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At least 307 records · Page 17

Phosphonium-Based Polyzwitterions: Influence of Ionic Structure and Association on Mechanical Properties

This manuscript describes a synthetic strategy and structure–property investigation of unprecedented phosphonium-based zwitterionic homopolymers (polyzwitterions) and random copolymers (zwitterionomers). Free radical polymerization of 4-(diphenylphosphino)styrene (DPPS) provided neutral polymers containing reactive triarylphosphines. Quantitative postpolymerization alkylation of these pendant functionalities generated a library of polymers containing various concentrations of neutral phosphines, phosphonium ions, and phosphonium sulfobetaine zwitterions. The zwitterionic homo- and copolymers exhibited significantly higher glass transition temperatures (T g ) and enhanced mechanical reinforcement in comparison to neutral and phosphonium analogues. These changes in T g and mechanical properties were attributed to nanoscale morphological domains, which formed due to electrostatic interactions between zwitterionic groups, as revealed by X-ray scattering and broadband dielectric spectroscopy (BDS). BDS revealed increased static dielectric constants (>25) for the phosphonium zwitterionomers compared to ionomeric or neutral analogues. These high static dielectric constants for the solvent-free polyzwitterions supported their stronger polarization response in comparison with polymers containing neutral phosphines and phosphonium ions, and these interactions accounted for morphological differences and enhanced mechanical behavior. This work describes a versatile strategy for modulating electrostatic interactions with tunable mechanical properties for an unprecedented family of zwitterionic polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nitrogen-Doped PtNi Catalysts on Polybenzimidazole-Functionalized Carbon Support for the Oxygen Reduction Reaction in Polymer Electrolyte Membrane Fuel Cells

PtM (M = 3d transition metals) alloys are known as the promising oxygen reduction reaction catalysts and have been considered as the replacement of pure Pt catalysts for the commercialization of proton exchange membrane fuel cells. Although great progress has been made in the past three decades, the performance and durability of PtM catalysts still face stringent challenges from practical applications. Functionalization of a catalyst carbon support with nitrogen-contained groups can add charges onto its surface, which can be utilized to build a more complete ionomer/catalyst interface, to reduce the catalyst particle size, and to improve particle size distribution. Nitriding of PtNi catalysts can effectively improve the catalyst activity and stability by the modification of lattice strain. Hereby, we propose a synergistic approach of combining polybenzimidazole-grafted Vulcan XC72 carbon as the catalyst carbon support and the nitriding of PtNi to develop PtNiN/XC72-polybenzimidazole catalysts. Such PtNiN/XC72-PBI catalysts exhibit the excellent performance of fuel cell membrane electrode assembly (i.e., mass activity, 440 mA mgPt –1 ; electrochemical surface area, 51 m 2 gPt –1 ; and rated power density, 836 mW cm –2 ) as well as promising catalyst stability. The developed PtNiN/XC72-PBI meets the US DOE 2020 targets of mass activity for the fuel cell catalysts. This work provides a novel approach and a promising pathway on the development of the catalyst using such a synergistic approach-modification of the catalyst structure by nitrogen doping and functionalization of carbon support by polybenzimidazole for both high performance and high durability.

25 ENERGY STORAGE↗

Anisotropic Dynamics and Mechanics of Macromolecular Crystals Containing Lattice-Patterned Polymer Networks

The mechanical and functional properties of many crystalline materials depend on cooperative changes in lattice arrangements in response to external perturbations. However, the flexibility and adaptiveness of crystalline materials are limited. Additionally, the bottom-up, molecular-level design of crystals with desired dynamic and mechanical properties at the macroscopic level remains a considerable challenge. To address these challenges, we had previously integrated mesoporous, cubic ferritin crystals with hydrogel networks, resulting in hybrid materials (polymer integrated crystals or PIX) which could undergo dramatic structural changes while maintaining crystalline periodicity and display efficient self-healing. Here, the dynamics and mechanics of these ferritin-PIX were devoid of directionality, which is an important attribute of many molecular and macroscopic materials/devices. In this study, we report that such directionality can be achieved through the use of ferritin crystals with anisotropic symmetries (rhombohedral or trigonal), which enable the templated formation of patterned hydrogel networks in crystallo. The resulting PIX expand and contract anisotropically without losing crystallinity, undergo prompt bending motions in response to stimuli, and self-heal efficiently, capturing some of the essential features of sophisticated biological devices like skeletal muscles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Novel High Barrier Films for Packaging Food and Medicine

Long manned missions require food packaging to maintain food safety, nutrition, and acceptability for the length of 3-5 years1,2 while the shelf life assigned by NASA for current provisions is 18-24 months1. The focus of this design project was to make a polymer film specifically to function as a high oxygen barrier to later be included in an improved multi-layer packaging system of other specialized polymers with capabilities to allow for a 5-year shelf-life. To qualify as a high oxygen barrier film and to be a successful design for the future packaging, the resulting film is required to have an oxygen transmission rate (OTR) less than 0.06 cc/ m2/24 hr/atm, the standard for the current packaging3. This new film was designed to have a decreased permeability by increasing the “tortuous path” a gas molecule travels to permeate through a film. The increase in the “tortuous path” of a gas molecule is accomplished by introducing a 2D material additive. The additive chosen for this project was hexagonal boron nitride (h-BN) which exfoliates into boron nitride nanosheets (BNNs). Nylon 6 was chosen as the candidate for the matrix. This project is required to determine the best methods to synthesize the sample film and then to test the OTR of the film to determine if this design was successful. This project examined methods for pulverizing polymer resin pellets, h-BN exfoliation, and film fabrication using a hot press. This report includes the exfoliation and analysis of h-BN, procedural preparations for films, and a modeling study of estimated OTR of the h-BN/Nylon. The work in this report did not yield a high barrier composite film because of the laboratory closure in response to COVID -19 guidance but provides a concise method of the additive preparation and film synthesis. This gives a good starting point for future research in high barrier films by 2D additive composites.

Polymer, Nylon, PET, boron nitride, nanocomposite↗

A&L Annual Report: Kapton Strength

Exploding Foil Initiator (EFI) systems function by launching a polymer flyer (often referred to as a slapper) at a high explosive (HE) pellet, which is intended to shock-initiate the HE. Flyer characteristics (e.g., shape, planarity, etc.) are extremely important in this respect, governing their ability to initiate the HE. Polymer models currently used in these systems are largely unvalidated, potentially compromising the integrity of magneto-hydrodynamic (MHD) predictions of EFI function. An improved EFI MHD modelling capability is expected to: (1) expedite optimization of EFI-based initiation system design, (2) enable consideration of EFI-related aging and corresponding lifetime predictions, and (3) potentially minimize the number of costly experiments required to certify EFI designs. To address this knowledge gap, several years ago we began a computational project to develop a higher-fidelity model for Kapton, a Polyimide copolymer most commonly employed as the flyer material in EFI devices.

36 MATERIALS SCIENCE↗

Design of robust and versatile hydrocarbon-based single-ion-conducting polymer electrolytes

Hydrocarbon-based polymers offer several advantages, including lower environmental impacts, cost effectiveness, and the ability to finely tune properties. Here, we have developed trifluoromethanesulfonimide (TFSI)-functionalized poly(norbornene) (PNB) polymers utilizing a specifically designed oxa-Michael addition of a vinyl TFSI anion to an alcohol. Our results reveal that PNB-TFSI derivatives exhibit superior thermal stability and mechanical robustness compared with Nafion. The optimized PNB-TFSI-H-48 polymer (IEC 1.86 mmol/g) exhibits equivalent performance to Nafion as an anode ionomer in a proton exchange membrane fuel cell. Exchanging the counter ion to Li + enables PNB-TFSI to be used for Li-ion battery applications. Propylene carbonate plasticized PNB-TFSI derivatives achieve an Li-ion conductivity of over 10 −5 S/cm at 30°C. This Li polymer electrolyte exhibits excellent electrochemical stability (5 V vs. Li + /Li) and good cycling in a Li symmetric cell. These results highlight the potential and rational design of PNB-TFSI polymers for next-generation energy storage and conversion technologies.

08 HYDROGEN↗

Designing Physicochemically‐Ordered Interphases for High‐Performance Composites

To enhance the mechanical properties of carbon fiber‐reinforced polymer composites, a physicochemical scaffold is designed incorporating microscopically architected chemically reactive nanofibers that act as a multiscale bridge between the carbon fibers and the matrix. Thermally activated nanofibers leverage their morphologically driven mechanochemical properties to form covalent bonds with adjacent polymer molecules, creating a co‐continuous network that dramatically enhances fiber‐matrix load transfer. By meticulously controlling the nanofiber architecture through variable surface area, functional group availability, and polymer chain alignment effects, the extent of covalent bonding between nanofibers and the matrix is manipulated ultimately resulting in improved carbon fiber‐matrix adhesion. Further, the concept was validated using polyacrylonitrile nanofibers within an acrylonitrile butadiene styrene matrix in a discontinuous carbon fiber‐reinforced composite system. Nanomechanical studies using atomic force microscopy and low‐field nuclear magnetic resonance spectroscopy confirmed immobilized, chemically transferred, and ordered nanostructures at the interphase. The resulting composites demonstrated ≈56% and ≈175% improvements in tensile strength and toughness, respectively, compared to composites without nanofiber. Comprehensive thermal, rheological, and X‐ray scattering analyses, along side all‐atomic molecular dynamics simulations, revealed the fundamental mechanisms behind these improvements in mechanical behavior. The versatility and efficacy of the approach have the potential to address longstanding interphase challenges in the composite industry.

36 MATERIALS SCIENCE↗

Polymeric membranes for CO 2 separation and capture

Over the past decade, CO 2 separation and capture have become the new bandwagon for polymer science and membrane research. This review presents the fundamentals of CO 2 /gas separation in polymeric membranes and discusses how these principles underpin opportunities and challenges for post-combustion carbon capture (CO 2 /N 2 ), hydrogen purification (CO 2 /H 2 ), and natural gas and biogas sweetening (CO 2 /CH 4 ). Emerging polymeric membrane materials are discussed, including a few polymers containing a high content of polar functional groups (i.e., ether oxygen-rich polymers and polymeric ionic liquids), shape-persisting glassy polymers (i.e., perfluoropolymers, thermally rearranged polymers, iptycene-containing polymers), and reactive polymers featuring facilitated transport. Moreover, the promising candidates for each CO 2 separation application are highlighted. Lastly, the permeability-selectivity data reviewed were plotted against their 2008 and 2019 upper bounds.

08 HYDROGEN↗

Over 15% Efficiency Polymer Solar Cells Enabled by Conformation Tuning of Newly Designed Asymmetric Small‐Molecule Acceptors

Abstract The prosperous period of polymer solar cells (PSCs) has witnessed great progress in molecule design methods to promote power conversion efficiency (PCE). Designing asymmetric structures has been proved effective in tuning energy level and morphology, which has drawn strong attention from the PSC community. Two hepta‐ring and octa‐ring asymmetric small molecular acceptors (SMAs) (IDTP‐4F and IDTTP‐4F) with S‐shape and C‐shape confirmations are developed to study the relationship between conformation shapes and PSC efficiencies. The similarity of absorption and energy levels between two SMAs makes the conformation a single variable. Additionally, three wide‐bandgap polymer donors (PM6, S1, and PM7) are chosen to prove the universality of the relationship between conformation and photovoltaic performance. Consequently, the champion PCE afforded by PM7: IDTP‐4F is as high as 15.2% while that of PM7: IDTTP‐4F is 13.8%. Moreover, the S‐shape IDTP‐4F performs obviously better than their IDTTP‐4F counterparts in PSCs regardless of the polymer donors, which confirms that S‐shape conformation performs better than the C‐shape one. This work provides an insight into how conformations of asymmetric SMAs affect PCEs, specific functions of utilizing different polymer donors to finely tune the active‐layer morphology and another possibility to reach an excellent PCE over 15%.

Guo, Qing↗

Synthesis of hyperbranched polymer films via electrodeposition and oxygen-tolerant surface-initiated photoinduced polymerization

Hypothesis Hyperbranched polymers, not only possess higher functionality, but are also easier to prepare compared to dendrimers and dendric polymers. Combining electrodeposition and surface-initiated photoinduced electron transfer-reversible addition-fragmentation chain transfer (SI-PET-RAFT) polymerization is hypothesized to be a novel strategy for preparing hyperbranched polymer films on conductive surfaces without degassing. Experiments In this study, polymer brush grafted films with four different architectures (i.e. linear, branched, linear- block -branched, and branched- block -linear) were prepared on gold-coated glass substrates using electrodeposition, followed by SI-PET-RAFT polymerization. The resulting film structure and thickness, surface topology, absorption property, and electrochemical behavior were confirmed by spectroscopy, microscopy, microbalance technique, and impedance measurement. Findings These hyperbranched polymer brushes were capable of forming a thicker but more uniformly covered films compared to linear polymer brush films, demonstrating that hyperbranched polymer films can be potentially useful for fabricating protective polymer coatings on various conductive surfaces.

36 MATERIALS SCIENCE↗

Single polymer sorbent fibers for high performance and rapid direct air capture

Polymers of intrinsic microporosity (PIM) fibers featuring amidoxime and amine functionalities were formulated into high-performance CO 2 adsorbents. Fiber sorbents were composed of a single porous polymer component functionalized with molecular amines to increase the CO 2 capture uptake and kinetics. Here we report the highest CO 2 uptake capacity (3.3 wt% (0.8 mmol g –1 ) CO 2 at 400 ppm) among all PIM-based and single polymeric sorbents to date. Moreover, the sorbents exhibited rapid CO 2 adsorption rates (capturing 90% of its total capacity within 7 min.) and cost efficient and reproducible regeneration (at 70 °C) which are essential for reducing the cost of direct air capture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

New sterically hindered polyvinylamine-containing membranes for CO 2 capture from flue gas

Amine-containing facilitated transport membranes can have both high permeability and selectivity due to the reversible reaction between CO 2 and amino groups for effective carbon capture from flue gas. In this study, we have developed an improved method for the synthesis of high-molecular-weight sterically hindered polyvinylamine (PVAm) as the new fixed-site carrier in thin-film composite membranes for CO 2 capture. Commercially available PVAm was N-monomethylated into poly-N-methyl-N-vinylamine (PVAm-CH 3 ) using the stepwise reductive amination with a highly polar fluorinated alcohol as the solvent to enhance the equilibrium shift to the formation of the imine intermediate. The method prevented over-alkylation, resulting in the increased yield of the target product. PVAm-CH 3 exhibited excellent CO 2 facilitation with a CO 2 permeability of 445.7 Barrer (1 Barrer = 3.349 x 10 –16 mol m m –2 s –1 Pa –1 ) and a CO 2 /N 2 selectivity of 70.3, which are above the Robeson 2008 upper bound. The PVAm-CH 3 solution retained a sufficiently high viscosity after incorporating the aminoacid salt, 2-(1-piperazinyl)ethylamine sarcosinate (PZEA-Sar), as the mobile carrier for the membrane coating on nanoporous polyethersulfone (PES) substrates without any penetration issues. The resultant thin-film composite PVAm-CH3/PZEA-Sar membrane with a thickness of approximately 170 nm exhibited a superior CO 2 performance of 1071 GPU (1 GPU = 3.349 x 10 –10 mol m –2 s –1 Pa –1 ) and a CO 2 /N 2 selectivity of 183 at 57°C and a feed gas pressure of 111.64 kPa (1.5 psig). This PVAm-CH 3 /PZEA-Sar membrane surpassed the latest redefined 2019 CO 2 /N 2 upper bound and outperformed other polymer-based membranes. Density functional theory calculations also demonstrated that PVAm-CH 3 showed a stronger preference, relative to PVAm, toward the more efficient bicarbonate pathway. Thus, the steric hindrance effect of PVAm-CH 3 enhanced the solubility of CO 2 in the polymer matrix and resulted in the higher CO 2 permeance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Self-assembly of cocontinuous nanostructured copolymer templates with compositional and architectural dispersity. Final Report

Cocontinuous nanostructured materials in which multiple domains of different materials simultaneously span three dimensional space offer opportunities to achieve combined properties not possible with a single homogeneous material. These architectures have importance in a broad range of energy-relevant technologies including batteries, supercapacitors, fuel cells, separation membranes, and catalysts. Achieving such structures in polymeric materials has been of long-standing interest in the field, due to both the inherently attractive properties of cocontinuous polymer morphologies as well as their ability to serve as templates for other functional nanostructured materials. Our work on this project has established that randomly-linked polymer architectures constructed from two immiscible polymer strands provide robust and highly tunable approaches to disordered cocontinuous nanostructures. In particular, we developed a detailed understanding of how the parameters (linker functionality and strand length, asymmetry, and dispersity) of randomly-linked networks controlled the breadth of the cocontinuous window over which both phases remain percolated. We further characterized how these nanostructures undergo orientation, while retaining cocontinuity, under mechanical deformation. We also compared their behavior to that of random multi-block polymers of linear architecture, which show similar propensity to form disordered nanostructures, albeit over narrower ranges of parameter space. Finally, we have explored the development of functional polymer nanostructures and composites based in part on the fundamental understanding obtained via this project.

36 MATERIALS SCIENCE↗

Tailoring Hierarchical Structure and Rare Earth Affinity of Compositionally Identical Polymers via Sequence Control

Macromolecule sequence, structure, and function are inherently intertwined. While well-established relationships exist in proteins, they are more challenging to define for synthetic polymer nanoparticles due to their molecular weight, sequence, and conformational dispersities. Furthermore, to explore the impact of sequence on nanoparticle structure, we synthesized a set of 16 compositionally identical, sequence-controlled polymers with distinct monomer patterning of dimethyl acrylamide and a bioinspired, structure-driving di(phenylalanine) acrylamide (FF). Sequence control was achieved through multiblock polymerizations, yielding unique ensembles of polymer sequences which were simulated by kinetic Monte Carlo simulations. Systematic analysis of the global (tertiary- and quaternary-like) structure in this amphiphilic copolymer series revealed the effect of multiple sequence descriptors: the number of domains, the hydropathy of terminal domains, and the patchiness (density) of FF within a domain, each of which impacted both chain collapse and the distribution of single- and multichain assemblies. Furthermore, both the conformational freedom of chain segments and local-scale, β-sheet-like interactions were sensitive to the patchiness of FF. To connect sequence, structure, and target function, we evaluated an additional series of nine sequence-controlled copolymers as sequestrants for rare earth elements (REEs) by incorporating a functional acrylic acid monomer into select polymer scaffolds. We identified key sequence variables that influence the binding affinity, capacity, and selectivity of the polymers for REEs. Collectively, these results highlight the potential of and boundaries of sequence control via multiblock polymerizations to drive primary sequence ensembles hierarchical structures, and ultimately the functionality of compositionally identical polymeric materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Carbon nanotube biocompatibility in plants is determined by their surface chemistry

Abstract Background Agriculture faces significant global challenges including climate change and an increasing food demand due to a growing population. Addressing these challenges will require the adoption of transformative innovations into biotechnology practice, such as nanotechnology. Recently, nanomaterials have emerged as unmatched tools for their use as biosensors, or as biomolecule delivery vehicles. Despite their increasingly prolific use, plant-nanomaterial interactions remain poorly characterized, drawing into question the breadth of their utility and their broader environmental compatibility. Results Herein, we characterize the response of Arabidopsis thaliana to single walled carbon nanotube (SWNT) exposure with two different surface chemistries commonly used for biosensing and nucleic acid delivery: oligonucleotide adsorbed-pristine SWNTs, and polyethyleneimine-SWNTs loaded with plasmid DNA (PEI-SWNTs), both introduced by leaf infiltration. We observed that pristine SWNTs elicit a mild stress response almost undistinguishable from the infiltration process, indicating that these nanomaterials are well-tolerated by the plant. However, PEI-SWNTs induce a much larger transcriptional reprogramming that involves stress, immunity, and senescence responses. PEI-SWNT-induced transcriptional profile is very similar to that of mutant plants displaying a constitutive immune response or treated with stress-priming agrochemicals. We selected molecular markers from our transcriptomic analysis and identified PEI as the main cause of this adverse reaction. We show that PEI-SWNT response is concentration-dependent and, when persistent over time, leads to cell death. We probed a panel of PEI variant-functionalized SWNTs across two plant species and identified biocompatible SWNT surface functionalizations. Conclusions While SWNTs themselves are well tolerated by plants, SWNTs surface-functionalized with positively charged polymers become toxic and produce cell death. We use molecular markers to identify more biocompatible SWNT formulations. Our results highlight the importance of nanoparticle surface chemistry on their biocompatibility and will facilitate the use of functionalized nanomaterials for agricultural improvement. Graphical Abstract

59 BASIC BIOLOGICAL SCIENCES↗

Bio-Based Polymers with Performance-Advantaged Properties

Bio-based compounds with unique chemical functionality can be obtained through selective transformations of plant and other non-fossil, biogenic feedstocks for the development of new polymers to displace those produced from fossil carbon feedstocks. Although substantial efforts have been invested to produce bio-based polymers that are chemically identical to and directly replace those from petroleum, a long-pursued goal is to synthesize new, sustainable, bio-based polymers that either functionally replace or exhibit performance advantages relative to incumbent polymers. Owing to anthropogenic climate change and the environmental consequences of global plastics pollution, the need to realize a bio-based materials economy at scale is critical. To that end, in this Review we describe the concept of performance-advantaged, bio-based polymers (PBPs), highlighting examples wherein superior performance is facilitated by the inherent chemical functionality of bio-based feedstocks. We focus on PBPs with C–O and C–N inter-unit chemical bonds, as these are often readily accessible from bio-based feedstocks, which are heteroatom-rich relative to petroleum-derived feedstocks. Finally, we outline guiding principles and challenges to aid progress in the development of PBPs.

bio-based feedstock↗

Integrating Emerging Polymer Chemistries for the Advancement of Recyclable, Biodegradable, and Biocompatible Electronics

Abstract Through advances in molecular design, understanding of processing parameters, and development of non‐traditional device fabrication techniques, the field of wearable and implantable skin‐inspired devices is rapidly growing interest in the consumer market. Like previous technological advances, economic growth and efficiency is anticipated, as these devices will enable an augmented level of interaction between humans and the environment. However, the parallel growing electronic waste that is yet to be addressed has already left an adverse impact on the environment and human health. Looking forward, it is imperative to develop both human‐ and environmentally‐friendly electronics, which are contingent on emerging recyclable, biodegradable, and biocompatible polymer technologies. This review provides definitions for recyclable, biodegradable, and biocompatible polymers based on reported literature, an overview of the analytical techniques used to characterize mechanical and chemical property changes, and standard policies for real‐life applications. Then, various strategies in designing the next‐generation of polymers to be recyclable, biodegradable, or biocompatible with enhanced functionalities relative to traditional or commercial polymers are discussed. Finally, electronics that exhibit an element of recyclability, biodegradability, or biocompatibility with new molecular design are highlighted with the anticipation of integrating emerging polymer chemistries into future electronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonlinear Shear Rheology of Entangled Polymer Rings

Steady-state shear viscosity η($\bar{γ}$) of unconcatenated ring polymer melts as a function of the shear rate $\bar{γ}$ 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 η ~ $\bar{γ}$ –0.56 ± 0.02 , independent of chain length, for Weissenberg numbers up to about 10 2 . Nonequilibrium molecular dynamics simulations using the bead-spring model reveal a similar behavior with η ~ $\bar{γ}$ -0.57 ± 0.08 for 4 ≤ Z ≤ 57. Viscosity decreases with chain length for high $\bar{γ}$. In our experiments, we see the onset of this regime, and in simulations, which we extended to Wi ~ 10 4 , the nonuniversality is fully developed. In addition to a naive scaling theory yielding for the universal regime η ~ $\bar{γ}$ –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 $\bar{γ}$. 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/$\bar{γ}$. 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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗