Star Polymer Melts Research Articles

Unexpected Stress Overshoot in Extensional Flow of Star Polymer Melts.

Previous studies have shown that the nonlinear rheological behavior of 3-arm star polymer melts in fast extensional flow is identical to that of linear polymers with the same span molecular weight, because the star polymers are highly aligned and have a similar conformation as the corresponding linear polymers. However, with more arms, it would be more difficult for the stars to be aligned like linear chains, and the nonlinear extensional rheology of star polymers with more arms under large deformations has not been investigated yet. Here we show that the star polystyrene (8-10 arms) melts behave differently from the linear polystyrenes. A transient stress overshoot is observed in the fast extensional flow, probably due to the difference in entanglement density near and far away from the branch point.

Capillary filling of star polymer melts in nanopores

The topology of a polymer profoundly influences its behavior. However, its effect on imbibition dynamics remains poorly understood. In the present work, capillary filling (during imbibition and following full imbibition) of star polymer melts was investigated by molecular dynamics simulations with a coarse-grained model. The reversal of imbibition dynamics observed for linear-chain systems was also present for star polymers. Star polymers with short arms penetrate slower than the prediction of the Lucas–Washburn equation, while systems with long arms penetrate faster. The radius of gyration increases during confined flow, indicating the orientation and disentanglement of arms. In addition, the higher the functionality of the star polymer, the more entanglement points are retained. Besides, a stiff region near the core segments of the stars is observed, which increases in size with functionality. The proportion of different configurations of the arms (e.g., loops, trains, tails) changes dramatically with the arm length and degree of confinement but is only influenced by the functionality when the arms are short. Following full imbibition, the different decay rates of the self-correlation function of the core-to-end vector illustrate that arms take a longer time to reach the equilibrium state as the functionality, arm length, and degree of confinement increase, in agreement with recent experimental findings. Furthermore, the star topology induces a stronger effect of adsorption and friction, which becomes more pronounced with increasing functionality.

Confinement effect of inter-arm interactions on glass formation in star polymer melts.

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Molecular Dynamics Study of Star Polymer Melts under Start-up Shear

Molecular Dynamics Study of Star Polymer Melts under Start-up Shear

When Polymer Chains Are Highly Aligned: A Perspective on Extensional Rheology

We provide a Perspective on recent findings in extensional rheology for polymer melts and solutions with different macromolecular architectures. For linear polymer systems, we focus on the argument of flow-induced friction reduction and provide our comments from an experimental point of view. For branched polymers, we provide our understanding on how to control extensional viscosity for polymers with different zero-shear-rate viscosity based on recent experimental results of star and comb polymer melts. For ring polymers, we summarize the recent progress in extensional rheology and provide our view on what would be interesting for further investigation. On the basis of the above results and discussions, we show that extensional rheology is complicated for even very simple molecular architectures. More data from both experiments and simulations are important for improvement of a fundamental understanding and development of theories, which is essential for molecular design of polymer materials.

Primitive Chain Network Simulations of Entangled Melts of Symmetric and Asymmetric Star Polymers in Uniaxial Elongational Flows

Ianniruberto and Marrucci developed a theory whereby entangled branched polymers behave like linear ones in fast elongational flows. In order to test such prediction, Huang et al. performed elongational measurements on star polymer melts, indeed revealing that, in fast flows, the elongational viscosity is insensitive to the molecular structure, provided the molecular weight of the backbone is the same. Inspired by these studies, we here report on results obtained with multi-chain slip-link simulations for symmetric and asymmetric star polymer melts, as well as calculations of the Rouse time of the examined branched structures. The simulations semi-quantitatively reproduce the experimental data if the Kuhn-segment orientation-induced reduction of friction (SORF) is accounted for. The observed insensitivity of the nonlinear elongational viscosity to the molecular structure for the same span molar mass may be due to several factors. In the symmetric case, the calculated Rouse time of the star marginally differs from that of the linear molecule, so that possible differences in the observed stress fall within the experimental uncertainty. Secondly, it is possible that the flow-induced formation of hooked star pairs makes the effective Rouse time of the aggregate even closer to that of the linear polymer because the friction center moves towards the branchpoint of the star molecule. In the asymmetric case, it is shown that the stress contributed by the short arms is negligible with respect to that of the long ones. However, such stress-reduction is balanced by a dilution effect whereby the unstretched arms reduce SORF as they decrease the Kuhn-segment order parameter of the system. As a result of that dilution, the stress contributed by the backbone is larger. The two effects compensate one another so that the overall stress is virtually the same as the other architectures.

Cross-correlation corrected friction in (generalized) Langevin models.

We propose a route for parameterizing isotropic (generalized) Langevin [(G)LE] thermostats with the aim to correct the dynamics of coarse-grained (CG) models with pairwise conservative interactions. The approach is based on the Mori-Zwanzig formalism and derives the memory kernels from Q-projected time correlation functions. Bottom-up informed (GLE and LE) thermostats for a CG star-polymer melt are investigated, and it is demonstrated that the inclusion of memory in the CG simulation leads to predictions of polymer diffusion in quantitative agreement with fine-grained simulations. Interestingly, memory effects are observed in the diffusive regime. We demonstrate that previously neglected cross-correlations between the "irrelevant" and the CG degree of freedom are important and lie at the origin of shortcomings in previous CG simulations.

Effects of interaction strength of associating groups on linear and star polymer dynamics.

A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. Here, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead-spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 kBT. We find that, for all melts and blends, interaction of a few kBT between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few kBT and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.

Size and Shape Characteristics of Polystyrene and Poly(ethylene oxide) Star Polymer Melts Studied By Atomistic Simulations

Front Cover: Schematic illustration of the shape transformation of polystyrene stars in melt, by increasing the number of arms f, from the prolate (stars with 4 arms) to the spherical objects (stars with 32 arms). The star polymer melts are studied by means of atomistic molecular dynamics simulations, capturing the indispensable chemical details. This is reported by Eirini Gkolfi, Petra Bačová, and Vagelis Harmandaris in article 2000067.

Star topology increases ballistic resistance in thin polymer films

Polymeric films with greater impact and ballistic resistance are highly desired for numerous applications, but molecular configurations that best address this need remain subject to debate. We study the resistance to ballistic impact of thin polymer films using coarse-grained molecular dynamics simulations, investigating melts of linear polymer chains and star polymers with varying number (2≤f≤16) and degree of polymerization (10≤M≤50) of the arms. We show that increasing the number of arms f or the length of the arms M both result in greater specific penetration energy within the parameter ranges studied. Greater interpenetration of chains in stars with larger f allows energy to be dissipated predominantly through rearrangement of the stars internally, rather than chain sliding. During film deformation, stars with large f show higher energy absorption rates soon after contact with the projectile, whereas stars with larger M have a delayed response where dissipation arises primarily from chain sliding, which results in significant back face deformation. Our results suggest that stars may be advantageous for tuning energy dissipation mechanisms of ultra-thin films. These findings set the stage for a topology-based strategy for the design of impact-resistant polymer films.

Dynamic heterogeneity and collective motion in star polymer melts.

While glass formation of linear chain polymer melts has widely been explored, comparatively little is known about glass formation in star polymer melts. We study the segmental dynamics of star polymer melts via molecular dynamics simulations and examine the cooperative nature of segmental motion in star melts. In particular, we quantify how the molecular architecture of star polymers, i.e., the number of arms and the length of those arms, affects the glass transition temperature Tg, the non-Gaussian nature of molecular displacements, the collective string-like motion of monomers, and the role of chain connectivity in the cooperative motion. Although varying the number of arms f and the molecular mass Ma of the star arms can significantly influence the average star molecular shape, all our relaxation data can be quantitatively described in a unified way by the string model of glass formation, an activated transport model that derives from the Adam-Gibbs model, where the degree of cooperative motion is identified with the average length L of string-like particle exchange motions observed in our simulations. Previous work has shown the consistency of the string model with simulations of linear polymers at constant volume and constant pressure, as well as for thin supported polymer films and nanocomposites with variable polymer-surface interactions, where there are likewise large mobility gradients as in the star polymer melts studied in the present paper.

The relaxation times of unentangled polymer melts with different molecular architectures

Monte Carlo algorithm is adopted to simulate linear, ring, H-shaped and three-arm star polymer melts, and the dependence of relaxation times defined by different methods on polymer size is investigated. Statistical and dynamic properties of several unentangled polymer melts are also revealed for comparison. It is obviously that the numerical difference is small when relaxation times defined by the ratio of maximum mean-square end-to-end distance of several polymers as a function of corresponding mean-square radius of gyration, and data for different architectures collapse onto a universal curve in unentangled regime. The relaxation times for several polymer exhibits weak dependence on architecture. However, the special relationship cannot be found through the relaxation times defined by the position of the intersection of g2 and g3, end-to-end correlation function and mean-square radius of gyration, with stronger architecture dependence. The correctness of the relationship is also reflected by mean-square monomer displacement. The result provides a new understanding of the correlation between relaxation time and polymer size.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts.

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius , packing length p, pair correlation function , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Coarse-Grained Simulations of Three-Armed Star Polymer Melts and Comparison with Linear Chains.

Melts of three-armed star polymers have been simulated using a coarse-grained model parameterized by atomistic simulations of polyethylene. The bonds between the highly coarse-grained, and hence soft, polymer beads are explicitly prevented from crossing by the TWENTANGLEMENT algorithm. The three melts of symmetric stars, differing in the lengths of the arms, are compared against five melts of linear polymers with comparable dimensions to study the impact of branched architecture on self-diffusion and bulk rheological properties. Differently from the power-law relation between the viscosity and molecular mass of linear chains, the star polymers in our simulations follow an exponential mass-viscosity relation and show qualitative agreement with the storage and loss moduli for stars with far longer arms from experiments. The stress relaxation dynamics of the stars are also compared with theoretical analysis in terms of Rouse modes.

A comparative study of thermodynamic, conformational, and structural properties of bottlebrush with star and ring polymer melts.

Thermodynamic, conformational, and structural properties of bottlebrush polymer melts are investigated with molecular dynamics simulations and compared to linear, regular star, and unknotted ring polymer melts to gauge the influence of molecular topology on polymer melt properties. We focus on the variation of the backbone chain length, the grafting density along the backbone, and the length of the side chains at different temperatures above the melt glass transition temperature. Based on these comparisons, we find that the segmental density, isothermal compressibility, and isobaric thermal expansion of bottlebrush melts are quantitatively similar to unknotted ring polymer melts and star polymer melts having a moderate number ( f = 5 to 6) of arms. These similarities extend to the mass scaling of the chain radius of gyration. Our results together indicate that the configurational properties of bottlebrush polymers in their melt state are more similar to randomly branched polymers than linear polymer chains. We also find that the average shape of bottlebrush polymers having short backbone chains with respect to the side chain length is also rather similar to the unknotted ring and moderately branched star polymers in their melt state. As a general trend, the molecular shape of bottlebrush polymers becomes more spherically symmetric when the length of the side chains has a commensurate length as the backbone chain. Finally, we calculate the partial static structure factor of the backbone segments and we find the emergence of a peak at the length scales that characterizes the average distance between the backbone chains. This peak is absent when we calculate the full static structure factor. We characterize the scaling of this peak with parameters characterizing the bottlebrush molecular architecture to aid in the experimental characterization of these molecules by neutron scattering.

A note on hydrodynamics from dissipative particle dynamics

We calculate current correlation functions (CCFs) of dissipative particle dynamics (DPD) and compare them with results of molecular dynamics (MD) and solutions of linearized hydrodynamic equations. In particular, we consider three versions of DPD, the empirical/classical DPD, coarse-grained (CG) DPD with radial-direction interactions only and full (radial, transversal, and rotational) interactions between particles. To facilitate quantitative discussions, we consider specifically a star-polymer melt system at a moderate density. For bonded molecules, it is straightforward to define the CG variables and to further derive CG force fields for DPD within the framework of the Mori-Zwanzig formalism. For both transversal and longitudinal current correlation functions (TCCFs and LCCFs), we observe that results of MD, DPD, and hydrodynamic solutions agree with each other at the continuum limit. Below the continuum limit to certain length scales, results of MD deviate significantly from hydrodynamic solutions, whereas results of both empirical and CG DPD resemble those of MD. This indicates that the DPD method with Markovian force laws possibly has a larger applicability than the continuum description of a Newtonian fluid. This is worth being explored further to represent generalized hydrodynamics.

Network formation and gelation in telechelic star polymers.

We investigate the efficiency of gelation and network formation in telechelic star polymer melt, where the tips of polymer arms are dipoles while the rest of the monomers are uncharged. Our work is motivated by the experimental observations [A. Kulkarni et al., Macromolecules 48, 6580 (2015)] in which rheological studies of telechelic star polymers of poly-(L-lactide), a bio-degradable polymer, showed a drastic increase in elastic properties (up to 2000 times) compared to corresponding star polymers without the telechelic arm ends. In contrast to previous studies, we avoid using effective attractive Lennard-Jones potentials or dipolar potentials to model telechelic interactions. Instead we use explicit Coulomb positive and negative charges at the tip of polymer-arms of our bead-spring model of star polymers. By our simulations we show that the dipoles at the tip of star arms aggregate together to form clusters of dipoles. Each cluster has contributions from several stars, and in turn each star contributes to several clusters. Thus the entire polymer melt forms a connected network. Network forming tendencies decrease with a decrease of the value of the effective charge constituting the dipole: this can be experimentally realized by choosing a different ionomer for the star tip. We systematically varied the value of dipole charges, the fraction of star-arms with dipoles at the tip, and the length of the arms. The choice of explicit charges in our calculations enables us to make better quantitative predictions about the onset of gelation; moreover we get qualitatively distinct results about structural organization of dipoles within a dipole-cluster.

Computing the non-Markovian coarse-grained interactions derived from the Mori-Zwanzig formalism in molecular systems: Application to polymer melts.

Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. More specifically, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. However, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.

Microscopic Picture of Constraint Release Effects in Entangled Star Polymer Melts

The constraint release (CR) effect in entangled branched polymers is generally described by the widely accepted dynamic tube dilation (DTD) theory based on the tube model, which predicts the stress relaxation function reasonably well, but not the dielectric or arm end-to-end vector relaxation. The microscopic picture of entanglement dynamics even in the simple case of star polymers is still not fully resolved. In this work, we first perform molecular dynamics (MD) simulations of symmetric star polymer melts using the Kremer–Grest bead–spring model. The entanglement events are analyzed microscopically using the persistent close contacts between mean paths of neighboring polymer strands. The resulting survival probability function of these entanglements or close contacts shows reasonably good agreement with the stress relaxation function, which provides qualitative evidence for the binary picture of entanglements. On the basis of this understanding, we further investigate the star arm retraction and CR effects using the coarse-grained single-chain slip-spring model originally developed by Likhtman and also a simplified single-chain stochastic model. In both MD and slip-spring simulations we verified the mechanism proposed by Shanbhag et al. that constraint release events lead to the insertion of new entanglements in between the branch points and deepest entanglements so that the last remaining deepest entanglements are deleted by relatively shallow arm retractions. Our simulations further revealed that for the entanglements sitting on a target star arm, only those destroyed by the free end of the given arm dominate the arm end-to-end vector relaxation, while the broad constraint release spectrum, together with the excluded volume of entanglements and the reflecting boundary at the branch point, produces an accelerated drift of the mean positions of these specific entanglements toward the arm-end, which is an essential mechanism for understanding the relaxation of star polymers in concentrated solutions or melts. Our findings call for an examination of the microscopic foundation of conventional DTD picture and inspire the development of quantitative theories with consideration of more microscopic details.