Self-Diffusion in Binary Blends of Cyclic and Linear Polymers

High-Performance Flexible Sulfur Cathodes with Robust Electrode Skeletons Built by a Hierarchical Self-Assembling Slurry

The electrochemical performance of lithium-sulfur batteries is fundamentally determined by the structural and mechanical stability of their composite sulfur cathodes. However, the development of cost-effective strategies for realizing robust hierarchical composite electrode structures remains highly challenging due to uncontrollable interactions among the components. The present work addresses this issue by proposing a type of self-assembling electrode slurry based on a well-designed two-component (polyacrylonitrile and polyvinylpyrrolidone) polar binder system with carbon nanotubes that forms hierarchical porous structures via optimized water-vapor-induced phase separation. The electrode skeleton is a highly robust and flexible electron-conductive network, and the porous structure provides hierarchical ion-transport channels with strong polysulfide trapping capability. Composite sulfur cathodes prepared with a sulfur loading of 4.53 mg cm-2 realize a very stable specific capacity of 485 mAh g-1 at a current density of 3.74 mA cm-2 after 1000 cycles. Meanwhile, a composite sulfur cathode with a high sulfur loading of 14.5 mg cm-2 in a lithium-sulfur pouch cell provides good flexibility and delivers a high capacity of 600 mAh g-1 at a current density of 0.72 mA cm-2 for 78 cycles.

Regulating Polysulfide Diffusion and Deposition via Rational Design of Core-Shell Active Materials in Li-S Batteries

Polar host materials with strong adsorption capacity of polysulfides are designed to limit the shuttle effect in sulfur cathodes. However, a critical problem is to control diffusion and deposition of lithium polysulfides during cycling, which significantly impacts cycling stability and sulfur utilization. Here, we report using a sequential adsorption-guided self-assembly to design two types of core-shell sulfur particles with opposite polysulfide adsorption gradients to explore quantitatively the regulation of polysulfide diffusion and deposition. We show that a positive core-shell design of sulfur particles (PCSD@SP), i.e., polysulfide adsorption capability decreasing from the interior to the exterior of the host, is more effective in restricting polysulfide diffusion and regulating polysulfide deposition than the negative core-shell counterpart (NCSD@SP). As a result, the PCSD@SP electrode with a sulfur loading of 7 mg cm^-2 exhibits a stable areal capacity of 6 mAh cm^-2 over 130 cycles at 0.2C. At intermittent discharge/charge, the PCSD@SP electrode retains excellent stability compared with the NCSD@SP. We conclude that rational design of positive core-shell active materials can be used to regulate polysulfide diffusion and deposition to boost electrochemical reaction dynamics and performance. The reported findings will be of immediate benefit to a range of researchers in the design of high-performance lithium-sulfur batteries.

Accelerating the crystallization kinetics of linear polylactides by adding cyclic poly (L-lactide): Nucleation, plasticization and topological effects

Polylactide is one of the most versatile biopolymers, but its slow crystallization limits its temperature usage range. Hence finding ways to enhance it is crucial to widen its applications. Linear and cyclic poly (L-lactide) (l-PLLA and c-PLLA) of similarly low molecular weights (MW) were synthesized by ring-opening polymerization of L-lactide, and ring-expansion methodology, respectively. Two types of blends were prepared by solution mixing: (a) l-PLLA/c-PLLA, at extreme compositions (rich in linear or in cyclic chains), and (b) blends of each of these low MW materials with a commercial high MW linear PLA. The crystallization of the different blends was evaluated by polarized light optical microscopy and differential scanning calorimetry. It was found, for the first time, that in the l-PLLA rich blends, small amounts of c-PLLA (i.e., 5 and 10 wt%) increase the nucleation density, nucleation rate (1/τ₀), spherulitic growth rate (G), and overall crystallization rate (1/τ_50%), when compared to neat l-PLLA, due to a synergistic effect (i.e., nucleation plus plasticization). In contrast, the opposite effect was found in the c-PLLA rich blends. The addition of small amounts of l-PLLA to a matrix of c-PLLA chains causes a decrease in the nucleation density, 1/τ₀, G, and 1/τ_50% values, due to threading effects between cyclic and linear chains. Small amounts of l-PLLA and c-PLLA enhance the crystallization ability of a commercial high MW linear PLA without affecting its melting temperature. The l-PLLA only acts as a plasticizer for the PLA matrix, whereas c-PLLA has a synergistic effect in accelerating the crystallization of PLA that goes beyond simple plasticization. The addition of small amounts of c-PLLA affects not only PLA crystal growth but also its nucleation due to the unique cyclic chains topology.

Threading-Unthreading Transition of Linear-Ring Polymer Blends in Extensional Flow

Adding small amounts of ring polymers to a matrix of their linear counterparts is known to increase the zero-shear-rate viscosity because of linear-ring threading. Uniaxial extensional rheology measurements show that, unlike its pure linear and ring constituents, the blend exhibits an overshoot in the stress growth coefficient. By combining these measurements with ex-situ small-angle neutron scattering and nonequilibrium molecular dynamics simulations, this overshoot is shown to be driven by a transient threading-unthreading transition of rings embedded within the linear entanglement network. Prior to unthreading, embedded rings deform affinely with the linear entanglement network and produce a measurably stronger elongation of the linear chains in the blend compared to the pure linear melt. Thus, rings uniquely alter the mechanisms of transient elongation in linear polymers.

Local Effects of Ring Topology Observed in Polymer Conformation and Dynamics by Neutron Scattering-A Review

The physical properties of polymers depend on a range of both structural and chemical parameters, and in particular, on molecular topology. Apparently simple changes such as joining chains at a point to form stars or simply joining the two ends to form a ring can profoundly alter molecular conformation and dynamics, and hence properties. Cyclic polymers, as they do not have free ends, represent the simplest model system where reptation is completely suppressed. As a consequence, there exists a considerable literature and several reviews focused on high molecular weight cyclics where long range dynamics described by the reptation model comes into play. However, this is only one area of interest. Consideration of the conformation and dynamics of rings and chains, and of their mixtures, over molecular weights ranging from tens of repeat units up to and beyond the onset of entanglements and in both solution and melts has provided a rich literature for theory and simulation. Experimental work, particularly neutron scattering, has been limited by the difficulty of synthesizing well-characterized ring samples, and deuterated analogues. Here in the context of the broader literature we review investigations of local conformation and dynamics of linear and cyclic polymers, concentrating on poly(dimethyl siloxane) (PDMS) and covering a wide range of generally less high molar masses. Experimental data from small angle neutron scattering (SANS) and quasi-elastic neutron scattering (QENS), including Neutron Spin Echo (NSE), are compared to theory and computational predictions.

Stress relaxation in symmetric ring-linear polymer blends at low ring fractions

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 η ( ϕ R * ) / η L of the blend with respect to the linear melt viscosity η _L at ring overlap volume fraction ϕ R * increases proportionally to the square root of ring molecular weight M w , R . 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.

Shear Rheology of Unentangled and Marginally Entangled Ring Polymer Melts from Large-Scale Nonequilibrium Molecular Dynamics Simulations

We present results for the steady state shear rheology of non-concatenated, unentangled and marginally entangled ring poly(ethylene oxide) (PEO) melts from detailed, atomistic nonequilibrium molecular dynamics (NEMD) simulations, and compare them to the behavior of the corresponding linear melts. The applied flow field spans a wide range of shear rates, from the linear (Newtonian) to the highly non-linear (described by a power law) regime. For all melts studied, rings are found to exhibit shear thinning but to a lesser degree compared to linear counterparts, mostly due to their reduced deformability and stronger resistance to alignment in the direction of flow. These features are attributed to the more compact structure of ring molecules compared to linear chains; the latter are capable of adopting wider and more open conformations even under shear due to the freedom provided by the free ends. Similar to linear melts, rings also exhibit a first and a second normal stress coefficient; the latter is negative. The ratio of the magnitude of the two coefficients remains practically constant with shear rate and is systematically higher than the corresponding one for linear melts. Emphasis was also given to the statistics of terminal (re-orientational) relaxation times which we computed by analyzing all chains in the simulated systems one by one; it was demonstrated that long time dynamics are strongly heterogeneous both for rings and (especially) linears. Repeating the analysis under flow conditions, and as expected, we found that the applied flow field significantly suppresses dynamic heterogeneity, especially for high shear rates well beyond the Newtonian plateau. Finally, a detailed geometrical analysis revealed that the average population of ring-ring threading events in the longest melt studied here (the PEO-5k ring) remains practically unaffected by the imposed flow rate even at strong shear rates, except for multi-threadings which disappear. To further analyze this peculiar and rather unexpected effect, we computed the corresponding survival times and penetration lengths, and found that the overwhelming majority of threadings under shear are extremely weak constraints, as they are characterized by very small penetration lengths, thus also by short survival times. They are expected therefore to play only a minor (if any) role on chain dynamics.

Surface Segregation of Cyclic Chains in Binary Melts of Thin Polymer Films: The Influence of Constituent Concentration

We carry out extensive molecular dynamics simulations of thin films of bead-spring models of binary mixtures composed of cyclic and linear polymer chains. We study the equilibrium behavior of the polymer chains for two very different chain lengths, which resemble short (10-mers) and long (100-mers) chains, at different concentrations of the binary mixture. We clearly show how the concentration variable affects the enrichment of either of the two polymer species at the interface, and also how the chain length influences this process.

What Happens When Threading is Suppressed in Blends of Ring and Linear Polymers?

Self-diffusivity of a large tracer ring polymer, D r , immersed in a matrix of linear polymers with N l monomers each shows unusual length dependence. D r initially increases, and then decreases with increasing N l . To understand the relationship between the nonmonotonic variation in D r and threading by matrix chains, we perform equilibrium Monte Carlo simulations of ring-linear blends in which the uncrossability of ring and linear polymer contours is switched on (non-crossing), or artificially turned off (crossing). The D r ≈ 6 . 2 × 10 - 7 N l 2 / 3 obtained from the crossing simulations, provides an upper bound for the D r obtained for the regular, non-crossing simulations. The center-of-mass mean-squared displacement ( g 3 ( t ) ) curves for the crossing simulations are consistent with the Rouse model; we find g 3 ( t ) = 6 D r t . Analysis of the polymer structure indicates that the smaller matrix chains are able to infiltrate the space occupied by the ring probe more effectively, which is dynamically manifested as a larger frictional drag per ring monomer.

DNA as a Model for Probing Polymer Entanglements: Circular Polymers and Non-Classical Dynamics

Double-stranded DNA offers a robust platform for investigating fundamental questions regarding the dynamics of entangled polymer solutions. The exceptional monodispersity and multiple naturally occurring topologies of DNA, as well as a wide range of tunable lengths and concentrations that encompass the entanglement regime, enable direct testing of molecular-level entanglement theories and corresponding scaling laws. DNA is also amenable to a wide range of techniques from passive to nonlinear measurements and from single-molecule to bulk macroscopic experiments. Over the past two decades, researchers have developed methods to directly visualize and manipulate single entangled DNA molecules in steady-state and stressed conditions using fluorescence microscopy, particle tracking and optical tweezers. Developments in microfluidics, microrheology and bulk rheology have also enabled characterization of the viscoelastic response of entangled DNA from molecular levels to macroscopic scales and over timescales that span from linear to nonlinear regimes. Experiments using DNA have uniquely elucidated the debated entanglement properties of circular polymers and blends of linear and circular polymers. Experiments have also revealed important lengthscale and timescale dependent entanglement dynamics not predicted by classical tube models, both validating and refuting new proposed extensions and alternatives to tube theory and motivating further theoretical work to describe the rich dynamics exhibited in entangled polymer systems.

Surface enrichment driven by polymer topology

We report a molecular dynamics simulation study of free-standing films of a blend of linear and cyclic polymer chains. We find that the composition of linear chains at the interface is enhanced relative to their bulk value for short chains but is depleted for long chains. Our findings are in agreement with recent experimental evidence reported for blends of short linear and cyclic polystyrene chains and highlight the genuine surface behavior in the short chain-length regime where theoretical predictions are more difficult. We highlight surface enrichment at low-energy surfaces as the result of competition between different entropic and enthalpic contributions to the interfacial free energy of the system.

The influence of small amounts of linear polycaprolactone chains on the crystallization of cyclic analogue molecules

C-PCL/L-PCL blends show a synergistic decrease in their isothermal crystallization rates as compared to the expectation of a simple mixing law due to the threading effect of the linear on the cyclic chains.

Universal scaling of crowding-induced DNA mobility is coupled with topology-dependent molecular compaction and elongation

Using single-molecule fluorescence microscopy and particle-tracking techniques, we elucidate the role DNA topology plays in the diffusion and conformational dynamics of crowded DNA molecules. We focus on large (115 kbp), double-stranded ring and linear DNA crowded by varying concentrations (0-40%) of dextran (10, 500 kDa) that mimic cellular conditions. By tracking the center-of-mass and measuring the lengths of the major and minor axes of single DNA molecules, we characterize both DNA mobility reduction as well as crowding-induced conformational changes (from random spherical coils). We reveal novel topology-dependent conformations, with single ring molecules undergoing compaction to ordered spherical configurations ∼20% smaller than dilute random coils, while linear DNA elongates by ∼2-fold. Surprisingly, these highly different conformations result in nearly identical exponential mobility reduction dependent solely on crowder volume fraction Φ, revealing a universal critical crowding concentration of Φc≅ 2.3. Beyond Φc DNA exhibits topology-independent conformational relaxation dynamics despite highly distinct topology-driven conformations. Our collective results reveal that topology-dependent conformational changes, unique to crowded environments, enable DNA to overcome the classically expected mobility reduction that high-viscosity crowded environments impose. Such coupled universal dynamics suggest a mechanism for DNA to maintain sufficient mobility required for wide-ranging biological processes despite severe cellular crowding.

Threading of Ring Poly(ethylene oxide) Molecules by Linear Chains in the Melt

We report results from an atomistic molecular dynamics simulation study of ring-linear poly(ethylene oxide) (PEO) melts followed by a topological reduction to ensembles of primitive paths and a detailed geometric analysis using vector calculus, which reveals considerable cyclic threading by the linear chains. The simulations have been conducted using ring-linear PEO blends of the same size, over a series of molecular lengths and compositions. For PEO melts characterized by molecular weight (MW) greater than 10044 g/mol, in particular, our computations reveal the occurrence of multiple threading events (penetrations). We further find that the time it takes a linear molecule that threads a cyclic one to fully pass through the latter can be more than 1 order of magnitude larger than the corresponding relaxation time of the ring in its own melt. Our analysis implies that dynamics in ring-linear polymer blends is highly heterogeneous, with many of the threadings being long-lived and with the linear chains (even when present in small amounts) dramatically obstructing the mobility of rings.

Extraction of self-diffusivity in systems with nondiffusive short-time behavior

We consider a toy model that captures the short-time nondiffusive behavior seen in many physical systems, to study the extraction of self-diffusivity from particle trajectories. We propose and evaluate a simple method to automatically detect the transition to diffusive behavior. We simulate the toy model to generate data sets of varying quality and test different methods of extracting the self-diffusion coefficient and characterizing its uncertainty. We find that weighted least-squares with statistical bootstrap is the most accurate and efficient means for analyzing the trajectory data. The analysis suggests an iterative recipe for designing simulations to conform to a specified level of accuracy.

Synthesis of a molecular charm bracelet via click cyclization and olefin metathesis clipping

We describe the synthesis of a polycatenated cyclic polymer, a structure that resembles a molecular charm bracelet. Ruthenium-catalyzed ring-opening metathesis polymerization of an amino-containing cyclic olefin monomer in the presence of a chain transfer agent generated an alpha,omega-diazide functionalized polyamine. Cyclization of the resulting linear polyamine using pseudo-high-dilution copper-catalyzed click cyclization produced a cyclic polymer in 19% yield. The click reaction was then further employed to remove linear contaminants from the cyclic polymer using azide- and alkyne-functionalized scavenging resins, and the purified cyclic polymer product was characterized by gel permeation chromatography, (1)H NMR spectroscopy, and IR spectroscopy. Polymer hydrogenation and conversion to the corresponding polyammonium species enabled coordination and interlocking of diolefin polyether fragments around the cyclic polymer backbone using ruthenium-catalyzed ring-closing olefin metathesis to afford a molecular charm bracelet structure. This charm bracelet complex was characterized by (1)H NMR spectroscopy, and the catenated nature of the small rings was confirmed using two-dimensional diffusion-ordered NMR spectroscopy.

Conformational free energy of melts of ring-linear polymer blends

The conformational free energy of ring polymers in a blend of ring and linear polymers is investigated using the bond-fluctuation model. Previously established scaling relationships for the free energy of a ring polymer are shown to be valid only in the mean-field sense, and alternative functional forms are investigated. It is shown that it may be difficult to accurately express the total free energy of a ring polymer by a simple scaling argument, or in closed form.