Polymer Length Research Articles

A Computer Simulation Study on Deposition Patterns of Cyclic Diblock Copolymer Solution Nanodroplets: Influence of Polymer Length and Concentration

A Computer Simulation Study on Deposition Patterns of Cyclic Diblock Copolymer Solution Nanodroplets: Influence of Polymer Length and Concentration

Folding behaviors of two-dimensional flexible polymers.

Unlike one-dimensional polymers, the theoretical framework on the behaviors of two-dimensional (2D) polymers is far from completeness. In this study, we model single-layer flexible 2D polymers of different sizes and examine their scaling behaviors in solution, represented by Rg ∼ Lν, where Rg is the radius of gyration and L is the side length of a 2D polymer. We find that the scaling exponent ν is 0.96 for a good solvent and 0.64 for under poor solvent condition. Interestingly, we observe a previously unnoticed phenomenon: under intermediate solvent conditions, the 2D polymer folds to maintain a flat structure, and as L becomes larger, multiple folded structures emerge. We introduce a shape parameter Q to diagram the relationship of folded structures with the polymer size and solvent condition. Theoretically, we explain the folding transitions by the competition between bending and solvophobic free energies.

Intrinsic Synergy and Selectivity for the Inhibition of Cancer Cell Growth Generated by a Polymer Ligand of Proximal Enzymes.

A fundamental understanding of the design of polymer ligands of proximal enzymes is essential for the precise targeting of cancer cells, but it is still in its infancy. In this study, we systematically investigated the contribution of the chain length, ligand density, and ligand ratio of proximal enzyme-targeted polymers to the efficacy, synergy, and selectivity for the inhibition of cancer cell proliferation. The results revealed that employing a moderate chain length as a scaffold allowed for an intrinsically high efficacy and synergy of proximal enzyme-targeted polymers, in contrast to single enzyme-targeted polymers that prefer longer chain length for efficacy. The synergy obtained in proximal enzyme targeting was not provided by the combination of the corresponding small molecules. Moreover, the maturation of the synergistic efficacy of the proximal enzyme-targeted polymers also improved selectivity. This study proposes a rational design for polymer inhibitors and/or ligands for cancer cells with a high efficacy and selectivity.

Deposition temperature-mediated growth of helically shaped polymers and chevron-type graphene nanoribbons from a fluorinated precursor

Graphene nanoribbons (GNRs) of precise size and shape, critical for controlling electronic properties and future device applications, can be realized via precision synthesis on surfaces using rationally designed molecular precursors. Fluorine-bearing precursors have the potential to form GNRs on nonmetallic substrates suitable for device fabrication. Here, we investigate the deposition temperature-mediated growth of a new fluorine-bearing precursor, 6,11-diiodo-1,4-bis(2-fluorophenyl)-2,3-diphenyltriphenylene (C42H24F2I2), into helically shaped polymer intermediates and chevron-type GNRs on Au(111) by combining scanning tunneling microscopy, X-ray photoelectron spectroscopy, and density functional theory simulations. The fluorinated precursors do not adsorb on the Au(111) surface at lower temperatures, necessitating an optimum substrate temperature to achieve maximum polymer and GNR lengths. We compare the adsorption behavior with that of pristine chevron precursors and discuss the effects of C-H and C-F bonds. The results elucidate the growth mechanism of GNRs with fluorine-bearing precursors and establish a foundation for future synthesis of GNRs on nonmetallic substrates.

A first proof of knot localization for polymers in a nanochannel

Abstract Based on polymer scaling theory and numerical evidence, Orlandini, Tesi, Janse van Rensburg and Whittington conjectured in 1996 that the limiting entropy of knot-type K lattice polygons is the same as that for unknot polygons, and that the entropic critical exponent increases by one for each prime knot in the knot decomposition of K. This Knot Entropy (KE) conjecture is consistent with the idea that for unconfined polymers, knots occur in a localized way (the knotted part is relatively small compared to polymer length). For full confinement (to a sphere or box), numerical evidence suggests that knots are much less localized. Numerical evidence for nanochannel or tube confinement is mixed, depending on how the size of a knot is measured. Here we outline the proof that the KE conjecture holds for polygons in the ∞ x 2 x 1 lattice tube and show that knotting is localized when a connected-sum measure of knot size is used. Similar results are established for linked polygons. This is the first model for which the knot entropy conjecture has been proved.

Fluidification of entangled polymers by loop extrusion

Loop extrusion is one of the main processes shaping chromosome organization across the cell cycle, yet its role in regulating deoxyribonucleic acid (DNA) entanglement and nucleoplasm viscoelasticity remains overlooked. We simulate entangled solutions of linear polymers under the action of generic loop extruding factors (LEFs) with a model that fully accounts for topological constraints and LEF-DNA uncrossability. We discover that extrusion drives the formation of bottlebrushlike structures which significantly lower the entanglement and effective viscosity of the system through an active fluidification mechanism. Interestingly, this fluidification displays an optimum at one LEF every 300–3000 base pairs. In marked contrast with entangled linear chains, the viscosity of extruded chains scales linearly with polymer length, yielding up to 1000-fold fluidification in our system. Our results illuminate how intrachain loop extrusion contributes to actively modulate genome entanglement and viscoelasticity . Published by the American Physical Society 2024

Electrolyte-Electrocatalyst Interfacial Effects of Polymeric Materials for Tandem CO2 Capture and Conversion Elucidated Using In Situ Electrochemical AFM.

Integrating CO2 capture and electrochemical conversion has been proposed as a strategy to reduce the net energy required for CO2 regeneration in traditional CO2 capture and conversion schemes and can be coupled with carbon-free renewable electricity. Polyethylenimine (PEI)-based materials have been previously studied as CO2 capture materials and can be integrated in these reactive capture processes. PEI-based electrolytes have been found to significantly increase the CO2 loading, and impact selectivity and rate of product formation when compared to the conventional aqueous electrolytes. However, the influence of these materials at the catalyst-electrode interface is currently not well understood. In this study, PEI-based electrolytes were prepared and their impact on the morphology of a silver electrode performing electrochemical CO2 reduction (CO2R) was studied using in situ electrochemical atomic force microscopy (EC-AFM). The presence of PEI on the electrode surface could be distinguished based on nanomechanical properties (DMT modulus), and changes were observed as negative polarization was applied, revealing a reorganization of the PEI chains due to electrostatic interactions. These changes were impacted by the electrolyte composition, including the addition of supporting electrolyte KHCO3 salt, as well as CO2 captured by the PEI-based electrolyte, which minimized the change in surface mechanical properties and degree of PEI alignment on the electrode surface. The changes in surface mechanical properties were also dependent on the PEI polymer length, with higher molecular weight PEI showing different reconfiguration than the shorter polymer brushes. The study highlights that the choice of polymer material, the electrolyte composition, and CO2 captured impact the near-electrode environment, which has implications for CO2R, and presents EC-AFM as a new tool that can be used to probe the dynamic behavior of these interfaces during electrocatalysis.

Surface Orthogonal Patterning and Bidirectional Self-Assembly of Nanoparticles Tethered by V-Shaped Diblock Copolymers.

We investigated the surface orthogonal patterning and bidirectional self-assembly of binary hairy nanoparticles (NPs) constructed by uniformly tethering a single NP with multiple V-shaped AB diblock copolymers using Brownian dynamics simulations in a poor solvent. At low concentration, the chain collapse and microphase separation of binary polymer brushes can lead to the patterning of the NP surface into A- and B-type orthogonal patches with various numbers of domains (valency), n = 1-6, that adopt spherical, linear, triangular, tetrahedral, square pyramidal, and pentagonal pyramidal configurations. There is a linear relationship between the valency and the average ratio of NP diameter to the polymers' unperturbed root-mean-square end-to-end distance for the corresponding valency. The linear slope depends on the grafting density and is independent of the interaction parameters between polymers. At high concentration, the orthogonal patch NPs serve as building blocks and exhibit directional attractions by overlapping the same type of domains, resulting in self-assembly into a series of fascinating architectures depending on the valency and polymer length. Notably, the 2-valent orthogonal patch NPs have the bidirectional bonding ability to form the two-dimensional (2D) square NP arrays by two distinct pathways. Simultaneously patching A and B blocks enables the one-step formation of 2D square arrays via bidirectional growth, whereas step-by-step patching causes the directional formation of 1D chains followed by 2D square arrays. Moreover, the gap between NPs in the 2D square arrays is related to the polymer length but independent of the NP diameter. These 2D square NP arrays are of significant value in practical applications such as integrated circuit manufacturing and nanotechnology.

Quantitative Comparison of the Hydration Capacity of Surface-Bound Dextran and Polyethylene Glycol.

We have quantified and compared the hydration capacity (i.e., capability to incorporate water molecules) of the two surface-bound hydrophilic polymer chains, dextran (dex) and poly(ethylene glycol) (PEG), in the form of poly(l-lysine)-graft-dextran (PLL-g-dex) and poly(l-lysine)-graft-poly(ethylene glycol) (PLL-g-PEG), respectively. The copolymers were attached to a negatively charged silica-titania surface through the electrostatic interaction between the PLL backbone and the surface in neutral aqueous media. While the molecular weights of PLL and PEG were fixed, that of dex and the grafting density of PEG or dex on the PLL were varied. The hydration capacity of the polymer chains was quantified through the combined experimental approach of optical waveguide lightmode spectroscopy (OWLS) and quartz crystal microbalance with dissipation monitoring (QCM-D) to yield a value for areal solvation (Ψ), i.e., mass of associated solvent molecules within the polymer chains per unit substrate area. For the two series of copolymers with comparable stretched chain lengths of hydrophilic polymers, namely, PLL(20)-g-PEG(5) and PLL(20)-g-dex(10), the Ψ values gradually increased as the initial grafting density on the PLL backbone increased or as g decreased. However, the rate of increase in Ψ was higher for PEG than dextran chains, which was attributed to higher stiffness of the dextran chains. More importantly, the number of water molecules per hydrophilic group was clearly higher for PEG chains. Given that the -CH2CH2O- units that make up the PEG chains form a cage-like structure with 2-3 water molecules, these "strongly bound" water molecules can account for the slightly more favorable behavior of PEG compared to dextran in both aqueous lubrication and antifouling behavior of the copolymers.

The function of CozE proteins is linked to lipoteichoic acid biosynthesis in Staphylococcus aureus.

Coordinated membrane and cell wall synthesis is vital for maintaining cell integrity and facilitating cell division in bacteria. However, the molecular mechanisms that underpin such coordination are poorly understood. Here we uncover the pivotal roles of the staphylococcal proteins CozEa and CozEb, members of a conserved family of membrane proteins previously implicated in bacterial cell division, in the biosynthesis of lipoteichoic acids (LTA) and maintenance of membrane homeostasis in Staphylococcus aureus. We establish that there is a synthetic lethal relationship between CozE and UgtP, the enzyme synthesizing the LTA glycolipid anchor Glc2DAG. By contrast, in cells lacking LtaA, the flippase of Glc2DAG, the essentiality of CozE proteins was alleviated, suggesting that the function of CozE proteins is linked to the synthesis and flipping of the glycolipid anchor. CozE proteins were indeed found to modulate the flipping activity of LtaA in vitro. Furthermore, CozEb was shown to control LTA polymer length and stability. Together, these findings establish CozE proteins as novel players in membrane homeostasis and LTA biosynthesis in S. aureus.IMPORTANCELipoteichoic acids are major constituents of the cell wall of Gram-positive bacteria. These anionic polymers are important virulence factors and modulators of antibiotic susceptibility in the important pathogen Staphylococcus aureus. They are also critical for maintaining cell integrity and facilitating proper cell division. In this work, we discover that a family of membrane proteins named CozE is involved in the biosynthesis of lipoteichoic acids (LTAs) in S. aureus. CozE proteins have previously been shown to affect bacterial cell division, but we here show that these proteins affect LTA length and stability, as well as the flipping of glycolipids between membrane leaflets. This new mechanism of LTA control may thus have implications for the virulence and antibiotic susceptibility of S. aureus.

Optimizing Binding among Bimolecular Tethered Complexes.

Tethered motion is ubiquitous in nature, offering controlled movement and spatial constraints to otherwise chaotic systems. The enhanced functionality and practical utility of tethers has been exploited in biotechnology, catalyzing the design of novel biosensors and molecular assembly techniques. While notable technological advances incorporating tethered motifs have been made, a theoretical gap persists within the paradigm, hindering a comprehensive understanding of tethered-based technologies. In this work, we focus on the characterization of the binding kinetics of two tethered molecules functionalized to a hard surface. Using a mean-field approximation, the binding time of such bimolecular system is determined analytically. Furthermore, estimates of the grafting site separation and polymer lengths which expedite binding are provided. These estimates, along with the analytical theories and frameworks established here, have the potential to improve efficacy in self-assembly methods in DNA nanotechnology and can be extended to more biologically specific endeavors including targeted drug-delivery and molecular sensing.

Translocation of two-dimensional active polymers through nanopores using Langevin dynamics simulations.

The translocation of polymers through nanopores is a complex process influenced by various factors. In this study, the translocation behavior of a two-dimensional active polymer chain, comprised of a head active Brownian particle (ABP) and a tail passive polymer chain, through a nanopore is studied using Langevin dynamics simulations. Results show that the effect of the self-propulsion force of the ABP on the translocation differs significantly from the driving force inside the pore for traditional polymer translocations. Specifically, the translocation time τ initially increases with increasing the magnitude fs of the self-propulsion force and then decreases with a further increase in fs. A small fs lowers the potential barrier for the translocation and thus promotes slow translocations, whereas a large fs directly pulls the polymer chain through the nanopore following the scaling relation τ ∝ fs-1. Moreover, two asymptotic scaling relations between τ and polymer length N, τ ∝ Nα, are found, with the exponent α of about 2.5 for small fs or long N and the exponent α of about 1.4 for short active polymers with large fs. We discover that the slow rotation of the ABP accelerates the translocation process.

Nonlinear Elastic Bottlebrush Polymer Hydrogels Modulate Actomyosin Mediated Protrusion Formation in Mesenchymal Stromal Cells.

The nonlinear elasticity of many tissue-specific extracellular matrices is difficult to recapitulate without the use of fibrous architectures, which couple strain-stiffening with stress relaxation. Herein, bottlebrush polymers are synthesized and crosslinked to form poly(ethylene glycol)-based hydrogels and used to study how strain-stiffening behavior affects human mesenchymal stromal cells (hMSCs). By tailoring the bottlebrush polymer length, the critical stress associated with the onset of network stiffening is systematically varied, and a unique protrusion-rich hMSC morphology emerges only at critical stresses within a biologically accessible stress regime. Local cell-matrix interactions are quantified using 3D traction force microscopy and small molecule inhibitors are used to identify cellular machinery that plays a critical role in hMSC mechanosensing of the engineered, strain-stiffening microenvironment. Collectively, this study demonstrates how covalently crosslinked bottlebrush polymer hydrogels can recapitulate strain-stiffening biomechanical cues at biologically relevant stresses and be used to probe how nonlinear elastic matrix properties regulate cellular processes.

Translocation of polymers through a wide-open conical pore

The transport of biomolecules across a cell membrane is an important phenomenon that plays a pivotal role in the functioning of biological cells. In this paper, we investigate such processes by modeling the translocation of polymers through a conical channel, directed from the wider opening to the narrow end of the conical channel. We use the molecular dynamics approach to study the problem. The effect of the different conical pore geometry and polymer lengths on translocation dynamics is determined from the behavior of the total translocation time, τ, and the waiting time distributions, w(s). The escape of polymer segments from the narrow end of the conical channel is tracked by studying the escape velocity profile (〈v i 〉). To demonstrate the asymmetric pore effects on the translocation dynamics, we compare the translocation process from both the terminals: the wider-opening and the narrow-end of the conical channel. We find striking differences in the translocation dynamics for both processes, which are in agreement with the experimental study. We have accounted for the effect of various rigidity, and increasing length of a polymer chain, on both types of processes. This computational study can be used to underline the translocation process from different conical pores.

Fine tuning of the net charge alternation of polyzwitterion surfaced lipid nanoparticles to enhance cellular uptake and membrane fusion potential

ABSTRACT Lipid nanoparticles (LNPs) coated with functional and biocompatible polymers have been widely used as carriers to deliver oligonucleotide and messenger RNA therapeutics to treat diseases. Poly(ethylene glycol) (PEG) is a representative material used for the surface coating, but the PEG surface-coated LNPs often have reduced cellular uptake efficiency and pharmacological activity. Here, we demonstrate the effect of pH-responsive ethylenediamine-based polycarboxybetaines with different molecular weights as an alternative structural component to PEG for the coating of LNPs. We found that appropriate tuning of the molecular weight around polycarboxybetaine-modified LNP, which incorporated small interfering RNA, could enhance the cellular uptake and membrane fusion potential in cancerous pH condition, thereby facilitating the gene silencing effect. This study demonstrates the importance of the design and molecular length of polymers on the LNP surface to provide effective drug delivery to cancer cells.

Plastic hinge behavior of rectangular CFRP-confined RC columns: Meso-scale modelling and formulation

The ultimate rotation capacity, depending on the plastic hinge length, is a vital factor in the seismic design of flexural members. This paper focuses on the investigation of the plastic hinge length and size effect of rectangular carbon fiber-reinforced polymer (CFRP)-confined reinforced concrete (RC) columns. Firstly, considerable scatter and evident bias of the calculation results were found after evaluating existing models for calculating the plastic hinge length of FRP-confined RC columns. Accordingly, a meso-scale numerical approach was developed, with concrete heterogeneity considered, to investigate the influences of the confinement ratio and corner radius on the plastic hinge length and size effect of rectangular CFRP-confined RC columns. Results show that columns having different cross-sectional sizes exhibit similar failure patterns, and the region of lateral crack propagation for columns with lower confinement ratios is larger than that for columns with higher confinement ratios. The actual plastic hinge length is determined based on the yielding zone of reinforcement, the crushing zone of concrete, and the localization zone of curvature, while the localization zone of curvature is employed to determine the real plastic hinge zone. The size effect is found to exist in the plastic hinge length ratio, and it is weakened with the increase of the corner radius, which can be attributed to the fact that columns with higher corner ratios have more effective confinement. Taking into account the size effect, a new model for calculating the ultimate drift ratio of CFRP-confined RC columns was proposed based on an assumption of curvature distribution and presented accurate predictions.

Depletion Interactions at Interfaces Induced by Ferromagnetic Colloidal Polymers.

The pair-interaction force profiles for two non-magnetic colloids immersed in a suspension of ferromagnetic colloidal polymers are investigated via Langevin simulations. A quasi-two-dimensional approach is taken to study the interface case and a range of colloidal size ratios (non-magnetic:magnetic) from 6:1 up to 20:1 have been considered in this work. Simulations show that when compared with non-magnetic suspensions, the magnetic polymers strongly modify the depletion force profiles leading to strongly oscillatory behavior. Larger polymer densities and size ratios increase the range of the depletion forces, and in general, also their strength; the force barrier peaks at short distances show more complex behavior. As the length of the ferromagnetic polymers increases, the force profiles become more regular, and stable points with their corresponding attraction basins develop. The number of stable points and the distance at which they occur can be tuned through the modification of the field strength H and the angle θ formed by the field and the imaginary axis joining the centers of the two non-magnetic colloids. When not constrained, the net forces acting on the two colloids tend to align them with the field till θ=0∘. At this angle, the force profiles turn out to be purely attractive, and therefore, these systems could be used as a funneling tool to form long linear arrays of non-magnetic particles. Torsional forces peak at θ=45∘ and have minimums at θ=0∘ as well as θ=90∘ which is an unstable orientation as slight deviations will evolve towards θ→0∘. Nonetheless, results suggest that the θ=90∘ orientation could be easily stabilized in several ways. In such a case, the stable points that the radial force profiles exhibit for this orthogonal orientation to the field could be used to control the distance between the two large colloids: their position and number can be controlled via H. Therefore, suspensions made of ferromagnetic colloidal polymers can be also useful in the creation of magnetic colloidal tweezers or ratchets. A qualitative explanation of all the observed phenomena can be provided in terms of how the geometrical constraints and the external field modify the conformations of the ferromagnetic polymers near the two large particles, and in turn, how both factors combine to create unbalanced Kelvin forces that oscillate in strength with the distance between the two non-magnetic colloids.

A molecular dynamics study on the solid–liquid polymer interface: insight into the effect of surface roughness scale and polymer chain length on interfacial thermal resistance

Understanding the role of surface morphology and molecular structure interface thermal transport is essential for designing thermal management materials. In the present work, models of solid–liquid interfaces were created by placing liquid n-alkane between two platinum crystals. The effect of different levels of crystal surface roughness–flat, small, and large-scale grooves–and polymer chain lengths, under varying solid–liquid affinity, on the interface thermal resistance (ITR) were assessed using non-equilibrium molecular dynamics simulations. The overall trend confirmed that grooved surfaces have higher ITR than flat surfaces at low affinity, and lower ITR values were observed at high affinity. Large grooves enabled more favourable polymer orientations than those of small grooves, resulting in a smaller ITR. However, long chains did not facilitate heat transfer normal to the interface because they preferentially aligned parallel to it. For efficient heat transfer, a balance between the roughness scale and polymer length must be considered.

Effect of GFRP bar diameter and concrete cover on bond and development length in UHPFRC

This study investigates the bond strength and development length of glass fiber-reinforced polymer (GFRP) sand-coated bars embedded into ultra-high-performance fiber-reinforced concrete (UHPFRC) with 2% steel fibers. A total of 42 notched beams following the RILEM RC5 standard bond test method were fabricated. The study focused on three GFRP bar sizes (#4, 5 and 8) with diameters (db) of 13.5 mm, 17.3 mm and 27.0 mm, while varying the concrete cover to the center of the bar (C) from 20 mm to 55 mm, which results in C/db ratio ranging from 1.0 to 3.7. Three embedment lengths (Le) for each case were used: 4db, 9db and 14db. The study established a correlation between development length (Ld) and (C/db). All beams, except for four, failed by splitting bond failure as would be expected. ACI440.11–22 code equations significantly overestimated bond strength at low (Le/db) ratios and underestimated it at high (Le/db) ratios as well as overestimated Ld by factors of 2.0 to 3.5. The Michaud et al. (2021) design equation for Ld which is intended for UHPFRC had limitations in that it does not account for C or db. As such, at lower C/db ratios (i.e. at small concrete covers), it underestimated Ld while at higher C/db ratios (i.e. at larger cover), it overestimated Ld. A new general equation for Ld has been developed using the combined database, accounting for all critical parameters.

Particle Size-Dependent Electrophoresis in Polymer Solutions.

It has long been known that the electrophoretic velocity of a charged particle is independent of its size under the thin-Debye-layer limit. This so-called Smoluchowski velocity is, however, valid only for Newtonian fluids. A couple of recent theoretical studies predict the rheology-induced particle size dependence of electrophoresis in non-Newtonian fluids. This work presents the first experimental demonstration of such dependence in viscoelastic poly(ethylene oxide) (PEO) solutions. Three different-sized particles are observed to travel at the same electrophoretic velocity in a Newtonian buffer through a rectangular microchannel. In contrast, their measured electrophoretic velocities in the PEO solution exhibit an increasing trend for larger particles, which is consistent with theoretical prediction. This particle size dependence is found to grow with an increasing concentration or length of the PEO polymer. Both trends are attributed to enhanced fluid elasticity, as characterized by the increasing elasticity number.