Rheology and Microscopic Topology of Entangled Polymeric Liquids

A possible strategy for generating polymer chains with an entanglement-free structure

We propose a possible strategy that may experimentally generate long polymeric chains with an entanglement-free structure. The basic idea is designing the conditions to restrict polymer chains from growing along the surface with an obviously concave curvature. This strategy is proved to effectively reduce the chance of forming both inter- and intra-molecular entanglements, which is quite similar to the self-avoiding random walking of chains on a two dimensional plane. We believe that this kind of chain growth strategy may supply a kind of possible explanation on the formation of the entanglement-free structure of chromosomes, which also have tremendously large molecular weight. Besides, this study also guides experimentalists on synthesizing specific entanglement-free functional polymeric or biological materials.

Effect of Slip-Spring Parameters on the Dynamics and Rheology of Soft, Coarse-Grained Polymer Models

Highly coarse-grained (hCG) linear polymer models allow for accessing long time and length scales by dissipative particle dynamics (DPD). This top-down strategy exploits the universal equilibrium behavior of long, flexible macromolecules by accounting only for the relevant interactions, such as molecular connectivity, and by parametrizing their strength via coarse-grained invariants, such as the mean-squared end-to-end distance. The description of the dynamics of long, entangled polymers, however, poses a challenge because (i) the noncrossability of the molecular backbones is not enforced by the soft interactions of an hCG model and (ii) the rheology involves multiple time and length scales, such as the Rouse-like dynamics on short scales and the reptation dynamics on long scales. One popular technique to effectively mimic the effect of entanglements in linear polymer melts via hCG models is slip-springs, and quantitative agreement with simulations that explicitly account for the noncrossability of molecular contours, experiments, and theoretical predictions has been achieved by identifying the time, length, and energy scales of the hCG model and adjusting the number of slip-springs per macromolecule. In the present work, we study how the spatial extent and the mobility of slip-springs affect the dynamics and discuss their implications in the choice of the degree of coarse-graining in computationally efficient hCG models.

Experiments and Modeling of Flow-Enhanced Nucleation in LLDPE

A computational and experimental framework for quantifying flow-enhanced nucleation (FEN) in polymers is presented and demonstrated for an industrial-grade linear low-density polyethylene (LLDPE). Experimentally, kinetic measurements of isothermal crystallization were performed by using fast-scanning calorimetry (FSC) for melts that were presheared at various strain rates. The effect of shear on the average conformation tensor of the melt was modeled with the discrete slip-link model (DSM). The conformation tensor was then related to the acceleration in nucleation kinetics by using an expression previously validated with nonequilibrium molecular dynamics (NEMD). The expression is based on the nematic order tensor of Kuhn segments, which can be obtained from the conformation tensor of entanglement strands. The single adjustable parameter of the model was determined by fitting to the experimental FSC data. This expression accurately describes FEN for the LLDPE, representing a significant advancement toward the development of a fully integrated processing model for crystallizable polymers.

Fingerprinting Brownian Motions of Polymers under Flow

We present a quantitative approach to the self-dynamics of polymers under steady flow by employing a set of complementary reference frames and extending the spherical harmonic expansion technique to dynamic density correlations. Application of this method to nonequilibrium molecular dynamics simulations of polymer melts reveals a number of universal features. For both unentangled and entangled melts, the center-of-mass motions in the flow frame are described by superdiffusive, anisotropic Gaussian distributions, whereas the isotropic component of monomer self-dynamics in the center-of-mass frame is strongly suppressed. Spatial correlation analysis shows that the heterogeneity of monomer self-dynamics increases significantly under flow.

Single-walled carbon nanotube reptation dynamics in submicron sized pores from randomly packed mono-sized colloids

Studying the Brownian motion of fibers and semi-flexible filaments in porous media is the key to understanding the transport and mechanical properties in a variety of systems. The motion of semi-flexible filaments in gel-like porous media including polymer networks and cell cytoskeleton has been studied theoretically and experimentally, whereas the motion of these materials in packed-colloid porous media, advanced foams, and rock-like systems has not been thoroughly studied. Here we use video microscopy to directly visualize the reptation and transport of intrinsically fluorescent, semiflexible, semiconducting single-walled carbon nanotubes (SWCNTs) in the sub-micron pores of packed colloids as fixed obstacles of packed-colloid porous media. By visualizing the filament motion and Brownian diffusion at different locations in the pore structures, we study how the properties of the environment, like the pore shape and pore structure of the porous media, affect SWCNT mobility. These results show that the porous media structure controls SWCNT reorientation during Brownian diffusion. In packed-colloid pores, SWCNTs diffuse along straight pores and bend across pores; conversely, in gel pores, SWCNTs consistently diffuse into curved pores, displaying a faster parallel motion. In both gel and packed-colloid porous media, SWCNT finite stiffness enhances SWCNT rotational diffusion and prevents jamming, allowing for inter-pore diffusion.

Geometric Predictors of Knotted and Linked Arcs

Inspired by how certain proteins “sense” knots and entanglements in DNA molecules, here, we ask if local geometric features that may be used as a readout of the underlying topology of generic polymers exist. We perform molecular simulations of knotted and linked semiflexible polymers and study four geometric measures to predict topological entanglements: local curvature, local density, local 1D writhe, and nonlocal 3D writhe. We discover that local curvature is a poor predictor of entanglements. In contrast, segments with maximum local density or writhe correlate as much as 90% of the time with the shortest knotted and linked arcs. We find that this accuracy is preserved across different knot types and also under significant spherical confinement, which is known to delocalize essential crossings in knotted polymers. We further discover that nonlocal 3D writhe is the best geometric readout of the knot location. Finally, we discuss how these geometric features may be used to computationally analyze entanglements in generic polymer melts and gels.

Superstretchable Elastomer from Cross-linked Ring Polymers

The stretchability of polymeric materials is critical to many applications such as flexible electronics and soft robotics, yet the stretchability of conventional cross-linked linear polymers is limited by the entanglements between polymer chains. We show using molecular dynamics simulations that cross-linked ring polymers are significantly more stretchable than cross-linked linear polymers. Compared to linear polymers, the entanglements between ring polymers do not act as effective cross-links. As a result, the stretchability of cross-linked ring polymers is determined by the maximum extension of polymer strands between cross-links, rather than between trapped entanglements as in cross-linked linear polymers. The more compact conformation of ring polymers before deformation also contributes to the increase in stretchability.

Slip-Spring Hybrid Particle-Field Molecular Dynamics for Coarse-Graining Branched Polymer Melts: Polystyrene Melts as an Example

The topology of chains significantly modifies the dynamical properties of polymer melts. Here, we extend a recently developed efficient simulation method, namely the slip-spring hybrid particle-field (SS-hPF) model, to study the structural and dynamical properties of branched polymer melts over large spatial-temporal scales. In the coarse-grained SS-hPF simulation of polymers, the bonded potentials are derived by iterative Boltzmann inversion from the underlying fine-grained model. The nonbonded potentials are computed from a density functional field instead of pairwise interactions used in standard molecular dynamics simulations, which increases the computational efficiency by a factor of 10-20. The entangled dynamics is lost due to the soft-core nature of density functional field interactions. It is recovered by a multichain slip-spring model that is rigorously parametrized from existing experimental or simulation data. To quantitatively predict the relaxation and diffusion of branched polymers, which are dominated by arm retraction rather than chain reptation, the slip-spring algorithm is augmented to improve the polymer dynamics near the branch point. Multiple dynamical observables, e.g., diffusion coefficients, arm relaxations, and tube survival probabilities, are characterized in an example coarse-grained model of symmetric and asymmetric star-shaped polystyrene melts. Consistent dynamical behaviors are identified and compared with theoretical predictions. With a single rescaling factor, the prediction of diffusion coefficients agrees well with the available experimental measurements. In this work, an efficient approach is provided to build chemistry-specific coarse-grained models for predicting the dynamics of branched polymers.

Validation and Refinement of Unified Analytic Model for Flexible and Semiflexible Polymer Melt Entanglement

We combine molecular dynamics simulations and topological analyses (TA) to validate and refine a recently proposed unified analytic model [Hoy, R. S.; Kröger, M. Phys. Rev. Lett. 2020, 124, 147801] for the reduced entanglement length, tube diameter, and plateau modulus of polymer melts. While the functional forms of the previously published expressions are insensitive to the choice of the TA method and N _e -estimator, obtaining better statistics and eliminating all known sources of systematic error in the N _e -estimation alters their numerical coefficients. Our revised expressions quantitatively match bead-spring simulation data over the entire range of chain stiffnesses for which systems remain isotropic, semiquantitatively match all available experimental data for flexible, semiflexible, and stiff polymer melts (including new data for conjugated polymers that lie in a previously unpopulated stiffness regime), and outperform previously developed unified scaling theories.

Two-step heat fusion kinetics and mechanical performance of thermoplastic interfaces

Thermoplastic polymers and composites are ubiquitous in the industry for their reshaping and fusing capabilities at elevated temperatures. The quality of heat-fused thermoplastic interfaces is of great concern for adhesion, coating, and welding applications, especially those between dissimilar materials. Kinetic evolution of the microstructures defines the mechanical performance of heat-fusion thermoplastic interfaces, which is studied here using polyethylene and polypropylene as an example. Key factors such as the viscosity and compatibility of polymers and the time and temperature of fusion are discussed by combining molecular-level simulations and structural-level hot-compression experiments. Inter-diffusion and entanglement of polymer chains are identified as the two elementary kinetic steps of the fusion, which dominate the control on the stiffness and strength of the interfaces, respectively. Experimental data shows that the quality of fused interfaces can be improved by reducing the viscosity and the interaction parameter. Following the same set of time-scaling relations as identified in the simulations, the two-step characteristics and their effects on the stiffness and strength are experimentally validated. Both simulation and the experiment results show that Young's modulus of fused interfaces recovers faster than the strength that is controlled by polymer entanglement to a large extent, rather than diffusion. These findings add insights into the design of fusion processes, laying the ground for the applications of thermoplastic polymers and composites.

Molecular weaving

Historically, the interlacing of strands at the molecular level has mainly been limited to coordination polymers and DNA. Despite being proposed on a number of occasions, the direct, bottom-up assembly of molecular building blocks into woven organic polymers remained an aspirational, but elusive, target for several decades. However, recent successes in two-dimensional and three-dimensional molecular-level weaving now offer new opportunities and research directions at the interface of polymer science and molecular nanotopology. This Perspective provides an overview of the features and potential of the periodic nanoscale weaving of polymer chains, distinguishing it from randomly entangled polymer networks and rigid crystalline frameworks. We review the background and experimental progress so far, and conclude by considering the potential of molecular weaving and outline some of the current and future challenges in this emerging field.

Predicting the Plateau Modulus from Molecular Parameters of Conjugated Polymers

The relationship between Kuhn length l k , Kuhn monomer volume v 0, and plateau modulus G N 0, initially proposed by Graessley and Edwards for flexible polymers, and extended by Everaers, has a large gap in experimental data between the flexible and stiff regimes. This gap prevents the prediction of mechanical properties from the chain structure for any polymer in this region. Given the chain architecture, including a semiflexible backbone and side chains, conjugated polymers are an ideal class of material to study this crossover region. Using small angle neutron scattering, oscillatory shear rheology, and the freely rotating chain model, we have shown that 12 polymers with aromatic backbones populate a large part of this gap. We also have shown that a few of these polymers exhibit nematic ordering, which lowers G N 0. When fully isotropic, these polymers follow a relationship between l k , v 0, and G N 0, with a simple crossover proposed in terms of the number of Kuhn segments in an entanglement strand N e.

Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design

In recent years, the synthesis of monomer sequence-defined polymers has expanded into broad-spectrum applications in biomedical, chemical, and materials science fields. Pursuing the characterization and inverse design of these polymer systems requires our fundamental understanding not only at the individual monomer level, but also considering the chain scales, such as polymer configuration, self-assembly, and phase separation. However, our accessibility to this field is still rudimentary due to the limitations of traditional design approaches, the complexity of chemical space along with the burdened cost and time issues that prevent us from unveiling the underlying monomer sequence-structure-property relationships. Fortunately, thanks to the recent advancements in molecular dynamics simulations and machine learning (ML) algorithms, the bottlenecks in the tasks of establishing the structure-function correlation of the polymer chains can be overcome. In this review, we will discuss the applications of the integration between ML techniques and coarse-grained molecular dynamics (CGMD) simulations to solve the current issues in polymer science at the chain level. In particular, we focus on the case studies in three important topics-polymeric configuration characterization, feed-forward property prediction, and inverse design-in which CGMD simulations are leveraged to generate training datasets to develop ML-based surrogate models for specific polymer systems and designs. By doing so, this computational hybridization allows us to well establish the monomer sequence-functional behavior relationship of the polymers as well as guide us toward the best polymer chain candidates for the inverse design in undiscovered chemical space with reasonable computational cost and time. Even though there are still limitations and challenges ahead in this field, we finally conclude that this CGMD/ML integration is very promising, not only in the attempt of bridging the monomeric and macroscopic characterizations of polymer materials, but also enabling further tailored designs for sequence-specific polymers with superior properties in many practical applications.

Topological Friction and Relaxation Dynamics of Spatially Confined Catenated Polymers

We study catenated ring polymers confined inside channels and slits with Langevin dynamics simulations and address how the contour position and size of the interlocked or physically linked region evolve with time. We show that the catenation constraints generate a drag, or topological friction, that couples the contour motion of the interlocked regions. Notably, the coupling strength decreases as the interlocking is made tighter, but also shorter, by confinement. Though the coupling strength differs for channel and slit confinement, the data outline a single universal curve when plotted against the size of the linked region. Finally, we study how the relaxation kinetics changes after one of the rings is cut open and conclude that considering interlocked circular polymers is key for isolating the manifestations of topological friction. The results ought to be relevant for linked biomolecules in experimental or biological confining conditions.

Facile equilibration of well-entangled semiflexible bead-spring polymer melts

The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [Auhl et al., J. Chem. Phys. 119, 12718-12728 (2003)] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with N ≃ 40N_e and chain stiffnesses all the way up to the isotropic-nematic transition using simulations of no more than 100 × 10⁶ time steps. For semiflexible chains, our method is several times faster than the standard DBH; we exploit this speedup to develop improved expressions for Kremer-Grest melts' chain-stiffness-dependent Kuhn length ℓ_K and entanglement length N_e.

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.

Simu-D: A Simulator-Descriptor Suite for Polymer-Based Systems under Extreme Conditions

We present Simu-D, a software suite for the simulation and successive identification of local structures of atomistic systems, based on polymers, under extreme conditions, in the bulk, on surfaces, and at interfaces. The protocol is built around various types of Monte Carlo algorithms, which include localized, chain-connectivity-altering, identity-exchange, and cluster-based moves. The approach focuses on alleviating one of the main disadvantages of Monte Carlo algorithms, which is the general applicability under a wide range of conditions. Present applications include polymer-based nanocomposites with nanofillers in the form of cylinders and spheres of varied concentration and size, extremely confined and maximally packed assemblies in two and three dimensions, and terminally grafted macromolecules. The main simulator is accompanied by a descriptor that identifies the similarity of computer-generated configurations with respect to reference crystals in two or three dimensions. The Simu-D simulator-descriptor can be an especially useful tool in the modeling studies of the entropy- and energy-driven phase transition, adsorption, and self-organization of polymer-based systems under a variety of conditions.

Tunable Knot Segregation in Copolyelectrolyte Rings Carrying a Neutral Segment

We use Langevin dynamics simulations to study the knotting properties of copolyelectrolyte rings carrying neutral segments. We show that by solely tuning the relative length of the neutral and charged blocks, one can achieve different combinations of knot contour position and size. Strikingly, the latter is shown to vary nonmonotonically with the length of the neutral segment; at the same time, the knot switches from being pinned at the block's edge to becoming trapped inside it. Model calculations relate both effects to the competition between two adversarial mechanisms: the energy gain of localizing one or more of the knot's essential crossings on the neutral segment and the entropic cost of such localization. Tuning the length of the neutral segment sets the balance between the two mechanisms and hence the number of localized essential crossings, which in turn modulates the knot's size. This general principle ought to be useful in more complex systems, such as multiblock copolyelectrolytes, to achieve a more granular control of topological constraints.

Topological and physical links in soft matter systems

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.

Heterogeneous Dynamics of Polymer Melts Exerted by Chain Loops Anchored on the Substrate: Insights from Molecular Dynamics Simulation

Understanding polymer-substrate interfacial dynamics at the molecular level is crucial for tailoring the properties of polymer ultrathin films (PUFs). Herein, through coarse-grained molecular dynamics simulation, the effect of length (N_loop) and rigidity (K_loop) of loop chains on the dynamics of linear chains is systematically explored, in which the loop chains are adsorbed on a solid substrate and the linear chains are covered on the loop chains. It is found that there is an optimal K_loop, which strongly confines the motion of the linear chains. Meanwhile, compared to increasing the rigidity of the loop chains, increasing the length of the loop chains can more effectively confine the motion of the linear chains. More interestingly, we observe that the mismatch of the length (ΔN) and rigidity (ΔK) between the loop and linear chains leads to dynamic asymmetry (ΔD_c). The relationship between the ΔN, ΔK, and ΔD_c are found to follow the mathematical expression of ΔD_c ∼ (ΔN)^α(ΔK)^β, in which the values of α and β are around 4.58 and 0.83, separately. Remarkably, using the Gaussian process regression model, we construct a master curve of diffusion coefficient on the segmental and chain length scales of the linear chains as a function of N_loop and K_loop, which is further validated by our simulated prediction. In general, this work provides a fundamental understanding of polymer interfacial dynamics at the molecular level, enlightening some rational principles for manipulating the physical properties of PUFs.

Fracture in Silica/Butadiene Rubber: A Molecular Dynamics View of Design-Property Relationships

Despite intense investigation, the mechanisms governing the mechanical reinforcement of polymers by dispersed nanoparticles have only been partially clarified. This is especially true for the ultimate properties of the nanocomposites, which depend on their resistance to fracture at large deformations. In this work, we adopt molecular dynamics simulations to investigate the mechanical properties of silica/polybutadiene rubber, using a quasi-atomistic model that allows a meaningful description of bond breaking and fracture over relatively large length scales. The behavior of large nanocomposite models is explored systematically by tuning the cross-linking, grafting densities, and nanoparticle concentration. The simulated stress-strain curves are interpreted by monitoring the breaking of chemical bonds and the formation of voids, up to complete rupture of the systems. We find that some chemical bonds, and particularly the S-S linkages at the rubber-nanoparticle interface, start breaking well before the appearance of macroscopic features of fracture and yield.

Shear-Thinning in Oligomer Melts-Molecular Origins and Applications

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations of single chains in shear flow, we identify which of these phenomena are of collective nature and arise through interchain interactions and which are already present in dilute systems. Building upon these microscopic simulations, we identify by means of the Irving-Kirkwood formula the corresponding macroscopic stress tensor for a non-Newtonian polymer fluid. Shear-thinning effects in oligomer melts are also demonstrated by macroscopic simulations of channel flows. The latter have been obtained by the discontinuous Galerkin method approximating macroscopic polymer flows. Our study confirms the influence of microscopic details in the molecular structure of short polymers such as chain flexibility on macroscopic polymer flows.

Crystallization of Polymers under the Influence of an External Force Field

We simulated the crystallization and melting behavior of entangled polymer melts using molecular dynamics where each chain is subject to a force dipole acting on its ends. This mimics the deformation of chains in a flow field but represents a well-defined equilibrium system in the melt state. Under weak extension within the linear response of the chains, the mechanical work done on the system is about two orders of magnitude smaller as compared with the heat of fusion. As a consequence, thermodynamic and simple arguments following the secondary nucleation model predict only small changes of the crystalline phase. By contrast, an increase of the stem length up to a factor of two is observed in our simulations. On the other hand, the lamellar thickening induced by the external force is proportional to the increase of the entanglement length in the melt prior to crystallization as measured by the primitive path method. While the mechanical work done on the system is only a small perturbation for thermodynamics of polymer crystallization, the change of the primitive path is large. This suggests that a strong increase in the lamellar thickness induced, by external deformation, a topological rather than a thermodynamic origin.

Sequence-Engineering Polyethylene-Polypropylene Copolymers with High Thermal Conductivity Using a Molecular-Dynamics-Based Genetic Algorithm

Polymer sequence engineering is emerging as a potential tool to modulate material properties. Here, we employ a combination of a genetic algorithm (GA) and atomistic molecular dynamics (MD) simulation to design polyethylene-polypropylene (PE-PP) copolymers with the aim of identifying a specific sequence with high thermal conductivity. PE-PP copolymers with various sequences at the same monomer ratio are found to have a broad distribution of thermal conductivities. This indicates that the monomer sequence has a crucial effect on thermal energy transport of the copolymers. A non-periodic and non-intuitive optimal sequence is indeed identified by the GA, which gives the highest thermal conductivity compared with any regular block copolymers, for example, diblock, triblock, and hexablock. In comparison to the bulk density, chain conformations, and vibrational density of states, the monomer sequence has the strongest impact on the efficiency of thermal energy transport via inter- and intra-molecular interactions. Our work highlights polymer sequence engineering as a promising approach for tuning the thermal conductivity of copolymers, and it provides an example application of integrating atomistic MD modeling with the GA for computational material design.