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We combine linear viscoelastic measurements and modelling in order to explore the dynamics of blends of the same-molecular-weight ring and linear polymers in the regime of the low volume fraction (0.3 or lower) of the ring component. The stress relaxation modulus is affected by the constraint release (CR) of both rings and linear components due to the motion of linear chains. We develop a CR-based model of ring-linear blends that predicts the stress relaxation function in the low fraction regime of ring component in excellent agreement with experiments. Rings trapped by their entanglements with linear chains can only relax by linear-chain-induced constraint release, resulting in much slower relaxation of rings than of linear chains. The relative viscosity [Formula: see text] of the blend with respect to the linear melt viscosity η(L) at ring overlap volume fraction [Formula: see text] increases proportionally to the square root of ring molecular weight [Formula: see text]. Our experimental results clearly demonstrate that it is possible to enhance the viscosity and simultaneously the structural relaxation time of linear polymer melts by adding a small fraction of ring polymers. These results not only provide fundamental insights into the physics of the CR process but also suggest ways to fine-tune the flow properties of linear polymers by means of adding rings.

In the melt state at equilibrium, entangled nonconcatenated ring macromolecules adapt more compact conformations compared to their linear analogs and do not form an entanglement network. We show here that, when subjected to uniaxial stretching, they exhibit a unique response, which sets them apart from any other polymer. Remarkably, whereas both linear and ring polymers strain-harden, the viscosity of the rings increases dramatically (the melt thickens) at very low stretch rates due to the unraveling of their conformations along the stretching direction. At high rates, stretching leads to viscosity thinning similar to that of entangled linear polymers, albeit with subtle differences.

We investigate the influence of the environment on the relaxation dynamics of well-defined H-polymers diluted in a matrix of linear chains. The molar mass of the linear chain matrix is systematically varied and the relaxation dynamics of the H-polymer is probed by means of linear viscoelastic measurements, with the aim to understand its altered motion in different blends, compared to its pure melt state. Our results indicate that short unentangled linear chains accelerate the relaxation of both the branches and the backbone of the H-polymers by acting as an effective solvent. On the other hand, the relaxation of the H-polymer in an entangled matrix is slowed-down, with the degree of retardation depending on the entanglement number of the linear chains. We show that this retardation can be quantified by considering that the H-polymers are moving in a dilated tube at the rhythm of the motion of the linear matrix.

The state‐of‐the‐art understanding of entangled linear polymers is based on the concept of physical network formation from entanglements. The physical network is characterized by aplateau modulus in linear viscoelastic (LVE) measurements. However, linking the two free ends of a linear polymer, thereafter called a ring polymer, has dramatic consequences. For example, non-concatenated rings have much lower zero‐shear‐rate viscosity compared to their linear entangled counterparts. A plateau modulus is not observed in LVE measurements for ring polymers [1].Due to the difficulties in synthesis, which leads to very limited amount of samples, well‐defined ring polymers have never been studied in extensional flow. In this work, we present the first results of extensional rheology of a ring polystyrene (PS) melt with the molecular weight 185k(Ring‐185k). We show that the ring PS is surprisingly strain hardening in extensional flow, and reaches the same extensional steady state viscosity as its linear counterpart (Lin‐185k) when the stretch rate is fast enough. We further present the extensional rheology of blends made of Ring‐185k and Lin‐185k, with weight fraction of 5%, 20%, and 30% of Ring‐185k, respectively. We show that in the transient stress‐strain responses, stress overshoot is observed for the samples containing 20% and 30% Ring‐185k, while the stress overshoot is not observed for the pure Ring‐185k and Lin‐185k.The present results shed light into the fascinating flow properties of polymers without free ends, while they also advance the state‐of‐the‐art in polymer physics. At the same time, they open the route for understanding the response of folded proteins and chromosome territories under strong external fields.

The intrinsic viscosity of cyclic polystyrenes (C-PS) and linear polystyrenes (L-PS) with molecular weight (MW) ranging from 16K to 370K was measured in THF using size exclusion chromatography coupled with a triple detection system. The C-PS samples were prepared by a ring-closure reaction of telechelic linear precursor synthesized by anionic polymerization. As-synthesized C-PS samples after the ring-closure reaction contain various byproducts, and they were fractionated by liquid chromatography at the critical condition to obtain highly pure C-PS. While the intrinsic viscosity of L-PS agrees well with the literature data, C-PS shows significantly lower value than the literature values. The Mark–Houwink exponent of C-PS is 0.67, somewhat lower than 0.70 for L-PS in the good solvent over the MW range examined. Therefore, the ratio of the intrinsic viscosity of C-PS to L-PS (g′ = [η]C/[η]L) in THF is not MW independent but decreases as MW increases (0.63 ≥ [η]C/[η]L ≥ 0.57). The trend of intrinsic viscosity agrees well with the computer simulation result. The discrepancy in [η]C from the literature values can largely be attributed to the contamination of linear byproducts in the earlier studies.

We report on a novel synthetic route to synthesize relatively large quantities of polystyrene (PS) star polymers with targeted arm functionality and molar mass and their theological properties in the molten state. The synthetic route involves grafting styrene monomers onto a modified (aliphatic, alternating) polyketone backbone with a specific number of initiating grafting sites using controlled atom transfer radical polymerization (ATRP). Several polyketone precursors were used. This resulted in a large array of star polystyrenes with nonspherical cores and varying average arm length and number of arms. Their linear viscoelasticity was investigated and discussed in the context of the known response of anionically synthesized stars. Using a powerful characterization toolbox, including state-of-the-art interaction chromatography, rheometry, and tube modeling via the branch-on-branch (BoB) algorithm, we have assessed the viscoelasticity of these star polymers quantitatively. In particular, we have demonstrated a variability in molecular structure, which differs substantially from their anionically synthesized counterparts. Hence, whereas this new family of star polymers is not recommended for fundamental studies of polymer physics such as the molecular origin of relaxation mechanisms without prior extensive fractionation, they could be used in studies of mixtures as well as industrially relevant processing operations that require large amounts of polymeric stars.

We present a systematic investigation of well-characterized, experimentally pure polystyrene (PS) rings with molar mass of 161 000 g/mol in dilute solutions. We measure the ring form factor at θ - and good-solvent conditions as well as in a polymeric solvent (linear PS of roughly comparable molar mass) by means of small-angle neutron scattering (SANS). Additional dynamic light scattering (DLS) measurements support the SANS data and help elucidate the role of solvent quality and solution preparation. The results indicate the increase of ring dimensions as the solvent quality improves. Furthermore, the experimental form factors in both θ -solvent and linear matrix behave as ideal rings and are fully superimposable. The nearly Gaussian conformations of rings in a melt of linear chains provide evidence of threading of linear chains through rings. The latter result has implications for the dynamics of ring-linear polymer mixtures.

We present systematic, unique linear and nonlinear shear rheology data of an experimentally pure ring polystyrene and its linear precursor. This polymer was synthesized anionically and characterized by interaction chromatography and fractionation at the critical condition. Its weight-average molar mass is 84 kg/mol; i.e., it is marginally entangled (entanglement number Z ≈ 5). Its linear viscoelastic response appears to be better described by the Rouse model (accounting for ring closure) rather than the lattice-animal-based model, suggesting a transition from unentangled to entangled ring dynamics. The failure of both models in the terminal region may reflect the remaining unlinked linear contaminants and/or ring–ring interpenetration. The viscosity evolution at different shear rates was measured using a homemade cone-partitioned plate fixture in order to avoid edge fracture instabilities. Our findings suggest that rings are much less shear thinning compared to their linear counterparts, whereas both obey...

This work describes the determination of the band broadening function (BBF) in a size exclusion chromatograph fitted with 2 mixed-gel columns, a light scattering (LS) detector, and a differential refractometer (DR). The raw data were the chromatograms of 4 narrow polystyrene standards. First, the interdetector volume shift was indirectly estimated from its upper and lower limiting values. Then, for each of the standards, their ‘‘local’’ BBFs were estimated by application of an existing theoretical method. Each local BBF is an assumed elution-volume invariant in the narrow ranges of the analyzed standards and is represented by an exponentially-modified Gaussian of standard deviation rBB and exponential decay sBB. Finally, a ‘‘global’’ BBF (valid for the complete fractionation range) was interpolated from the local BBF parameters. For increasing elution volumes, the global BBF exhibits an increasing rBB and a decreasing sBB. In addition, the asymmetry factor [sBB=rBB] and the global variance [r2 BB þ s2 BB] both decrease with elution volume. Fil: Yossen, Mariana Matilde. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico Para la Industria Química; Argentina Fil: Vega, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Chang, Taihyun. Pohang University of Science and Technology; Corea del Sur Fil: Meira, Gregorio Raul. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina

After many years of intense research, most aspects of the motion of entangled polymers have been understood. Long linear and branched polymers have a characteristic entanglement plateau and their stress relaxes by chain reptation or branch retraction, respectively. In both mechanisms, the presence of chain ends is essential. But how do entangled polymers without ends relax their stress? Using properly purified high-molar-mass ring polymers, we demonstrate that these materials exhibit self-similar dynamics, yielding a power-law stress relaxation. However, trace amounts of linear chains at a concentration almost two decades below their overlap cause an enhanced mechanical response. An entanglement plateau is recovered at higher concentrations of linear chains. These results constitute an important step towards solving an outstanding problem of polymer science and are useful for manipulating properties of materials ranging from DNA to polycarbonate. They also provide possible directions for tuning the rheology of entangled polymers.

High molecular weight dumbbell shaped polymers were prepared by atom transfer radical polymerization (ATRP) to grow branches from repeat units of end blocks of a symmetric triblock copolymer. The triblock copolymer itself was prepared by polymer-polymer coupling of a commercially obtained alpha,omega-end functionalized polystyrene as central block with end-functionalized poly(chloromethylstyrene) that we synthesized by nitroxide-mediated polymerization. Temperature gradient interaction chromatography (TGIC) enabled the estimation of the terminal hydroxyl functionality of the high molecular weight alpha,omega-difunctional polystyrene as 75%. Size exclusion chromatography (SEC) and H-1 NMR enabled the determination of molecular weights and verification of the structures of the intermediate and the cleaved products. Size exclusion chromatography coupled with light scattering (SEC-LS) and scanning force microscopy (SFM) were used to confirm that the desired dumbbell architecture was obtained.

To probe the effect of junction point functionality in miktoarm star block copolymer architecture on chain conformation and morphology, a series of AnBn miktoarm star copolymers where A arms are PS blocks and B arms are PI blocks were investigated. The overall series including a diblock and the star block copolymers can be represented by AnBn where n = 1, 2, 4, and 16. These materials were produced by synthesizing a single batch of living PS arms and a single batch of living PI arms and then linking them together with chlorosilane coupling agents of different functionality. Thus, all PS arms are identical and all PI arms are identical across the entire series of materials. All stars in the series have equal numbers of PS and PI arms, and the volume fractions of all the samples in the series (nearly 0.50 PS by volume) are identical within experimental error. All the materials were found, via small-angle X-ray scattering and transmission electron microscopy, to form lamellar morphologies. A significant increase in lamellar spacing with increasing junction point functionality (n) was found in this series of materials and can be attributed to molecular crowding near the junction point.

The synthesis of an H-shaped polybutadiene homopolymer as well as its detailed structural characterization is investigated. Anionic polymerization techniques together with chlorosilane linking agents were used for the production of the material. After each reaction step samples were taken and analyzed by size exclusion chromatography (SEC), membrane osmometry (MO), NMR, and temperature gradient interaction chromatography (TGIC). According to the characterization by SEC, MO, and NMR, the H-polymer showed a high degree of structural uniformity after purification by fractionation, and no significant amounts of differently branched byproducts could be detected. The TGIC analysis however revealed the presence of large amounts of structures, mainly with lower branching degree. We also found that a significant isotope effect exists in the TGIC retention between deuterated and hydrogenous polymers. In our case, where the H-polymer is partially deuterated, the TGIC analysis enabled us to resolve all the side products. Comparison of the different analysis methods indicates that the precise structural analysis of branched model polymers such as the H-polymer requires more sophisticated methods than used in the past.

Steady-state shear viscosity (γ˙) of unconcatenated ring polymer melts as a function of the shear rate γ˙ is studied by a combination of experiments, simulations, and theory. Experiments using polystyrenes with Z ≈ 5 and Z ≈ 11 entanglements indicate weaker shear thinning for rings compared to linear polymers exhibiting power law scaling of shear viscosity ∼γ˙-0.56 ± 0.02, independent of chain length, for Weissenberg numbers up to about 102. Nonequilibrium molecular dynamics simulations using the bead-spring model reveal a similar behavior with ∼γ˙-0.57 ± 0.08 for 4 ≤ Z ≤ 57. Viscosity decreases with chain length for high γ˙. In our experiments, we see the onset of this regime, and in simulations, which we extended to Wi ∼104, the nonuniversality is fully developed. In addition to a naive scaling theory yielding for the universal regime ∼γ˙-0.57, we developed a novel shear slit model explaining many details of observed conformations and dynamics as well as the chain length-dependent behavior of viscosity at large γ˙. The signature feature of the model is the presence of two distinct length scales: the size of tension blobs and much larger thickness of a shear slit in which rings are self-consistently confined in the velocity gradient direction and which is dictated by the size of a chain section with relaxation time 1/γ˙. These two length scales control the two normal stress differences. In this model, the chain length-dependent onset of nonuniversal behavior is set by tension blobs becoming as small as about one Kuhn segment. This model explains the approximate applicability of the Cox-Merz rule for ring polymers.