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Star polymers are an interesting class of polymers to study based on their shape and dynamics. We use complementary techniques to study the polymer dynamics of star polymers with shorter side chains and compare them with linear counterparts.
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.
Polymers with precisely controlled structure and function are in high demand across a diverse array of applications spanning the life sciences and nanotechnology. One prototypical example is a class of branched block copolymers known as miktoarm stars (μ-stars), which contain two or more arm compositions connected at a common junction. Miktoarm stars have attracted considerable attention since their physical properties can be different from conventional linear block copolymers. This perspective highlights the latest developments and historical context in the field of miktoarm star polymers, including design strategies, synthetic techniques, and advanced characterization tools used to avoid common preparation pitfalls and tailor properties for emerging applications. Furthermore, our contemporary perspective on μ-star polymers is a resource for inspiring future research into this exciting class of materials at the intersection of chemistry, physics, and advanced technology.
A library of polyester-based A(BA') n asymmetric miktoarm star polymers was synthesized with A, A' = poly(l-lactide) (PLLA) as the semicrystalline hard blocks and B = poly(4-methylcaprolactone) (PMCL) as the soft segment using a grafting-through platform known as μSTAR. The synthetic versatility of μSTAR enabled a systematic investigation of architectural design parameters, in particular the number of BA' arms (n), while holding the A, A', and B block lengths constant. The value of n has a pronounced impact on the mechanical properties of these high-molecular-weight miktoarm materials. Tensile toughness increases with n, an effect likely related to bridging, as the modulus drops because the hard-block volume fraction decreases. Furthermore, these insights expand our understanding of architecture effects in sustainable thermoplastic elastomers.
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. In this study, 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 k B T. We find that, for all melts and blends, interaction of a few k B T 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 k B T 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.
Emulsions have wide applications in the food, cosmetics, and pharmaceutical industries. Emulsions stabilized with polymers having different architectures, such as linear diblock and triblock copolymers, branched polymers, star polymers, graft polymers, and densely grafted bottlebrush polymers, have been used for encapsulation, delivery, and as templates for polymerization reactions. Furthermore, stimuli-responsive polymers have been used for on-demand demulsification and emulsion engineering. In this review, we highlight the developments in the past decade that used polymers with advanced architectures as multi-functional emulsifiers.
We present an investigation into the dynamic relaxation mechanisms of a polybutadiene blend composed of a four-arm star (10 wt. %) and a linear polymer matrix in the presence of an applied shear flow. Our focus was the response of the star polymer, which cannot be unambiguously assessed via linear viscoelastic measurements since the signature of the star polymer can barely be detected due to the dominant contribution of the linear matrix. By utilizing small-angle neutron scattering (SANS) coupled with a Couette shear device and a deuterated matrix polymer, we investigated the dynamics of the minority star component of the blend. Our results confirm that the stars deform anisotropically with increasing shear rate. We have compared the SANS data with predictions from the well-established scattering adaptation of the state-of-the-art tube model for entangled linear polymer melts undergoing shear, i.e., Graham, Likhtman, Milner, and McLeish (GLaMM) approach, appropriately modified following earlier studies in order to apply to the star. This modified model, GLaMM-R, includes the physics necessary to understand stress relaxation in both the linear and nonlinear flow regimes, i.e., contour length fluctuations, constraint release, convective constraint release, and chain retraction. The full scattering signal is due to the minority star component and, although the contribution of the linear chains is hidden from the neutron scattering, they still influence the star polymer molecular dynamics, with the applied shear rate ranging from approximately 8 to 24 s –1 , below the inverse relaxation time of the linear component. This study provides another confirmation that the combination of rheology and neutron scattering is an indispensable tool for investigating the nonlinear dynamics of complex polymeric systems.
We introduce ToPolyAgent, a multi-agent AI framework for performing coarse-grained molecular dynamics (MD) simulations of topological polymers through natural language instructions. By integrating large language models (LLMs) with domain-specific computational tools, ToPolyAgent supports both interactive and autonomous simulation workflows across diverse polymer architectures, including linear, ring, brush, and star polymers, as well as dendrimers. The system consists of four LLM-powered agents: a Config Agent for generating initial polymer–solvent configurations, a Simulation Agent for executing LAMMPS-based MD simulations and conformational analyses, a Report Agent for compiling markdown reports, and a Workflow Agent for streamlined autonomous operations. Interactive mode incorporates user feedback loops for iterative refinements, while autonomous mode enables end-to-end task execution from detailed prompts. We demonstrate ToPolyAgent's versatility through case studies involving diverse polymer architectures under varying solvent conditions, thermostats, and simulation lengths. Furthermore, we highlight its potential as a research assistant by directing it to investigate the effect of interaction parameters on the linear polymer conformation, and the influence of grafting density on the persistence length of the brush polymer. By coupling natural language interfaces with rigorous simulation tools, ToPolyAgent lowers barriers to complex computational workflows and advances AI-driven materials discovery in polymer science. It lays the foundation for autonomous and extensible multi-agent scientific research ecosystems.
The diffusion of nanoparticles in a polymer matrix is an area of current interest. However, a complete understanding is still limited as it is often difficult to quantify the much slower motion of nanoparticles in a polymer matrix. To combat this problem, we have developed a protocol to measure the diffusion coefficient of soft nanoparticles in a linear polymer matrix. Recently developed synthetic control over soft nanoparticle structures combined with this protocol provides a pathway to separately elucidate the effects of the molecular weight and nanoparticle softness on its diffusive behavior. These results indicate that the nanoparticle softness and deformability dictate its motion. Increasing the cross-linking density of the nanoparticle for all molecular weights increases its hardness and suppresses its motion in the linear matrix. Additionally, the nanoparticle molecular weight dependence deviates from the exponential dependence for star polymers suggesting that these nanoparticles benefit from the cooperative motion of the matrix to open pathways for the nanoparticle. Finally, comparison of these experimentally determined values to the Stokes–Einstein theory demonstrates that the nanoparticles diffuse much slower than a hard sphere. This is interpreted to indicate that there exist additional interactions between the nanoparticle and polymer matrix that are not captured by Stokes–Einstein, including threading or entanglement of the linear chain with the nanoparticle.
A material system for performing layer-spread experiments on brush particle bilayers is presented and used to determine the diffusion constant of brush particles in the melt state. Selective deuteration of the core and shell of organo-silica nanoparticles grafted with poly(methyl methacrylate) was used to match the scattering length density of the core and the polymer canopy layer. This subdued the scattering of particle cores (i.e., formfactor scattering) and enabled the analysis of the interdiffusion kinetics using neutron reflectivity. For low molecular grafts, i.e., grafts with a molecular weight below the entanglement limit, the interdiffusion kinetics revealed both a sub- and Fickian diffusion regime. The former was attributed to the local dynamics that was constrained by the slow-moving cores of neighboring brush particles that acted as long-lived physical cross-links. No transition to Fickian diffusion was observed for entangled systems, even at prolonged annealing times. This suggested a higher level of kinetic restraint in entangled brush particle melts as compared to, for example, star polymers with a comparable chain length for which Fickian diffusion has been reported under similar conditions.
We report the synthesis and temperature-dependent morphologies of a series of polylactide--poly (-decalactone)--polylactide (LDL) triblock copolymers with M n = 16.0 – 18.1 kg / mol and volume fractions f L = 0.27 – 0.31 and associated core-shell bottlebrush (csBB) polymers, which derive from enchaining LDL triblocks through a polymerizable midchain functionality. While the LDL triblocks form micellar Frank-Kasper A15 and phases due to the conformational asymmetry of this monomer pair, the csBB morphologies sensitively depend on the backbone degree of polymerization ( N bb ). At low N bb values, micellar Frank-Kasper phases with the brush backbone situated in the matrix domain are stable, albeit with a modest reduction in the mean interfacial curvature evidenced by a to A15 order-to-order transition. However, larger N bb values drive csBBs to form hexagonally packed cylinders phases. This N bb -dependent phase behavior is rationalized in terms of a star-to-bottlebrush transition. At low N bb values, the csBBs are akin to star polymers with pointlike junctions that can support complex micelle packings. As N bb increases, the csBBs adopt cylindrical molecular geometries with extended backbones situated in the matrix domain that prefer hexagonally packed cylinders morphologies. Published by the American Physical Society 2024
In our previous DOE-supported project (DE-SC0016208), we demonstrated that a particular architecture dubbed ‘randomly end-linked copolymer networks’ (RECNs) led to especially robust self-assembly of disordered cocontinuous nanostructures. Such structures, wherein both microphases are fully percolating in three dimensions, are attractive for a wide-variety of energy-relevant applications including purification membranes, separators in batteries and fuel cells, catalyst supports, and high surface area electrodes. In the current project we sought to substantially extend our fundamental understanding of how different types of randomness in blocky copolymer architecture contribute to the robust formation of disordered cocontinuous nanostructures. To do so, we filled in the sizable gap between the previously studied cases of randomly linked linear multiblock copolymers and RECNs by studying two intermediate cases: (i) random miktoarm star polymers, which contain dispersity in the number of the two chemically-incompatible strands located at each junction and therefore the preferred interfacial curvature of each polymer, and (ii) randomly branched copolymers, which also possess bridging strands that stretch across domains and apply local ‘elastic’ forces to the interfaces. In addition, we studied a different network architecture, statistically crosslinked copolymer networks, that is more straightforward to prepare using chain growth polymerization methods, enabling more facile formation of cocontinuous nanostructures. Finally, we extended our approaches from model systems based on polystyrene and poly(lactic acid) to copolymer architectures containing either (i) polysulfone, an engineering polymer that provides excellent mechanical properties for membrane applications, or (ii) polyacrylonitrile, providing a convenient route to nanoporous carbon materials.
Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing non-equilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a novel self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: (1) coarse-graining star polymers at challenging levels of coarse-graining while preserving non-equilibrium statistics, and (2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.
Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions of soft colloids having the same hydrodynamic size yields a liquid-togel-to-re-entrant liquid transition. In particular, the dynamic state diagram of 1,4-polybutadiene star-linear polymer mixtures was determined with the help of linear viscoelastic and small-angle Xray scattering experiments. While keeping the star polymers below their nominal overlap concentration, a gel was formed upon increasing the linear polymer content. Further addition of linear chains yielded a re-entrant liquid. This unexpected behavior was rationalized by the interplay of three possible phenomena: (i) depletion interactions, driven by the size disparity between the stars and the polymer length scale which is the mesh size of its entanglement network; (ii) colloidal deswelling due to the increased osmotic pressure exerted onto the stars; and (iii) a concomitant progressive suppression of the depletion efficiency on increasing the polymer concentration due to reduced mesh size, hence a smaller range of attraction. Our results unveil an exciting new way to tailor the flow of soft colloids and highlight a largely unexplored path to engineer soft colloidal mixtures.
Block polymers assemble into a variety of phase-separated morphologies based on volume fraction (φ) and interactions (χ) of the respective blocks. The arrangement of three different polymer blocks could either be a 3-arm star, with each block having one terminus attached to a common junction point or a linear A-B-C architecture. A versatile strategy is reported to synthesize a series of well-defined graft polymers that lie along the unexplored continuum between a 3-arm star and an A-B-C linear triblock polymer architecture. Using the technique of single-molecule insertion, precise control over the position of graft arm C along the B chain was achieved. A series of discrete graft polymers (PMMA-b-PS-g-PEO) with fixed φ and prescribed ω values that lie on the continuum between a 3-arm star (ω = 0) and linear triblock polymer (ω = 1) were synthesized. Morphological studies using small-angle X-ray scattering and conventional and energy-filtered transmission electron microscopy reveal the transition between lamellae, perforated lamellae, and cylindrical morphologies with systematic variation in the ω values, a trend attributed to the topological frustration and the associated χ values between the three blocks. Molecular dynamic simulations of coarse-grained models were found to predict phase diagrams that are consistent with the experimentally observed morphologies. Furthermore, our results suggest that changes in ω lead to topological frustration which is an important additional new design parameter that can be used to tune the morphology of multiblock polymers in addition to φ and χ.
Polymer single-chain nanoparticles (SCNPs) have found a wide range of applications spanning catalysts, sensors and nanomedicine. The generation of structured SCNPs from star-shaped polymers with diverse architectures and functionalities affords a new avenue to expand the emerging research area. The large-scale synthesis of structured SCNPs is described by the electrostatics-mediated intramolecular crosslinking of three types of 3-armed star-shaped polymers (T-P4VP, T-PS-b-P4VP, and T-P4VP-b-PS), whose configuration is tunable from spherical to cage-shaped to dumbbell-shaped and star-shaped. The structured SCNPs are amphiphilic and can be used as solid surfactants to stabilize different types of emulsions.
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