Linear Polymer Chains Research Articles

Sliding dynamics of ring chain on graft polymer in rotaxane

Rotaxane is a mechanically interlocked molecule in which rings are threaded on the axial linear polymer chain, and a characteristic feature of rotaxane is that ring can slide along the axial chain. In this study, molecular dynamics simulations are performed to investigate the sliding dynamics of ring on a regular/random graft polymer with graft density f and side chain length Ns. The mean-square displacement g3(t) of ring exhibits a novel sub-diffusion behavior in the intermediate time range due to the interaction between the branches and ring, and the sub-diffusive regime occurs at g3(t)∼((Nc−1)*b2)2, qualitatively, where Nc is the number of monomers between two adjacent side chains and b is bond length. For ring chain sliding along either a regular graft polymer or a random one, the sliding dynamic of ring relies strongly on the side chain length Ns、graft density f、ring size as well as the distribution of branches in the graft polymer. The diffusion coefficient D of ring decreases with the increase of Ns or f. However, ring slides faster along the regular graft polymer than that random one, because the dense side chains in the random graft polymer greatly hinder the ring's mobility. The effect of regular distribution on the improved diffusion gets most obvious when the side-chain length is middle. These results may provide a fundamental view for the understanding the effect of topological structure of axial graft polymer chain on the sliding dynamics of ring in rotaxane.

Metamorphosis of a Commodity Plastic like PVC to Efficient Catalytic Single-Chain Nanoparticles.

We perform the conversion of a commodity plastic of common use in pipes, window frames, medical devices, flexible hoses, etc. like polyvinyl chloride (PVC) to single-chain nanoparticles (SCNPs). SCNPs are versatile, protein-mimetic soft nano-objects of growing interest for catalysis, sensing, and nanomedicine, among other uses. We demonstrate that the metamorphosis process -as induced through metal-free click chemistry- leads to well-defined, uniform SCNPs that are stable during storage in the solid state for months. All the conversion process (from PVC isolation to PVC-SCNPs synthesis) can be run in a green, dipolar aprotic solvent and involving, when required, a simple mixture of ethanol and water (1/1 vol.) as non-solvent. The resulting PVC-SCNPs are investigated as recyclable, metalloenzyme-mimetic catalysts for several representative Cu(II)-catalyzed organic reactions. The method could be valid for the metamorphosis and valorization of other commodity plastics in which it is feasible to install azide functional groups in their linear polymer chains.

Metamorphosis of a Commodity Plastic like PVC to Efficient Catalytic Single‐Chain Nanoparticles

AbstractWe perform the conversion of a commodity plastic of common use in pipes, window frames, medical devices, flexible hoses, etc. like polyvinyl chloride (PVC) to single‐chain nanoparticles (SCNPs). SCNPs are versatile, protein‐mimetic soft nano‐objects of growing interest for catalysis, sensing, and nanomedicine, among other uses. We demonstrate that the metamorphosis process ‐as induced through metal‐free click chemistry‐ leads to well‐defined, uniform SCNPs that are stable during storage in the solid state for months. All the conversion process (from PVC isolation to PVC‐SCNPs synthesis) can be run in a green, dipolar aprotic solvent and involving, when required, a simple mixture of ethanol and water (1/1 vol.) as non‐solvent. The resulting PVC‐SCNPs are investigated as recyclable, metalloenzyme‐mimetic catalysts for several representative Cu(II)‐catalyzed organic reactions. The method could be valid for the metamorphosis and valorization of other commodity plastics in which it is feasible to install azide functional groups in their linear polymer chains.

All-polymer nanocomposites having superior strength, toughness and ultralow energy dissipation

Toughening polymers has attracted significant interest. Traditionally, polymer toughness is enhanced by constructing polymer networks or introducing sacrificial bonds into the chains between crosslink points. These strategies, though, introduce pronounced energy dissipation and associated heat, both of which are undesirable under long-term cyclic loading, for example at the interface of implants in the human body. By incorporating single-chain nanoparticles (SCNPs) into linear polymer chains to generate all-polymer nanocomposites (APNCs), we have been able to achieve high strength, high toughness with low energy dissipation. Using a combination of simulation and experimental results, we are advancing a “SCNPs effect” where tightly cross-linked SCNPs produce a modulus contrast to achieve strengthening and toughening. Benefitting from the soft interface, the penetrable and deformable SCNPs cause the surrounding polymer chains to move in concert, significantly reducing the interfacial friction to achieve low energy dissipation. The intramolecular cross-linking of the SCNPs and adhesion between the SCNPs and polymer matrix are critical for realizing such high-performance systems. Based on a Gaussian regression model and back propagation (BP) neural network, the mechanical strength can be predicted and is supported by simulations. The APNC concept described can be applied to elastomers and gels, broadening its utilization in high-cycle and low-dissipation applications, like soft robots, flexible sensors and cartilage replacements, and artificial heart valves.

Thermally Reversible Cross-Linking of Recyclable Polyamide Materials Based on Schiff Base and Diels-Alder Reactions.

Recyclability of cross-link polymer materials is essential to alleviate environmental pollution caused by discarded or damaged polymers. Herein, a facile method for producing recyclable polyamide materials is developed. Linear polymer chains are constructed by Schiff base reaction between glutaraldehyde (GD) and furandiamine (FD). The linear polymer chains are crosslinked by bismaleimide (BM) to give rise to polyamide material, named GF-BMs. The resulting GF-BMs polyamide material possesses strong tensile strength (78MPa) and good solvent resistance from room temperature to 135 °C. Especially, the thermally reversible Diels-Alder covalent bonds and dynamic imine bonds in the polymer network have a synergistic effect on fast-reprocessing, self-healing, and recyclability, which provides a new idea for recyclable materials.

Open Linear Polymer Host-Guest Interactions Sensed by Luminescent Silver Nanodots.

The selectivity of the linear polymer chain toward its binding moieties has been considered negligible; thus, a clear demonstration showing the best-fit binding of a linear polymer to its guest counterpart is still unknown. Luminescent poly(acrylic acid) (PAA)-stabilized silver nanodots (PAA-AgNDs) have been applied as a turn-on sensor to monitor the interaction between the PAA chain and its binding cations. The binding of cations ions to the PAA chain may cross-link the linear PAA chain via coordination with carboxylate, which increases the rigidity of the polymer chain, retards the nonradiative decay of PAA-AgNDs, and consequently enhances the emission of silver nanodots while inducing a blue-shift of its emission spectrum. For the first time, we have demonstrated that a linear polymer chain can act as an open host to selectively bind to its best-matching cations. Specifically, among Group 2 cations (Mg2+, Ca2+, Sr2+, Ba2+), calcium ions show the strongest bonding to the PAA polymer chain. Our research suggests that, with extra rigidity, the polymer improves its chemical stability as calcium ions cross-linked the linear polymer. Meanwhile, it has also been demonstrated that luminescent silver nanodots can be excellent probes for the detection of polymer activities with straightforward and simple visualization methods.

Influence of solvent quality on the swelling and deswelling and the shear modulus of semi-dilute solution cross-linked poly(vinyl acetate) gels.

We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the hydrogel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory-Huggins mean field theory or the Flory-Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized.

Benzoxazine/amine-based polymer networks featuring stress-relaxation and reprocessability

Amines as additives in benzoxazines are known to beneficially affect the polymerization temperature and furthermore to allow for partially reversible reaction steps yielding however a non-dynamic polybenzoxazine network. This contribution proves that the polymerization behavior of a two-component polymer of the polyetheramine Jeffamine® ED-600 and a bisphenol-A-based benzoxazine features stress-relaxation and reprocessability usually known from vitrimers. With the aim to gain a deeper understanding of the material properties of this system and the corresponding polymer structure, the reaction mechanism of a monofunctional benzoxazine and monoamine model system was studied revealing at first primary, and then secondary amine induced opening of oxazine rings, leading at first to linear polymer chains and then to covalently crosslinked networks. Both consist of repeated phenolic benzoxazine/amine motifs with permanently incorporated polyetheramine chains that do not impact the mechanical properties, compared to pure polybenzoxazine. Thermal, spectroscopic, and extraction analyses show that the addition of Jeffamine® reduces the polymerization temperature and introduces material properties such as reprocessability at the same time. Stress-relaxation measurements support the assumption that the reprocessability point to vitrimer-like molecular processes. The material shows rapid stress-relaxation of up to 11 s, a corresponding bond-exchange activation energy of 146 kJ/mol, and a topology freezing temperature of 97°C.

A photocured bio-based shape memory thermoplastics for reversible wet adhesion

Development of reversible wet or underwater adhesives remains a grand challenge, because weakened intermolecular interactions by water molecules or/and low effective contact area cause poor interface to the wet surfaces, which significantly decreases adhesive strength. Herein, a new photocured, bio-based shape memory polymer (SMP) that shows both chemical and structural wet adhesion to various types of surfaces is developed. The SMP is polymerized from three monomers to form linear polymer chains dangled with hydrophobic side chains. The hydrogen acceptor and donor groups in the chains form hydrogen bonding with the surfaces, which is protected by the hydrophobic chains in the interface. The SMP shows tunable phase transition temperature (Tg) of 17–38 °C. In a rubbery state above Tg, the adhesive forms conformable contact with the targeted surfaces. Below Tg, a transition to a glassy state locks the conformed shapes to largely increase the effective contact area. As a result, the adhesive exhibits long-term underwater adhesion of >15 days with the best adhesion strength of ∼0.9 MPa. Its applications in leak repair, underwater on-skin sensors were demonstrated. This new, general strategy would pave avenues to designing bio-based, long-lasting, and reversible adhesives from renewable feedstocks for widespread applications.

Interfacial Photopolymerization: A Method for Light-Based Printing of Thermoplastics.

Ultraviolet (UV) printing of photopolymers is a widely adopted manufacturing method because of its high resolution and throughput. However, available printable photopolymers are typically thermosets, resulting in challenges in postprocessing and recycling of printed structures. Here, we present a new process called interfacial photopolymerization (IPP) which enables photopolymerization printing of linear chain polymers. In IPP, a polymer film is formed at the interface between two immiscible liquids, one containing a chain-growth monomer and the other containing a photoinitiator. We demonstrate the integration of IPP in a proof-of-concept projection system for printing of polyacrylonitrile (PAN) films and rudimentary multi-layer shapes . IPP shows in-plane and out-of-plane resolutions comparable to conventional photoprinting methods. Cohesive PAN films with number-average molecular weights greater than 15 kg mol-1 are obtained, and to our knowledge this is the first report of photopolymerization printing of PAN. A macrokinetics model of IPP is developed to elucidate the transport and reaction rates involved and evaluate how reaction parameters affect film thickness and print speed. Last, demonstration of IPP in a multilayer scheme suggests its suitabiliy for three-dimensional printing of linear-chain polymers.

From Glow to Growth: Chemiluminescence Induced Cationic Polymerization Using Ferrocenium Salt

AbstractChemiluminescence (CL) has recently emerged as a novel light source for triggering various photoreactions with appealing features such as the elimination of continuous power supply and complex instrumentation. Here, CL‐induced cationic photopolymerization using ferrocenium salts as unimolecular photoinitiators is reported. The ferrocenium salts, facilely synthesized via ligand exchange reactions, absorb the visible light emitted from CL reactions and generate Lewis acids capable of initiating the cationic polymerization of oxirane and vinyl monomers. The presented method can be applied to create linear polymer chains and cross‐linked luminescent polymer networks, which have significant potential in the fabrication of new polymeric materials and various bioapplications.

High thermal conductivity and excellent mechanical properties of liquid crystal co‐polyester based on hydron bond

AbstractHigh thermal conductivity liquid crystal polymer has become a hot topic in electronic device research. Herein, we introduce a series of thermotropic liquid crystals synthesized by diphenyl diol, m‐phthalic acid, and 5‐hydroxyisophthalic acid. The intermolecular forces are tuned by adjusting the ratio (0, 20%, 40%, 60%, 80%, 100%) of monomers containing hydrogen bond donors in copolymers. The formation and dissociation of hydrogen bonds are analyzed from the red shift and blue shift of infrared spectra at variable temperatures. The thermal conductivity is increased to 0.31 Wm−1 k−1. Meanwhile, its mechanical properties and thermal stability have improved significantly. A sharp increment of 2120% in tensile strength was observed, the maximum tensile strength is 17.39 MPa. While Young's modulus increased from 0.26 to 1.224 GPa. The increase in intermolecular forces is the main reason for this result. Moreover,X‐raysingle‐crystal diffraction, polarizing microscope, differential scanning calorimetry, and thermogravimetric analysis (TGA) were also analyzed to further explore the thermal conduction mechanism. The formation of hydrogen bonds makes the linear polymer chain segments undergo reversible cross‐linking, which affects their crystallization behavior and provides more thermal conduction pathways. By controlling the number of hydrogen bond donors to control the cross‐linking density, the thermal conductivity and mechanical properties can be greatly improved.

Strong, Supertough and Self‐Healing Biomimetic Layered Nanocomposites Enabled by Reversible Interfacial Polymer Chain Sliding

AbstractDespite the remarkable progress in ultrastrong mechanical laminate materials, the simultaneous achievement of toughness, stretchability and self‐healing properties in biomimetic layered nanocomposites remains a great challenge due to the intrinsic limitations of their hard essences and lack of effective stress transfer at the organic‐inorganic fragile boundary. Here, an ultratough nanocomposite laminate is prepared by constructing chain‐sliding cross‐linking at the interface between sulfonated graphene nanosheets and polyurethane layers based on the ring molecules sliding on the linear polymer chains to release stresses. Unlike traditional supramolecular bonding toughening with limited sliding spacing, our strategy enables interfacial molecular chains reversible slippage when the inorganic nanosheets bear stretching force, providing sufficient interlayer spatial distance for relative sliding to dissipate more energy. The resulting laminates exhibit strong strength (22.33 MPa), supertoughness (219.08 MJ m−3), ultrahigh stretchability (>1900 %) and self‐healing ability (99.7 %), which far surpass most of reported synthetic and natural laminate materials. Moreover, the fabricated proof‐of‐concept electronic skin shows excellent flexibility, sensitivity and healability for human physiological signals monitoring. This strategy breaks through the challenge that traditional layered nanocomposites are intrinsically stiff and opens up the functional application of layered nanocomposites in flexible devices.

Strong, Supertough and Self-Healing Biomimetic Layered Nanocomposites Enabled by Reversible Interfacial Polymer Chain Sliding.

Despite the remarkable progress in ultrastrong mechanical laminate materials, the simultaneous achievement of toughness, stretchability and self-healing properties in biomimetic layered nanocomposites remains a great challenge due to the intrinsic limitations of their hard essences and lack of effective stress transfer at the organic-inorganic fragile boundary. Here, an ultratough nanocomposite laminate is prepared by constructing chain-sliding cross-linking at the interface between sulfonated graphene nanosheets and polyurethane layers based on the ring molecules sliding on the linear polymer chains to release stresses. Unlike traditional supramolecular bonding toughening with limited sliding spacing, our strategy enables interfacial molecular chains reversible slippage when the inorganic nanosheets bear stretching force, providing sufficient interlayer spatial distance for relative sliding to dissipate more energy. The resulting laminates exhibit strong strength (22.33 MPa), supertoughness (219.08 MJ m-3 ), ultrahigh stretchability (>1900 %) and self-healing ability (99.7 %), which far surpass most of reported synthetic and natural laminate materials. Moreover, the fabricated proof-of-concept electronic skin shows excellent flexibility, sensitivity and healability for human physiological signals monitoring. This strategy breaks through the challenge that traditional layered nanocomposites are intrinsically stiff and opens up the functional application of layered nanocomposites in flexible devices.

Tuning the Thermometric Features in 1D Luminescent EuIII and TbIII Coordination Polymers through Different Bridge Phosphine Oxide Ligands.

TbIII and EuIII systems have been investigated as ratiometric luminescent temperature probes in luminescent coordination polymers due to TbIII → EuIII energy transfer (ET). To help understand how ion-ion separation, chain conformation as well as excitation channel impact their thermometric properties, herein, [Eu(tfaa)3(μ-L)Tb(tfaa)3]n one-dimensional (1D) coordination polymers (tfaa- = trifluoroacetylacetonate, and L = [(diphenylphosphoryl)R](diphenyl)phosphine oxide, R = ethyl - dppeo - or butyl - dppbo) were synthesized. The short μ-dppeo bridge ligand leads to a more linear 1D polymeric chain, while the longer μ-dppbo bridge leads to tighter packed chains. As the temperature rises from 80 K, upon direct TbIII excitation at 488 nm, the TbIII emission intensity decreases, while the EuIII emission intensity increases after 160 and 200 K when L = dppeo or dppbo, respectively. The temperature-dependent emission intensities, due to TbIII → EuIII ET, enable the development of ratiometric luminescent temperature probes featuring maximum relative thermal sensitivity up to 3.8% K-1 (250 K, L = dppbo, excitation at 488 nm). On the other hand, the same system displays maximum thermal sensitivity up to 3.5% K-1 (323 K) upon ligand excitation at 300 nm. Thus, by changing the excitation channel and bridge ligand that leads to modification of the polymer conformations, the maximum relative thermal sensitivity can be tuned.

Effects of Accelerated Aging on Thermal, Mechanical and Shape Memory Properties of Cyanate-Based Shape Memory Polymer: III Vacuum Thermal Cycling.

Shape memory polymers (SMPs) with intelligent deformability have shown great potential in the field of aerospace, and the research on their adaptability to space environments has far-reaching significance. Chemically cross-linked cyanate-based SMPs (SMCR) with excellent resistance to vacuum thermal cycling were obtained by adding polyethylene glycol (PEG) with linear polymer chains to the cyanate cross-linked network. The low reactivity of PEG overcame the shortcomings of high brittleness and poor deformability while endowing cyanate resin with excellent shape memory properties. The SMCR with a glass transition temperature of 205.8 °C exhibited good stability after vacuum thermal cycling. The SMCR maintained a stable morphology and chemical composition after repeated high-low temperature cycle treatments. The SMCR matrix was purified by vacuum thermal cycling, which resulted in an increase in its initial thermal decomposition temperature by 10-17 °C. The continuous vacuum high and low temperature relaxation of the vacuum thermal cycling increased the cross-linking degree of the SMCR, which improved the mechanical properties and thermodynamic properties of SMCR: the tensile strength of SMCR was increased by about 14.5%, the average elastic modulus was greater than 1.83 GPa, and the glass transition temperature increased by 5-10 °C. Furthermore, the shape memory properties of SMCR after vacuum thermal cycling treatment were well maintained due to the stable triazine ring formed by the cross-linking of cyanate resin. This revealed that our developed SMCR had good resistance to vacuum thermal cycling and thus may be a good candidate for aerospace engineering.

A hydrogel electrolyte with ultrahigh ionic conductivity and transference number benefit from Zn2+ “highways” for dendrite-free Zn-MnO2 battery

Aqueous zinc ion batteries (AZIBs) have been regarded as promising energy storage devices owing to high safety and abundant resources. However, it still remains a great challenge to solve the issue of Zn dendrites. So far, some efforts have been made to inhibit dendrites using hydrogels as electrolytes. Nevertheless, it’s more challenging to improve ionic conductivity of hydrogel electrolyte to ensure it’s high enough to provide an environment for rapid transmission of Zn2+. Therefore, new strategies that can simultaneously solve above problems must be explored. Herein, a semi-interpenetrating network P(PEGMEA-AM)/PAM hydrogel electrolyte (s-PPMHE) with molecular chain designability was innovatively constructed. Abundant functional C-O-C groups in linear polymer chain of s-PPMHE can reduce the electrostatic potential of hydrated Zn2+ and release trapped Zn2+, thus significantly accelerating Zn2+ migration with an ultrahigh transference number (tZn2+ = 0.82). Thanks to the unique structural design, s-PPMHE has good mechanical stability and coordination ability with Zn2+, which is conducive to constructing ion migration channels and immobilizing water molecules, thus alleviating water-related parasitic reactions. The theoretical calculation results reveal that s-PPMHE can regulate Zn2+ electric field distribution and boost desolvation kinetics. Therefore, the Zn||s-PPMHE||MnO2 cells exhibit excellent electrochemical performance involving high average coulombic efficiency of 98.9% and ultrahigh specific capacity of ∼ 300 mAh/g at 0.05C (97% of theoretical capacity). Furthermore, s-PPMHE delivers excellent ionic conductivity of 82.65 mS/cm and over 350 h zinc stripping/plating cycling properties. Moreover, the flexible pouch AZIBs based on s-PPMHE show stable voltage under different conditions. This work provides a novel and exploratory strategy for design of hydrogel electrolyte at molecular chain level, and opens up a new avenue to design functional hydrogel matrix for high-performance electrochemical devices.

A Facile yet Versatile Strategy to Construct Liquid Hybrid Energy-Saving Windows for Strong Solar Modulation.

Smart windows with light management and indoor solar heating modulation capacities are of paramount importance for building energy conservation. Thermochromic poly(N-isopropylacrylamide) (PNIPAm) hydrogel smart windows exhibit advantages of the relatively suitable transition temperature of 32 °C, high cost-effective and automatic passive sunlight regulation, but sustain slow response rate and unsatisfactory solar modulation efficiency. Herein, a strategy of one-step copolymerization of NIPAm and different olefine acids (OA) using reverse atom transfer radical polymerization method is developed to fabricate various chain/microparticle hybrids (CMH) for liquid energy-saving windows. Synergetic mechanisms of thermal-induced dissolution and aggregation of linear polymer chains integrated with water capture and release of microgel particles contribute to tunable light-scattering behaviors and adaptive solar modulation. Without any post-treatment, the as-prepared poly(N-isopropylacrylamide-co-acrylic acid) (P(NIPAm-co-AA))-based CMH suspension is injected into sandwich glass to construct energy-saving windows, which exhibits appreciated near-room-temperature transition (26.7 °C), rapid response (5 s), extraordinary luminous transmittance (91.5%), and solar modulation efficiency (85.8%), resulting in a substantial decline of indoor temperature of 24.5 °C in simulation experiment. Combining the versatile strategy with flexible adjustment on transition temperature, multifarious P(NIPAm-co-OA)-based CMH windows with eminent light management capacity are obtained. This work will powerfully promote the development and renovation of energy-efficient windows.

A computational package for measuring Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP)

Many materials, like polymer melts, solutions, biopolymers and textiles, are composed of entangled filaments. The entanglement in these systems significantly affects their mechanical properties and their function. We introduce the Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP) software, that enables to measure the topological and geometrical complexity in such systems. In particular, this software enables the computation of the Writhe, the Gauss linking integral and the Jones polynomial of each filament or pair of filaments in the system, whether they are open or closed. In particular, for systems employing Periodic Boundary Conditions (PBC), the software also allows to compute the total pairwise entanglement in PBC, using the Periodic linking number and the Periodic Writhe. For linear (open) chains, TEPPP can calculate all these topological parameters (including the Jones polynomial) without any closure scheme. In addition, TEPPP also enables measuring self and pairwise entanglement at different length-scales along a chain or a pair of chains. With appropriate preprocessing of input files, the code can also be used for star or branched architectures. We provide examples of how the code is used and we present results on the entanglement effect in polymers obtained using this package. We show how TEPPP can be used to measure the topological entanglement of linear polymer chains in a melt, revealing subtle entanglement transitions never seen before. We also used TEPPP to analyze the effect of knotting and its location in diblock copolymer melts, which reveals that knotting localization transition coincides with lamellar-disorder transition in these systems. Finally, we use TEPPP to reveal some of the topological structure of the SARS-CoV-2 Spike protein, which points to interesting structure in a region that contains the S1/S2 cleavage site. Program summaryProgram Title: Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP) softwareCPC Library link to program files:https://doi.org/10.17632/ygdbpnhpzw.1Developer's repository link:https://github.com/TEPPP-softwareLicensing provisions: BSD 3-clauseProgramming language: C++Supplementary material:Nature of problem: Measuring single and pairwise entanglement and knotting in systems of linear or ring filaments (open or closed curves) in 3-space or in systems employing Periodic Boundary Conditions (PBC) at different length scales.Solution method: TEPPP can be used to measure topological entanglement complexity in single or multi-chain filament systems in 3-space or in systems employing PBC. Given as input the coordinates of the curves, TEPPP can compute the Gauss linking integral, the Writhe, the Jones polynomial, the Periodic Linking Number and the Periodic Writhe. Also, TEPPP can measure effects of local linking and knotting using scanning methods along the chains.

Molecular dynamics simulations of the monomer density profiles of knotted ring polymer chains confined in a slit of two parallel walls with one attractive and another repulsive surface.

We have used Molecular Dynamics simulations to obtain the monomer density profiles for real linear and ring polymer chains of 360 monomers length with different topological structures such as simple knots: 31, 61, 91, 10124, complex knots 313151 and twisted knots with n = 10 and n = 20 in a slit geometry of two parallel walls with one attractive and another repulsive surface. We have used Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software to perform simulations with the Verlet integration algorithm. The interactions between monomers were simulated as Lennard-Jones 12-6 potential, for bonds we have used Finitely Extensible Nonlinear Elastic (FENE) potential and the interaction with the walls was taken into account via Lennard-Jones 9-3 potential. We observed that topologically complex polymers have lower monomer density profiles near the attractive wall, but at some distance in the direction to the repulsive wall this tendency changes to the opposite. We showed that most complex twisted knots have two maxima in narrow slits. In the wide slits we do not observe such relation for twisted knots at higher temperatures. These results are important for better understanding the nature of the depletion forces which arise in a slit geometry of two parallel walls with one attractive and one repulsive wall.