in alignment, distribution, and extent of crystallization.

Influence of the carbon nanofiller surface curvature on the initiation of crystallization in thermoplastic polymers

The segments of crystallizable polyimide tend to lay parallel to the graphene nanofiller surface and this tendency is stronger than for carbon nanotubes.

Disentanglement of Linear Polymer Chains Toward Unentangled Crystals

Large scale and long time molecular dynamics simulations and primitive path analysis are used to investigate the disentanglement of long linear polymer chains during their crystallization from the melt state. In general, two competitive processes, a slow decrease of average entanglement length during cooling caused by stiffening of chains and a strong increase during crystallization, can be observed. In both homogeneous and heterogeneous nucleation, disentanglement occurs via forming folds from locally unentangled segments and continues in postcrystallization processes (slow reorganization), in particular, during annealing. Re-entanglement processes after melting are slow and can lead to memory effects in heating-recooling protocols such as self-seeding.

Morphological changes during annealing of polyethylene nanocrystals

Polymer crystals are metastable and exhibit morphological changes when being annealed. To observe morphological changes on molecular scales we started from small nanometer-sized crystals of highly folded long-chain polymers. Micron-sized stripes consisting of monolayers or stacks of several layers of flat-on oriented polyethylene nanocrystals were generated via evaporative dewetting from an aqueous dispersion. We followed the morphological changes in time and at progressively higher annealing temperatures by determining the topography and viscoelastic properties of such assemblies of nanocrystals using atomic force microscopy. Due to smallness and high surface-to-volume ratio of the nanocrystals, already at 75 °C, i.e. about 60 degrees below the nominal melting point, the lateral size of the crystal coarsened. Intriguingly, this occurred without a noticeable reduction in the number of folds per polymer chain. Starting at around 110 °C, chain folds were progressively removed leading to crystal thickening. At higher temperatures, but still below the melting point, prolonged annealing allowed for surface diffusion of molten polymers on the initially bare substrate, leading eventually to the disappearance of crystals. We compared these results to the behavior of the same nanocrystals annealed in an aqueous dispersion and to bulk samples.

Crystallization of alkane melts induced by carbon nanotubes and graphene nanosheets: a molecular dynamics simulation study

The crystallization of alkane melts on carbon nanotubes (CNT) and the surface of graphene nanosheets (GNS) is investigated using molecular dynamics (MD) simulations. The crystallization process of the alkane melts is analyzed in terms of the bond-orientational order parameter, atomic radial distribution for the CNT/alkane, atomic longitudinal distribution for the GNS/alkane, and diffusion properties. The dimensional effects of the different carbon-based nanostructures on the crystallization of alkane melts are shown. It is found that one-dimensional CNT has a stronger ability to induce the crystallization of the polymer than that of two-dimensional GNS, which provides a support at molecular level for the experimental observation [Li et al., J. Am. Chem. Soc., 2006, 128, 1692 and Xu et al., Macromolecules, 2010, 43, 5000]. From the MD simulations, we also find that the crystallization of alkane molecules has been completed with the highly cooperative processes of adsorption and orientation.

Size distribution of folded chain crystal nuclei of polyethylene on active centers

Kinetic equations describing temporal evolution of the size distribution of crystalline nuclei of folded chain polyethylene on active centers are solved numerically. Basic characteristics of nucleation processes (the total number of supercritical nuclei and the size distribution of nuclei) are determined and compared with the experimental data. It is shown that even though the total number of supercritical nuclei coincides with the experimental data, the size distribution prediction fails. This is caused by the fact that the total number of nuclei (usually used in analysis of the experimental data), in contrast to the size distribution of nuclei, represents an integral quantity. Using the experimental data of the steady state size distribution of nuclei enables us to determine thermodynamic parameters (especially interfacial energies) of the studied system more precisely and consequently to correct kinetic parameters to get coincidence of kinetic model with the experimental data in both, the total number of supercritical nuclei and also the size distribution of nuclei.