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704 KiB

Open AccessArticle

Unfolding Kinetics of a Wormlike Chain under Elongational Flow

by Theo Odijk

Polymers 2017, 9(6), 190; https://doi.org/10.3390/polym9060190 - 26 May 2017

Cited by 2 | Viewed by 4767

Abstract

A simple theory of the unfolding kinetics of a semi-flexible polymer chain is presented in terms of a Kramers type picture for the energy of elongation. The hydrodynamic interactions are discussed in terms of slender body theory. It turns out that the elongation [...] Read more.

A simple theory of the unfolding kinetics of a semi-flexible polymer chain is presented in terms of a Kramers type picture for the energy of elongation. The hydrodynamic interactions are discussed in terms of slender body theory. It turns out that the elongation of the chain is basically linear in time and independent of the viscosity. The former prediction agrees with experiments on the stretching dynamics of DNA under planar elongational flow. Nevertheless, the theory overestimates the experimental rate by a significant amount for reasons that are unclear. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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5378 KiB

Open AccessArticle

Carbon Nanotube Length Governs the Viscoelasticity and Permeability of Buckypaper

by Zhiqiang Shen, Magnus Röding, Martin Kröger and Ying Li

Polymers 2017, 9(4), 115; https://doi.org/10.3390/polym9040115 - 23 Mar 2017

Cited by 20 | Viewed by 7849

Abstract

The effects of carbon nanotube (CNT) length on the viscoelasticity and permeability of buckypaper, composed of (5,5) single-walled CNTs (SWCNTs), are systematically explored through large-scale coarse-grained molecular dynamics simulations. The SWCNT length is found to have a pronounced impact on the structure of [...] Read more.

The effects of carbon nanotube (CNT) length on the viscoelasticity and permeability of buckypaper, composed of (5,5) single-walled CNTs (SWCNTs), are systematically explored through large-scale coarse-grained molecular dynamics simulations. The SWCNT length is found to have a pronounced impact on the structure of buckypapers. When the SWCNTs are short, they are found to form short bundles and to be tightly packed, exhibit high density and small pores, while long SWCNTs are entangled together at a low density accompanied by large pores. These structure variations contribute to distinct performances in the viscoelasticity of buckypapers. The energy dissipation for buckypapers with long SWCNTs under cyclic shear loading is dominated by the attachment and detachment between SWCNTs through a zipping-unzipping mechanism. Thus, the viscoelastic characteristics of buckypapers, such as storage and loss moduli, demonstrate frequency- and temperature-independent behaviors. In contrast, the sliding-friction mechanism controls the energy dissipation between short SWCNTs when the buckypaper is under loading and unloading processes. Friction between short SWCNTs monotonically increases with rising length of SWCNTs and temperature. Therefore, the

tan δ

, defined as the ratio of the loss modulus over the storage modulus, of buckypaper with short SWCNTs also increases with the increment of temperature or SWCNT length, before the SWCNTs are entangled together. The permeability of buckypapers is further investigated by studying the diffusion of structureless particles within buckypapers, denoted by the obstruction factor (

β

). It is found to be linearly dependent on the volume fraction of SWCNTs, signifying a mass-dominated permeability, regardless of the structure variations induced by different SWCNT lengths. The present study provides a comprehensive picture of the structure-property relationship for buckypapers composed of SWCNTs. The methodology could be used for designing multifunctional buckypaper-based devices. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1724 KiB

Open AccessArticle

Buckling a Semiflexible Polymer Chain under Compression

by Ekaterina Pilyugina, Brad Krajina, Andrew J. Spakowitz and Jay D. Schieber

Polymers 2017, 9(3), 99; https://doi.org/10.3390/polym9030099 - 11 Mar 2017

Cited by 11 | Viewed by 7450

Abstract

Instability and structural transitions arise in many important problems involving dynamics at molecular length scales. Buckling of an elastic rod under a compressive load offers a useful general picture of such a transition. However, the existing theoretical description of buckling is applicable in [...] Read more.

Instability and structural transitions arise in many important problems involving dynamics at molecular length scales. Buckling of an elastic rod under a compressive load offers a useful general picture of such a transition. However, the existing theoretical description of buckling is applicable in the load response of macroscopic structures, only when fluctuations can be neglected, whereas membranes, polymer brushes, filaments, and macromolecular chains undergo considerable Brownian fluctuations. We analyze here the buckling of a fluctuating semiflexible polymer experiencing a compressive load. Previous works rely on approximations to the polymer statistics, resulting in a range of predictions for the buckling transition that disagree on whether fluctuations elevate or depress the critical buckling force. In contrast, our theory exploits exact results for the statistical behavior of the worm-like chain model yielding unambiguous predictions about the buckling conditions and nature of the buckling transition. We find that a fluctuating polymer under compressive load requires a larger force to buckle than an elastic rod in the absence of fluctuations. The nature of the buckling transition exhibits a marked change from being distinctly second order in the absence of fluctuations to being a more gradual, compliant transition in the presence of fluctuations. We analyze the thermodynamic contributions throughout the buckling transition to demonstrate that the chain entropy favors the extended state over the buckled state, providing a thermodynamic justification of the elevated buckling force. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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2111 KiB

Open AccessArticle

Demixing by a Nematic Mean Field: Coarse-Grained Simulations of Liquid Crystalline Polymers

by Abelardo Ramírez-Hernández, Su-Mi Hur, Julio C. Armas-Pérez, Monica Olvera de la Cruz and Juan J. De Pablo

Polymers 2017, 9(3), 88; https://doi.org/10.3390/polym9030088 - 3 Mar 2017

Cited by 20 | Viewed by 8411

Abstract

Liquid crystalline polymers exhibit a particular richness of behaviors that stems from their rigidity and their macromolecular nature. On the one hand, the orientational interaction between liquid-crystalline motifs promotes their alignment, thereby leading to the emergence of nematic phases. On the other hand, [...] Read more.

Liquid crystalline polymers exhibit a particular richness of behaviors that stems from their rigidity and their macromolecular nature. On the one hand, the orientational interaction between liquid-crystalline motifs promotes their alignment, thereby leading to the emergence of nematic phases. On the other hand, the large number of conﬁgurations associated with polymer chains favors formation of isotropic phases, with chain stiffness becoming the factor that tips the balance. In this work, a soft coarse-grained model is introduced to explore the interplay of chain stiffness, molecular weight and orientational coupling, and their role on the isotropic-nematic transition in homopolymer melts. We also study the structure of polymer mixtures composed of stiff and ﬂexible polymeric molecules. We consider the effects of blend composition, persistence length, molecular weight and orientational coupling strength on the melt structure at the nano- and mesoscopic levels. Conditions are found where the systems separate into two phases, one isotropic and the other nematic. We conﬁrm the existence of non-equilibrium states that exhibit sought-after percolating nematic domains, which are of interest for applications in organic photovoltaic and electronic devices. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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8701 KiB

Open AccessArticle

Trapping a Knot into Tight Conformations by Intra-Chain Repulsions

by Liang Dai and Patrick S. Doyle

Polymers 2017, 9(2), 57; https://doi.org/10.3390/polym9020057 - 10 Feb 2017

Cited by 16 | Viewed by 5867

Abstract

Knots can occur in biopolymers such as DNA and peptides. In our previous study, we systematically investigated the effects of intra-chain interactions on knots and found that long-range repulsions can surprisingly tighten knots. Here, we use this knowledge to trap a knot into [...] Read more.

Knots can occur in biopolymers such as DNA and peptides. In our previous study, we systematically investigated the effects of intra-chain interactions on knots and found that long-range repulsions can surprisingly tighten knots. Here, we use this knowledge to trap a knot into tight conformations in Langevin dynamics simulations. By trapping, we mean that the free energy landscape with respect to the knot size exhibits a potential well around a small knot size in the presence of long-range repulsions, and this potential can well lead to long-lived tight knots when its depth is comparable to or larger than thermal energy. We tune the strength of intra-chain repulsion such that a knot is weakly trapped. Driven by thermal fluctuations, the knot can escape from the trap and is then re-trapped. We find that the knot switches between tight and loose conformations—referred to as “knot breathing”. We use a Yukawa potential to model screened electrostatic interactions to explore the relevance of knot trapping and breathing in charged biopolymers. We determine the minimal screened length and the minimal strength of repulsion for knot trapping. We find that Coulomb-induced knot trapping is possible to occur in single-stranded DNA and peptides for normal ionic strengths. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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3984 KiB

Open AccessArticle

Entropic Interactions between Two Knots on a Semiflexible Polymer

by David Richard, Stefanie Stalter, Jonathan Tammo Siebert, Florian Rieger, Benjamin Trefz and Peter Virnau

Polymers 2017, 9(2), 55; https://doi.org/10.3390/polym9020055 - 9 Feb 2017

Cited by 9 | Viewed by 6816

Abstract

Two knots on a string can either be separated or intertwined, and may even pass through each other. At the microscopic scale, such transitions may occur spontaneously, driven by thermal fluctuations, and can be associated with a topological free energy barrier. In this [...] Read more.

Two knots on a string can either be separated or intertwined, and may even pass through each other. At the microscopic scale, such transitions may occur spontaneously, driven by thermal fluctuations, and can be associated with a topological free energy barrier. In this manuscript, we study the respective location of a trefoil (

3_{1}

) and a figure-eight (

4_{1}

) knot on a semiflexible polymer, which is parameterized to model dsDNA in physiological conditions. Two cases are considered: first, end monomers are grafted to two confining walls of varying distance. Free energy profiles and transition barriers are then compared to a subset of free chains, which contain exactly one

3_{1}

and one

4_{1}

knot. For the latter, we observe a small preference to form an intertwined state, which can be associated with an effective entropic attraction. However, the respective free energy barrier is so small that we expect transition events to occur spontaneously and frequently in polymers and DNA, which are highly knotted for sufficient strain lengths. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1194 KiB

Open AccessArticle

Thermodynamics of a Compressible Maier-Saupe Model Based on the Self-Consistent Field Theory of Wormlike Polymer

by Ying Jiang, Cristina Greco, Kostas Ch. Daoulas and Jeff Z. Y. Chen

Polymers 2017, 9(2), 48; https://doi.org/10.3390/polym9020048 - 4 Feb 2017

Cited by 5 | Viewed by 6320

Abstract

This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions [...] Read more.

This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier–Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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7830 KiB

Open AccessArticle

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

by Benno Werlich, Mark P. Taylor, Timur Shakirov and Wolfgang Paul

Polymers 2017, 9(2), 38; https://doi.org/10.3390/polym9020038 - 25 Jan 2017

Cited by 16 | Viewed by 6849

Abstract

Local stiffness of polymer chains is instrumental in all structure formation processes of polymers, from crystallization of synthetic polymers to protein folding and DNA compactification. We present Stochastic Approximation Monte Carlo simulations—a type of flat-histogram Monte Carlo method—determining the density of states of [...] Read more.

Local stiffness of polymer chains is instrumental in all structure formation processes of polymers, from crystallization of synthetic polymers to protein folding and DNA compactification. We present Stochastic Approximation Monte Carlo simulations—a type of flat-histogram Monte Carlo method—determining the density of states of a model class of single semi-flexible polymer chains, and, from this, their complete thermodynamic behavior. The chains possess a rich pseudo phase diagram as a function of stiffness and temperature, displaying non-trivial ground-state morphologies. This pseudo phase diagram also depends on chain length. Differences to existing pseudo phase diagrams of semi-flexible chains in the literature emphasize the fact that the mechanism of stiffness creation matters. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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911 KiB

Open AccessArticle

What Happens When Threading is Suppressed in Blends of Ring and Linear Polymers?

by Benjamin Crysup and Sachin Shanbhag

Polymers 2016, 8(12), 409; https://doi.org/10.3390/polym8120409 - 25 Nov 2016

Cited by 9 | Viewed by 5059

Abstract

Self-diffusivity of a large tracer ring polymer,

D_{r}

, immersed in a matrix of linear polymers with

N_{l}

monomers each shows unusual length dependence.

D_{r}

initially increases, and then decreases with increasing

N_{l}

. To understand the relationship between [...] Read more.

Self-diffusivity of a large tracer ring polymer,

D_{r}

, immersed in a matrix of linear polymers with

N_{l}

monomers each shows unusual length dependence.

D_{r}

initially increases, and then decreases with increasing

N_{l}

. To understand the relationship between the nonmonotonic variation in

D_{r}

and threading by matrix chains, we perform equilibrium Monte Carlo simulations of ring-linear blends in which the uncrossability of ring and linear polymer contours is switched on (non-crossing), or artificially turned off (crossing). The

D_{r} \approx 6.2 \times 10^{- 7} N_{l}^{2 / 3}

obtained from the crossing simulations, provides an upper bound for the

D_{r}

obtained for the regular, non-crossing simulations. The center-of-mass mean-squared displacement (

g_{3} (t)

) curves for the crossing simulations are consistent with the Rouse model; we find

g_{3} (t) = 6 D_{r} t

. Analysis of the polymer structure indicates that the smaller matrix chains are able to infiltrate the space occupied by the ring probe more effectively, which is dynamically manifested as a larger frictional drag per ring monomer. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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6984 KiB

Open AccessArticle

Conformation Change, Tension Propagation and Drift-Diffusion Properties of Polyelectrolyte in Nanopore Translocation

by Pai-Yi Hsiao

Polymers 2016, 8(10), 378; https://doi.org/10.3390/polym8100378 - 24 Oct 2016

Cited by 10 | Viewed by 5998

Abstract

Using Langevin dynamics simulations, conformational, mechanical and dynamical properties of charged polymers threading through a nanopore are investigated. The shape descriptors display different variation behaviors for the cis- and trans-side sub-chains, which reflects a strong cis-trans dynamical asymmetry, especially when the [...] Read more.

Using Langevin dynamics simulations, conformational, mechanical and dynamical properties of charged polymers threading through a nanopore are investigated. The shape descriptors display different variation behaviors for the cis- and trans-side sub-chains, which reflects a strong cis-trans dynamical asymmetry, especially when the driving field is strong. The calculation of bond stretching shows how the bond tension propagates on the chain backbone, and the chain section straightened by the tension force is determined by the ratio of the direct to the contour distances of the monomer to the pore. With the study of the waiting time function, the threading process is divided into the tension-propagation stage and the tail-retraction stage. At the end, the drift velocity, diffusive property and probability density distribution are explored. Owing to the non-equilibrium nature, translocation is not a simple drift-diffusion process, but exhibits several intermediate behaviors, such as ballistic motion, normal diffusion and super diffusion, before ending with the last, negative-diffusion behavior. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1763 KiB

Open AccessArticle

Dynamics of DNA Squeezed Inside a Nanochannel via a Sliding Gasket

by Aiqun Huang, Walter Reisner and Aniket Bhattacharya

Polymers 2016, 8(10), 352; https://doi.org/10.3390/polym8100352 - 29 Sep 2016

Cited by 10 | Viewed by 6061

Abstract

We use Brownian dynamics (BD) simulation of a coarse-grained (CG) bead-spring model of DNA to study the nonequilibrim dynamics of a single DNA molecule confined inside a rectangular nanochannel being squeezed with a sliding gasket piston or “nanodozer”. From our simulations we extract [...] Read more.

We use Brownian dynamics (BD) simulation of a coarse-grained (CG) bead-spring model of DNA to study the nonequilibrim dynamics of a single DNA molecule confined inside a rectangular nanochannel being squeezed with a sliding gasket piston or “nanodozer”. From our simulations we extract the nonequilibrim density profile

c (x, t)

of the squeezed molecule along the channel axis (x-coordinate) and then analyze the non-equilibrium profile using a recently introduced phenomenological Nonlinear Partial Differential Equation (NPDE) model. Since the NPDE approach also fits the experimental results well and is numerically efficient to implement, the combined BD + NPDE methods can be a powerful approach to analyze details of the confined molecular dynamics. In particular, the overall excellent agreement between the two complementary sets of data provides a strategy for carrying out large scale simulation on semi-flexible biopolymers in confinement at biologically relevant length scales. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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434 KiB

Open AccessArticle

Microstructure of Sheared Entangled Solutions of Semiflexible Polymers

by Marc Lämmel, Evelin Jaschinski, Rudolf Merkel and Klaus Kroy

Polymers 2016, 8(10), 353; https://doi.org/10.3390/polym8100353 - 28 Sep 2016

Cited by 3 | Viewed by 5802

Abstract

We study the influence of finite shear deformations on the microstructure and rheology of solutions of entangled semiflexible polymers theoretically and by numerical simulations and experiments with filamentous actin. Based on the tube model of semiflexible polymers, we predict that large finite shear [...] Read more.

We study the influence of finite shear deformations on the microstructure and rheology of solutions of entangled semiflexible polymers theoretically and by numerical simulations and experiments with filamentous actin. Based on the tube model of semiflexible polymers, we predict that large finite shear deformations strongly affect the average tube width and curvature, thereby exciting considerable restoring stresses. In contrast, the associated shear alignment is moderate, with little impact on the average tube parameters, and thus expected to be long-lived and detectable after cessation of shear. Similarly, topologically preserved hairpin configurations are predicted to leave a long-lived fingerprint in the shape of the distributions of tube widths and curvatures. Our numerical and experimental data support the theory. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1775 KiB

Open AccessArticle

Role of Bending Energy and Knot Chirality in Knot Distribution and Their Effective Interaction along Stretched Semiflexible Polymers

by Saeed Najafi, Rudolf Podgornik, Raffaello Potestio and Luca Tubiana

Polymers 2016, 8(10), 347; https://doi.org/10.3390/polym8100347 - 22 Sep 2016

Cited by 16 | Viewed by 6809

Abstract

Knots appear frequently in semiflexible (bio)polymers, including double-stranded DNA, and their presence can affect the polymer’s physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only [...] Read more.

Knots appear frequently in semiflexible (bio)polymers, including double-stranded DNA, and their presence can affect the polymer’s physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only come under scrutiny in the last few years. In this manuscript, we study the interaction of two knots on a stretched semiflexible polymer, expanding some recent results on the topic. Specifically, we consider an idealization of a typical optical tweezers experiment and show how the bending rigidity of the chain—And consequently its persistence length—Influences the distribution of the entanglements; possibly more importantly, we observe and report how the relative chirality of the otherwise identical knots substantially modifies their interaction. We analyze the free energy of the chain and extract the effective interactions between embedded knots, rationalizing some of their pertinent features by means of simple effective models. We believe the salient aspect of the knot–knot interactions emerging from our study will be present in a large number of semiflexible polymers under tension, with important consequences for the characterization and manipulation of these systems—Be they artificial or biologica in origin—And for their technological application. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1087 KiB

Open AccessArticle

Particle-Based Modeling of Living Actin Filaments in an Optical Trap

by Thomas A. Hunt, Santosh Mogurampelly, Giovanni Ciccotti, Carlo Pierleoni and Jean-Paul Ryckaert

Polymers 2016, 8(9), 343; https://doi.org/10.3390/polym8090343 - 19 Sep 2016

Cited by 1 | Viewed by 5634

Abstract

We report a coarse-grained molecular dynamics simulation study of a bundle of parallel actin filaments under supercritical conditions pressing against a loaded mobile wall using a particle-based approach where each particle represents an actin unit. The filaments are grafted to a fixed wall [...] Read more.

We report a coarse-grained molecular dynamics simulation study of a bundle of parallel actin filaments under supercritical conditions pressing against a loaded mobile wall using a particle-based approach where each particle represents an actin unit. The filaments are grafted to a fixed wall at one end and are reactive at the other end, where they can perform single monomer (de)polymerization steps and push on a mobile obstacle. We simulate a reactive grand canonical ensemble in a box of fixed transverse area A, with a fixed number of grafted filaments

N_{f}

, at temperature T and monomer chemical potential

μ_{1}

. For a single filament case (

N_{f} = 1

) and for a bundle of

N_{f} = 8

filaments, we analyze the structural and dynamical properties at equilibrium where the external load compensates the average force exerted by the bundle. The dynamics of the bundle-moving-wall unit are characteristic of an over-damped Brownian oscillator in agreement with recent in vitro experiments by an optical trap setup. We analyze the influence of the pressing wall on the kinetic rates of (de)polymerization events for the filaments. Both static and dynamic results compare reasonably well with recent theoretical treatments of the same system. Thus, we consider the proposed model as a good tool to investigate the properties of a bundle of living filaments. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1759 KiB

Open AccessArticle

Stretching a Semiflexible Polymer in a Tube

by Runhua Li and Jizeng Wang

Polymers 2016, 8(9), 328; https://doi.org/10.3390/polym8090328 - 9 Sep 2016

Cited by 6 | Viewed by 6525

Abstract

How the statistical behavior of semiflexible polymer chains may be affected by force stretching and tube confinement is a classical unsolved problem in polymer physics. Based on the Odijk deflection theory and normal mode decomposition in terms of Fourier expansion, we have derived [...] Read more.

How the statistical behavior of semiflexible polymer chains may be affected by force stretching and tube confinement is a classical unsolved problem in polymer physics. Based on the Odijk deflection theory and normal mode decomposition in terms of Fourier expansion, we have derived a new compact formula for the extension of a wormlike chain of finite length strongly confined in a tube and simultaneously stretched by an external force. We have also suggested a new deflection length, which together with the force-extension relation is valid for a very extended range of the tube-diameter/persistence-length ratio comparing to the classic Odijk theory. The newly derived formula has no adjustable fitting parameters for the whole deflection regime; in contrast, the classic Odijk length needs different prefactors to fit the free energy and average extension, respectively. Brownian dynamics simulations based on the Generalized Bead-Rod (GBR) model were extensively performed, which justified the theoretical predictions. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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3202 KiB

Open AccessArticle

The Semiflexible Polymer Translocation into Laterally Unbounded Region between Two Parallel Flat Membranes

by Zhi-Yong Yang, Ai-Hua Chai, Yong-Fu Yang, Xiao-Mao Li, Ping Li and Run-Ying Dai

Polymers 2016, 8(9), 332; https://doi.org/10.3390/polym8090332 - 7 Sep 2016

Cited by 6 | Viewed by 5599

Abstract

Using the dynamic Monte Carlo method, we investigate dynamics of semiflexible polymer translocation through a nanopore into laterally unbounded region between two parallel flat membranes with separation R in presence of an electric field inside the pore. The average translocation time τ initially [...] Read more.

Using the dynamic Monte Carlo method, we investigate dynamics of semiflexible polymer translocation through a nanopore into laterally unbounded region between two parallel flat membranes with separation R in presence of an electric field inside the pore. The average translocation time τ initially decreases rapidly with increase of R in the range of R < 10 and then almost keeps constant for R ≥ 10, and the decline range increases with increase of dimensionless bending stiffness κ. We mainly study the effect of chain length N, κ and electric field strength E on the translocation process for R = 5. The translocation dynamics is significantly altered in comparison to an unconfined environment. We find τ ~ N^α, where the exponent α increases with increase of E for small κ. α initially increases slowly with increase of E and then keeps constant for moderate κ. α decreases with increase of E for large κ. However, α decreases with increase of κ under various E. In addition, we find τ ~ κ^β. β decreases with increase of N under various E. These behaviors are interpreted in terms of the probability distribution of translocation time and the waiting time of an individual monomer segment passing through the pore during translocation. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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6528 KiB

Open AccessArticle

Evaluation of Thermally Induced Degradation of Branched Polypropylene by Using Rheology and Different Constitutive Equations

by Jiri Drabek and Martin Zatloukal

Polymers 2016, 8(9), 317; https://doi.org/10.3390/polym8090317 - 24 Aug 2016

Cited by 19 | Viewed by 7889

Abstract

In this work, virgin as well as thermally degraded branched polypropylenes were investigated by using rotational and Sentmanat extensional rheometers, gel permeation chromatography and different constitutive equations. Based on the obtained experimental data and theoretical analysis, it has been found that even if [...] Read more.

In this work, virgin as well as thermally degraded branched polypropylenes were investigated by using rotational and Sentmanat extensional rheometers, gel permeation chromatography and different constitutive equations. Based on the obtained experimental data and theoretical analysis, it has been found that even if both chain scission and branching takes place during thermal degradation of the tested polypropylene, the melt strength (quantified via the level of extensional strain hardening) can increase at short degradation times. It was found that constitutive equations such as Generalized Newtonian law, modified White-Metzner model, Yao and Extended Yao models have the capability to describe and interpret the measured steady-state rheological data of the virgin as well as thermally degraded branched polypropylenes. Specific attention has been paid to understanding molecular changes during thermal degradation of branched polypropylene by using physical parameters of utilized constitutive equations. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1044 KiB

Open AccessFeature PaperArticle

Conformational Properties of Active Semiflexible Polymers

by Thomas Eisenstecken, Gerhard Gompper and Roland G. Winkler

Polymers 2016, 8(8), 304; https://doi.org/10.3390/polym8080304 - 12 Aug 2016

Cited by 100 | Viewed by 9790

Abstract

The conformational properties of flexible and semiflexible polymers exposed to active noise are studied theoretically. The noise may originate from the interaction of the polymer with surrounding active (Brownian) particles or from the inherent motion of the polymer itself, which may be composed [...] Read more.

The conformational properties of flexible and semiflexible polymers exposed to active noise are studied theoretically. The noise may originate from the interaction of the polymer with surrounding active (Brownian) particles or from the inherent motion of the polymer itself, which may be composed of active Brownian particles. In the latter case, the respective monomers are independently propelled in directions changing diffusively. For the description of the polymer, we adopt the continuous Gaussian semiflexible polymer model. Specifically, the finite polymer extensibility is taken into account, which turns out to be essential for the polymer conformations. Our analytical calculations predict a strong dependence of the relaxation times on the activity. In particular, semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics to the flexible polymer dynamics with increasing activity. This leads to a significant activity-induced polymer shrinkage over a large range of self-propulsion velocities. For large activities, the polymers swell and their extension becomes comparable to the contour length. The scaling properties of the mean square end-to-end distance with respect to the polymer length and monomer activity are discussed. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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993 KiB

Open AccessArticle

The Connection between Biaxial Orientation and Shear Thinning for Quasi-Ideal Rods

by Christian Lang, Joachim Kohlbrecher, Lionel Porcar and Minne Paul Lettinga

Polymers 2016, 8(8), 291; https://doi.org/10.3390/polym8080291 - 9 Aug 2016

Cited by 16 | Viewed by 6121

Abstract

The complete orientational ordering tensor of quasi-ideal colloidal rods is obtained as a function of shear rate by performing rheo-SANS (rheology with small angle neutron scattering) measurements on isotropic fd-virus suspensions in the two relevant scattering planes, the flow-gradient (1-2) and the flow-vorticity [...] Read more.

The complete orientational ordering tensor of quasi-ideal colloidal rods is obtained as a function of shear rate by performing rheo-SANS (rheology with small angle neutron scattering) measurements on isotropic fd-virus suspensions in the two relevant scattering planes, the flow-gradient (1-2) and the flow-vorticity (1-3) plane. Microscopic ordering can be identified as the origin of the observed shear thinning. A qualitative description of the rheological response by Smoluchowski, as well as Doi–Edwards–Kuzuu theory is possible, as we obtain a master curve for different concentrations, scaling the shear rate with the apparent collective rotational diffusion coefficient. However, the observation suggests that the interdependence of ordering and shear thinning at small shear rates is stronger than predicted. The extracted zero-shear viscosity matches the concentration dependence of the self-diffusion of rods in semi-dilute solutions, while the director tilts close towards the flow direction already at very low shear rates. In contrast, we observe a smaller dependence on the shear rate in the overall ordering at high shear rates, as well as an ever-increasing biaxiality. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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2157 KiB

Open AccessArticle

Finsler Geometry Modeling of Phase Separation in Multi-Component Membranes

by Satoshi Usui and Hiroshi Koibuchi

Polymers 2016, 8(8), 284; https://doi.org/10.3390/polym8080284 - 4 Aug 2016

Cited by 7 | Viewed by 5300

Abstract

A Finsler geometric surface model is studied as a coarse-grained model for membranes of three components, such as zwitterionic phospholipid (DOPC), lipid (DPPC) and an organic molecule (cholesterol). To understand the phase separation of liquid-ordered (DPPC rich)

L_{o}

and liquid-disordered (DOPC rich) [...] Read more.

A Finsler geometric surface model is studied as a coarse-grained model for membranes of three components, such as zwitterionic phospholipid (DOPC), lipid (DPPC) and an organic molecule (cholesterol). To understand the phase separation of liquid-ordered (DPPC rich)

L_{o}

and liquid-disordered (DOPC rich)

L_{d}

, we introduce a binary variable

σ (= \pm 1)

into the triangulated surface model. We numerically determine that two circular and stripe domains appear on the surface. The dependence of the morphological change on the area fraction of

L_{o}

is consistent with existing experimental results. This provides us with a clear understanding of the origin of the line tension energy, which has been used to understand these morphological changes in three-component membranes. In addition to these two circular and stripe domains, a raft-like domain and budding domain are also observed, and the several corresponding phase diagrams are obtained. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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7678 KiB

Open AccessArticle

Microscopic Dynamics and Topology of Polymer Rings Immersed in a Host Matrix of Longer Linear Polymers: Results from a Detailed Molecular Dynamics Simulation Study and Comparison with Experimental Data

by George D. Papadopoulos, Dimitrios G. Tsalikis and Vlasis G. Mavrantzas

Polymers 2016, 8(8), 283; https://doi.org/10.3390/polym8080283 - 4 Aug 2016

Cited by 32 | Viewed by 7680

Abstract

We have performed molecular dynamics (MD) simulations of melt systems consisting of a small number of long ring poly(ethylene oxide) (PEO) probes immersed in a host matrix of linear PEO chains and have studied their microscopic dynamics and topology as a function of [...] Read more.

We have performed molecular dynamics (MD) simulations of melt systems consisting of a small number of long ring poly(ethylene oxide) (PEO) probes immersed in a host matrix of linear PEO chains and have studied their microscopic dynamics and topology as a function of the molecular length of the host linear chains. Consistent with a recent neutron spin echo spectroscopy study (Goossen et al., Phys. Rev. Lett. 2015, 115, 148302), we have observed that the segmental dynamics of the probe ring molecules is controlled by the length of the host linear chains. In matrices of short, unentangled linear chains, the ring probes exhibit a Rouse-like dynamics, and the spectra of their dynamic structure factor resemble those in their own melt. In striking contrast, in matrices of long, entangled linear chains, their dynamics is drastically altered. The corresponding dynamic structure factor spectra exhibit a steep initial decay up to times on the order of the entanglement time τ_e of linear PEO at the same temperature but then they become practically time-independent approaching plateau values. The plateau values are different for different wavevectors; they also depend on the length of the host linear chains. Our results are supported by a geometric analysis of topological interactions, which reveals significant threading of all ring molecules by the linear chains. In most cases, each ring is simultaneously threaded by several linear chains. As a result, its dynamics at times longer than a few τ_e should be completely dictated by the release of the topological restrictions imposed by these threadings (interpenetrations). Our topological analysis did not indicate any effect of the few ring probes on the statistical properties of the network of primitive paths of the host linear chains. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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477 KiB

Open AccessArticle

Mean-Square Radius of Gyration and Scattering Function of Semiflexible Ring Polymers of the Trefoil Knot

by Hiroki Abe and Daichi Ida

Polymers 2016, 8(8), 271; https://doi.org/10.3390/polym8080271 - 27 Jul 2016

Cited by 5 | Viewed by 6087

Abstract

A Monte Carlo study of the mean-square radius of gyration

R_{g}^{2}

and scattering function

P (k)

with k the magnitude of the scattering vector for semiflexible ring polymers of the trefoil knot was conducted by the use of the [...] Read more.

A Monte Carlo study of the mean-square radius of gyration

R_{g}^{2}

and scattering function

P (k)

with k the magnitude of the scattering vector for semiflexible ring polymers of the trefoil knot was conducted by the use of the discrete version of the Kratky–Porod (KP) wormlike ring model. The behavior of

R_{g}^{2}

and

P (k)

as functions of the reduced contour length

λ L

, defined as the total contour length L divided by the stiffness parameter

λ^{- 1}

, is clarified. A comparison is made of the results for the KP ring of the trefoil knot with those for the KP ring of the trivial knot and for the phantom KP ring without the topological constraints. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1736 KiB

Open AccessArticle

A Simple Analytical Model for Predicting the Collapsed State of Self-Attractive Semiflexible Polymers

by Wenjun Huang, Ming Huang, Qi Lei and Ronald G. Larson

Polymers 2016, 8(7), 264; https://doi.org/10.3390/polym8070264 - 16 Jul 2016

Cited by 16 | Viewed by 5908

Abstract

We develop an analytical model to predict the collapse conformation for a single semiflexible polymer chain in solution, given its length, diameter, stiffness, and self-attractiveness. We construct conformational phase diagrams containing three collapsed states, namely torus, bundle, and globule over a range of [...] Read more.

We develop an analytical model to predict the collapse conformation for a single semiflexible polymer chain in solution, given its length, diameter, stiffness, and self-attractiveness. We construct conformational phase diagrams containing three collapsed states, namely torus, bundle, and globule over a range of dimensionless ratios of the three energy parameters, namely solvent-water surface energy (

γ_{s}

), energy of bundle end folds (

γ_{e}

), and bending energy per unit length in a torus (

γ_{b}

). Our phase diagram captures the general phase behavior of a single long chain (>10 Kuhn lengths) at moderately high (order unity) dimensionless temperature, which is the ratio of thermal energy to the attractive interaction between neighboring monomers. We find that the phase behavior approaches an asymptotic limit when the dimensionless chain length to diameter ratio (L*) exceeds 300. We successfully validate our analytical results with Brownian Dynamics (BD) simulations, using a mapping of the simulation parameters to those used in the phase diagram. We evaluate the effect of three different bending potentials in the range of moderately high dimensionless temperature, a regime not been previously explored by simulations, and find qualitative agreement between the model and simulation results. We, thus, demonstrate that a rather simplified analytical model can be used to qualitatively predict the final collapsed state of a given polymer chain. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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5320 KiB

Open AccessArticle

Relaxation Dynamics of Semiflexible Fractal Macromolecules

by Jonas Mielke and Maxim Dolgushev

Polymers 2016, 8(7), 263; https://doi.org/10.3390/polym8070263 - 15 Jul 2016

Cited by 5 | Viewed by 6416

Abstract

We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin [...] Read more.

We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locally-dendritic structure that is more pronounced for higher stiffness. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1291 KiB

Open AccessArticle

Influence of Chain Stiffness, Grafting Density and Normal Load on the Tribological and Structural Behavior of Polymer Brushes: A Nonequilibrium-Molecular-Dynamics Study

by Manjesh K. Singh, Patrick Ilg, Rosa M. Espinosa-Marzal, Nicholas D. Spencer and Martin Kröger

Polymers 2016, 8(7), 254; https://doi.org/10.3390/polym8070254 - 8 Jul 2016

Cited by 32 | Viewed by 8867

Abstract

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be [...] Read more.

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equilibrium behavior of the model brushes, we first study the shearing behavior of flexible chains at different grafting densities covering brush and mushroom regimes. Next, we focus on the effect of chain stiffness on the tribological behavior of polymer brushes. The tribological properties are interpreted by means of the simultaneously recorded density profiles. We find that the friction coefficient decreases with increasing persistence length, both in velocity and separation-dependency studies, over the stiffness range explored in this work. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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2258 KiB

Open AccessFeature PaperArticle

System-Size Dependence of Helix-Bundle Formation for Generic Semiflexible Polymers

by Matthew J. Williams and Michael Bachmann

Polymers 2016, 8(7), 245; https://doi.org/10.3390/polym8070245 - 27 Jun 2016

Cited by 7 | Viewed by 6261

Abstract

Helical polymer bundles are an important fixture in biomolecular systems. The particular structural geometry of helix bundles is dependent on many factors including the length of the polymer chain. In this study, we performed Monte Carlo simulations of a coarse-grained model for helical [...] Read more.

Helical polymer bundles are an important fixture in biomolecular systems. The particular structural geometry of helix bundles is dependent on many factors including the length of the polymer chain. In this study, we performed Monte Carlo simulations of a coarse-grained model for helical polymers to determine the influence of polymer length on tertiary structure formation. Helical structures of semiflexible polymers are analyzed for several chain lengths under thermal conditions. Structural hyperphase diagrams, parametrized by torsion strength and temperature, are constructed and compared. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1770 KiB

Open AccessFeature PaperArticle

Predicting the Flory-Huggins χ Parameter for Polymers with Stiffness Mismatch from Molecular Dynamics Simulations

by Daniel J. Kozuch, Wenlin Zhang and Scott T. Milner

Polymers 2016, 8(6), 241; https://doi.org/10.3390/polym8060241 - 22 Jun 2016

Cited by 55 | Viewed by 12939

Abstract

The Flory–Huggins χ parameter describes the excess free energy of mixing and governs phase behavior for polymer blends and block copolymers. For chemically-distinct nonpolar polymers, the value of χ is dominated by the mismatch in cohesive energy densities of the monomers. For blends [...] Read more.

The Flory–Huggins χ parameter describes the excess free energy of mixing and governs phase behavior for polymer blends and block copolymers. For chemically-distinct nonpolar polymers, the value of χ is dominated by the mismatch in cohesive energy densities of the monomers. For blends of chemically-similar polymers, the entropic portion of χ, arising from non-ideal local packing, becomes more significant. Using polymer field theory, Fredrickson et al. predicted that a difference in backbone stiffness can result in a positive χ for chains consisting of chemically-identical monomers. To quantitatively investigate this phenomenon, we perform molecular dynamic (MD) simulations for bead-spring chains, which differ only in stiffness. From the simulations, we apply a novel thermodynamic integration to extract χ as low as

10^{- 4}

per monomer for blends with stiffness mismatch. To compare with experiments, we introduce a standardized effective monomer to map real polymers onto our bead-spring chains. The predicted χ agrees well with experimental values for a wide variety of pairs of chemically-similar polymers. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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5574 KiB

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Spatial Rearrangement and Mobility Heterogeneity of an Anionic Lipid Monolayer Induced by the Anchoring of Cationic Semiflexible Polymer Chains

by Xiaozheng Duan, Yang Zhang, Ran Zhang, Mingming Ding, Tongfei Shi, Lijia An, Qingrong Huang and Wen-Sheng Xu

Polymers 2016, 8(6), 235; https://doi.org/10.3390/polym8060235 - 17 Jun 2016

Cited by 3 | Viewed by 5110

Abstract

We use Monte Carlo simulations to investigate the interactions between cationic semiflexible polymer chains and a model fluid lipid monolayer composed of charge-neutral phosphatidyl-choline (PC), tetravalent anionic phosphatidylinositol 4,5-bisphosphate (PIP₂), and univalent anionic phosphatidylserine (PS) lipids. In particular, we explore how [...] Read more.

We use Monte Carlo simulations to investigate the interactions between cationic semiflexible polymer chains and a model fluid lipid monolayer composed of charge-neutral phosphatidyl-choline (PC), tetravalent anionic phosphatidylinositol 4,5-bisphosphate (PIP₂), and univalent anionic phosphatidylserine (PS) lipids. In particular, we explore how chain rigidity and polymer concentration influence the spatial rearrangement and mobility heterogeneity of the monolayer under the conditions where the cationic polymers anchor on the monolayer. We find that the anchored cationic polymers only sequester the tetravalent PIP₂ lipids at low polymer concentrations, where the interaction strength between the polymers and the monolayer exhibits a non-monotonic dependence on the degree of chain rigidity. Specifically, maximal anchoring occurs at low polymer concentrations, when the polymer chains have an intermediate degree of rigidity, for which the PIP₂ clustering becomes most enhanced and the mobility of the polymer/PIP₂ complexes becomes most reduced. On the other hand, at sufficiently high polymer concentrations, the anchoring strength decreases monotonically as the chains stiffen—a result that arises from the pronounced competitions among polymer chains. In this case, the flexible polymers can confine all PIP₂ lipids and further sequester the univalent PS lipids, whereas the stiffer polymers tend to partially dissociate from the monolayer and only sequester smaller PIP₂ clusters with greater mobilities. We further illustrate that the mobility gradient of the single PIP₂ lipids in the sequestered clusters is sensitively modulated by the cooperative effects between anchored segments of the polymers with different rigidities. Our work thus demonstrates that the rigidity and concentration of anchored polymers are both important parameters for tuning the regulation of anionic lipids. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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3576 KiB

Open AccessArticle

Effect of Geometrical Asymmetry on the Phase Behavior of Rod-Coil Diblock Copolymers

by Jingying Yu, Faqiang Liu, Ping Tang, Feng Qiu, Hongdong Zhang and Yuliang Yang

Polymers 2016, 8(5), 184; https://doi.org/10.3390/polym8050184 - 11 May 2016

Cited by 16 | Viewed by 5305

Abstract

The effect of geometrical asymmetry β (described by the length-diameter ratio of rods) on the rod-coil diblock copolymer phase behavior is studied by implementation of self-consistent field theory (SCFT) in three-dimensional (3D) position space while considering the rod orientation on the spherical surface. [...] Read more.

The effect of geometrical asymmetry β (described by the length-diameter ratio of rods) on the rod-coil diblock copolymer phase behavior is studied by implementation of self-consistent field theory (SCFT) in three-dimensional (3D) position space while considering the rod orientation on the spherical surface. The phase diagrams at different geometrical asymmetry show that the aspect ratio of rods β influences not only the order-disorder transition (ODT) but also the order-order transition (OOT). By exploring the phase diagram with interactions between rods and coils plotted against β, the β effect on the phase diagram is similar to the copolymer composition f. This suggests that non-lamellae structures can be obtained by tuning β, besides f. When the rods are slim compared with the isotropic shape of the coil segment (β is relatively large), the phase behavior is quite different from that of coil-coil diblock copolymers. In this case, only hexagonal cylinders with the coil at the convex side of the interface and lamella phases are stable even in the absence of orientational interaction between rods. The phase diagram is no longer symmetrical about the symmetric copolymer composition and cylinder phases occupy the large area of the phase diagram. The ODT is much lower than that of the coil-coil diblock copolymer system and the triple point at which disordered, cylinder and lamella phases coexist in equilibrium is located at rod composition f_R = 0.66. In contrast, when the rods are short and stumpy (β is smaller), the stretching entropy cost of coils can be alleviated and the phase behavior is similar to coil-coil diblocks. Therefore, the hexagonal cylinder phase formed by coils is also found beside the former two structures. Moreover, the ODT may even become a little higher than that of the coil-coil diblock copolymers due to the large interfacial area per chain provided by the stumpy rods, thus compensating the stretching entropy loss of the coils. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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488 KiB

Open AccessArticle

The Backfolded Odijk Regime for Wormlike Chains Confined in Rectangular Nanochannels

by Abhiram Muralidhar, Michael J. Quevillon and Kevin D. Dorfman

Polymers 2016, 8(3), 79; https://doi.org/10.3390/polym8030079 - 14 Mar 2016

Cited by 23 | Viewed by 6745

Abstract

We confirm Odijk’s scaling laws for (i) the average chain extension; (ii) the variance about the average extension; and (iii) the confinement free energy of a wormlike chain confined in a rectangular nanochannel smaller than its chain persistence length through pruned-enriched Rosenbluth method [...] Read more.

We confirm Odijk’s scaling laws for (i) the average chain extension; (ii) the variance about the average extension; and (iii) the confinement free energy of a wormlike chain confined in a rectangular nanochannel smaller than its chain persistence length through pruned-enriched Rosenbluth method (PERM) simulations of asymptotically long, discrete wormlike chains. In the course of this analysis, we also computed the global persistence length of ideal wormlike chains for the modestly rectangular channels that are used in many experimental systems. The results are relevant to genomic mapping systems that confine DNA in channel sizes around 50 nm, since fabrication constraints generally lead to rectangular cross-sections. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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Review

Jump to: Research

800 KiB

Open AccessReview

Statistical and Dynamical Properties of Topological Polymers with Graphs and Ring Polymers with Knots

by Tetsuo Deguchi and Erica Uehara

Polymers 2017, 9(7), 252; https://doi.org/10.3390/polym9070252 - 28 Jun 2017

Cited by 28 | Viewed by 7780

Abstract

We review recent theoretical studies on the statistical and dynamical properties of polymers with nontrivial structures in chemical connectivity and those of polymers with a nontrivial topology, such as knotted ring polymers in solution. We call polymers with nontrivial structures in chemical connectivity [...] Read more.

We review recent theoretical studies on the statistical and dynamical properties of polymers with nontrivial structures in chemical connectivity and those of polymers with a nontrivial topology, such as knotted ring polymers in solution. We call polymers with nontrivial structures in chemical connectivity expressed by graphs “topological polymers”. Graphs with no loop have only trivial topology, while graphs with loops such as multiple-rings may have nontrivial topology of spatial graphs as embeddings in three dimensions, e.g., knots or links in some loops. We thus call also such polymers with nontrivial topology “topological polymers”, for simplicity. For various polymers with different structures in chemical connectivity, we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We evaluate the ratio of the gyration radius to the hydrodynamic radius, which we expect to be universal from the viewpoint of the renormalization group. Furthermore, we show that the short-distance intrachain correlation is much enhanced for real topological polymers (the Kremer–Grest model) expressed with complex graphs. We then address topological properties of ring polymers in solution. We define the knotting probability of a knot K by the probability that a given random polygon or self-avoiding polygon of N vertices has the knot K. We show a formula for expressing it as a function of the number of segments N, which gives good fitted curves to the data of the knotting probability versus N. We show numerically that the average size of self-avoiding polygons with a fixed knot can be much larger than that of no topological constraint if the excluded volume is small. We call it “topological swelling”. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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11685 KiB

Open AccessReview

Theoretical Methods for Studying DNA Structural Transitions under Applied Mechanical Constraints

by Artem K. Efremov, Ricksen S. Winardhi and Jie Yan

Polymers 2017, 9(2), 74; https://doi.org/10.3390/polym9020074 - 21 Feb 2017

Cited by 3 | Viewed by 7536

Abstract

Recent progress in single-molecule manipulation technologies has made it possible to exert force and torque on individual DNA biopolymers to probe their mechanical stability and interaction with various DNA-binding proteins. It was revealed in these experiments that the DNA structure and formation of [...] Read more.

Recent progress in single-molecule manipulation technologies has made it possible to exert force and torque on individual DNA biopolymers to probe their mechanical stability and interaction with various DNA-binding proteins. It was revealed in these experiments that the DNA structure and formation of nucleoprotein complexes by DNA-architectural proteins can be strongly modulated by an intricate interplay between the entropic elasticity of DNA and its global topology, which is closely related to the mechanical constraints applied to the DNA. Detailed understanding of the physical processes underlying the DNA behavior observed in single-molecule experiments requires the development of a general theoretical framework, which turned out to be a rather challenging task. Here, we review recent advances in theoretical methods that can be used to interpret single-molecule manipulation experiments on DNA. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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2639 KiB

Open AccessReview

Theory of Semiflexible Filaments and Networks

by Fanlong Meng and Eugene M. Terentjev

Polymers 2017, 9(2), 52; https://doi.org/10.3390/polym9020052 - 5 Feb 2017

Cited by 50 | Viewed by 8958

Abstract

We briefly review the recent developments in the theory of individual semiflexible filaments, and of a crosslinked network of such filaments, both permanent and transient. Starting from the free energy of an individual semiflexible chain, models on its force-extension relation and other mechanical [...] Read more.

We briefly review the recent developments in the theory of individual semiflexible filaments, and of a crosslinked network of such filaments, both permanent and transient. Starting from the free energy of an individual semiflexible chain, models on its force-extension relation and other mechanical properties such as Euler buckling are discussed. For a permanently crosslinked network of filaments, theories on how the network responds to deformation are provided, with a focus on continuum approaches. Characteristic features of filament networks, such as nonlinear stress-strain relation, negative normal stress, tensegrity, and marginal stability are discussed. In the new area of transient filament network, where the crosslinks can be dynamically broken and re-formed, we show some recent attempts for understanding the dynamics of the crosslinks, and the related rheological properties, such as stress relaxation, yield stress and plasticity. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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854 KiB

Open AccessReview

Scattering and Gaussian Fluctuation Theory for Semiflexible Polymers

by Xiangyu Bu and Xinghua Zhang

Polymers 2016, 8(9), 301; https://doi.org/10.3390/polym8090301 - 13 Sep 2016

Cited by 3 | Viewed by 6787

Abstract

The worm-like chain is one of the best theoretical models of the semiflexible polymer. The structure factor, which can be obtained by scattering experiment, characterizes the density correlation in different length scales. In the present review, the numerical method to compute the static [...] Read more.

The worm-like chain is one of the best theoretical models of the semiflexible polymer. The structure factor, which can be obtained by scattering experiment, characterizes the density correlation in different length scales. In the present review, the numerical method to compute the static structure factor of the worm-like chain model and its general properties are demonstrated. Especially, the chain length and persistence length involved multi-scale nature of the worm-like chain model are well discussed. Using the numerical structure factor, Gaussian fluctuation theory of the worm-like chain model can be developed, which is a powerful tool to analyze the structure stability and to predict the spinodal line of the system. The microphase separation of the worm-like diblock copolymer is considered as an example to demonstrate the usage of Gaussian fluctuation theory. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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4553 KiB

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DNA as a Model for Probing Polymer Entanglements: Circular Polymers and Non-Classical Dynamics

by Kathryn Regan, Shea Ricketts and Rae M. Robertson-Anderson

Polymers 2016, 8(9), 336; https://doi.org/10.3390/polym8090336 - 7 Sep 2016

Cited by 26 | Viewed by 9950

Abstract

Double-stranded DNA offers a robust platform for investigating fundamental questions regarding the dynamics of entangled polymer solutions. The exceptional monodispersity and multiple naturally occurring topologies of DNA, as well as a wide range of tunable lengths and concentrations that encompass the entanglement regime, [...] Read more.

Double-stranded DNA offers a robust platform for investigating fundamental questions regarding the dynamics of entangled polymer solutions. The exceptional monodispersity and multiple naturally occurring topologies of DNA, as well as a wide range of tunable lengths and concentrations that encompass the entanglement regime, enable direct testing of molecular-level entanglement theories and corresponding scaling laws. DNA is also amenable to a wide range of techniques from passive to nonlinear measurements and from single-molecule to bulk macroscopic experiments. Over the past two decades, researchers have developed methods to directly visualize and manipulate single entangled DNA molecules in steady-state and stressed conditions using fluorescence microscopy, particle tracking and optical tweezers. Developments in microfluidics, microrheology and bulk rheology have also enabled characterization of the viscoelastic response of entangled DNA from molecular levels to macroscopic scales and over timescales that span from linear to nonlinear regimes. Experiments using DNA have uniquely elucidated the debated entanglement properties of circular polymers and blends of linear and circular polymers. Experiments have also revealed important lengthscale and timescale dependent entanglement dynamics not predicted by classical tube models, both validating and refuting new proposed extensions and alternatives to tube theory and motivating further theoretical work to describe the rich dynamics exhibited in entangled polymer systems. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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4472 KiB

Open AccessReview

Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation

by Johannes Zierenberg, Martin Marenz and Wolfhard Janke

Polymers 2016, 8(9), 333; https://doi.org/10.3390/polym8090333 - 6 Sep 2016

Cited by 38 | Viewed by 7127

Abstract

We review the current state on the thermodynamic behavior and structural phases of self- and mutually-attractive dilute semiflexible polymers that undergo temperature-driven transitions. In extreme dilution, polymers may be considered isolated, and this single polymer undergoes a collapse or folding transition depending on [...] Read more.

We review the current state on the thermodynamic behavior and structural phases of self- and mutually-attractive dilute semiflexible polymers that undergo temperature-driven transitions. In extreme dilution, polymers may be considered isolated, and this single polymer undergoes a collapse or folding transition depending on the internal structure. This may go as far as to stable knot phases. Adding polymers results in aggregation, where structural motifs again depend on the internal structure. We discuss in detail the effect of semiflexibility on the collapse and aggregation transition and provide perspectives for interesting future investigations. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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1771 KiB

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Semiflexible Polymers in the Bulk and Confined by Planar Walls

by Sergei A. Egorov, Andrey Milchev and Kurt Binder

Polymers 2016, 8(8), 296; https://doi.org/10.3390/polym8080296 - 10 Aug 2016

Cited by 26 | Viewed by 6016

Abstract

Semiflexible polymers in solution under good solvent conditions can undergo an isotropic-nematic transition. This transition is reminiscent of the well-known entropically-driven transition of hard rods described by Onsager’s theory, but the flexibility of the macromolecules causes specific differences in behavior, such as anomalous [...] Read more.

Semiflexible polymers in solution under good solvent conditions can undergo an isotropic-nematic transition. This transition is reminiscent of the well-known entropically-driven transition of hard rods described by Onsager’s theory, but the flexibility of the macromolecules causes specific differences in behavior, such as anomalous long wavelength fluctuations in the ordered phase, which can be understood by the concept of the deflection length. A brief review of the recent progress in the understanding of these problems is given, summarizing results obtained by large-scale molecular dynamics simulations and density functional theory. These results include also the interaction of semiflexible polymers with hard walls and the wall-induced nematic order, which can give rise to capillary nematization in thin film geometry. Various earlier theoretical approaches to these problems are briefly mentioned, and an outlook on the status of experiments is given. It is argued that in many cases of interest, it is not possible to describe the scaled densities at the isotropic-nematic transition as functions of the ratio of the contour length and the persistence length alone, but the dependence on the ratio of chain diameter and persistence length also needs to be considered. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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8244 KiB

Open AccessFeature PaperReview

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond

by Jörg Baschnagel, Hendrik Meyer, Joachim Wittmer, Igor Kulić, Hervé Mohrbach, Falko Ziebert, Gi-Moon Nam, Nam-Kyung Lee and Albert Johner

Polymers 2016, 8(8), 286; https://doi.org/10.3390/polym8080286 - 8 Aug 2016

Cited by 38 | Viewed by 9604

Abstract

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption [...] Read more.

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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10107 KiB

Open AccessFeature PaperReview

Semiflexible Biopolymers in Bundled Arrangements

by Jörg Schnauß, Tina Händler and Josef A. Käs

Polymers 2016, 8(8), 274; https://doi.org/10.3390/polym8080274 - 28 Jul 2016

Cited by 30 | Viewed by 8419

Abstract

Bundles and networks of semiflexible biopolymers are key elements in cells, lending them mechanical integrity while also enabling dynamic functions. Networks have been the subject of many studies, revealing a variety of fundamental characteristics often determined via bulk measurements. Although bundles are equally [...] Read more.

Bundles and networks of semiflexible biopolymers are key elements in cells, lending them mechanical integrity while also enabling dynamic functions. Networks have been the subject of many studies, revealing a variety of fundamental characteristics often determined via bulk measurements. Although bundles are equally important in biological systems, they have garnered much less scientific attention since they have to be probed on the mesoscopic scale. Here, we review theoretical as well as experimental approaches, which mainly employ the naturally occurring biopolymer actin, to highlight the principles behind these structures on the single bundle level. Full article

(This article belongs to the Special Issue Semiflexible Polymers)

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