The entanglement chain length and polymer composition
Dependence of entanglement chain length on polymer composition of linear, amorphous polymers - Rheology
RHEOLOGY↗
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Chain entanglements enable regeneration of high-performance thermosets
Thermoset plastics underpin structural materials, electronics and transportation, yet the permanent covalent networks that prevent flow and provide dimensional stability also make them difficult to recycle without sacrificing performance. In this work we show that high-performance thermosets can be built around dense chain entanglements, the physical interlacing of long polymer strands, rather than dense permanent crosslinks, with only a small number of selectively cleavable junctions preserving connectivity. Long, rigid, entangled polyolefin backbones generated by frontal polymerization form glassy polymers with high stiffness, high toughness and excellent creep suppression yet can be fully deconstructed into soluble, linear oligomers. Varying oligomer length and end-group chemistry enables their reuse as re-entangling building blocks that regenerate thermosets with thermal and mechanical properties that remain unchanged across generations. The strategy further extends to high-temperature fibre-reinforced composite matrices and additively manufactured structures, establishing chain entanglement as a design principle for durable, regenerable thermosets.
36 MATERIALS SCIENCE↗
Improving Miscibility of Polymer Donor and Polymer Acceptor by Reducing Chain Entanglement for Realizing 18.64 % Efficiency All Polymer Solar Cells
All-polymer solar cells have experienced rapid development in recent years by the emergence of polymerized small molecular acceptors (PSMAs). However, the strong chain entanglements of polymer donors (P D s) and polymer acceptors (P A s) decrease the miscibility of the resulting polymer mixtures, making it challenging to optimize the blend morphology. Herein, we designed three P A s, namely PBTPICm-BDD, PBTPICγ-BDD and PBTPICF-BDD, by smartly using a BDD unit as the polymerized unit to copolymerize with different Y-typed non-fullerene small molecular acceptors (NF-SMAs), thus achieving a certain degree of distortion and giving the polymer system enough internal space to reduce the entanglements of the polymer chains. Such effects increase the chances of the P D being interspersed into the acceptor material, which improve the solubility between the P D and P A . The PBTPICγ-BDD and PBTPICF-BDD displayed better miscibility with PBQx-TCl, leading to a well optimized morphology. As a result, high power conversion efficiencies (PCEs) of 17.50 % and 17.17 % were achieved for PBQx-TCl : PBTPICγ-BDD and PBQx-TCl : PBTPICF-BDD devices, respectively. In conclusion, with the addition of PYFT-o as the third component into PBQx-TCl : PBTPICγ-BDD blend to further extend the absorption spectral coverage and finely tune microstructures of the blend morphology, a remarkable PCE of 18.64 % was realized finally.
36 MATERIALS SCIENCE↗
Thin-Film Fracture Behavior for Diketopyrrolopyrrole Semiconducting Polymeric Films
Fracture energy, which quantifies a material’s resistance to the propagation of a pre-existing crack, is a key parameter for ensuring the mechanical reliability of stretchable organic electronic devices. However, most existing methods, such as a four-point bending fracture energy, utilized for measuring the fracture energy of semiconducting polymeric thin films are complicated by substrate effects, making it challenging to isolate the intrinsic behavior of the film from interfacial influences. In this study, we employed a pseudo free-standing pure shear method to systematically investigate the cohesive fracture energy of poly(diketopyrrolopyrrole-terthiophene) P(DPP-T)-based thin films to examine the effects of nanoconfinement, side chain length, degree of crystallinity, and strain rates. This method effectively eliminates substrate interference, enabling a direct assessment of the cohesive fracture energy of P(DPP-T) thin films. We found that thinner films and those with lower molecular weights exhibited significantly reduced fracture energies due to diminished chain entanglements. Additionally, films with shorter side chains displayed notably higher fracture energies, which were attributed to an increase in the degree of crystallinity. Finally, slower strain rates led to higher fracture energies, consistent with an enhanced stress relaxation. These insights offer practical guidelines for designing mechanically robust semiconducting polymers, contributing to the advancement of reliable, durable, flexible, and wearable electronic devices.
Zhang, Song [Univ. of Southern Mississippi, Hattie↗
Viscoelastic properties of entangled polymers - Ternary blends of monodisperse homopolymers
In a previous publication from this laboratory, the Rouse-Bueche-Zimm molecular theory of viscoelasticity has been extended by using a transient network model to apply to binary blends of monodisperse polymers with chain entanglements. The dynamics of the entanglements were modeled both by the enhanced frictional coefficients and by the additional elastic couplings. It was recognized that entanglements not only may form between chains of the same lengths (intracomponent entanglements) but also between those of different lengths (intercomponent entanglements). At a given intercomponent entanglement, the longer chain was assumed to have the frictional coefficient of the shorter chain. Similarly, for blends consisting of several monodisperse components with different molecular weights, such modifications are also required to predict their linear viscoelastic behavior. The frequency of these interactions is assumed to be proportional to the weight ratio of the respective component chains in the blend. Equations of motion are formulated for each component and solved numerically for the relaxation time spectra. Linear viscoelastic properties such as the dynamic mechanical moduli, stress relaxation moduli, and zero-shear viscosity can then be computed for these systems by linear summation of those of the components.
Soong, D.↗
SAN-Based Block Polymers as a Platform for Manufacturing Strong Isoporous Membranes
Ultrafiltration (UF) membranes are ubiquitous in water purification and bioprocessing. However, co-designing their mechanical and transport properties remains challenging because of the broad pore size distributions at the surface and within the bulk that result from nonsolvent-induced phase separation (NIPS) – their typical manufacturing process. These distributions influence the hydrodynamic resistance to water flow and the stress concentrations around the pores. Developing advanced UF membranes requires innovative molecular designs that offer control over the surface and bulk pores, as well as the mechanical properties of the load-bearing, polymer. Here, we introduce a platform for designing UF membranes by leveraging solution self-assembly of block polymers and chain architectures with pendant polar groups. The block polymers consist of a poly(styrene-co-acrylonitrile) hydrophobic block, which is known for its strength, and a poly(4-vinyl pyridine) hydrophilic block, which drives solution self-assembly. We focus on a series of block polymers with constant molecular weight, M n ≈ 115 kDa, SAN fraction, 75 wt.%, and varying acrylonitrile content, 0 to 40 mol%, to demonstrate that: (i) RAFT dispersion copolymerization of acrylonitrile and styrene provides a facile route to synthesize strong block polymers, (ii) incorporation of acrylonitrile into the hydrophobic block enhances membrane strength by facilitating chain entanglements and dipole-dipole interactions, and (iii) acrylonitrile alters the balance between membrane permeance and rejection, even when the membranes feature similar surface and bulk pores. Overall, our results provide insights into the molecular design of UF membranes with enhanced mechanical and separation properties, contributing to the development of materials for water and energy technologies.
deformation↗
Intermediate time sub-diffusion and stress relaxation in ring polymer melts
The slow dynamics of non-concatenated ring melts remains a frontier problem in polymer science with implications for many soft material environments including cellular biophysics. Here, in this work, we report large-scale simulations of model ring melts that analyze the monomer and center-of-mass (CM) mean square displacements (MSD) and stress relaxation function on intermediate time and length scales. The degree of dynamical slowing down is characterized by the maximally sub-diffusive fractional time scaling exponents. The data span an exceptionally wide range of ring degrees of polymerization and stiffnesses and are not successfully organized based on the classic measure linear chain entanglement, N/N e . Rather, we find that the crossover degree of polymerization, N D , based on ring macromolecular caging that successfully allows master curves to be constructed for the long-time CM self-diffusion constant also collapses these temporal dynamic scaling exponents. Different properties display different exponents and exhibit one or two regimes of linear variation with the logarithm of N D / N . A distinct crossover of the CM-MSD and stress relaxation exponents emerges at sufficiently large N or stiffness that is not found for the monomer MSD, indicating a novel form of dynamic decoupling. This crossover aligns with the predicted critical degree of polymerization for transitioning from a weak to strong caging regime, indicative of activated transport. The latter may reflect the emergence of an intermolecular collective contribution to stress in analogy with dense soft colloidal matter. Suggestions are made for future theoretical work to address the rich patterns of behavior discovered.
Anomalous diffusion↗
Minkowski vacuum entanglement and accelerated oscillator chains
Minkowski vacuum is empty from the perspective of Unruh-Minkowski photons, however, in the Rindler picture, it is filled with entangled pairs of Rindler photons. A ground-state atom uniformly accelerated through Minkowski vacuum can become excited by absorbing a Rindler photon (Unruh effect) or, in the alternative description, by emitting an Unruh-Minkowski photon (Unruh-Wald effect). We find an exact solution for the quantum evolution of a long chain of harmonic oscillators accelerated through Minkowski vacuum and for two chains accelerated in the opposite directions. We show how entanglement of Rindler photons present in Minkowski vacuum is transferred to the oscillators moving in causally disconnected regions. We also show that in the Unruh-Minkowski photon picture the process can be interpreted as if initial correlations between collective oscillator modes are transferred to the generated Unruh-Minkowski photons. Published by the American Physical Society 2025
Svidzinsky, Anatoly A. (ORCID:0000000247756767)↗
Understanding Viscoelasticity of an Entangled Silicone Copolymer via Coarse-Grained Molecular Dynamics Simulations
Entangled dynamics is important for understanding rheological properties of long-chain polymers. For entangled homopolymers, the classic tube-reptation model and its refinements have been successfully applied to quantify properties like diffusion coefficient and zero-rate viscosity. However, the application of such models to copolymers has been limited despite scientific and industrial importance. Here, we study the entangled melt dynamics of poly(dimethyl-co-diphenyl)siloxane random copolymer for a range of mean-composition-ratio ϕ of the diphenyl component via long-term molecular dynamics simulation with a recently developed coarse-grained model. We found that the segmental relaxation is heterogeneous at the monomeric level because of compositional fluctuations. However, at the chain-entanglement level and higher length scales, the viscoelastic response is homogeneous with compositional dependence only through the overall diphenyl fraction ϕ. The relaxation modulus of the entangled copolymer melt conforms to the Likhtman–McLeish model, and the viscosity predicted using our current coarse-grained parameters is in good quantitative agreement with experimental data.
Copolymers↗
Entanglement entropy of (2 +1)-dimensional SU(2) lattice gauge theory on plaquette chains
We study the entanglement entropy of Hamiltonian SU(2) lattice gauge theory in 2 +1 dimensions on linear plaquette chains and show that the entanglement entropies of both ground and excited states follow Page curves. The transition of the subsystem size dependence of the entanglement entropy from the area law for the ground state to the volume law for highly excited states is found to be described by a universal crossover function. Quantum many-body scars in the middle of the spectrum, which are present in the electric flux truncated Hilbert space, where the gauge theory can be mapped onto an Ising model, disappear when higher electric field representations are included in the Hilbert space basis. This suggests the continuum (2+1)-dimensional SU(2) gauge theory does not have such scarred states.
Astronomy & Astrophysics↗
Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain
In this work, we explore the interplay of confinement, string breaking and entanglement asymmetry on a 1D quantum Ising chain. We consider the evolution of an initial domain wall and show that, surprisingly, while the introduction of confinement through a longitudinal field typically suppresses entanglement, it can also serve to increase it beyond a bound set for free particles. Our model can be tuned to conserve the number of domain walls, which gives an opportunity to explore entanglement asymmetry associated with link variables. We study two approaches to deal with the non-locality of the link variables, either directly or following a Kramers-Wannier transformation that maps bond variables (kinks) to site variables (spins). We develop a numerical procedure for computing the asymmetry using tensor network methods and use it to demonstrate the different types of entanglement and entanglement asymmetry.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Floquet Engineering of Interactions and Entanglement in Periodically Driven Rydberg Chains
Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and quantum dynamics. We introduce a new Floquet engineering technique for systems in the blockade regime that provides control over novel forms of interactions and entanglement dynamics in such systems. Our approach is based on time-dependent control of Rydberg laser detuning and leverages perturbations around periodic many-body trajectories as resources for operator spreading. These time-evolved operators are utilized as a basis for engineering interactions in the effective Hamiltonian describing the stroboscopic evolution. As an example, we show how our method can be used to engineer strong spin exchange, consistent with the blockade, in a one-dimensional chain, enabling the exploration of gapless Luttinger liquid phases. In addition, we demonstrate that combining gapless excitations with Rydberg blockade can lead to dynamic generation of large-scale multipartite entanglement. Experimental feasibility and possible generalizations are discussed.
Floquet systems↗
The Work of Mechanical Degradation in Elongating Polymer Melts
Molecular dynamics simulations are used to study the mechanical degradation of well-entangled polymer melts during uniaxial extensional flow. Simulations measure the transient rise in extensional stresses and relate them to the molecular alignment and scission of chain backbones. Intermolecular entanglements couple chain scission in space and time, making degradation sensitive to deformation history and strain rate in ways not displayed by dilute polymer solutions. The rate of chain scission is nonmonotonic and peaks at strains corresponding to the maximum extensibility of entanglement segments but prior to the full extension of chain backbones. We measure a specific work per scission event w* and decompose it into separate contributions associated with chain alignment, chemical bond breaking, and scission-induced plasticity. We find chain scission in melts requires activating plastic dissipation that is multiple orders of magnitude larger than the chemical work required to break a covalent backbone bond. Our findings underscore the critical need to consider bulk polymer mechanics and rheology in designing efficient mechanical degradation and mechanochemical processes.
36 MATERIALS SCIENCE↗
The melt memory effects in polymer crystallization
This paper presents a systematic review of the literature on the melt memory effects observed in polymers, an area that has engendered considerable debate for over 50 years. Recent advances in experimental techniques have provided fresh insights into how a polymer's thermal history influences its recrystallization behavior. It has been observed that given other conditions unchanged, the crystallization temperature during recrystallization decreases with an increase in the melt temperature T s above the melting point T m until a critical melt temperature is attained. This phenomenon also extends to the half-time of crystallization and the secondary structures, such as lamellar thickness, of semi-crystalline polymers. Despite these findings, a comprehensive constitutive model that encapsulates polymer melt memory effects remains elusive. Cutting-edge instrumentation, including in situ small and wide-angle X-ray scattering, temperature-controlled Fourier transform infrared spectroscopy, and flash differential scanning calorimetry, have posed significant challenges to the traditional nucleation and growth models established in the 1970s. These models are foundational to our understanding of polymer crystallization, which is an integral part of polymer processing and production. In this review, the historical contours of this discourse are traced, with an examination of both the recent experimental breakthroughs and theoretical advancements pertinent to polymer melt memory effects. In conclusion, this paper delves into the prevailing theories of polymer nucleation and crystallization and engages with theoretical discussions and numerical simulations that attempt to elucidate and rationalize these melt memory phenomena.
36 MATERIALS SCIENCE↗
Large scale polymer toughening of two-dimensional materials revealed by in situ TEM fracture tests and multiscale simulations
Two-dimensional (2D) materials offer significant potential for applications in energy-harvesting devices, batteries, sensors, and transistors. However, their intrinsic brittleness makes them prone to mechanical failure, limiting their practical use. In this work, we perform in situ transmission electron microscopy (TEM) fracture tests on monolayer MoSe2 and uncover an extrinsic toughening effect induced by an ultrathin adsorbed polystyrene adlayer. This adlayer substantially enhances the fracture resistance of the 2D flakes. Through a combination of molecular dynamics simulations and finite element analysis, we elucidate the molecular mechanism behind this toughening effect. Further, it arises from the active crack-bridging behavior of entangled polymer chains and the formation of a fracture process zone that stabilizes crack propagation and increases the energy required for crack extension. The proposed toughening mechanism offers a pathway to improving the mechanical reliability of 2D material-based devices by mitigating the risk of sudden failure.
2D materials↗
Temporal entanglement transitions in the periodically driven Ising chain
Periodically driven quantum systems can host non-equilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover (TET) in a Floquet spin chain, which correspond to a quantum phase transition in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking. We identify the symmetry principles underlying these transitions: they appear when the driven Hamiltonian preserves global symmetry (here, ℤ2), the initial state respects this symmetry, and the reduced density matrix carries weight in both subsystem-parity sectors, with TET occurring precisely when the sector weights become equal (given the previous two conditions are also satisfied). Intriguingly, we find these transitions across a broad range of driving frequencies (from adiabatic to high-frequency regime) and independently of drive details, where they manifest as periodic, sharp entanglement spectrum reorganizations marked by the Schmidt-gap closure, a vanishing entanglement echo, and symmetry-quantum-number flips, while remaining invisible to conventional local observables. At high frequencies, the entanglement Hamiltonian acquires an intrinsic timescale decoupled from the drive period, rendering the transitions genuine steady-state features. Finite-size scaling reveals universal critical behavior with correlation-length exponent 𝜈 = 1, matching equilibrium Ising universality despite its emergence from purely dynamical mechanisms decoupled from static criticality. Furthermore, our work establishes TET as novel features in Floquet quantum matter.
36 MATERIALS SCIENCE↗
Power-Law Entanglement and Hilbert Space Fragmentation in Nonreciprocal Quantum Circuits
Quantum circuits utilizing measurement to evolve a quantum wave function offer a new and rich playground to engineer unconventional entanglement dynamics. Here, in this work, we introduce a hybrid, nonreciprocal setup featuring a quantum circuit, whose updates are conditioned on the state of a classical dynamical agent. In our example the circuit is represented by a Majorana quantum chain controlled by a classical N-state Potts chain undergoing pair flips. The local orientation of the classical spins controls whether randomly drawn local measurements on the quantum chain are allowed or not. This imposes a dynamical kinetic constraint on the entanglement growth, described by the transfer matrix of an N-colored loop model. It yields an equivalent description of the circuit by an SU(N)-symmetric Temperley-Lieb Hamiltonian or by a kinetically constrained surface growth model for an N-component height field. For N = 2, we find a diffusive growth of the half-chain entanglement toward a stationary profile S(L) ~ L 1/2 for L sites. For N ≥ 3, the kinetic constraints impose Hilbert space fragmentation, yielding subdiffusive growth toward S(L) ~ L 0.57 . This showcases how the control by a classical dynamical agent can enrich the entanglement dynamics in quantum circuits, paving a route toward novel entanglement dynamics in nonreciprocal hybrid circuit architectures.
1-dimensional spin chains↗
NMR (Nuclear Magnetic Resonance) and macromolecular migration in a melt or in concentrated solutions
The purpose of this paper is to analyze the migration process of long polymer molecules in a melt or in concentrated solutions as it may be observed from the dynamics of the transverse magnetization of nuclear spins linked to these chains. The low frequency viscoelastic relaxation of polymer systems is known to be mainly controlled by the mechanism of dissociation of topological constraints excited on chains and which are called entanglements. This mechanism exhibits a strong dependence upon the chain molecular weight. These topological constraints also govern the diffusion process of polymer chains. So, the accurate description of the diffusion motion of a chain may be a convenient way to characterize disentanglement processes necessarily involved in any model proposed to explain viscoelastic effects.
Addad, J. P. C.↗