Semiflexible Chains Research Articles

Kinetic models for semiflexible polymers in a half-plane

Based on a general discrete model for a semiflexible polymer chain, we introduce a formal derivation of a kinetic equation for semiflexible polymers in the half-plane via a continuum limit. It turns out that the resulting equation is the kinetic Fokker-Planck-type equation with the Laplace-Beltrami operator under a non-local trapping boundary condition. We then study the well-posedness and the long-chain asymptotics of the solutions of the resulting equation. In particular, we prove that there exists a unique measure-valued solution for the corresponding boundary value problem. In addition, we prove that the equation is hypoelliptic and the solutions are locally H\"older continuous near the singular boundary. Finally, we provide the asymptotic behaviors of the solutions for large polymer chains.

Changes in the structure of polysaccharides under different extraction methods

Changes in the structure of polysaccharides under different extraction methods

Removal of highly concentrated methylene blue dye by cellulose nanofiber biocomposites

The contamination of water by dyes in high concentrations is a worldwide concern, and it has prompted the development of efficient, economical, and environmentally friendly materials and technologies for water purification. The hydration and adsorption capacity for methylene blue (MB) in biocomposites (BCs) based on cellulose nanofiber (CNF) (0 to 2 wt%) were studied. BCs were synthesized through a simple and straightforward route and characterized by spectroscopy, microscopic techniques and thermogravimetric analysis, among others. Hydration studies showed that BCs prepared with 2 wt% of CNF can absorb large volumes of water, approximately 2274 % in the case of poly 2-acrylamide-2-methyl-1-propanesulfonic acid (PAMPS)-CNF and 2408 % in poly sodium 4-styrene sulfonate (PSSNa)-CNF. These BCs showed outstanding adsorption capacity for highly concentrated MB solutions (4536 mg g−1 PAMPS-CNF and 11,930 mg g−1 PSSNa-CNF). It was confirmed that the adsorption mechanism is through electrostatic interactions. Finally, BCs showed high MB adsorption efficiency after several sorption-desorption cycles and on a simulated textile effluent. Furthermore, the theoretical results showed a preferential interaction between MB and the semiflexible polymer chains at the lowest energy setting. The development and study of a new adsorbent material with high MB removal performance that is easy to prepare, economical and reusable for potential use in water purification treatments was successfully achieved.

General weak segregation theory with an application to monodisperse semi-flexible diblock copolymers.

A general theory has been developed for a polydisperse semi-flexible multi-block copolymer melt. Using the Bawendi-Freed approach to model semi-flexible chains, an expression for the Landau free energy is derived in the weak segregation regime, which includes density and orientation order-parameters. The orientation order-parameter is described in the smectic phase and in more complicated structures, such as the hexagonal phase. The Landau free energy contains contributions of two kinds of interactions. The first kind is the Flory-Huggins interaction, which describes the incompatibility of chemically different blocks and may induce microphase separation. The second kind is the Maier-Saupe interaction, which may induce nematic ordering. In the framework of the weak segregation limit, the Landau theory allows us to predict phase structures in the melt as a function of the composition, persistence length, and the strength of the Flory-Huggins and Maier-Saupe interaction. The general theory is applied to a simple system of monodisperse semi-flexible diblock copolymers. In several phase diagrams, a number of possible phase structures are predicted, such as the bcc, hexagonal, smectic-A, smectic-C, and nematic phase. The influence of the Maier-Saupe interaction on the microphase structure is thoroughly discussed.

Orientational Wetting and Topological Transitions in Confined Solutions of Semiflexible Polymers

Despite their considerable practical and biological applications, the link between molecular properties, assembly conditions and self-organized structure in confined polymer solutions remains elusive. Here, we explore the lyotropic nematic ordering of semi-flexible chains in spherical confinement for multiple contour lengths across a wide regime of concentrations. We uncover an original crossover from two distinct quadrupolar states, both characterized by regular tetrahedral patterns of surface topological defects, to either longitudinal, latitudinal or spontaneously-twisted bipolar structures with increasing densities. These transitions, along with the intermediary arrangements that they involve, are attributed to the combination of orientational wetting with subtle variations in their liquid-crystal (LC) elastic anisotropies. Our molecular simulations are corroborated by density functional calculations, and are quantified through the introduction of several order parameters as well as an unsupervised learning scheme for the localization of topological defects. Our results agree quantitatively with the predictions of continuum nematic elasticity theories, and evidence the extent to which the folding of macromolecules and the self-assembly of low-molecular-weight LCs may be guided by the same, universal principles.

Coiling of semiflexible paramagnetic colloidal chains.

Semiflexible filaments deform into a variety of configurations that dictate different phenomena manifesting at low Reynolds number. Harnessing the elasticity of these filaments to perform transport-related processes at the microfluidic scale requires structures that can be directly manipulated to attain controllable geometric features during their deformation. The configuration of semiflexible chains assembled from paramagnetic colloids can be readily controlled upon the application of external time-varying magnetic fields. In circularly rotating magnetic fields, these chains undergo coiling dynamics in which their ends close into loops that wrap inward, analogous to the curling of long nylon filaments under shear. The coiling is promising for the precise loading and targeted transport of small materials, however effective implementation requires an understanding of the role that field parameters and chain properties play on the coiling features. Here, we investigate the formation of coils in semiflexible paramagnetic chains using numerical simulations. We demonstrate that the size and shape of the initial coils are governed by the Mason and elastoviscous numbers, related to the field parameters and the chain bending stiffness. The size of the initial coil follows a nonmonotonic behavior with Mason number from which two regions are identified: (1) an elasticity-dependent nonlinear regime in which the coil size decreases with increasing field strength and for which loop shape tends to be circular, and (2) an elasticity-independent linear regime where the size increases with field strength and the shape become more elliptical. From the time scales associated to these regimes, we identify distinct coiling mechanisms for each case that relate the coiling dynamics to two other configurational dynamics of paramagnetic chains: wagging and folding behaviors.

Shock compression of semiflexible polymers.

We employ molecular dynamics simulations to investigate the shock compression of linear semiflexible polymers. While the propagation velocity of a shock primarily depends on density, both chain rigidity and chain orientation significantly influence the shock width and the final temperature of the system. In general, the shock wave triggers molecular buckling in chains oriented perpendicular to the compression front. Following the passage of the front, the semiflexible chains buckle with a wavelength that decreases with the compression speed as λm ∼ up-0.2, and subsequent relaxation leads to a banana-like liquid crystal phase. In ordered systems with molecules oriented perpendicular to the compression front, the shock width increases by a factor of up to 10 compared to a similar isotropic system, resulting in enhanced shock energy absorption. These findings indicate that chain stiffness plays a critical role in the impact absorption properties of polymeric materials.

Adsorption of Wormlike Chains onto Partially Permeable Membranes.

Reversible adsorption of a single stiff wormlike macromolecule to flat membranes with various permeabilities is considered theoretically. It is shown that the adsorbed layer microstructure is significantly different from either a flexible chain or a stiff chain adsorption at a solid surface. Close to the critical point, the adsorbing wormlike chain forms a strongly anisotropic proximal layer near the membrane in addition to a nearly isotropic distal layer. The proximal layer is characterized by the algebraic monomer concentration profile, c(x)∝x-β, due to the self-similar distribution of aligned polymer loops. For a perfectly penetrable membrane, β=1 which is different from β=4/3 obtained for semiflexible chain adsorption at a solid surface. Moreover, we establish that the critical exponent for a partially permeable membrane depends on its properties (porosity w) and propose an asymptotically exact theory (based on the generalized Edwards equation) predicting this dependence, β=β(w). We also develop a scaling theory elucidating, in particular, an intricate competition of loops and tails in both proximal and distal sublayers.

Conformation and dynamics of a tethered active polymer chain.

The conformational and dynamical properties of a tethered semiflexible polymer chain under tangential active force (f_{a}) are studied by using the Langevin dynamics simulation method. The head of the polymer is fixed near an infinite flat surface at z=0. The polymer is equilibrated first at f_{a}=0 and then subjected to the active force. Under the influence of the active force, the polymer is gradually compressed. Specially, for large f_{a} and large bending rigidity (k_{b}), the polymer is buckled into a quasihelical structure rotating around the z axis at the steady state. It is found that both the radius of the quasihelical structure (R) and the angular velocity of the rotation (ω) are nearly independent of the polymer length (N), but show scaling relations with f_{a} and k_{b}, i.e., R∝f_{a}^{-1/3}k_{b}^{1/3} and ω∝f_{a}^{4/3}k_{b}^{-1/3}, which are explained by simple dynamical models. Before reaching the steady state, it is further found that the buckling velocity of the polymer is proportional to f_{a} but roughly independent of k_{b} and N, then the buckling time (t_{b}) can be described by a scaling relation t_{b}∝Nf_{a}^{-1}. The underlying mechanism of the buckling process is revealed.

Detailed dynamics of discrete Gaussian semiflexible chains with arbitrary stiffness along the contour.

We revisit a model of semiflexible Gaussian chains proposed by Winkler et al., solve the dynamics of the discrete description of the model, and derive exact algebraic expressions for some of the most relevant dynamical observables, such as the mean-square displacement of individual monomers, the dynamic structure factor, the end-to-end vector relaxation, and the shear stress relaxation modulus. The mathematical expressions for the dynamic structure factor are verified by comparing them with results from Brownian dynamics simulations, reporting an excellent agreement. Then, we generalize the model to linear polymer chains with arbitrary stiffness. In particular, we focus on the case of a linear polymer with stiffness that changes linearly from one end of the chain to the other, and we study the same dynamical functions previously presented. We discuss different approaches to check whether a polymer has constant or heterogeneous stiffness along its contour. Finally, we provide expressions for the Lagrangian multipliers for Gaussian chains with variable stiffness and bond length, as well as for chains with torsion-like interactions. Overall, this work presents a new insight into a well-known model for semiflexible chains and provides tools that can be exploited to explore a much broader class of polymers or compare the predictions of the model with simulations of coarse-grained semiflexible polymers.

Sticker-and-spacer model for amyloid beta condensation and fibrillation.

A major pathogenic hallmark of Alzheimer's disease is the presence of neurotoxic plaques composed of amyloid beta (Aβ) peptides in patients' brains. The pathway of plaque formation remains elusive, though some clues appear to lie in the dominant presence of Aβ1 − 42 in these plaques despite Aβ1−40 making up approximately 90% of the Aβ pool. We hypothesize that this asymmetry is driven by the hydrophobicity of the two extra amino acids that are incorporated in Aβ1−42. To investigate this hypothesis at the level of single molecules, we have developed a molecular “sticker-and-spacer lattice model” of unfolded Aβ. The model protein has a single sticker that may reversibly dimerise and elongate into semi-flexible linear chains. The growth is hampered by excluded-volume interactions that are encoded by the hydrophilic spacers but are rendered cooperative by the attractive interactions of hydrophobic spacers. For sufficiently strong hydrophobicity, the chains undergo liquid-liquid phase-separation (LLPS) into condensates that facilitate the nucleation of fibers. We find that a small fraction of Aβ1−40 in a mixture of Aβ1−40 and Aβ1−42 shifts the critical concentration for LLPS to lower values. This study provides theoretical support for the hypothesis that LLPS condensates act as a precursor for aggregation and provides an explanation for the Aβ1−42-enrichment of aggregates in terms of hydrophobic interactions.

Theory of the Effects of Specific Attractions and Chain Connectivity on the Activated Dynamics and Selective Transport of Penetrants in Polymer Melts

We generalize and apply a microscopic force level statistical mechanical theory of activated spherical penetrant dynamics in glass-forming liquids to study the influence of semiflexible polymer connectivity and penetrant–polymer attractive interactions on the penetrant hopping rate. The detailed manner that attractions of highly variable strength and spatial range modify the penetrant size and polymer melt density (from the rubbery state to slightly beyond the kinetic glass transition) dependences of penetrant activation barriers is established. Of special interest are possible nonadditive consequences of physical bonding and steric caging, the degree of coupling of penetrant hopping and the Kuhn segment scale alpha relaxation process, the relative importance of local caging and long-range matrix collective elasticity as a function of penetrant size, and implications for optimizing transport selectivity. With increasing attraction strength, the repulsive caging-restriction effect on penetrant mobility is predicted to grow, in contrast to the effect of the equilibrium penetrant–matrix solvation shell size, which decreases. The former dynamical effect results in a significant enhancement of the importance of the local cage barrier, while the latter effect results in a decrease of the importance of the nonlocal collective elastic barrier. These two competing effects have a very strong influence on selective penetrant transport for different sized penetrants: selectivity varies nonmonotonically with attraction strength in the deeply supercooled state but decreases monotonically in the rubbery state and at fixed attraction strength, exhibits a nonmonotonic variation with the matrix packing fraction. By comparing results based on modeling the matrix as semiflexible polymer chains with analogous calculations using the same dynamical theory but for a disconnected hard sphere matrix, the effect of chain connectivity is revealed and found to have quantitative, but not qualitative, consequences on penetrant-activated dynamics.

Persistence length of semi-flexible polymer chains on Euclidean lattices

We have studied the persistence length behavior of semi-flexible linear polymers, represented by self-avoiding random walks (SAWs) on the square (d=2) and simple cubic (d=3) lattice. By employing the PERM Monte Carlo algorithm we have generated SAWs, changing the chain stiffness (characterized by the parameter s, related to each bend of a SAW). We have examined two quantities that measure persistence length of N-step SAWs: (1) ℓN, which is defined as an average length of straight parts of polymer chains, and (2) λN, defined as the mean projection of the end-to-end distance vector on the SAW’s first step. For each particular s, we have found that ℓN is a linear function of 1/N in both dimensions, d=2 and d=3, while λN is a linear function of 1/NΦeff, where Φeff≈0.3 in d=2 and Φeff≈0.82 in d=3. Sequences of ℓN and λN have been extrapolated in the range of very long chains, and we have established that, for each examined s, they converge to s dependent constants ℓp=ℓN→∞ and λp=λN→∞. We analyze dependence of ℓp and λp on the polymer stiffness s, and make a comparison between our findings and former results for studied quantities.

Compression-induced buckling of a semiflexible filament in two and three dimensions.

The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. For filaments in the low-temperature limit and under a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed state to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression. We determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates this transition. We find that the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble, the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show that the theory is highly sensitive to fluctuations in length in two dimensions and the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts.

Effects of ultrasonic on structure, chain conformation and morphology of pectin extracted from Premna microphylla Turcz

In this study, ultrasonic effects on structure, chain conformation and morphology of pectin extracted from Premna microphylla Turcz (PEP) and its probable mechanism were investigated. In the process of ultrasonic treatments, the chains of PEP were fractured rapidly within the initial 10 min and then the degradation rate gradually slowed down. The primary structure of PEP nearly remained unchanged after ultrasonic degradation. The rigid semi-flexible chains of PEP were converted into flexible chains, flexible coils, even compact coils. Sonication at low intensity for short time made PEP molecular chains curly collapse and tighten up. Long duration sonication at high intensity generated excessive small rigidness segments that mutually aggregated because of hydrogen bonds and inhibited the self-coiling of PEP chains. Atomic force microscopy (AFM) analysis supported the conformation transition of PEP chains. The results provided a fundamental basis for orientation design and process control of PEP structure.

Electrostatic Repulsion Slows Relaxations of Polyelectrolytes in Semidilute Solutions

We investigate the structure and dynamics of unentangled semidilute solutions of sodium polystyrenesulfonate (NaPSS) using small-angle neutron scattering (SANS) and neutron spin-echo (NSE) spectroscopy. The effects of electrostatic interactions and chain structure are examined as a function of ionic strength and polymer concentration, respectively. The SANS profiles exhibit a characteristic structural peak, signature of polyelectrolyte solutions, that can be fit with a combination of a semiflexible chain with excluded volume interactions form factor and a polymer reference interaction site model (PRISM) structure factor. We confirm that electrostatic interactions vary with ionic strength across solutions with similar geometries. The segmental relaxations from NSE deviate from theoretical predictions from Zimm and exhibit two scaling behaviors, with the crossover between the two regimes taking place around the characteristic structural peak. The chain dynamics are suppressed across the length scale of the correlation blob, and inversely related to the structure factor. These observations suggest that the highly correlated nature of polyelectrolytes presents an additional energy barrier that leads to de Gennes narrowing behavior.

Hydrodynamic and Polyelectrolyte Properties of Actin Filaments: Theory and Experiments.

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

Organized states arising from compression of single semiflexible polymer chains in nanochannels.

We use molecular dynamics simulation to probe the nonequilibrium physics of single nanochannel-confined semiflexible polymers in a homogeneous flow field. The flow field compresses the polymer against the end of the nanochannel, simulating an experiment of a nanochannel confined chain compressed against a slit barrier. The flow-based compression gives rise to a packing of the chain against the channel end that possesses a striking organization, consisting of interweaving of folds and circular coils. For stiff chains at low flow, we find that the organization is dominated by repeated hairpin folds. For stiff chains at higher flow, we observe that circular coils arise along with the folds, with folding and coiling domains becoming interwoven at the highest flow speeds. Chain organization is retained even when the chain persistence length is on order of the channel width. We show that the global polymer organization, consisting of a number of defined folds and coiled loops, arises from the minimization of the total chain free energy.

A particle-based computational model to analyse remodelling of the red blood cell cytoskeleton during malaria infections.

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments.

Dynamic behavior of tough polyelectrolyte complex hydrogels from chitosan and sodium hyaluronate

In this work, we investigated the dynamics of hydrogels from the polyelectrolyte complexation of sodium hyaluronate (HA) and chitosan under various temperature and salt concentration. Raising temperature and adding salt remarkably reduce the mechanical behavior of hydrogels. The stress relaxation of semi-flexible chain segments is accelerated at high temperature and salt concentration, which is controlled by thermally activated bond disassociation process. The flow activation energy determined from temperature-dependent dynamic light scattering decorrelation and rheological relaxation are in very good agreement. Our results suggest that the chain aggregations are physical crosslinked by surrounded semi-flexible chains, and their diffusion is highly hindered by the topological entanglements and ionic associations. The synergistic effect of aggregations diffusion and chain dynamics causes the slow macroscopic stress relaxation behavior of hydrogels before yield, independent of applied strain. Above yield, the amplitude of strain accelerates the stress relaxation, resulting in chain disentanglements and slipping.