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

Nonmonotonic Composition Dependence of Viscosity upon Adding Single-Chain Nanoparticles to Entangled Polymers

Well-characterized single-chain nanoparticles (SCNPs), synthesized from a linear polystyrene precursor through an intramolecular [4 + 4] thermal cycloaddition cross-linking reaction in dilute conditions, were added to entangled polystyrene melts at different concentrations. Starting from the pure linear melt, which is much more viscous than the melt of SCNPs, the zero-shear viscosity increased upon the addition of nanoparticles and reached a maximum before eventually dropping to the value of the SCNP melt. Molecular simulations reveal the origin of this unexpected behavior, which is the interplay of the very different compositional dependences of the dynamics of the two components. The SCNPs become much slower than the linear chains as their concentration decreases because they are threaded by the linear chains, reaching a maximum viscosity which is higher than that of the linear chains at a fraction of about 20%. This behavior is akin to that of single-loop ring polymers when added to linear matrices. This finding provides insights into the design and use of SCNPs as effective entropic viscosity modifiers of polymers and contributes to the discussion of the physics of loopy structures.

Dynamic-Bond-Mediated Chain Reptation Enhances Energy Dissipation of Elastomers

Vibrations with various frequencies in daily life and industry can cause health hazards and fatigue failure of critical structures, which requires the development of elastomers with high energy dissipation at desired frequencies. Current strategies relying on tuning characteristic relaxation time of polymer chains are mostly qualitative empirical methods, and it is difficult to precisely control damping performances. Here, we report a general strategy for constructing dynamic crosslinked polymer fluid gels that provide controllable ultrahigh energy dissipation. This is realized by dynamic-bond-mediated chain reptation of polymer fluids in a crosslinked network, where the characteristic time of chain reptation is dominated by the presence of well-defined dissociation time of dynamic bonds and almost independent of their molar mass. Using prototypical supramolecular polydimethylsiloxane elastomers, we demonstrate that dynamic crosslinked polymer fluid gels exhibit a controllable ultrahigh damping performance at desired frequencies (10-2~102 Hz), exceeding that of typical state-of-the-art silicone damping materials. Their shock absorption is over 300 % higher than that of commercial silicone rubber under the same impact force.

Mixing Linear Polymers with Rings and Catenanes: Bulk and Interfacial Behavior

We derive and parameterize effective interaction potentials between a multitude of different types of ring polymers and linear chains, varying the bending rigidity and solvent quality for the former species. We further develop and apply a density functional treatment for mixtures of both disconnected (chain-ring) and connected (chain-polycatenane) mixtures of the same, drawing coexistence binodals and exploring the ensuing response functions as well as the interface and wetting behavior of the mixtures. We show that worsening of the solvent quality for the rings brings about a stronger propensity for macroscopic phase separation in the linear-polycatenane mixtures, which is predominantly of the demixing type between phases of similar overall particle density. We formulate a simple criterion based on the effective interactions, allowing us to determine whether any specific linear-ring mixture will undergo a demixing phase separation.

Rotaxane Formation of Multicyclic Polydimethylsiloxane in a Silicone Network: A Step toward Constructing "Macro-Rotaxanes" from High-Molecular-Weight Axle and Wheel Components

Rotaxanes consisting of a high-molecular-weight axle and wheel components (macro-rotaxanes) have high structural freedom, and are attractive for soft-material applications. However, their synthesis remains underexplored. Here, we investigated macro-rotaxane formation by the topological trapping of multicyclic polydimethylsiloxanes (mc-PDMSs) in silicone networks. mc-PDMS with different numbers of cyclic units and ring sizes was synthesized by cyclopolymerization of a α,ω-norbornenyl-functionalized PDMS. Silicone networks were prepared in the presence of 10-60 wt % mc-PDMS, and the trapping efficiency of mc-PDMS was determined. In contrast to monocyclic PDMS, mc-PDMSs with more cyclic units and larger ring sizes can be quantitatively trapped in the network as macro-rotaxanes. The damping performance of a 60 wt % mc-PDMS-blended silicone network was evaluated, revealing a higher tan δ value than the bare PDMS network. Thus, macro-rotaxanes are promising as non-leaching additives for network polymers.

Miscibility and exchange chemical potential of ring polymers in symmetric ring-ring blends

Generally, differences of polymer topologies may affect polymer miscibility even with the same repeated units. In this study, the topological effect of ring polymers on miscibility was investigated by comparing symmetric ring-ring and linear-linear polymer blends. To elucidate the topological effect of ring polymers on mixing free energy, the exchange chemical potential of binary blends was numerically evaluated as a function of composition ϕ by performing semi-grand canonical Monte Carlo and molecular dynamics simulations of a bead-spring model. For ring-ring blends, an effective miscibility parameter was evaluated by comparing the exchange chemical potential with that of the Flory-Huggins model for linear-linear polymer blends. It was confirmed that in the mixed states satisfying χN > 0, ring-ring blends are more miscible and stable than the linear-linear blends with the same molecular weight. Furthermore, we investigated finite molecular weight dependence on the miscibility parameter, which reflected the statistical probability of interchain interactions in the blends. The simulation results revealed that the molecular weight dependence on the miscibility parameter was smaller in ring-ring blends. The effect of the ring polymers on miscibility was verified to be consistent with the change in the interchain radial distribution function. In ring-ring blends, it was indicated that the topology affected miscibility by reducing the effect of the direct interaction between the components of the blends.

To thread or not to thread? Effective potentials and threading interactions between asymmetric ring polymers

We use computer simulations to study a system of two unlinked ring polymers, whose length and bending stiffness are systematically varied. We derive the effective potentials between the rings, calculate the areas of minimal surfaces of the same, and characterize the threading between them. When the two rings are of the same kind, threading of a one ring through the surface of the other is immanent for small ring-ring separations. Flexible rings pierce the surface of the other ring several times but only shallowly, as compared to the stiff rings which pierce less frequently but deeply. Typically, the ring that is being threaded swells and flattens up into an oblate-like conformation, while the ring that is threading the other takes a shape of an elongated prolate. The roles of the threader and the threaded ring are being dynamically exchanged. If, on the other hand, the rings are of different kinds, the symmetry is broken and the rings tend to take up roles of the threader and the threaded ring with unequal probabilities. We propose a method how to predict these probabilities based on the parameters of the individual rings. Ultimately, our work captures the interactions between ring polymers in a coarse-grained fashion, opening the way to large-scale modelling of materials such as kinetoplasts, catenanes or topological brushes.

Topological digestion drives time-varying rheology of entangled DNA fluids

Understanding and controlling the rheology of polymeric complex fluids that are pushed out-of-equilibrium is a fundamental problem in both industry and biology. For example, to package, repair, and replicate DNA, cells use enzymes to constantly manipulate DNA topology, length, and structure. Inspired by this feat, here we engineer and study DNA-based complex fluids that undergo enzymatically-driven topological and architectural alterations via restriction endonuclease (RE) reactions. We show that these systems display time-dependent rheological properties that depend on the concentrations and properties of the comprising DNA and REs. Through time-resolved microrheology experiments and Brownian Dynamics simulations, we show that conversion of supercoiled to linear DNA topology leads to a monotonic increase in viscosity. On the other hand, the viscosity of entangled linear DNA undergoing fragmentation displays a universal decrease that we rationalise using living polymer theory. Finally, to showcase the tunability of these behaviours, we design a DNA fluid that exhibits a time-dependent increase, followed by a temporally-gated decrease, of its viscosity. Our results present a class of polymeric fluids that leverage naturally occurring enzymes to drive diverse time-varying rheology by performing architectural alterations to the constituents.

Understanding and controlling the rheology of polymeric complex fluids is of fundamental importance in both industry and biology. Here, Michieletto et al. show how to achieve time-dependent rheology of DNA solutions via enzymatically-driven architectural alterations by restriction endonucleases.

DNA Conformation Dictates Strength and Flocculation in DNA-Microtubule Composites

Polymer topology has been shown to play a key role in tuning the dynamics of complex fluids and gels. At the same time, polymer composites, ubiquitous in everyday life, have been shown to exhibit emergent desirable mechanical properties not attainable in single-species systems. Yet, how topology impacts the dynamics and structure of polymer composites remains poorly understood. Here, we create composites of rigid rods (microtubules) polymerized within entangled solutions of flexible linear and ring polymers (DNA) of equal length. We couple optical tweezers microrheology with confocal microscopy and scaled particle theory to show that composites with linear DNA exhibit a strongly nonmonotonic dependence of elasticity and stiffness on microtubule concentration due to depletion-driven polymerization and flocculation of microtubules. In contrast, composites containing ring DNA show a much more modest monotonic increase in elastic strength with microtubule concentration, which we demonstrate arises from the decreased conformational size and increased miscibility of rings.

Nonlinear rheometry of entangled polymeric rings and ring-linear blends

We present a comprehensive experimental rheological dataset for purified entangled ring polystyrenes and their blends with linear chains in nonlinear shear and elongation. In particular, data for shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of shear rate as well as molecular parameters (molar mass, blend composition and decreasing molar mass of linear component in blend). Over the extended parameter range investigated, rings do not exhibit clear transient undershoot in shear, in contrast to their linear counterparts and ring-linear blends. For the latter, the size of the undershoot and respective strain appear to increase with shear rate. Universal scaling of strain at overshoot and fractional overshoot (ratio of maximum to steady-state shear stress growth coefficient) indicates subtle differences in the shear-rate dependence between rings and linear polymers or their blends. The shear thinning behaviour of pure rings yields a slope nearly identical to predictions (-4/7) of a recent shear slit model and molecular dynamics simulations. Data for the second normal stress difference are reported for rings and ring-linear blends. While N ₂ is negative and its absolute value stays below that of N ₁ , as for linear polymers, the ratio -N ₂ /N ₁ is unambiguously larger for rings compared to linear polymer solutions with the same number of entanglements (almost by factor of two), in agreement with recent non-equilibrium molecular dynamics simulations. Further, -N ₂ exhibits slightly weaker shear rate dependence compared to N ₁ at high rates, and the respective power-law exponents can be rationalized in view of the slit model (3/7) and simulations (0.6), although further work is needed to unravel the molecular original of the observed behaviour. The comparison of shear and elongational stress growth coefficients for blends reflects the effect of ring-linear threading which leads to significant viscosity enhancement in elongation. Along the same lines, the elongational stress is much larger than the first normal stress in shear, and their ratio is much larger for rings and ring-linear blends compared to linear polymers. This conforms the interlocking scenario of rings and their important role in mechanically reinforcing linear matrices.

Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids

Ring polymers in dense solutions are among the most intriguing problems in polymer physics. Because of its natural occurrence in circular form, DNA has been extensively used as a proxy to study the fundamental physics of ring polymers in different topological states. Yet, torsionally constrained-such as supercoiled-topologies have been largely neglected so far. The applicability of existing theoretical models to dense supercoiled DNA is thus unknown. Here, we address this gap by coupling large-scale molecular dynamics simulations with differential dynamic microscopy of entangled supercoiled DNA plasmids. We find that, unexpectedly, larger supercoiling increases the size of entangled plasmids and concomitantly induces an enhancement in DNA mobility. These findings are reconciled as due to supercoiling-driven asymmetric and double-folded plasmid conformations that reduce interplasmid entanglements and threadings. Our results suggest a way to topologically tune DNA mobility via supercoiling, thus enabling topological control over the (micro)rheology of DNA-based complex fluids.

Dynamical Entanglement and Cooperative Dynamics in Entangled Solutions of Ring and Linear Polymers

Understanding how entanglements affect the behavior of polymeric complex fluids is an open challenge in many fields. To elucidate the nature and consequence of entanglements in dense polymer solutions, we propose a novel method: a "dynamical entanglement analysis" (DEA) to extract spatiotemporal entanglement structures from the pairwise displacement correlation of entangled chains. By applying this method to large-scale molecular dynamics simulations of linear and unknotted, nonconcatenated ring polymers, we find a strong and unexpected cooperative dynamics: the footprint of mutual entrainment between entangled chains. We show that DEA is a powerful and sensitive probe that reveals previously unnoticed and architecture-dependent spatiotemporal structures of dynamical entanglement in polymeric solutions. We also propose a mean-field approximation of our analysis that provides previously under-appreciated physical insights into the dynamics of generic entangled polymers. We envisage DEA will be useful to analyze the dynamical evolution of entanglements in generic polymeric systems such as blends and composites.

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.

Melt rheology of tadpole-shaped polystyrenes with different ring sizes

In this study, linear melt rheology of a single-tail tadpole-shaped polystyrene, ST-30/80, having ring and linear sizes of MR ∼ 30 kg mol-1 and ML ∼ 80 kg mol-1, respectively, was examined, and the effect of the ring size on rheological properties of tadpole polymers was discussed by comparing with the data of the previously reported tadpole samples having MR ∼ 60 kg mol-1. ST-30/80 exhibits an entanglement plateau and shows a clearly slower terminal relaxation than that of its component ring and linear polymers. When the zero-shear viscosity η0 for ST-30/80 is plotted against the molecular weight of a linear tail chain, the data point lies on the single curve of η0 for 4- and 6-arm star polymers and the single-tail tadpoles with MR ∼ 60 kg mol-1. These results suggest that the tadpole molecule in this study spontaneously forms a characteristic entanglement network, i.e., the intermolecular ring-linear threading, in the same manner as the previous tadpole samples, even though the size of the ring part is just slightly larger than the entanglement molecular weight (i.e., MR ∼ 1.8Me).

Threading-Induced Dynamical Transition in Tadpole-Shaped Polymers

The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring-linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in "chimeric" architectures. The simplest example of this family is a "tadpole"-shaped polymer, a single ring fused to the end of a single linear chain. We show that polymers with this architecture display a threading-induced dynamical transition that substantially slows chain relaxation. Our findings shed light on how threadings control dynamics and may inform design principles for chimeric polymers with topologically tunable bulk rheological properties.