Communication: When does a branched polymer become a particle?

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.

Atomistic Simulations of Polydisperse Lignin Melts Using Simple Polydisperse Residue Input Generator

Understanding the physics of lignin will help rationalize its function in plant cell walls as well as aiding practical applications such as deriving biofuels and bioproducts. Here, we present SPRIG (Simple Polydisperse Residue Input Generator), a program for generating atomic-detail models of random polydisperse lignin copolymer melts i.e., the state most commonly found in nature. Using these models, we use all-atom molecular dynamics (MD) simulations to investigate the conformational and dynamic properties of polydisperse melts representative of switchgrass (Panicum virgatum L.) lignin. Polydispersity, branching and monolignol sequence are found to not affect the calculated glass transition temperature, Tg. The Flory-Huggins scaling parameter for the segmental radius of gyration is 0.42 ± 0.02, indicating that the chains exhibit statistics that lie between a globular chain and an ideal Gaussian chain. Below Tg the atomic mean squared displacements are independent of molecular weight. In contrast, above Tg, they decrease with increasing molecular weight. Therefore, a monodisperse lignin melt is a good approximation to this polydisperse lignin when only static properties are probed, whereas the molecular weight distribution needs to be considered while analyzing lignin dynamics.

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.

Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition

We investigate a metallic glass-forming (GF) material (Al₉₀Sm₁₀) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, T_g. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the "hyperuniformity index" H of our liquid, which provides a quantitative measure of molecular "jamming". To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye-Waller parameter 〈u²〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u²〉 for heated crystalline Cu. This comparative analysis between H and 〈u²〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10^-3 as being analogous to the Lindemann criterion for both the melting of crystals and the "softening" of glasses. We further interpret the emergence of FS GF and liquid-liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid.

Polymer-Grafted Nanoparticles with Variable Grafting Densities for High Energy Density Polymeric Nanocomposite Dielectric Capacitors

Designing high energy density dielectric capacitors for advanced energy storage systems needs nanocomposite-based dielectric materials, which can utilize the properties of both inorganic and polymeric materials. Polymer-grafted nanoparticle (PGNP)-based nanocomposites alleviate the problems of poor nanocomposite properties by providing synergistic control over nanoparticle and polymer properties. Here, we synthesize "core-shell" barium titanate-poly(methyl methacrylate) (BaTiO₃-PMMA) grafted PGNPs using surface-initiated atom transfer polymerization (SI-ATRP) with variable grafting densities of (0.303 to 0.929) chains/nm² and high molecular masses (97700 g/mL to 130000 g/mol) and observe that low grafted density and high molecular mass based PGNP show high permittivity, high dielectric strength, and hence higher energy densities (≈ 5.2 J/cm³) as compared to the higher grafted density PGNPs, presumably due to their "star-polymer"-like conformations with higher chain-end densities that are known to enhance breakdown. Nonetheless, these energy densities are an order of magnitude higher than their nanocomposite blend counterparts. We expect that these PGNPs can be readily used as commercial dielectric capacitors, and these findings can serve as guiding principles for developing tunable high energy density energy storage devices using PGNP systems.

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.

Enhanced Dielectric Strength and Capacitive Energy Density of Cyclic Polystyrene Films

The maximum capacitive energy stored in polymeric dielectric capacitors, which are ubiquitous in high-power-density devices, is dictated by the dielectric breakdown strength of the dielectric polymer. The fundamental mechanisms of the dielectric breakdown, however, remain unclear. Based on a simple free-volume model of the polymer fluid state, we hypothesized that the free ends of linear polymer chains might act as “defect” sites, at which the dielectric breakdown can initiate. Thus, the dielectric breakdown strength of cyclic polymers should exhibit enhanced stability in comparison to that of their linear counterparts having the same composition and similar molar mass. This hypothesis is supported by the ∼50% enhancement in the dielectric breakdown strength and ∼80% enhancement in capacitive energy density of cyclic polystyrene melt films in comparison to corresponding linear polystyrene control films. Furthermore, we observed that cyclic polymers exhibit a denser packing density than the linear chain melts, an effect that is consistent with and could account for the observed property changes. Our work demonstrates that polymer topology can significantly influence the capacitive properties of polymer films, and correspondingly, we can expect polymer topology to influence the gas permeability, shear modulus, and other properties of thin films dependent on film density.

Solution properties of spherical gold nanoparticles with grafted DNA chains from simulation and theory

There has been a rapidly growing interest in the use of functionalized Au nanoparticles (NPs) as platforms in multiple applications in medicine and manufacturing. The sensing and targeting characteristics of these NPs, and the realization of precisely organized structures in manufacturing applications using such NPs, depend on the control of their surface functionalization. NP functionalization typically takes the form of polymer grafted layers, and a detailed knowledge of the chemical and structural properties of these layers is required to molecularly engineer the particle characteristics for specific applications. However, the prediction and experimental determination of these properties to enable the rational engineering of these particles is a persistent problem in the development of this class of materials. To address this situation, molecular dynamic simulations were performed based on a previously established coarse-grained single-stranded DNA (ssDNA) model to determine basic solution properties of model ssDNA-grafted NP-layers under a wide range of conditions. In particular, we emphasize the calculation of the hydrodynamic radius for ssDNA-grafted Au NPs as a function of structural parameters such as ssDNA length, NP core size, and surface coverage. We also numerically estimate the radius of gyration and the intrinsic viscosity of these NPs, which in combination with hydrodynamic radius estimates, provide valuable information about the fluctuating structure of the grafted polymer layers. We may then understand the origin of the commonly reported variation in effective NP "size" by different measurement methods, and then exploit this information in connection to material design and characterization in connection with the ever-growing number of applications utilizing polymer-grafted NPs.

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Designing high performance polymer nanocomposites by incorporating robustness-controlled polymeric nanoparticles: insights from molecular dynamics

Introducing polymeric nanoparticles into polymer matrices is an interesting topic, and the robustness of the polymeric nanoparticles is crucial for the properties of the polymer nanocomposites (PNCs). In this study, by incorporating star-shaped polymeric nanoparticles (SSPNs) into the polymer, the effect of the sphericity (η) and arm length (L) of the SSPNs on the mechanical properties of PNCs is systematically investigated, using a coarse-grained molecular dynamics simulation. In addition, the linear and spherical nanoparticles (NPs) are compared with SSPNs by fixing the approximate diameter and mass fraction of the NPs. The radial distribution function, the second virial coefficient, mean-squared displacement, bond autocorrelation function, and primitive path analysis are employed to systematically characterize the structure and dynamics of these new PNCs. It is found that the dispersion of the NPs is enhanced with the increase of η, and the entanglement density reaches maximum, which both contribute to the greatest mechanical reinforcing effect. More significantly, it is found that the classical Payne effect, namely the storage as a function of the strain amplitude, decreases remarkably, and with a much smaller loss factor for these SSPN filled polymer nanocomposites, compared to conventional PNCs filled with rigid NPs. Furthermore, the change of the arm length of the SSPNs is found to exhibit the same effect on the mechanical and viscoelastic properties, as the variation of the number of the arms. In general, this work shows that these new SSPN filled polymer nanocomposites can exceed conventional PNCs, by manipulating the robustness of the SSPNs using, for example, the number and length of the arms. This research may provide guidelines for the investigation of the structure-property relationships of the topological structure of polymeric nanoparticles.

Differences and similarities between mono-, bi- or tetrafunctional initiated cationic ring-opening polymerization of 2-oxazolines

Cationic ring-opening polymerization (CROP) is an interesting synthesis technique to obtain well-defined polymers with narrow molar mass distribution (MMD).

AIE-active macromolecules: designs, performances, and applications

Aggregation-induced emission (AIE) macromolecules as emerging luminescent materials gained increasing attention owing to their good processability, high brightness, wide functionality, and smart responsiveness, with great potential in many fields.

Glass transition of ion-containing polymer melts in bulk and thin films

Ion-containing polymers often are good glass formers, and the glass transition temperature is an important parameter to consider for practical applications, which prescribes the working temperature range for different mechanical and dynamic properties. In this work, we present a systematic molecular dynamics simulation study on the coupling of ionic correlations with the glass transition, based on a generic coarse-grained model of ionic polymers. The variation of the glass transition temperature is examined concerning the influence of the electrostatic interaction strength, charge fraction, and charge sequence. The interplay with the film thickness effect is also discussed. Our results reveal a few typical features about the glass transition process that are in qualitative agreement with previous studies, further highlighting the effects of counterion entropy at weak ionic correlations and physical crosslinking of ionic aggregates at strong ionic correlations. Detailed parametric dependencies are displayed, which demonstrate that introducing strong ionic correlations promotes vitrification while adopting a precise charge sequence and applying strong confinement with weak surface affinity reduce the glass transition temperature. Overall, our investigation provides an improved picture towards a comprehensive understanding of the glass transition in ion-containing polymeric systems from a molecular simulation perspective.

A simulation study of the self-assembly of ABC star terpolymers confined between two parallel surfaces

The phase behavior of ABC star terpolymers confined between two identical parallel surfaces is systematically studied using a simulated annealing method. Several phase diagrams are constructed for systems with different bulk phases or with different interfacial interaction strength ratios in the space of surface distance (D) and surface preference for different arms, or in the space of D and the arm-length ratio x. Phases, including tiling patterns [6.6.6], [8.8.4], [8.6.6; 8.6.4], [8.6.6; 8.6.4; 10.6.6; 10.6.4] and hierarchical lamellar structures of lamella + cylinders and lamella + rods, are identified both in the bulk and in the films. Our results suggest that the self-assembled structure of a phase is largely controlled by x, while an increase of the interfacial interaction strength ratio shifts the x-window for each phase to the smaller x side. The orientation of a confined phase depends on the "effective surface preference" which is a combined effect of the interfacial interaction strength ratio, the surface preference, and the entropic preference. In the case of neutral or weak "effective surface preference", phases with a perpendicular orientation are usually observed, while in the case of strong "effective surface preference" phases with a perpendicular orientation or also with outermost wetting-layers can be frequently observed under some circumstances.

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.

Conformation and dynamics of ring polymers under symmetric thin film confinement

Understanding the structure and dynamics of polymers under confinement has been of widespread interest, and one class of polymers that have received comparatively little attention under confinement is that of ring polymers. The properties of non-concatenated ring polymers can also be important in biological fields because ring polymers have been proven to be a good model to study DNA organization in the cell nucleus. From our previous study, linear polymers in a cylindrically confined polymer melt were found to segregate from each other as a result of the strong correlation hole effect that is enhanced by the confining surfaces. By comparison, our subsequent study of linear polymers in confined thin films at similar levels of confinements found only the onset of segregation. In this study, we use molecular dynamics simulation to investigate the chain conformations and dynamics of ring polymers under planar (1D) confinement as a function of film thickness. Our results show that conformations of ring polymers are similar to the linear polymers under planar confinement, except that ring polymers are less compressed in the direction normal to the walls. While we find that the correlation hole effect is enhanced under confinement, it is not as pronounced as the linear polymers under 2D confinement. Finally, we show that chain dynamics far above Tg are primarily affected by the friction from walls based on the monomeric friction coefficient we get from the Rouse mode analysis.

Design of nearly perfect hyperuniform polymeric materials

Disordered hyperuniform materials are exotic amorphous systems that simultaneously exhibit anomalous suppression of long-range density fluctuations, comparable in amplitude to that of crystals and quasi-crystalline materials, while lacking the translational order characteristic of simple liquids. We establish a framework to quantitatively predict the emergence of hyperuniformity in polymeric materials by considering the distribution of localized polymer subregions, instead of considering the whole material. We demonstrate that this highly tunable approach results in arbitrarily small long-range density fluctuations in the liquid state. Our simulations also indicate that long-ranged density fluctuation of the whole polymeric material is remarkably insensitive to molecular topology (linear chain, unknotted ring, star, and bottlebrush) and depends on temperature in an apparently near universal fashion. Our findings open the way for the creation of nearly perfect hyperuniform polymeric materials.

Mixing-demixing transition in polymer-grafted spherical nanoparticles

Polymer-grafted nanoparticles (PGNPs) can provide property profiles that cannot be obtained individually by polymers or nanoparticles (NPs). Here, we have studied the mixing-demixing transition of symmetric copolymer melts of polymer-grafted spherical nanoparticles by means of coarse-grained molecular dynamics simulation and a theoretical mean-field model. We find that a larger size of NPs leads to higher stability for a given number of grafted chains and chain lengths, reaching a point where demixing is not possible. Most importantly, the increase in the number of grafted chains, Ng, can initially favour the phase separation of PGNPs, but a further increase can lead to more difficult demixing. The reason is the increasing impact of an effective core that forms as the grafting density of the tethered polymer chains around the NPs increases. The range and exact values of Ng where this change in behaviour takes place depend on the NP size and the chain length of the grafted polymer chains. Our study elucidates the phase behaviour of PGNPs and in particular the influence of the grafting density on the phase behaviour of the systems, anticipating that it will open new doors in the understanding of these systems with implications in materials science and medicine.

Dynamic Equivalence between Soft Star Polymers and Hard Spheres

Understanding the dynamics of soft colloids, such as star polymers, dendrimers, and microgels, is of scientific and practical importance. It is known that the excluded volume effect plays a key role in colloidal dynamics. Here, we propose a condition of compressibility equivalence that provides a simple method to experimentally evaluate the excluded volume of soft colloids from a thermodynamic view. We apply this condition to survey the dynamics of a series of star polymer dispersions. It is found that, as the concentration increases, the slowing of the long-time self-diffusivity of the star polymer, normalized by the short-time self-diffusivity, can be mapped onto the hard-sphere behavior. This phenomenon reveals the dynamic equivalence between soft colloids and hard spheres, despite the apparent complexity of the interparticle interaction of the soft colloids. The methods for measuring the osmotic compressibility and the self-diffusivities of soft colloidal dispersions are also presented.

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.

Influence of knot complexity on glass-formation in low molecular mass ring polymer melts

We perform molecular dynamics simulations on a coarse-grained polymer melt to study the dynamics of glass-formation in ring polymer melts of variable knot complexity. After generating melts of non-concatenated polymeric rings having a range of minimum crossing number values, mc, we compute the coherent intermediate scattering function, the segmental α-relaxation time, fragility, and the glass transition temperature as a function of mc. Variation of knot complexity is found to have a pronounced effect on the dynamics of polymer melts since both molecular rigidity and packing are altered, primary physical factors governing glass-formation in polymeric materials.

Polymers on nanoparticles: structure & dynamics

Grafting polymers to nanoparticle surfaces influences properties from the conformation of the polymer chains to the dispersion and assembly of nanoparticles within a polymeric material. Recently, a small body of work has begun to address the question of how grafting polymers to a nanoparticle surface impacts chain dynamics, and the resulting physical properties of a material. This Review discusses recent work that characterizes the structure and dynamics of polymers that are grafted to nanoparticles and opportunities for future research. Starting from the case of a single polymer chain attached to a nanoparticle core, this Review follows the structure of the chains as grafting density increases, and how this structure slows relaxation of polymer chains and affects macroscopic material properties.

Continuous flow synthesis of core cross-linked star polymers via photo-induced copper mediated polymerization

A convenient method to synthesize core cross-linked star polymers via a continuous flow photopolymerization process is developed.

Hidden Hyperuniformity in Soft Polymeric Materials

We investigate the nature of long-range density fluctuations in melts of model "soft" polymers, specifically stars and bottlebrushes, over a wide temperature range by molecular dynamics simulation. The cores of the stars and the backbones of bottlebrush polymers are found to have a hyperuniform distribution; i.e., they exhibit anomalously small density fluctuations over a wide temperature range above the glass transition temperature. The hyperuniformity of these substituent polymer subregions is hidden since the fluid as a whole does not exhibit this property. These findings offer a strategy for the practical design of hyperuniform polymeric materials.

Dynamics of Architecturally Engineered All-Polymer Nanocomposites

We present nanocomposite materials formed by using glassy star-shaped polymers as nanofillers and dispersing them in soft matrices. The resulting "architecturally engineered" polymer nanocomposites structurally reside between the linear homopolymer blends and the conventional polymer nanocomposites with inorganic fillers, inducing reinforcement, which can be as strong as that of solid nanoparticles, or softening depending on the compactness and concentration of the nanoparticles. Such behavior can be traced back to the dynamical features at the local segmental and the chain level, which we investigated using neutron scattering over a wide range of time and length scales in the glassy and melt states of the nanocomposites. The local and segmental dynamics as well as the degree of chain-chain entanglements are all modified by the star-shaped fillers. The presented approach to tuning the physical properties of all-polymer-based nanocomposites is readily adaptable to other polymer architectures with immediate applications in numerous areas including gas separation membranes, tissue engineering, drug delivery, and functional coatings.

Polyelectrolyte association and solvation

There has been significant interest in the tendency of highly charged particles having the same charge to form dynamic clusters in solution, but an accepted theoretical framework that can account for this ubiquitous phenomenon has been slow to develop. The theoretical difficulties are especially great for flexible polyelectrolytes due to the additional complex coupling between the polyelectrolyte chain configurations and the spatial distribution of the ionic species in solution. For highly charged polyelectrolytes, this leads to the formation of a diffuse "polarizable" cloud of counter-ions around these polymers, an effect having significant implications for the function of proteins and other natural occurring polyelectrolytes, as emphasized long ago by Kirkwood and co-workers. To investigate this phenomenon, we perform molecular dynamics simulations of a minimal model of polyelectrolyte solutions that includes an explicit solvent and counter-ions, where the relative affinity of the counter-ions and the polymer for the solvent is tunable through the variation of the relative strength of the dispersion interactions of the polymer and ions. In particular, we find that these dispersion interactions can greatly influence the nature of the association between the polyelectrolyte chains under salt-free conditions. We calculate static and dynamic correlation functions to quantify the equilibrium structure and dynamics of these complex liquids. Based on our coarse-grained model of polyelectrolyte solutions, we identify conditions in which three distinct types of polyelectrolyte association arise. We rationalize these types of polyelectrolyte association based on the impact of the selective solvent affinity on the charge distribution and polymer solvation in these solutions. Our findings demonstrate the essential role of the solvent in the description of the polyelectrolyte solutions, as well as providing a guideline for the development of a more predictive theory of the properties of the thermodynamic and transport properties of these complex fluids.

Macromolecular 'size' and 'hardness' drives structure in solvent-swollen blends of linear, cyclic, and star polymers

In this paper, we apply molecular simulation and liquid state theory to uncover the structure and thermodynamics of homopolymer blends of the same chemistry and varying chain architecture in the presence of explicit solvent species. We use hybrid Monte Carlo (MC)/molecular dynamics (MD) simulations in the Gibbs ensemble to study the swelling of ∼12 000 g mol^-1 linear, cyclic, and 4-arm star polystyrene chains in toluene. Our simulations show that the macroscopic swelling response is indistinguishable between the various architectures and matches published experimental data for the solvent annealing of linear polystyrene by toluene vapor. We then use standard MD simulations in the NPT ensemble along with polymer reference interaction site model (PRISM) theory to calculate effective polymer-solvent and polymer-polymer Flory-Huggins interaction parameters (χ^eff) in these systems. As seen in the macroscopic swelling results, there are no significant differences in the polymer-solvent and polymer-polymer χ^eff between the various architectures. Despite similar macroscopic swelling and effective interaction parameters between various architectures, the pair correlation function between chain centers-of-mass indicates stronger correlations between cyclic or star chains in the linear-cyclic blends and linear-star blends, compared to linear chain-linear chain correlations. Furthermore, we note striking similarities in the chain-level correlations and the radius of gyration of cyclic and 4-arm star architectures of identical molecular weight. Our results indicate that the cyclic and star chains are 'smaller' and 'harder' than their linear counterparts, and through comparison with MD simulations of blends of soft spheres with varying hardness and size we suggest that these macromolecular characteristics are the source of the stronger cyclic-cyclic and star-star correlations.

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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Knot Energy, Complexity, and Mobility of Knotted Polymers

The Coulomb energy E C is defined by the energy required to charge a conductive object and scales inversely to the self-capacity C, a basic measure of object size and shape. It is known that C is minimized for a sphere for all objects having the same volume, and that C increases as the symmetry of an object is reduced at fixed volume. Mathematically similar energy functionals have been related to the average knot crossing number 〈m〉, a natural measure of knot complexity and, correspondingly, we find E C to be directly related to 〈m〉 of knotted DNA. To establish this relation, we employ molecular dynamics simulations to generate knotted polymeric configurations having different length and stiffness, and minimum knot crossing number values m for a wide class of knot types relevant to the real DNA. We then compute E C for all these knotted polymers using the program ZENO and find that the average Coulomb energy 〈E C〉 is directly proportional to 〈m〉. Finally, we calculate estimates of the ratio of the hydrodynamic radius, radius of gyration, and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric chains since these ratios should be useful in characterizing knotted polymers experimentally.

Application of the Eckart frame to soft matter: rotation of star polymers under shear flow

The Eckart co-rotating frame is used to analyze the dynamics of star polymers under shear flow, either in melt or solution and with different types of bonds. This formalism is compared with the standard approach used in many previous studies on polymer dynamics, where an apparent angular velocity ω is obtained from the relation between the tensor of inertia and angular momentum. A common mistake is to interpret ω as the molecular rotation frequency, which is only valid for rigid-body rotation. The Eckart frame, originally formulated to analyze the infrared spectra of small molecules, dissects different kinds of displacements: vibrations without angular momentum, pure rotation, and vibrational angular momentum (leading to a Coriolis cross-term). The Eckart frame co-rotates with the molecule with an angular frequency Ω obtained from the Eckart condition for minimal coupling between rotation and vibration. The standard and Eckart approaches are compared with a straight description of the star's dynamics taken from the time autocorrelation of the monomer positions moving around the molecule's center of mass. This is an underdamped oscillatory signal, which can be described by a rotation frequency ω_R and a decorrelation rate Γ. We consistently find that Ω coincides with ω_R, which determines the characteristic tank-treading rotation of the star. By contrast, the apparent angular velocity ω < Ω does not discern between pure rotation and molecular vibrations. We believe that the Eckart frame will be useful to unveil the dynamics of semiflexible molecules where rotation and deformations are entangled, including tumbling, tank-treading motions and breathing modes.

Influence of polymer architectures on diffusion in unentangled polymer melts

Recent simulations have indicated that the thermodynamic properties and the glassy dynamics of polymer melts are strongly influenced by the average molecular shape, as quantified by the radius of gyration tensor of the polymer molecules, and that the average molecular shape can be tuned by varying the molecular topology (e.g., ring, star, linear chain, etc.). In the present work, we investigate if the molecular shape is similarly a predominant factor in understanding the polymer center of mass diffusion D in the melt, as already established for polymer solutions. We find that all our D data for unentangled polymer melts having a range of topologies can be reasonably described as a power law of the polymer hydrodynamic radius, Rh. In particular, this scaling is similar to the scaling of D for a tracer sphere having a radius on the order of the chain radius of gyration, Rg. We conclude that the chain topology influences the molecular dynamics in as much as the polymer topology influences the average molecular shape. Experimental evidence seems to suggest that this situation is also true for entangled polymer melts.

Ring Polymers: Threadings, Knot Electrophoresis and Topological Glasses

Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physical consequences of such threadings are far-reaching: for instance, they lead to a topologically-driven glassy behaviour of ring polymer melts under pinning perturbations, while they can also account for the shape of experimentally observed patterns in two-dimensional gel electrophoresis of DNA knots.

Solution properties of star polyelectrolytes having a moderate number of arms

We investigate polyelectrolyte stars having a moderate number of arms by molecular dynamics simulations of a coarse-grained model over a range of polyelectrolyte concentrations, where both the counter-ions and solvent are treated explicitly. This class of polymeric materials is found to exhibit rather distinct static and dynamic properties from linear and highly branched star polyelectrolyte solutions emphasized in past studies. Moderately branched polymers are particle-like in many of their properties, while at the same time they exhibit large fluctuations in size and shape as in the case of linear chain polymers. Correspondingly, these fluctuations suppress crystallization at high polymer concentrations, leading apparently to an amorphous rather than crystalline solid state at high polyelectrolyte concentrations. We quantify the onset of this transition by measuring the polymer size and shape fluctuations of our model star polyelectrolytes and the static and dynamic structure factor of these solutions over a wide range of polyelectrolyte concentration. Our findings for star polyelectrolytes are similar to those of polymer-grafted nanoparticles having a moderate grafting density, which is natural given the soft and highly deformable nature of both of these "particles."