Critical Entanglement Research Articles

Flocculation Mechanism and Microscopic Statics Analysis of Polyacrylamide Gel in Underwater Cement Slurry

Zeta potential testing, Fourier infrared spectroscopy, and total organic carbon analysis were employed in this manuscript to explore the flocculation mechanism of polyacrylamide (PAM) on slurry with a high content of polycarboxylate ether (PCE). Through the combination of assessments of chemical bond shifts, adsorption indicators, and intrinsic viscosity of high-molecular-weight polymer systems, the microscale flocculation mechanisms of different PAM dosages in cement suspensions were elucidated, showcasing stages of “adsorption–lubrication–entanglement”. Initially (PAM < 0.3%), with PAM introduction, the polymer primarily underwent adsorption interactions, including hydrogen bonding between the ester group, amine group, and water molecules; chelation between the ester group and Ca2+ and Al3+ on the cement surface; and bridging between PAM’s long-chain structure and cement particles. As the PAM content increased, the cement particles’ adsorption capacity saturated (PAM < 0.67%). The entropy loss of polymer conformation could not be offset by adsorption energy, leading to its exclusion from the interface and depletion attractive forces. Slurry movement shifted from inter-particle motion to high-molecular-weight polymer sliding in interstitial fluid, forming a lubrication effect. With further PAM content no less than 0.67%, the polymer solution reached a critical entanglement concentration, and the contact of the rotation radius of the long-chain molecules led to entanglement domination. By introducing bridging adsorption, depletion attraction, and entanglement forces, the cohesion of cement-based polymer suspensions was subsequently determined. The results showed a linear correlation between cohesion and PAM concentration raised to powers of 0.30, 1.0, and 0.75 at different interaction stages, and a multiscale validation from microscopic flocculation mechanisms to macroscopic performance was finally completed through a comparative analysis with macroscopic anti-washout performance.

Transgressive Knowing

This issue's In-Dialogue represents the intentional epitomization of many conversations the Editorial Team has been having since JASC’s inception around what we mean by 'transformative'. As convenors of the dialogue Oliver Koenig and Megan Seneque invited a small group of individuals who, in their ongoing work, have been deeply immersed in exploring research and praxis paradigms that respond ethically, critically, and creatively to the intersecting crises of our time. Together, the group set out to explore the integrity of 'research' and 'practice', their critical entanglement and co-dependence, and the nature of practices that enable worlds to be created in certain ways. Rather than attempting to arrive at a consensual understanding, the dialogue that unfolds can be seen as a mirror of the world-making practice(s) that are characteristic of transformative research

Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories

We construct a class of solvable models for 2+1D quantum critical points by attaching 1+1D conformal field theories (CFTs) to fluctuating domain walls forming a “loop soup”. Specifically, our local Hamiltonian attaches gapless spin chains to the domain walls of a triangular lattice Ising antiferromagnet. The macroscopic degeneracy between antiferromagnetic configurations is split by the Casimir energy of each decorating CFT, which is usually negative and thus favors a short loop phase with a finite gap. However, we found a set of 1D CFT Hamiltonians for which the Casimir energy is effectively positive, making it favorable for domain walls to coalesce into a single “snake” which is macroscopically long and thus hosts a CFT with a vanishing gap. The snake configurations are geometrical objects also known as fully-packed self-avoiding walks or Hamiltonian walks which are described by an \mathrm{O}O(n=0) loop ensemble with a non-unitary 2+0D CFT description. Combining this description with the 1+1D decoration CFT, we obtain a 2+1D theory with unusual critical exponents and entanglement properties. Regarding the latter, we show that the log contributions from the decoration CFTs conspire with the spatial distribution of loops crossing the entanglement cut to generate a “non-local area law”. Our predictions are verified by Monte Carlo simulations.

Symmetry-resolved entanglement in critical non-Hermitian systems

The study of entanglement in the symmetry sectors of a theory has recently attracted a lot of attention since it provides better understanding of some aspects of quantum many-body systems. In this paper, we extend this analysis to the case of non-Hermitian models, in which the reduced density matrix $\rho_A$ may be non-positive definite and the entanglement entropy negative or even complex. Here we examine in detail the symmetry-resolved entanglement in the ground state of the non-Hermitian Su-Schrieffer-Heeger chain at the critical point, a model that preserves particle number and whose scaling limit is a $bc$-ghost non-unitary CFT. By combining bosonization techniques in the field theory and exact lattice numerical calculations, we analytically derive the charged moments of $\rho_A$ and $|\rho_A|$. From them, we can understand the origin of the non-positiveness of $\rho_A$ and naturally define a positive-definite reduced density matrix in each charge sector, which gives a well-defined symmetry-resolved entanglement entropy. As byproduct, we also obtain the analytical distribution of the critical entanglement spectrum.

Facilely prepare high-performance loose nanofiltration membranes through regulation of polymer chain entanglements

The membrane forming process was fundamentally affected by the thermodynamics of polymer solution, the core of which involved the governance of polymer chain entanglements in the solution. In this work, a high-performance loose nanofiltration (LNF) membrane with high water permeance and high separation accuracy was facilely fabricated by the regulation of polymer chain entanglements through only changing CaCO3 nanoparticle (nano-CaCO3) size in the casting solution. The degree of polymer chain entanglements was characterized by the critical entanglement viscosity of the casting solution. The solution viscosity was markedly increased with the decrease of nano-CaCO3 size and then significantly reduced when nano-CaCO3 disappeared. While the mutual diffusion rate between the non-solvent (acidic water) and the solvent was increased to bring about rapid phase inversion with increasing the viscosity of the casting solution. The high solution viscosity and rapid phase inversion, which was a unconventional phenomenon, leaded to the formation of LNF membranes with outstanding performance. The LNF membranes obtained had a pore diameter of 1.4 nm (MWCO = 1625 Da) and a high pure water permeance of 98 L·m−2·h−1·bar−1, accompanying an excellent separation accuracy of small molecule dyes and NaCl mixtures (the rejection is 99.9% for eriochrome black T (EBT, Mw = 461 Da) and 4.5% for NaCl). This work provides general guidance for the structural regulation of high-performance separation membranes.

Critical light-matter entanglement at cavity mediated phase transitions

We consider a model of a light-matter system, in which a system of fermions (or bosons) is coupled to a photonic mode that drives a phase transitions in the matter degrees of freedom. Starting from a simplified analytical model, we show that the entanglement between light and matter vanishes at small and large coupling strength, and shows a peak in the proximity of the transition. We perform numerical simulations for a specific model (relevant to both solid state and cold atom platforms), and show that the entanglement displays critical behavior at the transition, and features maximum susceptibility, as demonstrated by a maximal entanglement capacity. Remarkably, light-matter entanglement provides direct access to critical exponents, suggesting a novel approach to measure universal properties without direct matter probes.

Polymer segmental dynamics near the interface of silica particles in the particle/polymer composites

We demonstrate an approach to examine the local segmental dynamics of a polymer near the interface of an inorganic filler by observing the rotational dynamics of the fluorescent probe at the chain ends of polymer brushes grafted onto the surface of the filler particles. Localization of the fluorescent probe was realized by designing and synthesizing fluorophore-tethered polystyrene (PS) brushes anchored on the surface of silica particles of controlled sizes. Fluorophore-functionalized telechelic PS with an azide functionality at the other chain end was achieved via a combination of atom transfer radical polymerization and post-polymerization modification. The azide-bearing PS chains were tethered to alkyne-functionalized particles via copper-catalyzed cycloaddition reaction. The molecular weight of the grafted polymer chains was controlled to be less than the critical entanglement molecular weight, and the chain density was controlled to be low enough so that the observed dynamics was not perturbed by the polymer brush conformation and brush-matrix polymer entanglement. The polymer dynamics near the surface of the particles at low concentrations was closely examined in the bulk film geometry by employing imaging rotational fluorescence correlation microscopy (irFCM). The observed polymer dynamics near the interface were not altered in the inorganic/polymer composite geometry when the surface did not have favorable interaction with the matrix polymer. The presented rational design of the chemical route and examination of local dynamics highlight a feasible approach to construct material systems with high complexities towards a deeper understanding of composite materials.

Ground-state separability and criticality in interacting many-particle systems

We analyze exact ground state (GS) separability in general $N$ particle systems with two-site couplings. General necessary and sufficient conditions for full separability, in the form of one and two-site eigenvalue equations, are first derived. The formalism is then applied to a class of $SU(n)$-type interacting systems, where each constituent has access to $n$ local levels, and where the total number parity of each level is preserved. Explicit factorization conditions for parity-breaking GS's are obtained, which generalize those for $XYZ$ spin systems and correspond to a fundamental GS multilevel parity transition where the lowest $2^{n-1}$ energy levels cross. We also identify a multicritical factorization point with exceptional high degeneracy proportional to $N^{n-1}$, arising when the total occupation number of each level is preserved, in which any uniform product state is an exact GS. Critical entanglement properties (like full range pairwise entanglement) are shown to emerge in the immediate vicinity of factorization. Illustrative examples are provided.

Measurement-induced criticality in Z2 -symmetric quantum automaton circuits

We study entanglement dynamics in hybrid $\mathbb{Z}_2$-symmetric quantum automaton circuits subject to local composite measurements. We show that there exists an entanglement phase transition from a volume law phase to a critical phase by varying the measurement rate $p$. By analyzing the underlying classical bit string dynamics, we demonstrate that the critical point belongs to parity-conserving universality class. We further show that the critical phase with $p>p_c$ is related to the diffusion-annihilation process and is protected by the $\mathbb{Z}_2$-symmetric measurement. We give an interpretation of the entanglement entropy in terms of a two-species particle model and identify the coefficient in front of the critical logarithmic entanglement scaling as the local persistent coefficient. The critical behavior observed at $p\geq p_c$ and the associated dynamical exponents are also confirmed in the purification dynamics.

Synthesis of a hydrophobic association polymer with an inner salt structure for fracture fluid with ultra-high-salinity water

This study used a compound initiation free radical polymerization process to synthesize a hydrophobic association polymer (PDMA1) with good salt resistance for use in ultra-high salinity reservoirs. The critical association and entanglement concentrations of PDMA1 in deionized (DI) water were 1596 and 2799 mg/L, respectively. The properties of the polymer in simulated formation (SF) water were investigated using viscosity change and conductivity tests, and the apparent viscosity of the PDMA1 solution was investigated using apparent viscosity, viscoelasticity, and thixotropy experiments. To a certain extent, the apparent viscosity of the solution was found to be influenced by metal ions. Under total dissolved solids (TDS) concentrations of up to 239,500 ppm, when the polymer concentration exceeded the critical entanglement concentration, the apparent viscosity of the polymer remained close to that of DI water. Additionally, the viscosity of the PDMA1 solution was affected by different types of metal ions, and the polymer solution thickened owing to divalent cations. PDMA1 is resistant to salt owing to hydrophobic interaction, electrostatic shielding, and double-layer compression. The results of the thixotropy and viscoelasticity tests revealed the thixotropy loop area of the PDMA1 solution in SF water to be greater than that in DI water. Under these conditions, PDMA1 is mostly viscous at low shear frequencies and mostly elastic at high shear frequencies. The PDMA1 inner-salt hydrophobic association polymer can be utilized as a chemical agent for tertiary recovery and fracturing, processes in high-salinity reservoirs, particularly for aggravating fracturing fluid.

Multicriticality and quantum fluctuation in a generalized Dicke model

We consider an important generalization of the Dicke model in which multi-level atoms, instead of two-level atoms as in conventional Dicke model, interact with a single photonic mode. We explore the phase diagram of a broad class of atom-photon coupling schemes and show that, under this generalization, the Dicke model can become multicritical. For a subclass of experimentally realizable schemes, multicritical conditions of arbitrary order can be expressed analytically in compact forms. We also calculate the atom-photon entanglement entropy for both critical and non-critical cases. We find that the order of the criticality strongly affects the critical entanglement entropy: higher order yields stronger entanglement. Our work provides deep insight into quantum phase transitions and multicriticality.

Direct Observations of Segmental Dynamics at the Polymer–Substrate Interface Enabled by Localizing Fluorescent Probes with Polymer Brushes

We employed imaging rotational fluorescence correlation microscopy to directly observe the segmental dynamics of the polymer near the polymer–substrate interface using a probe-tethered polymer brush buried in bulk polymer films. The probe-tethered polymers grafted onto the polymer–substrate interface provide spatial selectivity to probe only the segmental dynamics of polymer near the polymer–substrate interface. The perturbation caused by the grafted polymer chains on the segmental dynamics of the polymer film near the interface was minimized by reducing the molecular weight of the polymer brush compared with the critical entanglement molecular weight of the polymer and grafted with a low grafting density (≈0.1 chains/nm²) using a “grafting-to” method, which allows precisely controlled and fully characterized polymer brush structures. In addition, the molecular weight of the brush polymer was further controlled to ≈10 kg/mol with the root-mean-square end-to-end distance of ≈5 nm to probe dynamics within 10 nm of the polymer–substrate interface. Polystyrene and poly(methyl methacrylate) films carrying rather unfavorable and similar surface energies, respectively, with the silane-modified silicon wafer substrates were investigated. The polymer dynamics near the interface characterized by the degrees of non-Arrhenius temperature dependence and nonexponential relaxation were not altered in both systems compared with those of the bulk, suggesting that the polymer dynamics is not sensitive to moderate differences in enthalpic interaction between the polymer and the substrate.

Multivalent Assembly of Flexible Polymer Chains into Supramolecular Nanofibers.

Polymeric materials in nature regularly employ ordered, hierarchical structures in order to perform unique and precise functions. Importantly, these structures are often formed and stabilized by the cooperative summation of many weak interactions as opposed to the independent association of a few strong bonds. Here, we show that synthetic, flexible polymer chains with periodically placed and directional dynamic bonds collectively assemble into supramolecular nanofibers when the overall molecular weight is below the polymer's critical entanglement molecular weight. This causes bulk films of long polymer chains to have faster dynamics than films of shorter polymer chains of identical chemical composition. The formation of nanofibers increases the bulk film modulus by over an order of magnitude and delays the onset of terminal flow by more than 100 °C, while still remaining solution processable. Systematic investigation of different polymer chain architectures and dynamic bonding moieties along with coarse-grained molecular dynamics simulations illuminate governing structure-function relationships that determine a polymer's capacity to form supramolecular nanofibers. This report of the cooperative assembly of multivalent polymer chains into hierarchical, supramolecular structures contributes to our fundamental understanding of designing biomimetic functional materials.

Effect of entanglement upon branching on dispersibility, β-nucleating and mechanically strengthening ability of polystyrene in isotactic polypropylene

Polymers with benzene rings have the potential to act as macromolecular β-nucleating agents and rigid organic particles for isotactic polypropylene (iPP). The dispersibility in iPP matrix is a key factor for their β-nucleating efficiency and mechanically strengthening ability. In this paper, comb-like branched polystyrenes (cPSs) with different side chain lengths were introduced into iPP. The effect of entanglement upon branching on dispersibility, β-nucleating and mechanically strengthening ability of PS in iPP was investigated in detail. Compared with the linear polystyrene with the same length of backbone, the incorporation of side chains intensifies the entanglement between cPS chains, not facilitating their dispersion in iPP matrix. However, short side chains (chain length lower than the critical chain entanglement molecular weight of PS) facilitate the interdiffusion between the cPS and iPP chains and ultimately lead to favorable dispersibility and high β-nucleating efficiency, as well as prominent toughening and reinforcing effect on iPP.

Entanglement and dynamics of diffusion-annihilation processes with Majorana defects

Coupling a many-body system to a thermal environment typically destroys the quantum coherence of its state, leading to an effective classical dynamics at the longest time scales. We show that systems with anyon-like defects can exhibit universal late-time dynamics that is stochastic, but fundamentally non-classical, because some of the quantum information about the state is topologically protected from the environment. Our coarse-grained model describes one-dimensional systems with domain-wall defects carrying Majorana modes. These defects undergo Brownian motion due to coupling with a bath. Since the fermion parity of a given pair of defects is nonlocal, it cannot be measured by the bath until the two defects happen to come into contact. We examine how such a system anneals to zero temperature via the diffusion and pairwise annihilation of Majorana defects, and we characterize the nontrivial entanglement structure that arises in such stochastic processes. Separately, we also investigate simplified "quantum measurement circuits" in one or more dimensions, involving repeated pairwise measurement of fermion parities for a lattice of Majoranas. The dynamics of these circuits can be solved by exact mappings to classical loop models. They yield analytically tractable examples of measurement-induced phase transitions, with critical entanglement structures that are governed by nonunitary conformal fixed points. In the system of diffusing and annihilating Majorana defects, the relaxation to the ground state is analogous to coarsening in a classical 1D Ising model via domain wall annihilation. Here, however, configurations are labeled not only by the defect positions but by a nonlocal entanglement structure. The resulting dynamical process is a new universality class for the coarsening of topological domain walls, whose universal properties can be obtained from an exact mapping.

Study on the formation and structural evolution of bead‐on‐string in electrospun polysulfone mats

Bead‐on‐string is a desirable morphology for some emerging applications of electrospun mats such as superhydrophobic surfaces. In this study, the bead‐on‐string morphology in electrospun polysulfone (PSU) mats was investigated and correlated with the solution concentration, voltage and feed rate. PSU/dimethylformamide solutions with different concentrations (4, 5.5, 7, 15, 18 and 20 wt% PSU) were electrospun at a constant feed rate (3.5 mL h–1) and voltage (15 kV). Critical chain overlap and entanglement concentrations were found to be 3.65 and 7.12 wt% PSU, respectively. The bead‐on‐string morphology was detected in the concentration range 7–18 wt% PSU, in close agreement with theoretical estimations. The evolution of the bead‐on‐string morphology in mats prepared from 15 wt% PSU solution and electrospun at three feed rates (i.e. 1.5, 2.5 and 3.5 mL h–1) and voltages (i.e. 12.5, 15 and 18 kV) were also studied. The results showed that the beads appear less in number as either the feed rate or the voltage increases. In addition, the morphology of the beads revealed a transition from a spherical to a spindle‐like appearance with an increase in voltage. The effect of feed rate on bead geometry, however, was revealed to depend on the applied voltage. © 2020 Society of Chemical Industry

Rheological aspects in fabricating pullulan-whey protein isolate emulsion suitable for electrospraying: Application in improving β-carotene stability

Beta-carotene has been used as a food colorant and functional ingredient, but these applications are limited due to its poor stability. The aim of this work was to improve the stability of β-carotene by encapsulating it in electrosprayed particles. The electrohydrodynamic behavior of pullulan solution was studied and the influence of encapsulation and core-to-wall ratio on the stability of β-carotene at different temperatures and relative humidity were investigated. The specific viscosity of the polymer solution increased linearly with the concentration until 5% w/w concentration. The critical entanglement concentration of the pullulan was found to be 4.58% wt. Among the various concentrations of pullulan studied, 3% w/w pullulan solution yielded spherical, monodisperse nanoparticles. Electrosprayed particles with 1:50 core-to-wall ratio had highest encapsulation efficiency. The rate of β-carotene loss displayed first order reaction kinetic within 14 days, while displayed diffusion limited mode after 14 days storage. The retention of β-carotene from the electrosprayed particles accelerated markedly with decreasing temperatures and relative humidity. This study provides a strategy for the preparation of promising electrosprayed particles to improve the stability of β-carotene.

Exact solution of the extended dimer Bose–Hubbard model with multi-body interactions

It is shown that the extended one-dimensional dimer Bose–Hubbard model with multi-body interactions can be solved exactly by using the algebraic Bethe ansatz mainly due to the site-permutation S2 symmetry. The solution for the model with up to three-particle hopping and three-body on-site interaction is explicitly shown. As an example of the application, lower part of the excitation energy levels and the ground-state entanglement measure of the standard Bose–Hubbard Hamiltonian with the attractive two-body on-site interaction plus the three-body on-site interaction for 100 bosons with variation of the control parameter are calculated by using the exact solution. It is shown that the attractive three-body on-site interaction reinforces the critical point entanglement of the system, which may be helpful for design of an optical lattice for ultracold atoms or a tuneable superconducting quantum interference device with maximal entanglement.

Molecular Dynamics Test of the Stress-Thermal Rule in Polyethylene and Polystyrene Entangled Melts

Anisotropic thermal transport induced by deformation and the linear relation between the thermal conductivity and stress tensors, also known as the stress-Thermal rule (STR), are tested via molecular dynamics simulations in well-entangled linear polyethylene (PE) and polystyrene (PS) melts subjected to extensional flow. We propose a method to determine the stress in deformed molecular melts, a key component missing in prior simulation studies on thermal transport in polymers that prevented verification of the STR. We compare our results with available data from previous experimental and simulation studies. Thermal conductivity (TC) is found to increase (decrease) in the direction parallel (perpendicular) to the imposed stretch. We find that the STR is valid for both PE and PS over a wide range of deformation rates and stress levels. In direct agreement with experimental evidence and the STR, we observe that for a given strain, the anisotropy in TC increases with the strain rate. Surprisingly, our results for PE question the universal behavior with respect to polymer chemistry suggested by experiments by showing a significantly higher proportionality constant (the stress-Thermal coefficient) between stress and anisotropy in TC. We argue that this discrepancy can be explained by the high degree of entanglement interactions in PE affecting the transport of energy at the molecular level. Our conjecture is tested by studying an entangled linear PS melt, a polymer with a much lower entanglement plateau, for which thermal transport experimental results are available. For PS, the normalized stress-Thermal coefficient is found to be commensurate with the experimental value. Finally, we test the fundamental molecular hypothesis of preferential energy transport along the backbone of polymer chains used to formulate the STR, which was prompted by early experimental evidence showing an increase in TC with chain length. We are able to establish that the increase in TC with chain length in PE melts fades as the system becomes entangled (i.e., TC remains constant beyond the critical entanglement chain length that marks the transition to entanglement-dominated rheological behavior). Our findings are of key importance in developing robust molecular-To-continuum methodologies for the study of nonisothermal macroscopic flows that are extremely relevant to polymer manufacturing processes.

Preparation of long‐chain branched poly(ethylene terephthalate): Molecular entanglement structure and toughening mechanism

Poly(ethylene terephthalate) (PET) was long‐chain branched (LCB) by ring‐opening reaction with both pyromellitic dianhydride and tetrahydrophthalic acid diglycidyl ester as chain extenders through reactive melt processing. It was found that with the increase of chain extenders dosage, the intrinsic viscosity of PET increased and melt index decreased greatly, while both the tensile strength and impact strength of PET were remarkably improved. The elastic modulus (G′) and viscous modulus (G″) were enhanced by chain branching. Compared with PET, the complex viscosities of LCB‐PET were much higher at full frequency range, and obvious shear thinning was presented. The Cole–Cole curve deviated from the semicircular shape and the curve end was inclined to upward in high viscosity region, indicating the formation of the multiple hierarchical structures. The molecular weight of the branch (MB) was much greater than critical entanglement molecular weight (M e), which essentially confirmed the existence of LCB structure and fairly strong molecular entanglement in the LCB‐PET molecular chain. When subjected to external force, the entanglement point, acting as physical crosslinking point between the molecules, was in favor of increasing the molecular interaction, reducing the molecular slippage, and bearing a large deformation. POLYM. ENG. SCI., 59:1190–1198 2019. © 2019 Society of Plastics Engineers