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Semiflexible Polymers II

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A special issue of Polymers (ISSN 2073-4360). This special issue belongs to the section "Polymer Physics and Theory".

Deadline for manuscript submissions: closed (15 August 2022) | Viewed by 37807

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Prof. Dr. Martin Kröger

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Guest Editor

Polymer Physics, Department of Materials, ETH Zurich, Leopold-Ruzicka-Weg 4, CH-8093 Zurich, Switzerland
Interests: polymer physics; computational physics; applied mathematics; stochastic differential equations; coarse-graining; biophysics
Special Issues, Collections and Topics in MDPI journals

Dr. Panayotis Benetatos

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Co-Guest Editor

Department of Physics, Kyungpook National University, Daugu, Republic of Korea
Interests: statistical mechanics of polymers; semiflexible polymers; elasticity

Special Issue Information

Dear Colleagues,

Further to the success of the Special Issue of Polymers “Semiflexible Polymers”, we are delighted to open a new Special Issue entitled “Semiflexible Polymers II”.

Semiflexible chains serve as a coarse-grained representation of macromolecules whenever random or self-avoiding walk statistics do not apply, i.e., when the dimensions of a macromolecule do not significantly exceed its persistence length. Semiflexibility also manifests itself when a polymer is strongly stretched, or when it is confined by boundaries. Prominent systems containing semiflexible chains are various biomolecules, such as DNA and the cytoskeletal filaments (F-actin, nanotubes, intermediate filaments), dendronized polymers, and their networks and brushes. Semiflexible chains are an integral part of polymer physics education. However, even if fundamental results have been obtained for linear semiflexible chains, the number of open issues is larger. The minimal theoretical model which acts as the classical paradigm in the field is the wormlike chain (WLC), a locally inextensible fluctuating one-dimensional curve with bending stiffness. Despite its appeal and success with long dsDNA, however, it is inadequate to describe the conformations and elasticity of many semiflexible systems. Electrostatic interactions, quenched or reversible inhomogeneities along the polymer contour, supramolecular structures (e.g., actin bundles, DNA nanotubes, which themselves may act as semiflexible building blocks of higher order assemblies), cross-links, helicity, and twist stiffness modify the simple uniform WLC behavior. Besides thermal and possibly quenched disorder, semiflexible polymers in living matter also experience active noise. The polymer itself may have activity, converting chemical energy to mechanical work, or it can be passive interacting with an active environment.

This Special Issue is concerned with the statics and dynamics, simulation and application of semiflexible polymers in the WLC framework and beyond, including linear, branched, ring, thick polymers and their networks or gels. Topics may include polymer solution or scaling behavior, knots, entanglements, interactions, lattice and continuous representations, buckling, bond breaking, translocation, scattering properties in both equilibrium and out-of-equilibrium situations. Papers may also address semiflexible chains subjected to flow and external stimuli or fields, semiflexible chains in composites or in biological systems, subjected to confinement, or as part of nematic or other networks. Ideally, contributions will focus on fundamental results, algorithms, mechanisms, statistical physics, and/or applications that will help to compile the current state of the art. Both original contributions and reviews are welcome.

Prof. Dr. Martin Kröger
Assoc. Prof. Panayotis Benetatos
Guest Editors

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Keywords

Semiflexible polymers
Wormlike polymers
Polymer brushes
Polymer physics
Bending
Buckling
Tumbling
Translocation
Networks
Entanglements
Liquid crystals
Composites
Confinement
Actin filaments
DNA
Supramolecular structures
Bundles
Electrostatic interactions
Active matter
Twist
Helicity
Disorder
Phase transitions

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Published Papers (14 papers)

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Research

23 pages, 5635 KiB

Open AccessArticle

Hydrodynamic and Polyelectrolyte Properties of Actin Filaments: Theory and Experiments

by Ernesto Alva, Annitta George, Lorenzo Brancaleon and Marcelo Marucho

Polymers 2022, 14(12), 2438; https://doi.org/10.3390/polym14122438 - 16 Jun 2022

Cited by 3 | Viewed by 2382

Abstract

Actin filament’s polyelectrolyte and hydrodynamic properties, their interactions with the biological environment, and external force fields play an essential role in their biological activities in eukaryotic cellular processes. In this article, we introduce a unique approach that combines dynamics and electrophoresis light-scattering experiments, an extended semiflexible worm-like chain model, and an asymmetric polymer length distribution theory to characterize the polyelectrolyte and hydrodynamic properties of actin filaments in aqueous electrolyte solutions. A fitting approach was used to optimize the theories and filament models for hydrodynamic conditions. We used the same sample and experimental conditions and considered several g-actin and polymerization buffers to elucidate the impact of their chemical composition, reducing agents, pH values, and ionic strengths on the filament translational diffusion coefficient, electrophoretic mobility, structure factor, asymmetric length distribution, effective filament diameter, electric charge, zeta potential, and semiflexibility. Compared to those values obtained from molecular structure models, our results revealed a lower value of the effective G-actin charge and a more significant value of the effective filament diameter due to the formation of the double layer of the electrolyte surrounding the filaments. Contrary to the data usually reported from electron micrographs, the lower values of our results for the persistence length and average contour filament length agree with the significant difference in the association rates at the filament ends that shift to sub-micro lengths, which is the maximum of the length distribution. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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11 pages, 885 KiB

Open AccessArticle

Constraint Release for Reptating Filaments in Semiflexible Networks Depends on Background Fluctuations

by Tina Händler, Cary Tutmarc, Jessica S. Freitag, David M. Smith and Jörg Schnauß

Polymers 2022, 14(4), 707; https://doi.org/10.3390/polym14040707 - 12 Feb 2022

Viewed by 1944

Abstract

Entangled semiflexible polymer networks are usually described by the tube model, although this concept has not been able to explain all experimental observations. One of its major shortcomings is neglecting the thermal fluctuations of the polymers surrounding the examined test filament, such that disentanglement effects are not captured. In this study, we present experimental evidence that correlated constraint release which has been predicted theoretically occurs in entangled, but not in crosslinked semiflexible polymer networks. By tracking single semiflexible DNA nanotubes embedded both in entangled and crosslinked F-actin networks, we observed different reptation dynamics in both systems, emphasizing the need for a revision of the classical tube theory for entangled polymer solutions. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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14 pages, 527 KiB

Open AccessArticle

Grafted Semiflexible Nunchucks with a Magnetic Bead Attached to the Free End

by Mohammadhosein Razbin and Panayotis Benetatos

Polymers 2022, 14(4), 695; https://doi.org/10.3390/polym14040695 - 11 Feb 2022

Cited by 1 | Viewed by 1737

Abstract

Semiflexible nunchucks are block copolymers, which consist of two long blocks of high bending stiffness jointed together by a short block of low bending stiffness. Semiflexible nunchucks that consist of two DNA nanorods jointed by a short segment of double-stranded (ds) DNA and confined in two dimensions have been used in recent experiments by Fygenson and coworkers as a tool to magnify the bending fluctuations of the linking dsDNA, which in turn are used to deduce the persistence length of dsDNA. In a recent theoretical analysis, we showed that in a semiflexible nunchuck with one end grafted, the fluctuations of the position of the free end that is transverse to the grafting direction exhibit a pronounced bimodality, provided that the bending stiffness of the hinge is not very large. In this article, we theoretically analyse a grafted semiflexible nunchuck with a magnetic bead attached to its free end. We show that a transverse magnetic field induces an asymmetry in the bimodal distribution of the transverse fluctuations of the free end. This asymmetry is very sensitive to interactions with a magnetic field and, in principle, could be used in magnetometry (the measurement of a magnetic field or the magnetic moment of the bead). We also investigate how the response of the bimodal distribution of the transverse fluctuations of the free end to a magnetic field depends on the bending stiffness of the nunchuck hinge. In addition, we analyse the closely related systems of a single filament and two filaments jointed at a kink point with one end grafted and the other end attached to a magnetic bead. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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13 pages, 2050 KiB

Open AccessArticle

From Strain Stiffening to Softening—Rheological Characterization of Keratins 8 and 18 Networks Crosslinked via Electron Irradiation

by Iman Elbalasy, Nils Wilharm, Erik Herchenhahn, Robert Konieczny, Stefan G. Mayr and Jörg Schnauß

Polymers 2022, 14(3), 614; https://doi.org/10.3390/polym14030614 - 4 Feb 2022

Cited by 6 | Viewed by 2392

Abstract

Networks of crosslinked keratin filaments are abundant in epithelial cells and tissues, providing resilience against mechanical forces and ensuring cellular integrity. Although studies of in vitro models of reconstituted keratin networks have revealed important mechanical aspects, the mechanical properties of crosslinked keratin structures remain poorly understood. Here, we exploited the power of electron beam irradiation (EBI) to crosslink in vitro networks of soft epithelial keratins 8 and 18 (k8–k18) filaments with different irradiation doses (30 kGy, 50 kGy, 80 kGy, 100 kGy, and 150 kGy). We combined bulk shear rheology with confocal microscopy to investigate the impact of crosslinking on the mechanical and structural properties of the resultant keratin gels. We found that irradiated keratin gels display higher linear elastic modulus than the unirradiated, entangled networks at all doses tested. However, at the high doses (80 kGy, 100 kGy, and 150 kGy), we observed a remarkable drop in the elastic modulus compared to 50 kGy. Intriguingly, the irradiation drastically changed the behavior for large, nonlinear deformations. While untreated keratin networks displayed a strong strain stiffening, increasing irradiation doses shifted the system to a strain softening behavior. In agreement with the rheological behavior in the linear regime, the confocal microscopy images revealed fully isotropic networks with high percolation in 30 kGy and 50 kGy-treated keratin samples, while irradiation with 100 kGy induced the formation of thick bundles and clusters. Our results demonstrate the impact of permanent crosslinking on k8–k18 mechanics and provide new insights into the potential contribution of intracellular covalent crosslinking to the loss of mechanical resilience in some human keratin diseases. These insights will also provide inspiration for the synthesis of new keratin-based biomaterials. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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13 pages, 1752 KiB

Open AccessArticle

Compression and Stretching of Confined Linear and Ring Polymers by Applying Force

by Wenduo Chen, Xiangxin Kong, Qianqian Wei, Huaiyu Chen, Jiayin Liu and Dazhi Jiang

Polymers 2021, 13(23), 4193; https://doi.org/10.3390/polym13234193 - 30 Nov 2021

Cited by 5 | Viewed by 2586

Abstract

We use Langevin dynamics to study the deformations of linear and ring polymers in different confinements by applying compression and stretching forces on their two sides. Our results show that the compression deformations are the results of an interplay among of polymer rigidity, degree of confinement, and force applied. When the applied force is beyond the threshold required for the buckling transition, the semiflexible chain under the strong confinement firstly buckles; then comes helical deformation. However, under the same force loading, the semiflexible chain under the weaker confinement exhibits buckling instability and shrinks from the folded ends/sides until it becomes three-folded structures. This happens because the strong confinement not only strongly reduces the buckling wavelength, but also increases the critical buckling force threshold. For the weakly confined polymers, in compression process, the flexible linear polymer collapses into condensed states under a small external force, whereas the ring polymer only shows slight shrinkage, due to the excluded volume interactions of two strands in the crowded states. These results are essential for understanding the deformations of the ring biomacromolecules and polymer chains in mechanical compression or driven transport. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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20 pages, 1609 KiB

Open AccessArticle

Shear-Thinning in Oligomer Melts—Molecular Origins and Applications

by Ranajay Datta, Leonid Yelash, Friederike Schmid, Florian Kummer, Martin Oberlack, Mária Lukáčová-Medvid’ová and Peter Virnau

Polymers 2021, 13(16), 2806; https://doi.org/10.3390/polym13162806 - 20 Aug 2021

Cited by 16 | Viewed by 3082

Abstract

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations of single chains in shear flow, we identify which of these phenomena are of collective nature and arise through interchain interactions and which are already present in dilute systems. Building upon these microscopic simulations, we identify by means of the Irving–Kirkwood formula the corresponding macroscopic stress tensor for a non-Newtonian polymer fluid. Shear-thinning effects in oligomer melts are also demonstrated by macroscopic simulations of channel flows. The latter have been obtained by the discontinuous Galerkin method approximating macroscopic polymer flows. Our study confirms the influence of microscopic details in the molecular structure of short polymers such as chain flexibility on macroscopic polymer flows. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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15 pages, 1358 KiB

Open AccessArticle

Densely Packed Tethered Polymer Nanoislands: A Simulation Study

by Nicolas Chen, Oleg Davydovich, Caitlyn McConnell, Alexander Sidorenko and Preston B. Moore

Polymers 2021, 13(15), 2570; https://doi.org/10.3390/polym13152570 - 1 Aug 2021

Viewed by 2325

Abstract

COordinated Responsive Arrays of Surface-Linked polymer islands (CORALS) allow for the creation of molecular surfaces with novel and switchable properties. Critical components of CORALs are the uniformly distributed islands of densely grafted polymer chains (nanoislands) separated by regions of bare surface. The grafting footprint and separation distances of nanoislands are comparable to that of the constituent polymer chains themselves. Herein, we characterize the structural features of the nanoislands and semiflexible polymers within to better understand this critical constituent of CORALs. We observe different characteristics of grafted semiflexible polymers depending on the polymer island’s size and distance from the center of the island. Specifically, the characteristics of the chains at the island periphery are similar to isolated tethered polymer chains (full flexible chains), while chains in the center of the island experience the neighbor effect such as chains in the classic polymer brush. Chains close to the edge of the islands exhibit unique structural features between these two regimes. These results can be used in the rational design of CORALs with specific interfacial characteristics and predictable responses to external stimuli. It is hoped that this the discussion of the different morphologies of the polymers as a function of distance from the edge of the polymer will find applications in a wide variety of systems. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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23 pages, 2528 KiB

Open AccessArticle

Blends of Semiflexible Polymers: Interplay of Nematic Order and Phase Separation

by Andrey Milchev, Sergei A. Egorov, Jiarul Midya, Kurt Binder and Arash Nikoubashman

Polymers 2021, 13(14), 2270; https://doi.org/10.3390/polym13142270 - 11 Jul 2021

Cited by 6 | Viewed by 2609

Abstract

Mixtures of semiflexible polymers with a mismatch in either their persistence lengths or their contour lengths are studied by Density Functional Theory and Molecular Dynamics simulation. Considering lyotropic solutions under good solvent conditions, the mole fraction and pressure is systematically varied for several [...] Read more.

κ

(the normalized persistence length) and chain length N. For binary mixtures with different chain length (i.e.,

N_{A} = 16

N_{B} = 32

or 64) but the same stiffness, isotropic-nematic phase coexistence is studied. For mixtures with the same chain length (

N = 32

) and large stiffness disparity (

κ_{B} / κ_{A} = 4.9

to 8), both isotropic-nematic and nematic-nematic unmixing occur. It is found that the phase diagrams may exhibit a triple point or a nematic-nematic critical point, and that coexisting phases differ appreciably in their monomer densities. The properties of the two types of chains (nematic order parameters, chain radii, etc.) in the various phases are studied in detail, and predictions on the (anisotropic) critical behavior near the critical point of nematic-nematic unmixing are made. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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11 pages, 1053 KiB

Open AccessArticle

Braiding Dynamics in Semiflexible Filament Bundles under Oscillatory Forcing

by Valentin M. Slepukhin and Alex J. Levine

Polymers 2021, 13(13), 2195; https://doi.org/10.3390/polym13132195 - 1 Jul 2021

Cited by 1 | Viewed by 1964

Abstract

We examine the nonequilibrium production of topological defects—braids—in semiflexible filament bundles under cycles of compression and tension. During these cycles, the period of compression facilitates the thermally activated pair production of braid/anti-braid pairs, which then may separate when the bundle is under tension. As a result, appropriately tuned alternating periods of compression and extension should lead to the proliferation of braid defects in a bundle so that the linear density of these pairs far exceeds that expected in the thermal equilibrium. Secondly, we examine the slow extension of braided bundles under tension, showing that their end-to-end length creeps nonmonotonically under a fixed force due to braid deformation and the motion of the braid pair along the bundle. We conclude with a few speculations regarding experiments on semiflexible filament bundles and their networks. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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17 pages, 509 KiB

Open AccessArticle

Orientational Fluctuations and Bimodality in Semiflexible Nunchucks

by Panayotis Benetatos and Mohammadhosein Razbin

Polymers 2021, 13(12), 2031; https://doi.org/10.3390/polym13122031 - 21 Jun 2021

Cited by 5 | Viewed by 3207

Abstract

Semiflexible nunchucks are block copolymers consisting of two long blocks with high bending rigidity jointed by a short block of lower bending stiffness. Recently, the DNA nanotube nunchuck was introduced as a simple nanoinstrument that mechanically magnifies the bending angle of short double-stranded (ds) DNA and allows its measurement in a straightforward way [Fygenson et al., Nano Lett. 2020, 20, 2, 1388–1395]. It comprises two long DNA nanotubes linked by a dsDNA segment, which acts as a hinge. The semiflexible nunchuck geometry also appears in dsDNA with a hinge defect (e.g., a quenched denaturation bubble or a nick), and in end-linked stiff filaments. In this article, we theoretically investigate various aspects of the conformations and the tensile elasticity of semiflexible nunchucks. We analytically calculate the distribution of bending fluctuations of a wormlike chain (WLC) consisting of three blocks with different bending stiffness. For a system of two weakly bending WLCs end-jointed by a rigid kink, with one end grafted, we calculate the distribution of positional fluctuations of the free end. For a system of two weakly bending WLCs end-jointed by a hinge modeled as harmonic bending spring, with one end grafted, we calculate the positional fluctuations of the free end. We show that, under certain conditions, there is a pronounced bimodality in the transverse fluctuations of the free end. For a semiflexible nunchuck under tension, under certain conditions, there is bimodality in the extension as a function of the hinge position. We also show how steric repulsion affects the bending fluctuations of a rigid-rod nunchuck. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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14 pages, 1811 KiB

Open AccessArticle

Comparison of Conformational Phase Behavior for Flexible and Semiflexible Polymers

by Dilimulati Aierken and Michael Bachmann

Polymers 2020, 12(12), 3013; https://doi.org/10.3390/polym12123013 - 16 Dec 2020

Cited by 10 | Viewed by 1878

Abstract

We employ the recently introduced generalized microcanonical inflection point method for the statistical analysis of phase transitions in flexible and semiflexible polymers and study the impact of the bending stiffness upon the character and order of transitions between random-coil, globules, and pseudocrystalline conformations. The high-accuracy estimates of the microcanonical entropy and its derivatives required for this study were obtained by extensive replica-exchange Monte Carlo simulations. We observe that the transition behavior into the compact phases changes qualitatively with increasing bending stiffness. Whereas the

Θ

collapse transition is less affected, the first-order liquid-solid transition characteristic for flexible polymers ceases to exist once bending effects dominate over attractive monomer-monomer interactions. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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29 pages, 5194 KiB

Open AccessArticle

Development of Coarse-Grained Models for Poly(4-vinylphenol) and Poly(2-vinylpyridine): Polymer Chemistries with Hydrogen Bonding

by Utkarsh Kapoor, Arjita Kulshreshtha and Arthi Jayaraman

Polymers 2020, 12(11), 2764; https://doi.org/10.3390/polym12112764 - 23 Nov 2020

Cited by 5 | Viewed by 4637

Abstract

In this paper, we identify the modifications needed in a recently developed generic coarse-grained (CG) model that captured directional interactions in polymers to specifically represent two exemplary hydrogen bonding polymer chemistries—poly(4-vinylphenol) and poly(2-vinylpyridine). We use atomistically observed monomer-level structures (e.g., bond, angle and torsion distribution) and chain structures (e.g., end-to-end distance distribution and persistence length) of poly(4-vinylphenol) and poly(2-vinylpyridine) in an explicitly represented good solvent (tetrahydrofuran) to identify the appropriate modifications in the generic CG model in implicit solvent. For both chemistries, the modified CG model is developed based on atomistic simulations of a single 24-mer chain. This modified CG model is then used to simulate longer (36-mer) and shorter (18-mer and 12-mer) chain lengths and compared against the corresponding atomistic simulation results. We find that with one to two simple modifications (e.g., incorporating intra-chain attraction, torsional constraint) to the generic CG model, we are able to reproduce atomistically observed bond, angle and torsion distributions, persistence length, and end-to-end distance distribution for chain lengths ranging from 12 to 36 monomers. We also show that this modified CG model, meant to reproduce atomistic structure, does not reproduce atomistically observed chain relaxation and hydrogen bond dynamics, as expected. Simulations with the modified CG model have significantly faster chain relaxation than atomistic simulations and slower decorrelation of formed hydrogen bonds than in atomistic simulations, with no apparent dependence on chain length. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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19 pages, 1764 KiB

Open AccessEditor’s ChoiceArticle

Topological Disentanglement of Linear Polymers under Tension

by Michele Caraglio, Boris Marcone, Fulvio Baldovin, Enzo Orlandini and Attilio L. Stella

Polymers 2020, 12(11), 2580; https://doi.org/10.3390/polym12112580 - 3 Nov 2020

Cited by 7 | Viewed by 2525

Abstract

We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semiflexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rules allow reconstructing the type and location of the knot moving on the chain Our theory is extensively benchmarked with corresponding molecular dynamics simulations and the results show a remarkable agreement between the simulations and the theoretical predictions of the model. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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19 pages, 952 KiB

Open AccessArticle

A Local-Exchange Model of Folding Chain Surface of Polymer Crystal Based on Worm-Like Chain Model within Single-Chain in Mean-Field Theory

by Hongyi Xiao, Xinghua Zhang and Dadong Yan

Polymers 2020, 12(11), 2555; https://doi.org/10.3390/polym12112555 - 30 Oct 2020

Viewed by 2444

Abstract

The structure of amorphous layer of folding surface controls the properties of the polymer lamellar crystal, which consists of chains with a loop conformation. The surface tension depends on the length and the distance between two injection points of the loop which involving the reptation motion and lateral exchange motion of the stems. In the present work, a local-exchange motion model based on the worm-like chain model is developed to investigate the effects of lateral motion of stems on the release the surface tension. The optimal distance between two injection points is determined by the balance of chain bending energy and conformational entropy. The numerical results provide evidences to the adjacent re-entry model for various loop lengths. A possible explanation involving density of injection points is proposed to interpret the mechanism. Full article

(This article belongs to the Special Issue Semiflexible Polymers II)

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