Wormlike Chain Research Articles

Self-Avoiding Wormlike Chain Confined in a Cylindrical Tube: Scaling Behavior.

Within a confining tube section, the multithreads of a strongly confined, backfolding polymer exert the excluded-volume repulsions on each other and produce physical properties that are very different from those of a confined ideal chain. The conformational properties of a such confined wormlike chain are of fundamental interest and are also practically useful in understanding the DNA confinement problems. Here, the excluded-volume effects are added to the standard wormlike-chain model by a self-consistent field theory. The numerical solutions are examined in light of their scaling properties.

Tunable Toughness of Model Fibers With Bio-Inspired Progressive Uncoiling Via Sacrificial Bonds and Hidden Length

Nature has a proven track record of advanced materials with outstanding mechanical properties, which has been the focus of recent research. A well-known trade-off between ultimate strength and toughness is one of the main challenges in materials design. Progress has been made by mimicking tough biological fibers by applying the concepts of (1) sacrificial bond and (2) hidden length, providing a so-called “safety-belt” for biological materials. Prior studies indicate a relatively common behavior across scales, from nano- to macro-, suggesting the potential of a generalized theoretical mechanistic framework. Here, we undertake molecular dynamics (MD) based simulation to investigate the mechanical properties of model nanoscale fibers. We explore representative models of serial looped or coiled fibers with different parameters—specifically number of loops, loop radii, cross-link strength, and fiber stiffness—to objectively compare strength, extensibility, and fiber toughness gain. Observing consistent saw-tooth like behavior, and adapting worm-like chain (WLC) mechanics (i.e., pseudo-entropic elasticity), a theoretical scaling relation which can describe the fiber toughness gain as a function of the structural factors is developed and validated by simulation. The theoretical model fits well with the simulation results, indicating that engineering the mechanical response based on controlled structure is possible. The work lays the foundation for the design of uniaxial metamaterials with tunable and predictable tensile behavior and superior toughness.

Applications of worm-like chain model in polymer physics

Saito, Takahashi and Yunoki developed the continuous version of worm-like chain (WLC) model that is very suitable for description of the polymer conformational properties affected by chain rigidity. By adjusting persistence length directly, the WLC model can depict the extensive range of chain conformations from flexible chains to rigid chains. It is widely accepted that more physical properties of real polymer can be obtained by utilizing coarse-grained model than Gaussian chain (GSC). This paper reviews the applications of the WLC model in the framework based on self-consistent field theory, which is an efficient method of theoretical exploration of phase separation in polymer system. It is noticed that the development of numerical schemes is in favor of solving modified diffusion equation that adjusts the probability distribution of polymers. In addition, we conclude the recent applications of the self-consistent field theory based on the WLC model as the following three points: phase transitions of liquid crystal polymer; the influences of surface curvature on polymer system that involves the chain orientation effects; self-assembly of worm-like block copolymer. These researches have been out of the range of the self-consistent field theory based on GSC model that has been used in a large number of theoretical studies. Finally, we present ideas of theoretical development in field theory simulations based on the WLC model in the future. It is universally acknowledged that chain rigidity is a key factor that influences the properties of structural stabilities in the meso-scale in articles. Theoretical researches determine the key physical mechanisms that play crucial roles in many experimental systems with attractively promising applications in practice, for systems such as liquid crystalline polymers and organic solar cell based on the conjugated polymers.

Characterisation of flexible fibre deformations in turbulence

The transport of deformable objects by a turbulent flow is common in environmental sciences which are interested, for instance, in the dynamics of plankton in the ocean, and in industry, such as the papermaking or textile industries. In this study, the deformations of flexible fibres in homogeneous isotropic turbulence are experimentally and numerically investigated, focusing on the local curvature κ. By comparing our results to the predictions for worm-like chain polymers in an ideal solvent, we are able to identify the role of the spatial and temporal correlations of the turbulent forcing. In particular, we show that these correlations are responsible for a straightening of long fibres which become statistically less distorted by turbulence as their length increases.

Molecular orientation dependent dynamic viscoelasticity in uni-axially drawn polycarbonate

Molecular orientation and dynamic modulus of the high and low temperature drawn polycarbonate splines were investigated using wide-angle X-ray diffraction (WAXD) and dynamic mechanical analysis (DMA). For high-temperature stretched splines, the storage modulus in the glassy state and the loss modulus in the rubbery state increased with increasing the orientation. No obvious regularity was observed for the low-temperature stretched ones. These behaviors could be interpreted by a relation between relaxation modulus and average orientation angle, which was derived from the elastic dumbbell model and wormlike chain model. Through associating the molecular orientation defined by Herman's factor with the storage modulus at the end of the glassy state plateau and the loss modulus at the tanδ peak respectively, the relationship between orientation and dynamic viscoelasticity of polycarbonate was built as well.

Sequence-Dependent Three Interaction Site Model for Single- and Double-Stranded DNA.

We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

Detecting Branching in Wormlike Micelles via Dynamic Scattering Methods.

Topological differences in a model series of wormlike micelles (WLMs) with varying degrees of branching are investigated via neutron spin echo (NSE) and dynamic light scattering (DLS). Branching was previously verified via microscopy, scattering methods, and rheology. NSE measurements reveal that on the shortest length scales, where WLMs are topologically similar, the dynamic behavior is independent of branching level. However, branching leads to deviations from wormlike chain behavior on length scales relevant to branching. These differences continue into the DLS regime, where two relaxation modes are observed. While measuring micellar branching is challenging, our measurements of segmental dynamics provide a direct dynamic measurement of WLM branching and demonstrate promise for future identification of topological changes in self-assembled materials.

Progressive Relaxation Behavior and Relaxation Dynamics of sPS Gels upon Controlled Heating.

Progressive relaxation behavior of syndiotactic polystyrene (sPS) chains in sPS gel was detected in the course of melting via the application of intrinsic fluorescence and fluorescence anisotropy techniques. The melting process included a dissociative process of the network at lower temperature and a relaxation process from helix to worm-like chains at higher temperature. The dynamics of structural relaxation behavior was discovered by intrinsic fluorescence technique, and an abrupt bend emerged at 58 °C on the Arrhenius plot. At temperatures lower than 58 °C, only the dissociation of the helical structure existed and the rate of relaxation from helix to worm-like conformation was negligible. At temperatures higher than 58 °C, the transition from helical chain to worm-like chain was the rate-determining step. The intrinsic fluorescence technique demonstrated its practicability in detecting kinetic processes of sPS/chloroform gel in the course of melting.

Adsorption and structure formation of semiflexible polymers on spherical surfaces

Rigid spheres with a short-range attractive potential are taken as a coarse-grained model of vesicles, which contain a solution of semiflexible polymers in their interior. Assuming good solvent conditions with an implicit description of the solvent, effective monomers experience bond-length and bond-angle potentials as well as excluded-volume interaction. Due to the attractive vesicle surface, phase separation occurs between a thin shell of adsorbed monomers at the surface and a rather dilute, and therefore, disordered polymer solution in the sphere interior. While at a planar attractive surface the wormlike chains would exhibit liquid crystalline (nematic and smectic) order, the curvature of the sphere frustrates this order, causing the existence of defects in the orientational order. In the dense monolayer of surface-attached polymers, the stiff chains acquire a curvature corresponding to banana-like shapes for rather small contour length, causing a local nematic order of biaxial type. These orderings are compared to related phenomena in spheres densely filled with semiflexible polymers. We complement the results obtained by Molecuar Dynamics simulations by corresponding Density Functional Theory calculations.

Mechanical transduction via a single soft polymer.

Molecular machines from biology and nanotechnology often depend on soft structures to perform mechanical functions, but the underlying mechanisms and advantages or disadvantages over rigid structures are not fully understood. We report here a rigorous study of mechanical transduction along a single soft polymer based on exact solutions to the realistic three-dimensional wormlike-chain model and augmented with analytical relations derived from simpler polymer models. The results reveal surprisingly that a soft polymer with vanishingly small persistence length below a single chemical bond still transduces biased displacement and mechanical work up to practically significant amounts. This "soft" approach possesses unique advantages over the conventional wisdom of rigidity-based transduction, and potentially leads to a unified mechanism for effective allosterylike transduction and relay of mechanical actions, information, control, and molecules from one position to another in molecular devices and motors. This study also identifies an entropy limit unique to the soft transduction, and thereby suggests a possibility of detecting higher efficiency for kinesin motor and mutants in future experiments.

Combined experimental and computational characterization of crosslinked collagen-based hydrogels.

Collagen hydrogels are widely used for in-vitro experiments and tissue engineering applications. Their use has been extended due to their biocompatibility with cells and their capacity to mimic biological tissues; nevertheless their mechanical properties are not always optimal for these purposes. Hydrogels are formed by a network of polymer filaments embedded on an aqueous substrate and their mechanical properties are mainly defined by the filament network architecture and the individual filament properties. To increase properties of native collagen, such as stiffness or strain-stiffening, these networks can be modified by adding crosslinking agents that alter the network architecture, increasing the unions between filaments. In this work, we have investigated the effect of one crosslinking agent, transglutaminase, in collagen hydrogels with varying collagen concentration. We have observed a linear dependency of the gel rigidity on the collagen concentration. Moreover, the addition of transglutaminase has induced an earlier strain-stiffening of the collagen gels. In addition, to better understand the mechanical implications of collagen concentration and crosslinkers inclusion, we have adapted an existing computational model, based on the worm-like chain model (WLC), to reproduce the mechanical behavior of the collagen gels. With this model we can estimate the parameters of the biopolymer networks without more sophisticated techniques, such as image processing or network reconstruction, or, inversely, predict the mechanical properties of a defined collagen network.

Solution Properties of Polysarcosine: From Absolute and Relative Molar Mass Determinations to Complement Activation

Polysarcosine (pSar) was one of the first polymers synthesized in a controlled living manner, but it was only recently when it was reconsidered as a promising alternative for poly(ethylene glycol) (PEG) in biomedical applications. Despite receiving more and more attention, very little is known about the solution properties of pSar, such as coil dimensions and thermodynamic interactions. In this article, we report on these properties of pSar with degrees of polymerization 50 < Xn < 400 that were prepared by controlled living ring-opening polymerization. The polymers are characterized by gel permeation chromatography (GPC), MALDI-TOF mass spectrometry, dynamic and static light scattering (SLS), and viscometry. The chain stiffness of pSar in PBS in terms of the Kuhn statistical segment length, lk, was estimated to lk = 1.5 nm by application of the Yamakawa–Fujii wormlike chain theory to the experimentally determined hydrodynamic radii, Rh, thus being higher than lk = 1.1 nm for PEG in PBS. Also, the second v...

Hairpins in the conformations of a confined polymer.

If a semiflexible polymer confined to a narrow channel bends around by 180°, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here, we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte-Carlo simulations of confined discrete wormlike chains. We develop a simple model that qualitatively explains the form of the extension distribution. The model shows that the tail of the distribution at short extensions is determined by conformations with one hairpin.

Evaluation of Blob Theory for the Diffusion of DNA in Nanochannels.

We have measured the diffusivity of λ-DNA molecules in approximately square nanochannels with effective sizes ranging from 117 nm to 260 nm at moderate ionic strength. The experimental results do not agree with the non-draining scaling predicted by blob theory. Rather, the data are consistent with the predictions of previous simulations of the Kirkwood diffusivity of a discrete wormlike chain model, without the need for any fitting parameters.

Polymer Semiflexibility Induces Nonuniversal Phase Transitions in Diblock Copolymers.

The order-disorder phase transition and the associated phase diagrams of semiflexible diblock copolymers are investigated using the wormlike chain model, incorporating concentration fluctuations. The free energy up to quartic order in concentration fluctuations is developed with chain-rigidity-dependent coefficients, evaluated using our exact results for the wormlike chain model, and a one-loop renormalization treatment is used to account for fluctuation effects. The chain length N and the monomer aspect ratio α directly control the strength of immiscibility (defined by the Flory-Huggins parameter χ) at the order-disorder transition and the resulting microstructures at different chemical compositions f_{A}. When monomers are infinitely thin (i.e., large aspect ratio α), the finite chain length N lowers the χN at the phase transition. However, fluctuation effects become important when chains have a finite radius, and a decrease in the chain length N elevates the χN at the phase transition. Phase diagrams of diblock copolymers over a wide range of N and α are calculated based on our fluctuation theory. We find that both finite N and α enhance the stability of the lamellar phase above the order-disorder transition. Our results demonstrate that polymer semiflexibility plays a dramatic role in the phase behavior, even for large chain lengths (e.g., N≈100).

Forceless Sadowsky strips are spherical.

We show that thin rectangular ribbons, defined as energy-minimizing configurations of the Sadowsky functional for narrow developable elastic strips, have a propensity to form spherical shapes in the sense that forceless solutions lie on a sphere. This has implications for ribbonlike objects in (bio)polymer physics and nanoscience that cannot be described by the classical wormlike chain model. A wider class of functionals with this property is identified.

Evidence for the extended de Gennes regime of a semiflexible polymer in slit confinement.

We use off-lattice, pruned-enriched Rosenbluth method (PERM) simulations to compute the confinement free energy of a real wormlike chain of effective width w and persistence length lp in a slit of height H. For slit heights much larger than the persistence length of the polymer and much smaller than the thermal blob size, the excess free energy of the confined chain is consistent with a modified version of the scaling theory for the extended de Gennes regime in a channel that reflects the blob statistics in slit confinement. Explicitly, for channel sizes [Formula: see text], the difference between the confinement free energy of the real chain and that of an ideal chain scales like w/H.

A cooperative transition from the semi-flexible to the flexible regime of polymer elasticity: Mitoxantrone-induced DNA condensation

We report a high cooperative transition from the semi-flexible to the flexible regime of polymer elasticity during the interaction of the DNA molecule with the chemotherapeutic drug Mitoxantrone (MTX). By using single molecule force spectroscopy, we show that the force-extension curves of the DNA-MTX complexes deviate from the typical worm-like chain behavior as the MTX concentration in the sample increases, becoming straight lines for sufficiently high drug concentrations. The behavior of the radius of gyration of the complexes as a function of the bound MTX concentration was used to quantitatively investigate the cooperativity of the condensation process. The present methodology can be promptly applied to other ligands that condense the DNA molecule upon binding, opening new possibilities in the investigation of this type of process and, more generally, in the investigation of phase transitions in polymer physics.

Mechanics and statistics of the worm-like chain

The worm-like chain model is a simple continuum model for the statistical mechanics of a flexible polymer subject to an external force. We offer a tutorial introduction to it using three approaches. First, we use a mesoscopic view, treating a long polymer (in two dimensions) as though it were made of many groups of correlated links or “clinks,” allowing us to calculate its average extension as a function of the external force via scaling arguments. We then provide a standard statistical mechanics approach, obtaining the average extension by two different means: the equipartition theorem and the partition function. Finally, we work in a probabilistic framework, taking advantage of the Gaussian properties of the chain in the large-force limit to improve upon the previous calculations of the average extension.

Study of Polyelectrolyte-Small Molecule Drug Binding with Wormlike Chain Model

Study of Polyelectrolyte-Small Molecule Drug Binding with Wormlike Chain Model