Dynamic heterogeneity and collective motion in star polymer melts

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.

Bidispersity Improves the Toughness and Impact Resistance of Star-Polymer Thin Films

Branched polymer architectures are used to tune the mechanical properties of impact-resistant thin films through parameters, such as chain length and grafting density. While chain dispersity affects molecular properties, such as interpenetration and entanglements, structure-property relationships accounting for dispersity are challenging to obtain experimentally and are often neglected in computational models. We employ molecular dynamics simulations to model the high-rate tensile elongation and nanoballistic impact of thin films composed of bidisperse star polymers with varying arm lengths. We find that, at fixed molecular weight, high dispersity can significantly enhance the toughness and impact resistance of the films without decreasing their elastic modulus. Bidisperse stars with fewer longer arms are less entangled, but stretch and interpenetrate for longer times during crazing, leading to increased toughness. These findings highlight controlled dispersity as a design strategy to improve the mechanical properties of polymer composites across Pareto fronts.

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.

Competing Effects of Molecular Additives and Cross-Link Density on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

The introduction of molecular additives into thermosets often results in changes in their dynamics and mechanical properties that can have significant ramifications for diverse applications of this broad class of materials such as coatings, high-performance composites, etc. Currently, there is limited fundamental understanding of how such additives influence glass formation in these materials, a problem of broader significance in glass-forming materials. To address this fundamental problem, here, we employ a simplified coarse-grained (CG) model of a polymer network as a model of thermoset materials and then introduce a polymer additive having the same inherent rigidity and polymer-polymer interaction strength as the cross-linked polymer matrix. This energetically "neutral" or "self-plasticizing" additive model gives rise to non-trivial changes in the dynamics of glass formation and provides an important theoretical reference point for the technologically more important case of interacting additives. Based on this rather idealized model, we systematically explore the combined effect of varying the additive mass percentage (m) and cross-link density (c) on the segmental relaxation dynamics and mechanical properties of a model thermoset material with additives. We find that increasing the additive mass percentage m progressively decreases both the glass-transition temperature Tg and the fragility of glass formation, a trend opposite to increasing c so that these thermoset variables clearly have a competing effect on glass formation in these model materials. Moreover, basic mechanical properties (i.e., bulk, shear, and tensile moduli) likewise exhibit a competitive variation with the increase of m and c, which are strongly correlated with the Debye-Waller parameter ⟨u2⟩, a measure of material stiffness at a molecular scale. Our findings prove beneficial in the development of structure-property relationships for the cross-linked polymers, which could help guide the design of such network materials with tailored physical properties.

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (T_g). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with T_g, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τ_α becomes almost a universal function of reduced temperature, (T - T_g)/T_g, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - T_g)/T_g. Evidently, T_g dominates both τ_α and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Decoding polymer self-dynamics using a two-step approach

The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. We show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a "two-step" approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.

Diffusion of polymer-grafted nanoparticles with dynamical fluctuations in unentangled polymer melts

The dynamics of polymer-grafted nanoparticles (PGNPs) in melts of unentangled linear chains were investigated by means of coarse-grained molecular dynamics simulations. The results demonstrated that the graft monomers closer to the particle surface relax more slowly than those farther away due to the constraint of the grafted surface and the confinement of the neighboring chains. Such heterogeneous relaxations of the surrounding environment would perturb the particle motion, making them fluctuating around their centers before they can diffuse through the melt. During such intermediate-time stage, the dynamics is subdiffusive while the distribution of particle displacements is Gaussian, which can be described by the popular fractional Brownian motion model. For the long-time Fickian diffusion, we found that the diffusivity D decreases with increasing grafting density Σ_g, grafted chain length N_g, and matrix chain length N_m. This is due to the fact that the diffusivity is controlled by the viscous drag of an effective core, consisting of the NP and the non-draining layer of graft segments, and that of the free-draining graft layer outside the "core". With increasing Σ_g, the PGNPs become harder with greater effective size and thinner free draining layer, resulting in a reduction in D. At extremely high Σ_g, the diffusivity can even be estimated by the diameter-renormalized Stokes-Einstein (SE) relation. With increasing N_g, both the effective core size and the thickness of the free-draining layer increase, leading to a reduction in diffusivity by D ∼ N-γg with 0.5 < γ < 1. Increasing N_m would lead to the enlargement of the effective core size but meanwhile result in the reduction of the free-draining layer thickness due to autophobic dewetting. The counteraction between these two opposite effects leads to only a slight reduction in the diffusivity, significantly different from the typical SE behavior where D ∼ N_m^-1. These findings bear significance in unraveling the fundamental physics of the anomalous dynamics of PGNPs in various polymers, including biological and synthetic.

Activation free energy gradient controls interfacial mobility gradient in thin polymer films

We examine the mobility gradient in the interfacial region of substrate-supported polymer films using molecular dynamics simulations and interpret these gradients within the string model of glass-formation. No large gradients in the extent of collective motion exist in these simulated films, and an analysis of the mobility gradient on a layer-by-layer basis indicates that the string model provides a quantitative description of the relaxation time gradient. Consequently, the string model indicates that the interfacial mobility gradient derives mainly from a gradient in the high-temperature activation enthalpy ΔH₀ and entropy ΔS₀ as a function of depth z, an effect that exists even in the high-temperature Arrhenius relaxation regime far above the glass transition temperature. To gain insight into the interfacial mobility gradient, we examined various material properties suggested previously to influence ΔH₀ in condensed materials, including density, potential and cohesive energy density, and a local measure of stiffness or u²(z)^-3/2, where u²(z) is the average mean squared particle displacement at a caging time (on the order of a ps). We find that changes in local stiffness best correlate with changes in ΔH₀(z) and that ΔS₀(z) also contributes significantly to the interfacial mobility gradient, so it must not be neglected.

Comparative experimental and computational study of synthetic and natural bottlebrush polyelectrolyte solutions

We systematically investigate model synthetic and natural bottlebrush polyelectrolyte solutions through an array of experimental techniques (osmometry and neutron and dynamic light scattering) along with molecular dynamics simulations to characterize and contrast their structures over a wide range of spatial and time scales. In particular, we perform measurements on solutions of aggrecan and the synthetic bottlebrush polymer, poly(sodium acrylate), and simulations of solutions of highly coarse-grained charged bottlebrush molecules having different degrees of side-branch density and inclusion of an explicit solvent and ion hydration effects. While both systems exhibit a general tendency toward supramolecular organization in solution, bottlebrush poly(sodium acrylate) solutions exhibit a distinctive "polyelectrolyte peak" in their structure factor, but no such peak is observed in aggrecan solutions. This qualitative difference in scattering properties, and thus polyelectrolyte solution organization, is attributed to a concerted effect of the bottlebrush polymer topology and the solvation of the polymer backbone and counterions. The coupling of the polyelectrolyte topological structure with the counterion distribution about the charged polymer molecules along with direct polymer segmental hydration makes their solution organization and properties "tunable," a phenomenon that has significant ramifications for biological function and disease as well as for numerous materials applications.

Supercooled melt structure and dynamics of single-chain nanoparticles: A computer simulation study

By using coarse-grained molecular dynamics simulations, we have investigated the structure and dynamics of supercooled single-chain cross-linked nanoparticle (SCNP) melts having a range of cross-linking degrees ϕ. We find a nearly linear increase in glass-transition temperature (T_g) with increasing ϕ. Correspondingly, we have also experimentally synthesized a series of polystyrene-based SCNPs and have found that the measured T_g estimated from differential scanning calorimetry is qualitatively consistent with the trend predicted by our simulation estimates. Experimentally, an increase in T_g as large as ΔT_g = 61 K for ϕ = 0.36 is found compared with their linear chain counterparts, indicating that the changes in dynamics with cross-links are quite appreciable. We attribute the increase in T_g to the enlarged effective hard-core volume and the corresponding reduction in the free volume of the polymer segments. Topological constraints evidently frustrate the local packing. In addition, the introduction of intra-molecular cross-linking bonds slows down the structural relaxation and simultaneously enhances the local coupling motion on the length scales within SCNPs. Consequently, a more pronounced dynamical heterogeneity (DH) is observed for larger ϕ, as quantified by measuring the dynamical correlation length through the four-point susceptibility parameter, χ₄. The increase in DH is directly related to the enhanced local cooperative motion derived from intra-molecular cross-linking bonds and structural heterogeneity derived from the cross-linking process. These results shed new light on the influence of intra-molecular topological constraints on the segmental dynamics of polymer melts.

Layers of Distinct Mobility in Densely Grafted Dendrimer Arborescent Polymer Hybrids

Melts of multiarm stars of 1,4-polybutadiene (dendrimer arborescent hybrids) with very high branching functionality (f) and small arm molar mass behave as jammed colloids and show distinct layers of segmental mobility. Three mobility layers were identified, comprising outer, intermediate, and near-core segments, all displaying a Vogel-Fulcher-Tammann temperature dependence. The respective glass temperatures increase as f^{1/2}. Our findings pave the way for further progress in this field by reconsidering previous theoretical treatments based on a single friction coefficient in hybrid nanoparticles such as densely grafted stars.

Hydrogen-Bonded Complexes of Star Polymers

The effect of molecular architecture, star versus linear, poly(ethylene oxide) (PEO) on the formation of hydrogen-bonded complexes with linear poly(methacrylic acid) (PMAA) is investigated experimentally and rationalized theoretically. Isothermal titration calorimetry reveals that at pH 2.5 interpolymer complexes (IPCs) of PMMA with a 6-arm star PEO (sPEO) contains ≈50% more polyacid than IPCs formed with linear PEO (lPEO). While the enthalpy of IPC formation is positive in both cases, its magnitude is ≈50% larger for sPEO/PMAA complexes that exhibit a lower dissociation constant than lPEO/polyacid complexes. These results are rationalized based on a higher localized density of hydrogen bonds formed between sPEO and the polyacid which prevents penetration of star molecules into PMAA coils. Accordingly, Fourier transform infrared results indicate approximately twofold excess of self-associated >COOH units over intermolecularly bonded >COOH units in sPEO-containing complexes. The excess of PMAA chains in IPCs and the percentage of self-associated carboxylic groups in sPEO/PMAA complexes both increase with polyacid molecular weight. Other findings, including a positive entropy, hysteresis in composition at strongly acidic pH, and progressive equilibration of IPCs at increased pH are consistent with the critical role of charge and release of water molecules in the formation of sPEO/PMAA and lPEO/PMAA complexes.

The microscopic origins of stretched exponential relaxation in two model glass-forming liquids as probed by simulations in the isoconfigurational ensemble

The origin of stretched exponential relaxation in supercooled glass-forming liquids is one of the central questions regarding the anomalous dynamics of these fluids. The dominant explanation for this phenomenon has long been the proposition that spatial averaging over a heterogeneous distribution of locally exponential relaxation processes leads to stretching. Here, we perform simulations of model polymeric and small-molecule glass-formers in the isoconfigurational ensemble to show that stretching instead emerges from a combination of spatial averaging and locally nonexponential relaxation. The results indicate that localities in the fluid exhibiting faster-than-average relaxation tend to exhibit locally stretched relaxation, whereas slower-than-average relaxing domains exhibit more compressed relaxation. We show that local stretching is predicted by loose local caging, as measured by the Debye-Waller factor, and vice versa. This phenomenology in the local relaxation of in-equilibrium glasses parallels the dynamics of out of equilibrium under-dense and over-dense glasses, which likewise exhibit an asymmetry in their degree of stretching vs compression. On the basis of these results, we hypothesize that local stretching and compression in equilibrium glass-forming liquids results from evolution of particle mobilities over a single local relaxation time, with slower particles tending toward acceleration and vice versa. In addition to providing new insight into the origins of stretched relaxation, these results have implications for the interpretation of stretching exponents as measured via metrologies such as dielectric spectroscopy: measured stretching exponents cannot universally be interpreted as a direct measure of the breadth of an underlying distribution of relaxation times.