Star Polymers: Experiment, Theory, and Simulation

Controllable Synthesis of Chain Center Dye-Labeled Star Polymers for Quantitative Examination of Interchain Conformation by Time-Resolved Fluorescence Resonance Energy Transfer

Using a "core-first" approach with atom transfer radical polymerization, fluorescent center-functional star polymers of equivalent molecular weight but with varying numbers of arms (di-, tri-, and tetra-arm) were prepared. The sensitivity of fluorescence, combined with a dye-labeling technique introducing a fluorescent donor (carbazole) and an acceptor (anthracene) at the center of poly(methyl methacrylate) (PMMA) chains, enabled the application of time-resolved fluorescence resonance energy transfer to obtain quantitative insights into the conformation of the star polymer chains in the film state. When the results of star-branched polymers were compared with those of linear polymers of identical type and molecular weight, the impact of branching on polymer behavior was isolated for examination. Although the star topology does not alter the average intercoil distance, it affects the distance dispersity. Star polymers with higher arm numbers display decreased dispersity from distance due to reduced intermolecular aggregation at their geometric centers. This study presents the first spectroscopic evidence regarding the distribution of geometric centers in star polymers, offering a physical understanding of chain interpenetration and entanglement within star polymers.

Nanostructured Single-ion Polymer Blend Electrolytes Composed of Polyanionic Particles and Low Molecular Weight PEO

The development of single-ion solid polymer electrolytes with high ion conductivity holds the key to the realization of safe, long-lasting, high-energy batteries. Here we introduce the use of core-shell nanostructured polyanionic particles, composed of polyanion asymmetric miktoarm stars with a large number of glassy polystyrene-based polyanion arms that complement longer poly(ethylene oxide), PEO, arms, as additives to low molecular weight, liquid PEO. Due to the proposed macromolecular design approach, the polyanion particles are well dispersed for wt % ≤ 55 that enables the formation of a nanostructured single-ion electrolyte with highly interconnected channels composed of liquid PEO that promotes fast ion transport. Noticeably, while the ion conductivity remains fairly unaffected and close to 10-5 S/cm at room temperature with nanoparticle loading, the shear modulus monotonically increases by several order of magnitudes indicating a very strong decoupling between the antagonistic properties of mechanical modulus and ion conductivity.

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.

How Does the Number of Arms Affect the Properties of Mikto-Arm Stars in a Selective Oligomeric Matrix? Insights from Atomistic Simulations

We present a simulation study of amphiphilic mikto-arm star copolymers in a selective polymer host. By means of atomistic molecular dynamics simulations, we examine the structural and dynamical properties of mikto-arm stars with varying number, n, of poly(ethylene oxide) (PEO) and polystyrene (PS) arms, (PEO) n (PS) n in a 33% wt blend with an oligomeric PEO host (o-PEO). As the number of arms increases, the stars resemble more spherical particles with less separated PEO and PS intramolecular domains. As a result of their internal morphology and associated geometrical constraints, the mikto-arm stars self-assemble either into cylindrical-like objects or a percolated network with increasing n, within the o-PEO matrix. The segmental dynamics is mostly governed by the star architecture and the heterogeneous local environment, formed by the intra- and intermolecular nanosegregation. We discuss the role of each factor and compare the results with previously published studies on mikto-arm stars.

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.

Single molecule electrophoresis of star polymers through nanopores: Simulations

We study the translocation of charged star polymers through a solid-state nanopore using coarse-grained Langevin dynamics simulations, in the context of using nanopores as high-throughput devices to characterize polymers based on their architecture. The translocation is driven by an externally applied electric field. Our key observation is that translocation kinetics is highly sensitive to the functionality (number of arms) of the star polymer. The mean translocation time is found to vary non-monotonically with polymer functionality, exhibiting a critical value for which translocation is the fastest. The origin of this effect lies in the competition between the higher driving force inside the nanopore and inter-arm electrostatic repulsion in entering the pore, as the functionality is increased. Our simulations also show that the value of the critical functionality can be tuned by varying nanopore dimensions. Moreover, for narrow nanopores, star polymers above a threshold functionality do not translocate at all. These observations suggest the use of nanopores as a high-throughput low-cost analytical tool to characterize and separate star polymers.

Thermodynamics of star polymer solutions: A coarse-grained study

We consider a coarse-grained (CG) model with pairwise interactions, suitable to describe low-density solutions of star-branched polymers of functionality f. Each macromolecule is represented by a CG molecule with (f + 1) interaction sites, which captures the star topology. Potentials are obtained by requiring the CG model to reproduce a set of distribution functions computed in the microscopic model in the zero-density limit. Explicit results are given for f = 6, 12, and 40. We use the CG model to compute the osmotic equation of state of the solution for concentrations c such that Φ_p=c∕c^*≲1, where c^* is the overlap concentration. We also investigate in detail the phase diagram for f = 40, identifying the boundaries of the solid intermediate phase. Finally, we investigate how the polymer size changes with c. For Φ_p≲0.3, polymers become harder as f increases at fixed reduced concentration c∕c^*. On the other hand, for Φ_p≳0.3, polymers show the opposite behavior: At fixed Φ_p, the larger the value of f, the larger their size reduction is.

Universal size properties of a star-ring polymer structure in disordered environments

We consider the complex polymer system, consisting of a ring polymer connected to the f_{1}-branched starlike structure, in a good solvent in the presence of structural inhomogeneities. In particular cases f_{1}=1 and f_{1}=2, such a system restores the synthesized tadpole-shaped polystyrenes [Doi et al., Macromolecules 46, 1075 (2013)MAMOBX0024-929710.1021/ma302511j]. We assume that structural defects are correlated at large distances x according to a power law x^{-a}. Applying the direct polymer renormalization approach, we evaluate the universal size characteristics such as the ratio of the radii of gyration of star-ring and star topologies, and compare the effective sizes of single arms in complex structures and isolated polymers of the same total molecular weight. The nontrivial impact of disorder on these quantities is analyzed.

Glass transition of polymers in bulk, confined geometries, and near interfaces

When cooled or pressurized, polymer melts exhibit a tremendous reduction in molecular mobility. If the process is performed at a constant rate, the structural relaxation time of the liquid eventually exceeds the time allowed for equilibration. This brings the system out of equilibrium, and the liquid is operationally defined as a glass-a solid lacking long-range order. Despite almost 100 years of research on the (liquid/)glass transition, it is not yet clear which molecular mechanisms are responsible for the unique slow-down in molecular dynamics. In this review, we first introduce the reader to experimental methodologies, theories, and simulations of glassy polymer dynamics and vitrification. We then analyse the impact of connectivity, structure, and chain environment on molecular motion at the length scale of a few monomers, as well as how macromolecular architecture affects the glass transition of non-linear polymers. We then discuss a revised picture of nanoconfinement, going beyond a simple picture based on interfacial interactions and surface/volume ratio. Analysis of a large body of experimental evidence, results from molecular simulations, and predictions from theory supports, instead, a more complex framework where other parameters are relevant. We focus discussion specifically on local order, free volume, irreversible chain adsorption, the Debye-Waller factor of confined and confining media, chain rigidity, and the absolute value of the vitrification temperature. We end by highlighting the molecular origin of distributions in relaxation times and glass transition temperatures which exceed, by far, the size of a chain. Fast relaxation modes, almost universally present at the free surface between polymer and air, are also remarked upon. These modes relax at rates far larger than those characteristic of glassy dynamics in bulk. We speculate on how these may be a signature of unique relaxation processes occurring in confined or heterogeneous polymeric systems.

Dextran-Polyacrylamide as Matrices for Creation of Anticancer Nanocomposite

Drug targeting to specific organs and tissues is one of the crucial endeavors of modern pharmacotherapy. Controlled targeting at the site of action and reduced time of exposure of nontargeted tissues increase the efficacy of the treatment and reduce toxicity and side effects, improving compliance and convenience. Nanocarriers based on the branched copolymers dextran-graft-polyacrylamide were synthesized and characterized and were tested on phagocytic cells. It was shown that these nanoparticles are actively captured by phagocytic cells and that they are not cytotoxic. The polymer nanoparticles loaded with cisplatin at different concentrations from 0.1 to 10 μg/mL yielded dose-dependent decrease in viability of chronic myelogenous leukemia and histiocytic lymphoma cells. The lowest percentage of viable cells was observed for lymphoma cells (22%). Taking into account the fact that our nanoparticles will act mainly on malignant phagocytic cells and do not affect healthy cells, they can thus potentially be used for the therapeutic treatment of tumor cells having phagocytic activity. The effect of nanosilver on cell viability was lower than the one of polymer/cisplatin composite. The data from the cytotoxic studies indicate that nanosilver induces toxicity in cells. However, when the copolymers were conjugated to both nanosilver and cisplatin, such a nanosystem displayed less cytotoxic effect compared to the conjugates of dextran-polyacrylamide and cisplatin.

Synthesis and Characterization of Multicomponent ABC- and ABCD-Type Miktoarm Star-Branched Polymers Containing a Poly(3-hexylthiophene) Segment

The new series of ABC-type miktoarm star polymer (ABC star, A = polyisoprene (PI), B = polystyrene (PS), and C = poly(3-hexylthiophene) (P3HT)) and ABCD-type miktoarm star polymer (ABCD star, A = PI, B = PS, C = poly(α-methylstyrene) (PαMS), and D = P3HT) could be synthesized by the combination of the controlled KCTP, anionic linking reaction, and Click chemistry. By the copper(I)-catalyzed Huisgen 1,3-dipolar cycloaddition click reaction of the azido-chain-end-functional P3HT (P3HT-N₃) with the alkyne-in-chain-functional AB diblock copolymer (A = PI and B = PS) (AB-alkyne) or alkyne-core-functional ABC miktoarm star polymer (A = PI, B = PS, and C = PαMS) (ABC-alkyne), the target ABC star and ABCD star, respectively, were obtained, as confirmed by size exclusion chromatography (SEC) and proton nuclear magnetic resonance (¹H NMR). The thermal and optical properties of these star polymers were examined by thermal gravimetric analysis (TGA) and UV-vis spectroscopy. The dynamic scattering calorimetry (DSC), atomic force micrograph (AFM) image, and grazing incidence small-angle X-ray scattering (GISAXS) results showed that the periodic P3HT fibril nanostructures rather than microphase separation occurred in the ABCD star film. In addition, it was found that highly crystalline P3HT domains aligned in the "edge-on" orientation, as supported by grazing incidence wide-angle X-ray scattering (GIWAXS).

Validity of the Stokes-Einstein Relation in Soft Colloids up to the Glass Transition

We investigate the dynamics of kinetically frozen block copolymer micelles of different softness across a wide range of particle concentrations, from the fluid to the onset of glassy behavior, through a combination of rheology, dynamic light scattering, and pulsed field gradient NMR spectroscopy. We additionally perform Brownian dynamics simulations based on an ultrasoft coarse-grained potential, which are found to be in quantitative agreement with experiments, capturing even the very details of dynamic structure factors S(Q,t) on approaching the glass transition. We provide evidence that for these systems the Stokes-Einstein relation holds up to the glass transition; given that it is violated for dense suspensions of hard colloids, our findings suggest that its validity is an intriguing signature of ultrasoft interactions.

Conformational and dynamical properties of ultra-soft colloids in semi-dilute solutions under shear flow

We investigate structural and dynamical properties of ultra-soft colloids in dilute and semi-dilute solutions by hybrid mesoscale simulations under linear shear flow. In particular, the influence of functionality on these properties is addressed. Our study combines molecular dynamics simulations for the solute with the multiparticle collision dynamics approach for the coarse-grained solvent. The star polymers exhibit large conformational and orientational changes in shear flow, which we characterize by the radius of gyration tensor and the alignment angle. These quantities show a universal dependence on a concentration- and functionality-dependent Weissenberg number with slight deviations at high shear rates. Moreover, the star polymers display a rotational dynamics with a shear-rate- and concentration-dependent rotation frequency. We attribute the concentration dependence to the screening of hydrodynamic interactions in semi-dilute star-polymer solutions.

Star copolymers in porous environments: scaling and its manifestations

We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair-correlation function g(x)~x(-a). Applying the field-theoretical renormalization group approach in d dimensions, we analyze different scenarios of scaling behavior working to first order of a double ɛ=4-d, δ=4-a expansion. We discuss the influence of the correlated disorder on the resulting scaling laws and possible manifestations such as diffusion-controlled reactions in the vicinity of absorbing traps placed on polymers as well as the effective short-distance interaction between star copolymers.

Osmotic shrinkage in star/linear polymer mixtures

Multiarm star polymers were used as model grafted colloidal particles with long hairs, to study their size variation due to osmotic forces arising from added linear homopolymers of smaller size. This is the origin of the depletion phenomenon that has been exploited in the past as a means to melt soft colloidal glasses by adding linear chains and analyzed using dynamic light scattering experiments and an effective interactions analysis yielding the depletion potential. Shrinkage is a generic phenomenon for hairy particles, which affects macroscopic properties and state transitions at high concentrations. In this work we present a small-angle neutron scattering study of star/linear polymer mixtures with different size ratios (varying the linear polymer molar mass) and confirm the depletion picture, i.e., osmotic star shrinkage. Moreover, we find that as the linear/star polymer size ratio increases for the same effective linear volume fraction (c/c* with c* the overlapping concentration), the star shrinkage is reduced whereas the onset of shrinkage appears to take place at higher linear polymer volume fractions. A theoretical description of the force balance on a star polymer in solution, accounting for the classic Flory contributions, i.e. elastic and excluded volume, as well as the osmotic force due to the linear chains, accurately predicts the experimental findings of reduced star size as a function of linear polymer concentration. This is done in a parameter-free fashion, in which the size of the cavity created by the star, and from which the chains are excluded, is related to the radius of the former from first principles.

Slow dynamics, aging, and crystallization of multiarm star glasses

Multiarm star polymers are model systems with tunable intermediate colloid to polymerlike character, exhibiting rich phase behavior, internal relaxations, and flow properties. An important puzzle for several years has been the lack of clear experimental proof of crystalline states despite strong theoretical predictions. We present unambiguous evidence via multispeckle dynamic light scattering (MSDLS) and small-angle neutron scattering (SANS) for such crystallization in a solvent of intermediate quality. An unexpected speed up of the short-time star diffusion observed in MSDLS was attributed by SANS to crystallization, via aging, of the multiam star glass. This delayed glass to crystal transition establishes a pathway for star crystallization that might be generic in colloidal glasses.

Barrier crossing by a star polymer

We analyze the dynamics of a star polymer of F arms trapped in a double well potential. Initially the molecule is confined to one of the minima and can cross over the barrier to the other side. We use the continuum version of the Rouse-Ham model and calculate the rate of crossing using the multidimensional approach due to Langer [Ann. Phys. (N.Y.) 54, 258 (1969)]. Finding the transition state for the process is shown to be equivalent to the solution of Newton's equations for F independent particles, moving in an inverted potential. For each star polymer, there is a critical barrier top curvature, below which the star crosses over in coiled conformation. The value of the critical curvature is determined by the first Rouse mode of the star. If the curvature is greater than this critical value, the saddle point for the crossing is a stretched conformation of the star. For the coiled transition state, the activation energy is proportional to the total arm length of the star. For the stretched transition state, as one increases the length of an arm of the star, the activation energy at first increases and then decreases. This results from the fact that in the stretched state, only one arm of the polymer is stretched across the top of the barrier, while others need not be. We calculate the rate by expanding the energy around the saddle up to second order in the fluctuations. As we use the continuum model, there are infinite modes for the polymer and, consequently, the prefactor has infinite products. We show that these infinite products can be reduced to a simple expression, and evaluated easily. However, the rate diverges near NTc due to the multifurcation, which results in more than one unstable mode. The cure for this divergence is to keep terms up to fourth order in the expansion of energy for these modes. Performing this, we have calculated the rate as a function of the length of the star. It is found that the rate has a nonmonotonic dependence on the length, suggesting that longer stars may actually cross over the barrier faster.

Asymmetric poly(ethylene-alt-propylene)-poly(ethylene oxide) micelles: a system with starlike morphology and interactions

We report on an experimental study of single particle properties and interactions of poly(ethylene-alt-propylene)-poly(ethylene oxide) (PEP-PEO) starlike micelles. The starlike regime is achieved by an extremely asymmetric block ratio (1:20) and the number of arms (functionality) is changed by varying the composition of the solvent (the interfacial tension). Small angle neutron scattering (SANS) data in the dilute regime can be modeled by assuming a constant density profile in the micellar core (compact core) and a starlike density profile in the corona (starlike shell). The starlike morphology of the corona is confirmed by a direct comparison with SANS measurements of dilute poly butadiene star solutions. Comparison of structure factors obtained by SANS measurements in the concentrated regime shows in addition that the interactions in the two systems are equivalent. Micellar structure factors at several packing fractions can be modeled by using the ultrasoft potential recently proposed for star polymers [Likos, Phys. Rev. Lett. 80, 4450 (1998)]. The experimental phase diagram of PEP-PEO micelles is quantitatively compared to theoretical expectations, finding good agreement for the location of the liquid-solid boundary and excellent agreement for the critical packing fraction where the liquid-to-bcc crystal transition takes place for f<70. The functionality, i.e., the coronal density, strongly influences the nature of the solid phase: for f<70 the system crystallizes into a bcc phase, high f>70 formation of amorphous arrested states prevents crystallization.

Hydrodynamic screening of star polymers in shear flow

The mutual effects of the conformations of a star polymer in simple shear flow and the deformation of the solvent flow field are investigated by a hybrid mesoscale simulation technique. We characterize the flow field near the star polymer as a function of its functionality (arm number) f . A strong screening of the imposed flow is found inside the star polymer, which increases with increasing f . To elucidate the importance of hydrodynamic screening, we compare results for hydrodynamic and random solvents. The dependence of the polymer orientation angle on the Weissenberg number shows a power law behavior with super-universal exponent --independent of hydrodynamic and excluded-volume interactions. In contrast, the polymer rotation frequency changes qualitatively when hydrodynamic interactions are switched on.