Semiflexible Polymers Research Articles

Structure and Mechanics of Bundled Semiflexible Polymer Networks

Fibrous networks of semiflexible polymers are prevalent in biological materials such as connective tissues, the cytoskeleton, and biofilm extracellular matrices. While the mechanical behavior of pe...

Nonmonotonic adsorption behavior of semiflexible polymers

We study the adsorption behavior of semiflexible polymer chains with finite concentrations onto a structureless, planar, and impenetrable surface using polymer density functional theory based on a discretization of the Kratky-Porod wormlike chain model. Adsorption characteristics are investigated at different attractive interactions between the surface and polymers of various intrinsic stiffnesses. We analyze the density distributions in the vicinity of the surface and find, in the adsorption regime (when the surface attraction is strong: ϵw≳ϵw c, where ϵw c is the critical surface potential of adsorption transition), a nonmonotonic adsorption behavior for polymer chains with various intrinsic stiffnesses: the adsorption amount first decreases and then increases with the intrinsic stiffness, and the minimum adsorption amount (as well as the maximum critical surface potential of adsorption transition) occurs at lp ∼ Δ (Δ and lp are the attractive range of surface potential and persistence length, respectively), while in the depletion regime (ϵw≪ϵw c), the depletion depth and range are increased monotonically with the intrinsic stiffness. Furthermore, we find βϵw c∼lp/Δ-0.185 for lp ⋗ Δ and βϵw c∼lp/Δ0.366 for lp < Δ.

Probing the Structure of Filamentous Nonergodic Gels by Dynamic Light Scattering

Mesh size is a crucial parameter that governs the behavior of gels made of semiflexible polymers. We show that the average mesh size of amyloid fibril gels can be extracted from simple dynamic ligh...

Structural Diversity of Native Major Ampullate, Minor Ampullate, Cylindriform, and Flagelliform Silk Proteins in Solution.

The foundations of silk spinning, the structure, storage, and activation of silk proteins, remain highly debated. By combining solution small-angle neutron and X-ray scattering (SANS and SAXS) alongside circular dichroism (CD), we reveal a shape anisotropy of the four principal native spider silk feedstocks from Nephila edulis. We show that these proteins behave in solution like elongated semiflexible polymers with locally rigid sections. We demonstrated that minor ampullate and cylindriform proteins adopt a monomeric conformation, while major ampullate and flagelliform proteins have a preference for dimerization. From an evolutionary perspective, we propose that such dimerization arose to help the processing of disordered silk proteins. Collectively, our results provide insights into the molecular-scale processing of silk, uncovering a degree of evolutionary convergence in protein structures and chemistry that supports the macroscale micellar/pseudo liquid crystalline spinning mechanisms proposed by the community.

Macromolecule crowding effects on the phase separation of semi-flexible polymer in spherical confined space

Current works focus on detecting macromolecule crowding effects on the phase separation of the mixture between semi-flexible polymer and crowders (hydrophilic polymers) in confined space by Monte Carlo simulations. With the increasing addition of crowders into the spherical confined space, the semi-flexible polymer was first compressed into a condensed state from the initial coil state, and then the condensed conformation expanded and deposited on the inner surface of the spherical confined space with an extended state. The phase diagram in the phase space of the volume fraction of crowders and the scaled radius of spherical confined space by crowder diameter, and the direct conformation transition of semi-flexible polymer have validated the phase transition process successfully. In addition, the deposition of extended conformation on the inner surface of the spherical confined space was qualified by the vertex density, its curve shifted along the radial direction with the increasing volume fraction of crowder. During the phase separation process, the critical volume fraction φ∗ relates to the crowder diameter approximately linearly and the relation between the critical volume fraction and the crowder diameter strongly depends on the size of the spherical confined space.

Critical properties of semi-flexible polymer chains situated within the simple cubic lattice

We have studied the critical properties of semi-flexible polymer chains whose elastic properties are brought out by the stiffness parameter s, and which are modelled by self-avoiding random walks (SAWs) in three-dimensional space. By applying the PERM Monte Carlo method, we have simulated the polymer chains by SAWs along the bonds of the simple cubic lattice, for a set of specific values for the stiffness parameter s. More precisely, we have examined behaviour of critical exponent νN, associated with the mean squared end-to-end distance of polymer chains of length N, as a function of s. Thus, we have established that νN monotonically decreases with N for s ⩾ 0.6, whereas the critical exponent νN displays a non-monotonic behaviour for s < 0.6. Values of νN, obtained for various s, have been extrapolated in the range of very long chains, and we have shown that obtained values ν = limN→∞νN do not depend on the polymer flexibility. Besides, we have calculated approximately the partition function for SAWs of length N, and examined its asymptotic behaviour, which turns out to be governed by the entropic critical exponent γ (associated with the total number of different polymer configurations), and the growth constant μ. We demonstrate that μ is a linear function of s, while γ does not depend on the polymer flexibility. Finally, we discuss and compare our results to those obtained previously for polymers on Euclidean lattices.

Scaling Limit of Semiflexible Polymers: A Phase Transition

We consider a semiflexible polymer in $\mathbb Z^d$ which is a random interface model with a mixed gradient and Laplacian interaction. The strength of the two operators is governed by two parameters called lateral tension and bending rigidity, which might depend on the size of the graph. In this article we show a phase transition in the scaling limit according to the strength of these parameters: we prove that the scaling limit is, respectively, the Gaussian free field, a "mixed" random distribution and the continuum membrane model in three different regimes.

Nematic ordering of worm-like polymers near an interface.

The phase behavior of semi-flexible polymers is integral to various contexts, from materials science to biophysics, many of which utilize or require specific confinement geometries as well as the orientational behavior of the polymers. Inspired by collagen assembly, we study the orientational ordering of semi-flexible polymers, modeled as Maier-Saupe worm-like chains, using self-consistent field theory. We first examine the bulk behavior of these polymers, locating the isotropic-nematic transition and delineating the limit of stability of the isotropic and nematic phases. This effort explains how nematic ordering emerges from the isotropic phase and offers insight into how different (e.g., mono-domain vs multi-domain) nematic phases form. We then clarify the influence of planar confinement on the nematic ordering of the polymers. We find that while the presence of a single confining wall does not shift the location of nematic transition, it aligns the polymers in parallel to the wall; above the onset of nematic transition, this preference tends to propagate into the bulk phase. Introducing a second, perpendicular, wall leads to a nematic phase that is parallel to both walls, allowing the ordering direction to be uniquely set by the geometry of the experimental setup. The advantage of wall-confinement is that it can be used to propagate mono-domain nematic phases into the bulk phase.

Simulation Study of Entanglement in Semiflexible Polymer Melts and Solutions

Multiple scaling arguments have been proposed to describe how the entanglement molecular weight depends on polymer architecture and concentration. The Lin–Noolandi (LN) scaling argument, well suppo...

Ordered aggregation of semiflexible ring-linear blends in ellipsoidal confinement

Coarse-grained molecular dynamics simulations are used to investigate the conformations of semiflexible ring-linear blends in ellipsoidal confinement. Ordered structures of semiflexible ring polymers (SRPs) in ring-linear blends rely strongly on the number density of blends (ρ), the chain length (Nlinear) and the bending energy (Kb,linear) of semiflexible linear polymers, as well as the curvature of confinement. For a low number density ρ, SRPs are immersed randomly in the matrix of linear polymers in ellipsoid confinement. However, for a high number density ρ, a complete separation of SRPs from flexible linear polymers occurs, and a highly ordered aggregation structure of SRPs at the equatorial plane is formed in the mixture of semiflexible linear polymers with large Kb,linear. These explicit ordered aggregations of SRPs in ellipsoidal confinement are induced by a delicate competition between the entropic excluded volume (depletion) effects and bending contributions. This investigation can help us understand the complicated conformations of ring-linear blends in ellipsoidal confinement.

Depletion-Induced Flocculation of Concentrated Emulsions Probed by Photon Density Wave Spectroscopy.

Stable, creaming-free oil in water emulsions with high volume fractions of oil (ϕ = 0.05-0.40, density matched to water) and polysorbate 80 as an emulsifier were characterized without dilution by Photon Density Wave spectroscopy measuring light absorption and scattering behavior, the latter serving as the basis for droplet size distribution analysis. The emulsion with ϕ = 0.10 was used to investigate flocculation processes induced by xanthan as a semi-flexible linear nonabsorbing polymer. Different time regimes in the development of the reduced scattering coefficient μs' could be identified. First, a rapid, temperature-dependent change in μs' during the depletion process was observed. Second, the further decrease of μs' follows a power law in analogy to a spinodal demixing behavior, as described by the Cahn-Hilliard theory.

Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent.

This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provides a consistent characterization of the domain growth. Our results indicate that the coarsening kinetics presents a scaling behaviour that is independent of the solvent quality parameter, in analogy to the time–temperature superposition principle. Interestingly, the domain growth in time follows a power-law behaviour that is approximately independent of the architecture for all the flexible systems; while it is steeper for the semiflexible chains. Nevertheless, the fractal nature of the dense regions emerging during the collapse exhibits the same scaling behaviour for all the macromolecules. This suggests that the faster growing length scale in the semiflexible chains originates just from a faster mass diffusion along the chain contour, induced by the local stiffness. The decay of the dynamic correlations displays scaling behavior with the growing length scale of the system, which is a characteristic signature in coarsening phenomena.

Glass transition temperature from the chemical structure of conjugated polymers

The glass transition temperature (Tg) is a key property that dictates the applicability of conjugated polymers. The Tg demarks the transition into a brittle glassy state, making its accurate prediction for conjugated polymers crucial for the design of soft, stretchable, or flexible electronics. Here we show that a single adjustable parameter can be used to build a relationship between the Tg and the molecular structure of 32 semiflexible (mostly conjugated) polymers that differ drastically in aromatic backbone and alkyl side chain chemistry. An effective mobility value, ζ, is calculated using an assigned atomic mobility value within each repeat unit. The only adjustable parameter in the calculation of ζ is the ratio of mobility between conjugated and non-conjugated atoms. We show that ζ correlates strongly to the Tg, and that this simple method predicts the Tg with a root-mean-square error of 13 °C for conjugated polymers with alkyl side chains.

How does stiffness of polymer chains affect their adsorption transition?

The adsorption transition and the structure of semiflexible adsorbed macromolecules are studied by a molecular dynamics simulation of a coarse-grained, bead-spring type model. Varying chain length N and stiffness κ (which is proportional to the persistence length ℓp in d = 3 dimensions) as well as the strength ϵwall of the adsorption potential, the adsorbed monomer fraction, orientational bond order parameter, and chain linear dimensions are studied. In the simulations, excluded volume interactions normally are included but can be "switched off," and thus, the influence of excluded volume (leading to deviations from predictions of the wormlike chain model) can be identified. It is shown that the variation in the adsorption threshold ϵwall cr with ℓp is compatible with the predicted law ϵwall cr∝ℓp -1/3. In the vicinity of the adsorption threshold, the coils are still three-dimensional, and for large ℓp, the effect of the excluded volume is almost negligible, while for strongly adsorbed chains it is always felt. Near the transition, the decay length of orientational correlations along the chain contour increases gradually from ℓp to 2ℓp. While the latter value is expected for strictly two-dimensional chains from the Kratky-Porod model, this model is inaccurate for the description of lateral chain dimensions of long, strongly adsorbed, semiflexible polymers due to its neglect of excluded volume. The significance of these findings for the interpretation of pertinent experiments is briefly discussed.

Unified Entanglement Scaling for Flexible, Semiflexible, and Stiff Polymer Melts and Solutions

The entanglement length Ne is a key parameter for all entangled polymer fluids for which no comprehensive scaling theory yet exists. We have pieces of a theory; the Lin-Noolandi (LN) argument predicts Ne scaling for flexible chains that agrees with data on polymer melts. There are arguments for how Ne should depend on polymer concentration, but which are not obviously consistent with LN. Morse scaling describes entanglement for solutions of stiff chains, consistent with data. Everaers proposed an ansatz that Ne depends only on the arclength concentration, as if chains were uncrossable threads of vanishing thickness. This ansatz is consistent with simulations of bead-spring chains, but not with LN, as it has no role for packing length, the central parameter in LN scaling. We propose a comprehensive scaling theory that includes LN in one limit, thread ansatz in another, and reduces to Morse scaling for stiff chains. One new ingredient is that the typical distance of closest approach between two chains is governed by the packing length or chain diameter, whichever is larger. If a chain is sufficiently flexible and bulky, the packing length is relevant; but for stiffened bead-spring chains without side groups, the packing length is smaller than the chain diameter, so thread scaling applies. Our approach presents a consistent physical picture of entanglements in all regimes as close encounters between two chains. For solutions, we determine the entanglement probability between chain segments, and consistently describe the crossover between the Edwards and semidilute regimes.

Competitive Substrate Binding Coordinates the Two Antagonistic Motors of the Bacterial Type IV Pilus

The bacterial type IV pilus is an intricate nano-machine that coordinates two antagonistic molecular motors to extend and retract a semi-flexible polymer to the environment. Filament retraction is driven by the strongest molecular motor known and used for a variety of tasks such as uptake of DNA, surface sensing, and motility. However, how both motors are coordinated to dynamically extend and retract pili is unknown. To fill this void, we genetically engineered a fluorescent label for the pilus fiber. This enables us to characterize the dynamic cycles of extension and retraction of the pilus in an unprecedented way. Careful characterization of pilus dynamics reveals that pili are short and individual cells make a new pilus every 10 seconds. This is in stark contrast to the current dogma of the field that was shaped by static cyro electron images. To explain this discrepancy, we introduce a simplistic three-state model that describes the mutually exclusive binding/unbinding of the motor proteins to the pilus machine by a Poisson process. We combined live cell super-resolution microscopy and Monte-Carlo simulations to determine the rate constants of the model. We explain how these rates determine biological function such as pilus length and rate of pilus assembly. Intriguingly, we find that the major throttle of pilus production is the unbinding step of the retraction motor. Furthermore, we measured pilus activity with and without surface contact by combining fluorescence microscopy and line-scanning optical tweezers. Cells show similar levels of pilus activity, overturning the current model that surface contact drives pilus retraction. Together, our results shape a comprehensive picture of the physical processes that determine pilus activity and suggest that the pilus was optimized for multitasking of different tasks such as DNA uptake and motility.

Scaling laws of entangled polysaccharides

We study the dilute solution properties and entangled dynamics of hydroxypropyl cellulose (HPC), a semiflexible polymer, in aqueous solution. Intrinsic viscosity data are consistent with a polymer in θ solvent with a Kuhn length ≃22 nm. The overlap concentration, estimated as the reciprocal of the intrinsic viscosity scales with the degree of polymerisation as c* ∝ N−0.9. We evaluate different methods for estimating the entanglement cross-over, following the de Gennes scaling and hydrodynamic scaling models, and show that these lead to similar results. Above the entanglement concentration, the specific viscosity, longest relaxation time and plateau modulus scale as ηsp ≃ N3.9c4.2, τ ≃ N3.9c2.4 and GP ≃ N0c1.9. A comparison with other polymers suggests that the rheological properties displayed by HPC are common to many polysaccharide systems of varying backbone composition, stiffness and solvent quality, as long as the effect of hyper-entanglements can be neglected. On the other hand, the observed scaling laws differ appreciably from those of synthetic flexible polymers in good or θ-solvent.

Semiflexible Polymers Interacting With Planar Surfaces: Weak versus Strong Adsorption.

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness as well as the strength of the adsorption potential are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter ) and the mean square gyration radius parallel, , and perpendicular, , to the wall. While for strongly adsorbed chains EV has negligible effect on f and , we find that is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that , and converge to their asymptotic values with corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.

Single chain in mean field simulation of flexible and semiflexible polymers: comparison with discrete chain self-consistent field theory.

Single chain in mean field (SCMF) simulation is a theoretical framework performing Monte Carlo moves of explicit polymer chains under quasi-instantaneously updated external fields which were originally imported from the self-consistent field theory (SCFT). Even though functional-based hybrid simulations are often used to compare the results of SCFT and MC simulation, the adoption of a finite number of coarse-grained segments makes direct comparison rather difficult. In this study, we perform SCMF simulation of block copolymers using various chain models and quantitatively compare it with discrete chain SCFT (DCSCFT) which finds the mean field solution of polymers with a finite number of segments. By comparing free energy and natural period of the symmetric block copolymer lamellar phase, we systematically show that DCSCFT serves as an intermediate step between SCMF simulation and SCFT. In addition, by adopting angle dependent bond potential, we perform SCMF simulation of semiflexible polymers using bead-spring and freely jointed chain models. As the chain stiffness increases, the lamellar phase tends to align perpendicular to the surfaces when confined between two neutral walls. We also investigate the effects of fluctuation and chain stiffness on the distribution of chain ends. The tendency of chain end segregation towards the surfaces turns out to increase as the chain stiffness increases for both homopolymer and block copolymer systems.

A comparative study of semi-flexible linear and ring polymer conformational change in an anisotropic environment.

We adopt a Langevin-dynamics based simulation to systematically study the conformational change of a semi-flexible probed polymer in a rod crowding environment. Two topologically different probed polymer types, linear and ring polymers, are specifically considered. Our results unravel the significance of the interplay of probed polymer's semi-flexibility and crowding anisotropy. Firstly, both ring and linear polymers show a non-trivial dimensional change including nonmonotonicity and collapse-swelling crossover as their stiffness increases. Secondly, we modulate rod crowder length to investigate the anisotropic effect. We reveal that the formation of an ordered parallel arrangement of the environment can effectively lead to a remarkable stretching effect on the probed polymer. The coupling between the crowding anisotropy-induced stretching and the polymer stiffness can account for the unusual swelling behavior. Lastly, nonmonotonic swelling and shape change of the ring polymer are analyzed. We find out that the ring polymer is subject to most pronounced swelling at robust stiffness. Moreover, the maximum prolate shape is also observed at the same robust location.