Linear Chain Research Articles

Low-Temperature Synthesis of Linear Carbon Chain inside Single-Walled Carbon Nanotubes

Linear carbon chain (LCC) has attracted much interest concerning its structure and applications. It has been reported that LCC possesses higher strength, elastic modulus, and stiffness than any known material, which provides a possibility for LCC as a new composite material, yet its chemical stability remains an issue [1]. Therefore, finding a method to efficiently synthesize LCC has become a meaningful research topic in recent years. A landmark study on LCC synthesis was given by using double-walled carbon nanotubes (DWCNTs) as the template combined with a high-temperature annealing treatment at 1460°C to acquire long chains composed of more than 6,000 carbon atoms [2]. Except for DWCNTs, LCC synthesis starting from single-walled carbon nanotubes (SWCNT) as templates was also reported. However, given the instability of SWCNTs at higher temperature [2] the synthesis efficiency is not as good as for DWCNTs. As far as we know, there is still no report on an efficient LCC synthesis inside SWCNTs. Herein, we report the low-temperature (400°C) efficient LCC synthesis starting from a SWCNT template.To this end, a SWCNT dispersion [3] underwent a surfactant exchange process and was fabricated into a SWCNT film by the filtration method. The SWCNT film was annealed under 400°C in an argon atmosphere to synthesize LCC. Raman spectroscopy (laser wavelength 532 nm) was used to characterize the efficiency of the LCC synthesis. A strong peak at 1863 cm-1 appeared after annealing, originating from the well-known C-mode of the linear carbon chain [4] thereby confirming its existence inside SWCNTs. SWCNTs synthesized by a low-pressure alcohol catalytic chemical vapor deposition (ACCVD) method [5] were also adopted for the LCC synthesis template, resulting in a similar LCC Raman peak at 1863 cm-1. We attribute this successful low-temperature LCC synthesis to the appropriate surfactant which could be encapsulated inside CNTs and converted to LCC during the annealing process.Keywords: Linear Carbon Chain, Single-walled Carbon Nanotubes, Surfactants

Effective Coupling Model to Treat the Odd-Even Effect on the Current-Voltage Response of Saturated Linear Carbon Chains Single-Molecule Junctions.

The calculation of the electrical charge transport properties of alkanes C n H 2n S 2 with (n = 4-11) was performed to understand the odd-even effect on its current-voltage response. The extended molecule and broadband limit models were used to describe the molecular junction and covalent coupling with the electrodes. It was shown that among the participating molecular orbitals, HOMO and HOMO-1 are the ones with the most charge transport contribution. Moreover, the odd-even effect is caused by the alternation of the eigenvalues of some frontier orbitals as a function of the number of carbons, especially the HOMO that dominates the electrical transport. It could also be noted that when the current is analyzed outside the resonance, the relationship with the number of carbons exponentially decays, confirming the reports in the literature. To the best of our knowledge, a first principle study of the odd-even effect in symmetric systems composed by linear saturated carbon chains covalently coupled to electrodes has not been reported yet.

Group Theoretic Approach towards the Balaban Index of Catacondensed Benzenoid Systems and Linear Chain of Anthracene

In this work, we present the analytical closed forms of the Balaban index for anthracene and catacondensed benzenoid systems using group theoretic techniques. The Balaban index is a distance-based topological index that provides valuable information about the properties of chemical structures. We emphasize the importance of determining analytical closed forms of the Balaban index for catacondensed benzenoid systems and linear chains of anthracene, as it enables a deeper understanding of these systems and their behavior. Our analysis utilizes the group action of the automorphism group of these chains on the set of vertices, which refer to the points where the chains intersect. In future work, we plan to determine the Balaban index of other polymeric linear chains using group theoretic techniques and extend the applications of this index to other fields, such as materials science and biology. It is clear that the Balaban index remains a valuable tool in theoretical and computational chemistry, and its applications are constantly evolving.

Antipolyphosphate monoclonal antibodies derived from autoimmune mice

BackgroundInorganic polyphosphates (polyPs) are linear chains of phosphates that accelerate blood clotting. Targeting polyP in vivo has been shown to reduce thrombosis. ObjectivesTo identify and characterize anti-polyP monoclonal antibodies that could be used as analytical tools and as antithrombotic agents. MethodsHybridomas were prepared from spleen cells from autoimmune NZBWF1/J female mice and screened for anti-polyP antibodies. Antibodies that bound polyP using enzyme-linked immunosorbent assay and pull-down assays were further characterized with plate binding, surface plasmon resonance, and plasma-based clotting assays. Antithrombotic potential was evaluated in a murine ferric chloride–induced carotid artery thrombosis model. ResultsOf 4 antibodies that bound polyP in our pull-down assay, 2 (PP2069 and PP2099) were available for further characterization. While analyzing these anti-polyP antibodies, we found secretory leukocyte peptidase inhibitor (SLPI) to be a common contaminant of these antibodies and that SLPI binds polyP. We removed SLPI quantitatively from our purified immunoglobulin G. Both PP2069 and PP2099 immunoglobulin G displayed high affinity for polyP but also bound to other polyanions such as DNA, heparin, and certain other glycosaminoglycans, indicating limited specificity. Both antibodies inhibited polyP-initiated plasma clotting in vitro. When tested in vivo in a mouse thrombosis model, however, neither PP2069 nor PP2099 exhibited a significant antithrombotic effect. ConclusionAutoimmune mice spontaneously produce antibodies against polyP. The 2 examples of anti-polyP monoclonal antibodies studied here not only bound to polyP with high affinity but also cross-reacted with DNA and heparin. Neither antibody protected against thrombosis in a mouse model, but they might have some utility for in vitro studies of polyP.

Transition metal centers with anharmonic elastic interactions in one-dimensional spin-crossover solids

An exact examination of a one-dimensional (1D) anharmonic elastic model describing the thermodynamic properties of spin-crossover (SCO) solids is presented. This elastic model incorporates both intra-chain and mean field inter-chain interactions, providing a more understanding of 1D SCO materials. Numerical findings for a linear chain of spins unveil intriguing features, such as a two-step-like transition. Extending the model to interacting chains leads to an additional term in the effective ligand field of the system’s Hamiltonian, thereby enhancing its predictive power by accounting for more elastic constants of interactions. This augmentation reinforces the model’s validity in capturing the spin-crossover phenomenon. Numerical results in this extended framework elucidate clearer two-step-like spin crossover transitions, with the HS_LS fraction of spins approaching maximum values at equilibrium temperature Teq.

Ligand Tail Controls the Conformation of Indium Sulfide Ultrathin Nanoribbons.

We report the conformational control of 2D ultrathin indium sulfide nanoribbons by tuning their amine ligands' alkyl chain. The initial orthorhombic InS nanoribbons bare n-octylamine ligands and display a highly curved geometry with a characteristic figure of eight shapes. Exchanging the native ligand by oleylamine induces their complete unfolding to yield flat board-shaped nanoribbons. Significant strain variations in the InS crystal structure accompany this shape-shifting. By tuning the linear alkyl chain length from 4 to 18 carbon atoms, we show using small-angle X-ray scattering in solution and transmission electron microscopy that the curvature of the nanoribbon subtly depends on the ligand-ligand interactions at the nanoribbon's surface. The curvature decreases gradually as the chain length increases, while carbon unsaturation has an unexpectedly significant effect at constant chain length. These experiments shed light on the critical role of the ligand monolayer on the curvature of ultrathin 2D crystalline nanosheets and demonstrate that weak supramolecular forces within the organic part of colloidal nanocrystals can dramatically impact their shape. This transduction mechanism, in which changes in the organic monolayer impact the shape of a nanocrystal, will help to devise new strategies to design stimuli-responsive systems that take advantage of both the flexibility of organic moieties and the physical properties of the inorganic core.

The third-order nonlinear optical responses of zinc porphyrin oligomers: Cycles vs linear chains

Porphyrins are widely used as potential nonlinear optical (NLO) materials because of their highly delocalized π electrons and feasible synthesis and functionalization with broad biological applications. A variety of linear and cyclic porphyrin derivatives have been synthesized, and the correlation between their structures and NLO properties awaits being disclosed. In this work, the electronic structures and third-order NLO properties of linear and cyclic butadiyne-linked zinc porphyrin oligomers have been studied by quantum chemical methods and sum-over-states model. The static second hyperpolarizability (<γ0>) increases exponentially with the number of zinc porphyrin units ([<γ0>n] = 0.67[<γ0>1]n2.63, n = 2 ∼ 6) in linear π-conjugated oligomers, and the <γ0> of the linear hexamer is about 74 times that of the monomer. Such enhancement of <γ0> in linear oligomers originates from closely-lying frontier molecular orbitals available for low energy electron excitations and strong charge transfer-based excitations across porphyrins. The <γ0>s of cyclic porphyrins are lower than that of the linear hexamer, though the interaction between the ring and the ligand enhances the <γ0> of some cyclic zinc porphyrin complexes. The large two-photon absorption cross sections confer on these zinc porphyrin derivatives excellent candidates for two-photon absorption applications.

Cyclophilin J limits linear ubiquitin signaling and controls colorectal cancer progression

Exorbitant sustained inflammation is closely linked to inflammation-associated disorders, including cancer. The initiation of gastrointestinal cancers such as colorectal cancer (CRC) is frequently accelerated by uncontrollable chronic inflammation which is triggered by excessive activation of nuclear factor kappa-B (NF-κB) signaling. Linear ubiquitin chains play an important role in activating canonical NF-κB pathway. The only known E3 complex, linear ubiquitin assembly complex (LUBAC) is responsible for the synthesis of linear ubiquitin chains, thus leading to the activation of NF-κB axis and promoting the development of inflammation and inflammation-associated cancers. We report here cyclophilin J (CYPJ) is a negative regulator of the LUBAC. The N-terminus of CYPJ binds to the second Npl4-like zinc finger (NZF2) domain of HOIP and the ubiquitin-like (UBL) domain of SHARPIN to disrupt the interaction between HOIP and SHARPIN and thus restrains linear ubiquitin chain synthesis and NF-κB activation. Cypj-deficient mice are highly susceptible to dextran sulfate sodium (DSS)-induced colitis and DSS plus azoxymethane (AOM)-induced colon cancer. Moreover, CYPJ expression is induced by hypoxia. Patients with high expression of both CYPJ and hypoxia-inducible factor-1α (HIF-1α) have longer overall survival and progression-free survival. These results implicate CYPJ as an unexpected robust attenuator of inflammation-driven tumorigenesis that exerts its effects by controlling linear ubiquitin chain synthesis in NF-κB signal pathway.

Toward a policy landscape to support the product‐as‐a‐service design process for a circular economy

AbstractDespite the widely recognized potential of product‐as‐a‐service (PaaS) business models to contribute to the circular economy, many industrial case studies have reported that several systemic factors tend to hinder product manufacturers from effectively designing such solutions. More specifically, factors such as linear value chains, organizational structures, and market and financial conditions tend to restrict the freedom of product manufacturers to design circular PaaS solutions effectively. In this article, we take a novel approach to advance the body of knowledge concerning the interactions between policies and circular PaaS designing. We first explore the potential of the existing policy landscape to support designing for a circular economy in the manufacturing industry. The results suggest that the existing policy landscape is primarily focused on regulating product design outcomes and is thus deemed unsuitable for supporting circular PaaS designing. Subsequently, we investigate the literature to uncover how internal and external systemic factors may hinder the implementation of the key facets of circular PaaS designing in the manufacturing industry. Based on these findings, we propose a prospective policy framework that includes a mix of complementary policy interventions that systemically target the identified internal and external factors to support the implementation of the key facets of circular PaaS designing.

Thermal decomposition behaviors of adamantane and 1-methyladamantane in oxygen atmosphere: ReaxFF molecular dynamics simulation

High energy density fuels (HEDFs) have garnered considerable interest in the aerospace applications due to their high density and effective heat dissipation capabilities. However, there is still no clear understanding of the pyrolysis and oxidation mechanisms of HEDFs. In this work, a computational strategy based on ReaxFF molecular dynamics reveals dehydrogenation and ring-opening reaction events for adamantane and 1-methyladamantane. A comparative analysis of the initial decomposition behavior, intermediate reaction mechanism, and final product distribution demonstrates that the decay of the reactants is dependent on temperature and oxygen concentration. The main decomposition pathways of adamantane and 1-methyladamantane involve multi-step dehydrogenation and ring opening by the following reaction: i. C10H16 → C10H15 → C7H10 + C3H5, ii. C10H16 → C10H12, iii. C11H18 → C11H16, iv. C11H18 → C11H15 → C2H4 + C9H11. C7H10, C3H5, and C9H11 undergo further bond-breaking reactions to form linear hydrocarbon chains. At low temperatures, C10H16 and C11H18 exhibit a preference for reacting with OH and HO2, accounting for 15 %–35 % of the reactions. At high temperatures, the preferred reaction for C10H16 and C11H18 is with O2, accounting for 33 %–64 % of the reactions. The bridge carbon atom acts as the initial dehydrogenation site for both adamantane and 1-methyladamantane, as well as the active site for ring opening. The decomposition energy barrier for 1-methyladamantane (108.16–130.39 kJ/mol) is lower than that for adamantane (130.72–142.61 kJ/mol). Our findings shed light on the complicated interplay of oxidation of adamantane and 1-methyladamantane.

Ring Structures of Metal Atom Doped C9, C11, and C13 Clusters from Ab Initio Calculations-The Finding of a Gd@C13 Magnetic Superatom Ring.

Pure C9 clusters have a linear chain structure. However, here, we report using ab initio calculations the transformation of a chain into a cyclic ring structure with the capping of Ca, Sr, and Ba atoms. Further calculations on neutral and charged clusters doped with Sc, Y, and La atoms show stabilization of a cation C9 isoelectronic cyclic ring capped with the metal (M) atom, but anion clusters doped with these trivalent atoms form a C10 like MC9 ring, which deforms to a necklace structure. Both the ring structures correspond to electronic shell closing with 20 delocalized valence electrons in a disk jellium model and have a large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap. Calculations of IR and Raman spectra show no imaginary frequency, suggesting that the structures are stable. Addition of two C atoms to the ring structure of LaC9 leads to a capped ring structure of the cation LaC11 and an open ring structure of the LaC11 anion. Further addition of two C atoms leads to a La@C13 cation as well as Ca@C13 and Sr@C13 neutral wheel-shaped rings with endohedral doping of the M atom. These novel ring structures have a large HOMO-LUMO gap of more than 4 eV and are magic with electronic shell closing corresponding to 28 delocalized valence electrons in a disk jellium model. There is π aromaticity in this ring satisfying 4n+2 (n = 3) Hückel's rule with 14 valence electrons. Interestingly, when the dopant is a Gd atom, there is a formation of a magnetic superatom ring Gd@C13 + with 7 μB magnetic moments due to seven 4f up-spin states of Gd being fully occupied. Bonding in these novel ring structures is discussed.

Cd-Ln (Ln = Pr, Sm, Yb and Nd) heteronuclear complexes based on the linear chain ether Schiff base: Structural regulation and fluorescence properties

Four structurally different Cd-Ln heteronuclear complexes based on the linear chain ether Schiff base ligand (bis(3-methoxysalicylidene)-3-oxapentane-1,5-diamine (H2L) and the co-ligands 4,4′-bipyridine (bipy) or isonicotinate (IN), with composition [PrCd2L2(CH3COO)2](NO3)·CH2Cl2 (1), {[SmCdL(bipy)(NO3)3]·CH2Cl2·CH3CH2OH}n (2), [YbCdL(IN)(NO3)(CH3COO)]n (3) and {[Nd2Cd2L2(IN)2(NO3)2(CH3OH)2(CH3COO)](NO3)}n (4), have been synthesized by interfacial diffusion methods. Structural regulation is achieved by changes in the co-ligands or Ln(III) ions of different radii: Single crystal X-ray analysis determined that 1 is a trinuclear cluster with the Pr(III) ion as a joint bridging of two CdL coordination units; 2 and 3 are both infinite one-dimensional zigzag coordination polymers consisting of CdLnL secondary units through coordination bridging bipy or IN; 4 is a two-dimensional graphene laminate structure formed by two types of CdNdL secondary units bridged by both IN and acetate simultaneously. In the solid state, the complexes 1–4 all exhibit fluorescence peaks based on H2L with blue shift and enhancement. The order of fluorescence peaks intensity of the complexes in N,N-dimethylformamide (DMF) solution is consistent with that in the solid state. Moreover, the corresponding characteristic emissions of Sm(III) ion in complex 2 can be observed in the fluorescence spectra in either solid state and DMF solution, indicating that [CdL] unit is suitable for the sensitization of Sm(III) ion.

Investigating the synergetic effect of tungsten oxide doping into the 1,3-dicarbonyl moiety grafted chitosan and phytic acid impregnated sodium alginate for efficient U(VI) adsorption

In this work, chemical modification of the chitosan with ethyl acetoacetate was performed through a base-catalyzed reaction in which epichlorohydrin facilitated the insertion as well as nucleophilic substitution reaction to graft the 1,3-dioxo moiety across the linear chains of the base biopolymer to establish specificity and selectivity for U(VI) removal. The modified chitosan (EAA-CS) was intercalated into phosphate rich alginate matrix (PASA). Later on, the WO3-doped composites with different WO3 to PASA mass ratio were prepared and characterized using FTIR, XPS, SEM-EDS, XRD, and elemental mapping analysis. WO3 significantly contributed to chemically stable inorganic-organic composites with improved porous texture. Among the prepared composites, MCPS-3 microspherical beads, having mass ratio of 30.0 % w/w, exhibited excellent sorption capacity for U(VI) at an optimal pH 4.5. The successful U(VI) sorption was validated by the existence of two U4f peaks at 392.25 and 381.36 eV due to U4f5/2 and U4f7/2 sub-peaks with an intensity ratio of 3:4, respectively. Batch mode sorption kinetics followed pseudo-second-order rate equation (R2 ≈ 0.99, qe,th ≈ 116.88 mg/g, k2 = 0.86 × 10−4 g/mg.min−1) and equilibrium sorption data aligns with Langmuir (R2 = 0.99, qm = 343.85 mg/g at 310 K and pH = 4.5, KL = 2.00 × 10−2 L/mg) and Temkin models (R2 ≈ 0.99). Thermodynamic parameters ΔHo (30.51 kJ/mol), ΔSo (0.19 kJ/mol.K) and ΔGo (−25.64, −26.89, and − 27.91 kJ/mol) at 298, 305, and 310 K, respectively, suggested that the uptake process is feasible, endothermic and spontaneous. Based on these findings, it is reasonable to conclude that MCPS-3 could be a better hydrogel-based biomaterial for appreciable uranium recovery.

Unified understanding of the impact of semiflexibility, concentration, and molecular weight on macromolecular-scale ring diffusion

Conformationally fluctuating, globally compact macromolecules such as polymeric rings, single-chain nanoparticles, microgels, and many-arm stars display complex dynamic behaviors due to their rich topological structure and intermolecular organization. Synthetic rings are hybrid objects with conformations that display both ideal random walk and compact globular features, which can serve as models of genomic DNA. To date, emphasis has been placed on the effect of ring molecular weight on their unusual behaviors. Here, we combine simulations and a microscopic force-level theory to build a unified understanding for how key aspects of ring dynamics depend on different tunable molecular properties including backbone rigidity, monomer concentration, degree of traditional entanglement, and molecular weight. Our large-scale molecular dynamics simulations of ring melts with very different backbone stiffnesses reveal unanticipated behaviors which agree well with our generalized theory. This includes a universal master curve for center-of-mass diffusion constants as a function of molecular weight scaled by a chemistry and thermodynamic state-dependent critical molecular weight that generalizes the concept of an entanglement cross-over for linear chains. The key physics is how backbone rigidity and monomer concentration induced changes of the entanglement length, interring packing, degree of interpenetration, and liquid compressibility slow down space-time dynamic-force correlations on macromolecular scales. A power law decay of the center-of-mass diffusion constant with inverse molecular weight squared is the first consequence, followed by an ultraslow activated hopping transport regime. Our results set the stage to address slow dynamics and kinetic arrest in different families of compact synthetic and biological polymeric systems.

On Volganism and Tectonics in the Evolution of the Guyots of the Magellan Seamounts (Pacific Ocean)

This report is devoted to the analysis of original geological materials on the Magellan Seamounts in the Pacific Ocean, obtained by the authors in numerous voyages of R/V ʺGelendzhikʺ. This chain of guyouts does not have a common volcanic basement and apparently was formed in the second half of the Early Cretaceous on the oldest (middle-last Jurassic) fragment of the Pacific plate. The main points of view on the genesis of the Magellan Mountains are as follows: either they originated at the crossing of the transform fractures, or the Pacific plate moved them from the southern hemisphere to their present-day position. Because of their high degree of study, the Magellan Seamounts are one of the key sites for understanding the mechanism of the origin of linear chains in the ocean. A comprehensive analysis of new geological on the Magellan Seamounts has established the important role of magmatism and tectonics in the formation of the modern morphological shapes, sedimentation and influence on the paleooceangraphy. The periodic renewal of these processes from the Early Cretaceous to Late Cenozoic can be traced in the cyclicity of sedimentation, the permanent growth of ore crusts and the formation of secondary volcanic domes and cones.

Synthesis of All‐Benzene Multi‐Macrocyclic Nanocarbons by Post‐Functionalization of meta‐Cycloparaphenylenes

AbstractExpanding the diversity of multi‐macrocyclic nanocarbons, particularly those with all‐benzene scaffolds, represents intriguing yet challenging synthetic tasks. Complementary to the existing synthetic approaches, here we report an efficient and modular post‐functionalization strategy that employs iridium‐catalyzed C−H borylation of the highly strained meta‐cycloparaphenylenes (mCPPs) and an mCPP‐derived catenane. Based on the functionalized macrocyclic synthons, a number of novel all‐benzene topological structures including linear and cyclic chains, polycatenane, and pretzelane have been successfully prepared and characterized, thereby showcasing the synthetic utility and potential of the post‐functionalization strategy.

Synthesis of All-Benzene Multi-Macrocyclic Nanocarbons by Post-Functionalization of meta-Cycloparaphenylenes.

Expanding the diversity of multi-macrocyclic nanocarbons, particularly those with all-benzene scaffolds, represents intriguing yet challenging synthetic tasks. Complementary to the existing synthetic approaches, here we report an efficient and modular post-functionalization strategy that employs iridium-catalyzed C-H borylation of the highly strained meta-cycloparaphenylenes (mCPPs) and an mCPP-derived catenane. Based on the functionalized macrocyclic synthons, a number of novel all-benzene topological structures including linear and cyclic chains, polycatenane, and pretzelane have been successfully prepared and characterized, thereby showcasing the synthetic utility and potential of the post-functionalization strategy.

Spatially Confined Assembly and Immobilization of Hierarchical Nanoparticle Architectures inside Microdroplets in Magnetic Fields.

Magnetic field-directed colloidal interactions offer facile tools for assembly of structures that range from linear chains to multidimensional hierarchical architectures. While the field-driven assembly of colloidal particles has commonly been investigated in unbounded media, a knowledge gap remains concerning such assembly in confined microenvironments. Here, we investigate how confinement of ferromagnetic nanoparticles in microspheres directs their magnetic assembly into hierarchical architectures. Microdroplets from polydimethylsiloxane (PDMS) liquid precursor containing dispersed iron oxide magnetic nanoparticles (MNPs) were placed in a static magnetic field leading to the formation of organized assemblies inside the host droplets. By changing the MNP concentrations, we revealed a sequence of microstructures inside the droplets, ranging from linear chains at a low MNP loading, transitioning to a combination of chains and networked bundles, to solely 3D bundles at high MNP loading. These experimental results were analyzed with the aid of COMSOL simulations where we calculated the potential energy to identify the preferred assembly conformations. The chains at high MNP loading minimized their energy by aggregating laterally to form bundles with their MNP dipoles being out-of-registry. We cured these PDMS droplets to immobilize the assemblies by forming soft microbeads. These microbeads constitute an "interaction toolbox" with different magnetic macroscale responses, which are governed by the structuring of the MNPs and their magnetic polarizability. We show that thanks to their ability to rotate by field-induced torque under a rotating field, these microbeads can be employed in applications such as optical modulators and microrollers.

Highly branched thermoresponsive polysaccharide derivative in water. Partly substituted highly branched cyclic dextrin ethylcarbamate

A thermoresponsive highly branched polysaccharide derivative was revealed from commercially available highly branched cyclic dextrin (HBCD), originally synthesized from amylopectin. Eight samples of partially substituted ethyl carbamate derivatives of HBCD (HEC) were prepared with a degree of substitution DS ranging from 0.27 to 1.46. Three samples with DS = 0.88, 1.05, and 1.22 showed LCST type phase separation in water. The intrinsic viscosity and form factor in water were typical of the hyperbranched structure. The intermolecular interactions between HEC and iodine or 1-anilinonaphthalene-8-sulfonic acid (ANS) were appreciably different from those of the linear analog (AEC), suggesting that the locally bent helical conformation of highly branched HEC chains has a different interaction with small molecules. The phase diagram of HEC-water systems was accidentally similar to that of the linear chain with the same molar mass and DS, although the one phase region of the branched polymer chain-poor solvent system is usually wider than that of the corresponding linear chain. This is likely due to the lower hydration nature of the polymer segment of HEC chains than that of the corresponding linear chain.

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. Published by the American Physical Society 2024