Semiflexible Polymers Research Articles

Laun's rule for predicting the first normal stress coefficient in complex fluids: A comprehensive investigation using fractional calculus

Laun's rule [H. M. Laun, “Prediction of elastic strains of polymer melts in shear and elongation,” J. Rheol. 30, 459–501 (1986).] is commonly used for evaluating the rate-dependent first normal stress coefficient from the frequency dependence of the complex modulus. We investigate the mathematical conditions underlying the validity of Laun's relationship by employing the time-strain–separable Wagner constitutive formulation to develop an integral expression for the first normal stress coefficient of a complex fluid in steady shear flow. We utilize the fractional Maxwell liquid model to describe the linear relaxation dynamics compactly and accurately and incorporate material nonlinearities using a generalized damping function of Soskey–Winter form. We evaluate this integral representation of the first normal stress coefficient numerically and compare the predictions with Laun's empirical expression. For materials with a broad relaxation spectrum and sufficiently strong strain softening, Laun's relationship enables measurements of linear viscoelastic data to predict the general functional form of the first normal stress coefficient but often with a noticeable quantitative offset. Its predictive power can be enhanced by augmenting the original expression with an adjustable power-law index that is based on the linear viscoelastic characteristics of the specific material being considered. We develop an analytical expression enabling the calculation of the optimal power-law index from the frequency dependence of the viscoelastic spectrum and the strain-softening characteristics of the material. To illustrate this new framework, we analyze published data for an entangled polymer melt and for a semiflexible polymer solution; in both cases our new approach shows significantly improved prediction of the experimentally measured first normal stress coefficient.

Highly flexible PEG-LifeAct constructs act as tunable biomimetic actin crosslinkers.

In vitro studies of actin filament networks crosslinked with dynamic actin binding proteins provide critical insights into cytoskeletal mechanics as well as inspiration for new adaptive materials design. However, discontinuous variance in the physiochemical properties of actin binding proteins impedes holistic relationships between crosslinker molecular parameters, network structure, and mechanics. Bio-synthetic constructs composed of synthetic polymer backbones and actin binding motifs would enable crosslinkers with engineered physiochemical properties to directly target the desired structure-property relationships. As a proof of concept, bio-synthetic crosslinkers composed of highly flexible polyethylene glycol (PEG) polymers functionalized with the actin binding peptide LifeAct, are explored as actin crosslinkers. Using bulk rheology and fluorescence microscopy, these constructs are shown to modulate actin filament network structure and mechanics in a contour length dependent manner, while maintaining the stress-stiffening behavior inherent to actin filament networks. These results encourage the design of more diverse and complex peptide-polymer crosslinkers to interrogate and control semi-flexible polymer networks.

Active motion of tangentially driven polymers in periodic array of obstacles

One key question about transport of active polymers within crowded environments is how spatial order of obstacles influences their conformation and dynamics when compared to disordered media. To this end, we computationally investigate the active transport of tangentially driven polymers with varying degrees of flexibility and activity in two-dimensional square lattices of obstacles. Tight periodic confinement induces notable conformational changes and distinct modes of transport for flexible and stiff active filaments. It leads to caging of low activity flexible polymers inside the inter-obstacle pores while promoting more elongated conformations and enhanced diffusion for stiff polymers at low to moderate activity levels. The migration of flexible active polymers occurs via hopping events, where they unfold to move from one cage to another, similar to their transport in disordered media. However, in ordered media, polymers are more compact and their long-time dynamics is significantly slower. In contrast, stiff chains travel mainly in straight paths within periodic inter-obstacle channels while occasionally changing their direction of motion. This mode of transport is unique to periodic environment and leads to more extended conformation and substantially enhanced long-time dynamics of stiff filaments with low to moderate activity levels compared to disordered media. At high active forces, polymers overcome confinement effects and move through inter-obstacle pores just as swiftly as in open spaces, regardless of the spatial arrangement of obstacles. We explain the center of mass dynamics of semiflexible polymers in terms of active force and obstacle packing fraction by developing an approximate analytical theory.

Interacting semi-flexible self-avoiding walks studied on a fractal lattice

Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, nonhomogeneous solution. The model is supplemented with bending energies and attractive-interaction energies between nonconsecutively visited pairs of nearest-neighboring sites (contacts). It captures the main features of a semi-flexible polymer subjected to variable solvent conditions. A hierarchical structure of the fractal lattice enabled the determination of the exact recurrence equations for the generating function, through which universal and local properties of the model were studied. An analysis of the recurrence equations showed that for all finite values of the considered energies and nonzero temperatures, the polymer resides in an expanded phase. The critical exponents of the expanded phase are universal and the same as those for ordinary self-avoiding walks on the same lattice found earlier. As a measure of local properties, the mean number of contacts per mean number of steps as well as the persistence length, are calculated as functions of Boltzmann weights associated with bending energies and attractive interactions between contacts. Both quantities are monotonic functions of stiffness weights for fixed interaction, and in the limit of infinite stiffness, the number of contacts decreases to zero, while the persistence length increases unboundedly.

Mechanical criticality of fiber networks at a finite temperature.

At zero temperature, spring networks with connectivity below Maxwell's isostatic threshold undergo a mechanical phase transition from a floppy state at small strains to a rigid state for applied shear strain above a critical strain threshold. Disordered networks in the floppy mechanical regime can be stabilized by entropic effects at finite temperature. We develop a scaling theory for this mechanical phase transition at finite temperature, yielding relationships between various scaling exponents. Using Monte Carlo simulations, we verify these scaling relations and identify anomalous entropic elasticity with sublinear T dependence in the linear elastic regime. While our results are consistent with prior studies of phase behavior near the isostatic point, the present work also makes predictions relevant to the broad class of disordered thermal semiflexible polymer networks for which the connectivity generally lies far below the isostatic threshold.

Ejection dynamics of a semiflexible polymer from a nanosphere

Ejection dynamics of a semiflexible polymer from a nanosphere

Stochastic Electrical Detection of Single Ion-Gated Semiconducting Polymers.

Semiconducting polymer chains constitute the building blocks for a wide range of electronic materials and devices. However, most of their electrical characteristics at the single-molecule level have received little attention. Elucidating these properties can help understanding performance limits and enable new applications. Here, coupled ionic-electronic charge transport is exploited to measure the quasi-1D electrical current through long single conjugated polymer chains as they form transient contacts with electrodes separated by ≈10nm. Fluctuations between internal conformations of the individual polymers are resolved as abrupt, multilevel switches in the electrical current. This behavior is consistent with the theoretical simulations based on the worm-like-chain (WLC) model for semiflexible polymers. In addition to probing the intrinsic properties of single semiconducting polymer chains, the results provide an unprecedented window into the dynamics of random-coil polymers and enable the use of semiconducting polymers as electrical labels for single-molecule (bio)sensing assays.

Phase behaviour of semiflexible lattice polymers in poor-solvent solution: Mean-field theory and Monte Carlo simulations.

We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d = 3. A gas-liquid transition is found in the temperature-density plane that is then interpreted in terms of real systems. Interestingly, we find this transition to be independent of the bending rigidity. Past classical Flory-Huggins and Flory mean-field results are shown to be particular cases of this more general framework. Perspectives in terms of guiding experimental results towards optimal conditions are also proposed.

Craze Extension Ratio of Semiflexible Polymer Glasses

Craze Extension Ratio of Semiflexible Polymer Glasses

Cluster Formation in Solutions of Polyelectrolyte Rings.

We use molecular dynamics simulations to explore concentrated solutions of semiflexible polyelectrolyte ring polymers, akin to the DNA mini-circles, with counterions of different valences. We find that the assembly of rings into nanoscopic cylindrical stacks is a generic feature of the systems, but the morphology and dynamics of such a cluster can be steered by the counterion conditions. In general, a small addition of trivalent ions can stabilize the emergence of clusters due to the counterion condensation, which mitigates the repulsion between the like-charged rings. Stoichiometric addition of trivalent ions can even lead to phase separation of the polyelectrolyte ring phase due to the ion-bridging effects promoting otherwise entropically driven clustering. On the other hand, monovalent counterions cause the formation of stacks to be re-entrant with density. The clusters are stable within a certain window of concentration, while above the window the polyelectrolytes undergo an osmotic collapse, disfavoring ordering. The cluster phase exhibits characteristic cluster glass dynamics with arrest of collective degrees of freedom but not the self-ones. On the other hand, the collapsed phase shows arrest on both the collective and single level, suggesting an incipient glass-to-glass transition, from a cluster glass of ring clusters to a simple glass of rings.

Mixing and demixing arising from compression of two semiflexible polymer chains in nanochannels.

We use molecular dynamics simulation to probe the non-equilibrium physics of two nanochannel-confined semiflexible polymers in a homogeneous flow field. We find that for sufficiently stiff chains the internal organization of the two chains takes the form of interwoven folds and circular coils. This organization can lead to mixing or demixing depending on chain stiffness and flow speed. At low and intermediate flow, the two chains adopt a folded configuration, which favours mixing. At high flow, the two chains adopt a predominantly coiled configuration. The coiled configuration results in demixing when the chains are compressed from an initially demixed condition and mixing when the chains are compressed from an initially mixed condition. We find that the mixing/demixing behaviour is governed by the ratio of the number of folded segments of one chain relative to the other at low flow and by the degree of coiling in both chains at high flow. For decreasing stiffness, the chains start to aggregate locally instead of mixing smoothly at low and intermediate flow. In the limit of completely flexible chains, the two chains either completely segregate at low flow, or adopt a locally demixed configuration consisting of large aggregates of one chain relative to the other that undergo complex stochastic dynamics, diffusing, disintegrating, and reforming at intermediate flow. The transition from complete segregation to the aggregate-dominated configuration occurs when the linear intra-chain ordering breaks down.

Thermodynamically controlled multiphase separation of heterogeneous liquid crystal colloids

Phase separation is a universal physical transition process whereby a homogeneous mixture splits into two distinct compartments that are driven by the component activity, elasticity, or compositions. In the current work, we develop a series of heterogeneous colloidal suspensions that exhibit both liquid-liquid phase separation of semiflexible binary polymers and liquid crystal phase separation of rigid, rod-like nanocellulose particles. The phase behavior of the multicomponent mixture is controlled by the trade-off between thermodynamics and kinetics during the two transition processes, displaying cholesteric self-assembly of nanocellulose within or across the compartmented aqueous phases. Upon thermodynamic control, two-, three-, and four-phase coexistence behaviors with rich liquid crystal stackings are realized. Among which, each relevant multiphase separation kinetics shows fundamentally different paths governed by nucleation and growth of polymer droplets and nanocellulose tactoids. Furthermore, a coupled multiphase transition can be realized by tuning the composition and the equilibrium temperature, which results in thermotropic behavior of polymers within a lyotropic liquid crystal matrix. Finally, upon drying, the multicomponent mixture undergoes a hierarchical self-assembly of nanocellulose and polymers into stratified cholesteric films, exhibiting compartmentalized polymer distribution and anisotropic microporous structure.

Molecular Relay Stations in Membrane Nanotubes: IRSp53 Involved in Actin-Based Force Generation.

Membrane nanotubes are cell protrusions that grow to tens of micrometres and functionally connect cells. Actin filaments are semi-flexible polymers, and their polymerisation provides force for the formation and growth of membrane nanotubes. The molecular bases for the provision of appropriate force through such long distances are not yet clear. Actin filament bundles are likely involved in these processes; however, even actin bundles weaken when growing over long distances, and there must be a mechanism for their regeneration along the nanotubes. We investigated the possibility of the formation of periodic molecular relay stations along membrane nanotubes by describing the interactions of actin with full-length IRSp53 protein and its N-terminal I-BAR domain. We concluded that I-BAR is involved in the early phase of the formation of cell projections, while IRSp53 is also important for the elongation of protrusions. Considering that IRSp53 binds to the membrane along the nanotubes and nucleates actin polymerisation, we propose that, in membrane nanotubes, IRSp53 establishes molecular relay stations for actin polymerisation and, as a result, supports the generation of force required for the growth of nanotubes.

Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain.

Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.

Determining glass transition in all-atom acrylic polymeric melt simulations using machine learning.

The functionality of many polymeric materials depends on their glass transition temperatures (Tg). In computer simulations, Tg is often calculated from the gradual change in macroscopic properties. Precise determination of this change depends on the fitting protocols. We previously proposed a robust data-driven approach to determine Tg from the molecular dynamics simulation data of a coarse-grained semiflexible polymer model. In contrast to the global macroscopic properties, our method relies on high-resolution microscopic details. Here, we demonstrate the generality of our approach by using various dimensionality reduction and clustering methods and apply it to an atomistic model of acrylic polymers. Our study reveals the explicit contribution of the side chain and backbone residues in influencing the determination of the glass transition temperature.

Marginal Distributions at the Tip of a Grafted Stiff Polymer: Analytical and Monte Carlo Investigations

AbstractThis study investigates the marginal distributions of grafted stiff polymer tips in a 2D embedding space using both analytical methods and Monte Carlo simulations. By mapping active Brownian particle (ABP) trajectories in the short‐time regime, analytical expressions for the elongation of the free end of the polymer under horizontal and vertical forces are derived and these expressions are validated using Monte Carlo simulations. These results indicate that the theoretical predictions match well with the simulation results when the chain length is short or the force is large. However, a slight discrepancy is observed between the theoretical and simulation results when the chain is extremely long, although the qualitative asymptotic results remain valid. Additionally, expressions are provided for the horizontal and vertical force versus displacement for the wormlike chain under the weakly bending approximation. This research provides insights into how the trajectories of an ABP correspond to the equilibrium configuration of a semiflexible polymer. These findings have potential applications in various fields, including biophysics and materials science, where understanding the behavior of grafted polymers is crucial.

Ring-linear mixtures of semiflexible rubber bands

During the synthesis of ring polymers, it is quite common to obtain mixtures containing both ring and linear molecules. Recent studies, including experiments and simulations, have shown that even small quantities of linear molecules can significantly influence the shape of ring polymers, ultimately altering their rheological response. To further explore this phenomenon, we investigated blends of semiflexible linear and ring filaments by using disordered assemblies of open and closed rubber bands. We employed x-ray tomography to analyze the structure of these mixtures, focusing on how the length and composition of linear bands influenced the overall mixture. In contrast to the behavior observed in fully-flexible polymers, our findings revealed that increasing the concentration of linear bands could actually decrease the average size of rings within a semiflexible ring-linear mixture. This outcome is attributable to a reduction in inter-ring threading, which naturally occurs as the proportion of rings diminishes. To validate our findings, we conducted molecular dynamics simulations on semiflexible ring-linear polymer mixtures in bulk. These simulations confirmed that our results stem from the semiflexibility of the bands or chains rather than confinement or athermal conditions.

Compression of a confined semiflexible polymer under direct and oscillating fields.

The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.

Impact of flexibility on the aggregation of polymeric macromolecules.

Dependence of the dimerization probability and the aggregation behavior of polymeric macromolecules on their flexibility is studied using Langevin dynamics simulations. It is found that the dimerization probability is a non-monotonic function of the polymers persistence length. For a given value of inter-polymer attraction strength, semiflexible polymers have lower dimerization probability relative to flexible and rigid polymers of the same length. The threshold temperature of the formation of aggregates in a many-polymer system and its dependence on the polymers persistence length is also investigated. The simulation results of two- and many-polymer systems are in good agreement and show how the amount of flexibility affects the dimerization and the aggregation behaviors of polymeric macromolecules.

Partition complex structure can arise from sliding and bridging of ParB dimers

In many bacteria, chromosome segregation requires the association of ParB to the parS-containing centromeric region to form the partition complex. However, the structure and formation of this complex have been unclear. Recently, studies have revealed that CTP binding enables ParB dimers to slide along DNA and condense the centromeric region through the formation of DNA bridges. Using semi-flexible polymer simulations, we demonstrate that these properties can explain partition complex formation. Transient ParB bridges organize DNA into globular states or hairpins and helical structures, depending on bridge lifetime, while separate simulations show that ParB sliding reproduces the multi-peaked binding profile observed in Caulobacter crescentus. Combining sliding and bridging into a unified model, we find that short-lived ParB bridges do not impede sliding and can reproduce both the binding profile and condensation of the nucleoprotein complex. Overall, our model elucidates the mechanism of partition complex formation and predicts its fine structure.