Dynamics of Star-Shaped Polystyrene Molecules: From Arm Retraction to Cooperativity

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.

Distinguishing between Linear and Star Polystyrenes with Unentangled Arms by Dynamic Oscillatory Shear Tests

Linear and nonlinear viscoelastic properties of star polystyrene (PS) melts with unentangled arms were measured by using small-amplitude and medium-amplitude oscillatory shear (SAOS and MAOS) tests. For comparison purposes, such tests were also conducted on entangled linear and star PS melts. Interestingly, the linear viscoelastic properties of unentangled star PS were quantitatively described using the Lihktman-McLeish model for entangled linear chains, indicating that unentangled stars were indistinguishable from linear chains by using relaxation spectra. By contrast, the relative intrinsic nonlinearity (Q0), one of the MAOS material functions, exhibited a difference between unentangled star and linear PS. When the maximum Q0 value (Q0,max) was plotted against the entanglement number of span molecules (Zs), unentangled star PS exhibited larger Q0,max values than linear PS, which was quantitatively predicted via the multimode K-BKZ model. Therefore, in the unentangled regime, star PS was concluded to be characterized by intrinsically higher relative nonlinearity than linear PS.

Decoding Polymer Architecture Effect on Ion Clustering, Chain Dynamics, and Ionic Conductivity in Polymer Electrolytes

Poly(ethylene oxide) (PEO)-based polymer electrolytes are a promising class of materials for use in lithium-ion batteries due to their high ionic conductivity and flexibility. In this study, the effects of polymer architecture including linear, star, and hyperbranched and salt (lithiumbis(trifluoromethanesulfonyl)imide (LiTFSI)) concentration on the glass transition (T _g), microstructure, phase diagram, free volume, and bulk viscosity, all of which play a significant role in determining the ionic conductivity of the electrolyte, have been systematically studied for PEO-based polymer electrolytes. The branching of PEO widens the liquid phase toward lower salt concentrations, suggesting decreased crystallization and improved ion coordination. At high salt loadings, ion clustering is common for all electrolytes, yet the cluster size and distribution appear to be strongly architecture-dependent. Also, the ionic conductivity is maximized at a salt concentration of [Li/EO ≈ 0.085] for all architectures, and the highly branched polymers displayed as much as three times higher ionic conductivity (with respect to the linear analogue) for the same total molar mass. The architecture-dependent ionic conductivity is attributed to the enhanced free volume measured by positron annihilation lifetime spectroscopy. Interestingly, despite the strong architecture dependence of ionic conductivity, the salt addition in the highly branched architectures results in accelerated yet similar monomeric friction coefficients for these polymers, offering significant potential toward decoupling of conductivity from segmental dynamics of polymer electrolytes, leading to outstanding battery performance.

Soft Character of Star-Like Polymer Melts: From Linear-Like Chains to Impenetrable Nanoparticles

The importance of microscopic details in the description of the behavior of polymeric nanostructured systems, such as hairy nanoparticles, has been lately discussed via experimental and theoretical approaches. Here we focus on star polymers, which represent well-defined soft nano-objects. By means of atomistic molecular dynamics simulations, we provide a quantitative study about the effect of chemistry on the penetrability of star polymers in a melt, which cannot be considered by generic coarse-grained models. The "effective softness" estimated for two dissimilar polymers is confronted with available literature data. A consistent picture about the star penetrability can be drawn when the star internal packing is taken into consideration besides the number and the length of the star arms. These findings, together with the recently introduced two-layer model, represent a step forward in providing a fundamental understanding of the soft character of stars and guiding their design toward advanced applications, such as in all-polymer nanocomposites.

Universal Polymeric-to-Colloidal Transition in Melts of Hairy Nanoparticles

Two different classes of hairy self-suspended nanoparticles in the melt state, polymer-grafted nanoparticles (GNPs) and star polymers, are shown to display universal dynamic behavior across a broad range of parameter space. Linear viscoelastic measurements on well-characterized silica-poly(methyl acrylate) GNPs with a fixed core radius (R_core) and grafting density (or number of arms f) but varying arm degree of polymerization (N_arm) show two distinctly different regimes of response. The colloidal Regime I with a small N_arm (large core volume fraction) is characterized by predominant low-frequency solidlike colloidal plateau and ultraslow relaxation, while the polymeric Regime II with a large N_arm (small core volume fractions) has a response dominated by the starlike relaxation of partially interpenetrated arms. The transition between the two regimes is marked by a crossover where both polymeric and colloidal modes are discerned albeit without a distinct colloidal plateau. Similarly, polybutadiene multiarm stars also exhibit the colloidal response of Regime I at very large f and small N_arm. The star arm retraction model and a simple scaling model of nanoparticle escape from the cage of neighbors by overcoming a hopping potential barrier due to their elastic deformation quantitatively describe the linear response of the polymeric and colloidal regimes, respectively, in all these cases. The dynamic behavior of hairy nanoparticles of different chemistry and molecular characteristics, investigated here and reported in the literature, can be mapped onto a universal dynamic diagram of f/[R_core³/ν₀)^1/4] as a function of (N_armν₀f)/(R_core³), where ν₀ is the monomeric volume. In this diagram, the two regimes are separated by a line where the hopping potential ΔU_hop is equal to the thermal energy, k_BT. ΔU_hop can be expressed as a function of the overcrowding parameter x (i.e., the ratio of f to the maximum number of unperturbed chains with N_arm that can fill the volume occupied by the polymeric corona); hence, this crossing is shown to occur when x = 1. For x > 1, we have colloidal Regime I with an overcrowded volume, stretched arms, and ΔU_hop > k_BT, while polymeric Regime II is linked to x < 1. This single-material parameter x can provide the needed design principle to tailor the dynamics of this class of soft materials across a wide range of applications from membranes for gas separation to energy storage.

Mikto-Arm Stars as Soft-Patchy Particles: From Building Blocks to Mesoscopic Structures

We present an atomistic molecular dynamics study of self-assembled mikto-arm stars, which resemble patchy-like particles. By increasing the number of stars in the system, we propose a systematic way of examining the mutual orientation of these fully penetrable patchy-like objects. The individual stars maintain their patchy-like morphology when creating a mesoscopic (macromolecular) self-assembled object of more than three stars. The self-assembly of mikto-arm stars does not lead to a deformation of the stars, and their shape remains spherical. We identified characteristic sub-units in the self-assembled structure, differing by the mutual orientation of the nearest neighbor stars. The current work aims to elucidate the possible arrangements of the realistic, fully penetrable patchy particles in polymer matrix and to serve as a model system for further studies of nanostructured materials or all-polymer nanocomposites using the mikto-arm stars as building blocks.

Supramolecular Polymer Brushes: Influence of Molecular Weight and Cross-Linking on Linear Viscoelastic Behavior

The origin of unique rheological response in supramolecular brush polymers is investigated using different polymer chemistries (poly(methyl acrylate) (PmA) and poly(ethylene glycol) (PEG)), topologies (linear or star), and molecular weights. A recently developed hydrogen-bonding moiety (1-(6-isocyanatohexyl)-3-(7-oxo-7,8-dihydro-1,8-naphthyridin-2-yl)-urea) (ODIN) was coupled to PmAs and PEGs to form supramolecular brush polymers, the backbone of which is formed by the associated moieties. At low molecular weights of monofunctionalized polymers (both PmA and PEG), the formed brushes are mostly composed of a thick backbone (with very short arms) and are surrounded by other similar brush polymers, which prevent them from diffusing and relaxing. Therefore, the monofunctionalized PmA with a low M_n does not show terminal flow even at the highest experimentally studied temperature (or at longest time scales). By increasing the length of the chains, supramolecular brushes with longer arms are obtained. Due to their lower density of thick backbones, these last ones have more space to move and their relaxation is therefore enhanced. In this work, we show that despite similarities between covalent and transient brush polymers, the elastic response in the latter does not originate from the brush entanglements with a large M_e (entanglement molecular weight), but it rather stems from the impenetrable rigid backbone and caging effect similar to the one described for hyperstars.

Spatio-temporal heterogeneities in nanosegregated single-molecule polymeric nanoparticles

The study of the coupling between structural and dynamical heterogeneities in nanostructured systems is essential for the design of hybrid materials with the desired properties. Here, we use atomistic molecular dynamics simulations to closely examine the dynamical heterogeneities in nanostructured single-molecule nanoparticles consisting of mikto-arm star copolymers with poly(ethylene oxide), PEO, and polystyrene, PS, arms. The particles exhibit an internally nanostructured morphology, resembling either "Janus-like" or "patchy-like" morphology when the functionality of the stars varies. The differences in the local environment result in strong intramolecular dynamical heterogeneities. In the proximity of the star core, geometric constraints promote unfavorable PEO:PS contacts that lead to a behavior similar to dynamically asymmetric miscible polymer blends or disordered copolymers. In contrast, further away from the core, the nanosegregation induces segmental dynamics very similar to the one found in the homopolymer star analogues.

Designing All-Polymer Nanostructured Solid Electrolytes: Advances and Prospects

Multi-phase nanostructured polymer electrolytes, where the one phase conducts ions while the other imparts the desired mechanical properties, are currently the most promising candidates for solid-state electrolytes in high-density lithium metal batteries. In contrast to homogeneous polymer electrolytes, where ion transport is coupled with polymer segmental dynamics and any attempt to improve conductivity via faster polymer motions results in a decrease in stiffness, nanostructured materials efficiently decouple these two antagonistic parameters. Nevertheless, for reasons discussed herein the synthesis of a polymer electrolyte that simultaneously has a shear modulus of G' ≈ GPa and an ion conductivity of σ > 10-4 S/cm (in the case dual ion conductor) or of σ > 10-5 S/cm (in the case of single-ion conductor) remains a challenge. This review focuses on recent designing strategies for the synthesis of all-polymer nanostructured electrolytes, and protocols for introducing a single-ion character in such materials.

A Critical Approach to Polymer Dynamics in Supramolecular Polymers

Over the past few years, the concurrent (1) development of polymer synthesis and (2) introduction of new mathematical models for polymer dynamics have evolved the classical framework for polymer dynamics once established by Doi-Edwards/de Gennes. Although the analysis of supramolecular polymer dynamics based on linear rheology has improved a lot recently, there are a large number of insecurities behind the conclusions, which originate from the complexity of these novel systems. The interdependent effect of supramolecular entities (stickers) and chain dynamics can be overwhelming depending on the type and location of stickers as well as the architecture and chemistry of polymers. This Perspective illustrates these parameters and strives to determine what is still missing and has to be improved in the future works.

Supramolecular Mimic for Bottlebrush Polymers in Bulk

A series of poly(tetrahydrofuran)s with molecular weights above entanglement molecular weight M _e were synthesized, and one of their end-groups was functionalized with a supramolecular entity so that the corresponding polymers form a brushlike structure suitable for comparison with conventional irreversible bottlebrush polymers. To compare their relaxation mechanisms, linear rheology was employed and showed that a hierarchical relaxation, which is usually observed in bottlebrush polymers, occurs in these materials, too. The polymer chain segments close to the supramolecular backbone are highly immobilized due to strong association in the center of polymer brush and cannot relax via reptation mechanism, which is mainly responsible for linear entangled polymer relaxations. Therefore, disentanglement can take much longer through contour length fluctuations and arm retraction processes similar to covalent bottlebrush polymers and combs. The relaxed ends of polymers then act as solvent to let the remaining segments of the polymeric brush undergo Rouse-like motions (constraint release Rouse). At longer times, additional plateau appears, which can be attributed to the relaxation of the entire supramolecular bottlebrush polymer via hopping or reptative motions. With an increase of temperature, viscoelastic solid behavior turns into viscoelastic liquid due to reversible depolymerization of the supramolecular backbone of the bottlebrush polymer. The elastic modulus (G' in the order of kPa) was much less than the values found for the entanglement plateau modulus of linear poly(tetrahydrofuran) (in order of MPa). This low modulus value, which exists up to very low frequencies (high temperatures), makes them a good candidate for supersoft elastomers.

Nanostructuring Single-Molecule Polymeric Nanoparticles via Macromolecular Architecture

Heterogeneous polymer-based nanoparticles comprise a very promising family of materials for a broad range of applications. Here, we present a detailed study of structural heterogeneities in nanostructured single-molecule nanoparticles in various environments by means of atomistic molecular dynamics simulations. The nanoparticles consist of mikto-arm star copolymers with two types of chemically incompatible arms, namely poly(ethylene oxide) (PEO) and polystyrene (PS), (PS) _n,(PEO) _n, where n is the number of arms. The immiscibility between the two components gives rise to intramolecularly nanostructured particles. The nanostructured objects resemble either "Janus-like" or "patchy-like" particles, depending on the number or the length of the arms (or both) as well as the interaction with the surrounding medium. The degree of intramolecular heterogeneity increases with increasing number of arms and with decreasing affinity of star components to the polymer host. We provide a detailed analysis of the internal structure of the star-shaped particles, focusing on the intramolecular packing and the spatial arrangement of the arms. The results of our study can be used to design heterogeneous, internally nanostructured particles with two phases of distinct static properties for challenging specific applications of next-generation materials.

Free Surface Relaxations of Star-Shaped Polymer Films

The surface relaxation dynamics of supported star-shaped polymer thin films are shown to be slower than the bulk, persisting up to temperatures at least 50 K above the bulk glass transition temperature T_{g}^{bulk}. This behavior, exhibited by star-shaped polystyrenes with functionality f=8 arms and molecular weights per arm M_{arm} Collapse

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Grants

• 9999-NIST Intramural NIST DOC

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Affiliation(s)

Emmanouil Glynos Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, P.O. Box 1385, 711 10 Heraklion, Crete, Greece
Kyle J. Johnson Department of Material Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA Biointeraces Institute, University of Michigan, Ann Arbor, Michigan 48109, USA
Bradley Frieberg Biointeraces Institute, University of Michigan, Ann Arbor, Michigan 48109, USA Macromolecular Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
Alexandros Chremos Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA
Suresh Narayanan Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis, Zografou, 15771, Athens Greece
Georgios Sakellariou National Renewable Energy Laboratory (NREL), Golden, Colorado 80401, USA
Peter F. Green Department of Material Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA Biointeraces Institute, University of Michigan, Ann Arbor, Michigan 48109, USA Macromolecular Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA National Renewable Energy Laboratory (NREL), Golden, Colorado 80401, USA

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Deciphering the dynamics of star molecules in shear flow

This work analyses the rotation of star polymers under shear flow, in melts, and in good solvent dilute solution. The latter is modeled by single molecule Brownian hydrodynamics, while melts are modeled using non-equilibrium molecular dynamics in closed (periodic) boxes and in open boundaries. A Dissipative Particle Dynamics (DPD) thermostat introduces pairwise monomer friction in melts at will, in directions normal and tangent to the monomer-monomer vectors. Although tangential friction is seldom modeled, we show that it is essential to control hydrodynamic effects in melts. We analyze the different sources of molecular angular momentum in solution and melts and distinguish three dynamic regimes as the shear rate [small gamma, Greek, dot above] is increased. These dynamic regimes are related with the disruption of the different relaxation mechanisms of the star in equilibrium. Although strong differences are found between harmonic springs and finitely extensible bonds, above a critical shear rate the star molecule has a "breathing" mode with successive elongations and contractions in the flow direction with frequency Ω. The force balance in the flow direction unveils a relation between Ω and the orientation angle. Using literature results for the tumbling of rings and linear chains, either in melt or in solution, we show that the relation is general. A different "tank-treading" dynamics determines the rotation of monomers around the center of mass of the molecule. We show that the tank-treading frequency does not saturate but keeps increasing with [small gamma, Greek, dot above]. This is at odds with previous studies which erroneously calculated the molecular angular frequency, used as a proxy for tank-treading.