Semiflexible Chains Research Articles

The Bending Energy of a Semi-Flexible Polymer Chain and the Polygons of the Polymer Chain

The Bending Energy of a Semi-Flexible Polymer Chain and the Polygons of the Polymer Chain - written by Pramod Kumar Mishra published on 2019/12/27 download full article with reference data and citations

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections.

We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.

Nucleation theory of polymer crystallization with conformation entropy

Based on classical nucleation theory, we propose a couple of theoretical models for the nucleation of polymer crystallization, i.e. one for a single chain system (Model S) and the other for a multi-chain system (Model M). In these models, we assume that the nucleus is composed of tails, loops and a cylindrical ordered region, and we evaluate the conformation entropy explicitly by introducing a transfer matrix. Using these two models, we evaluate the occurrence probability of critical nucleus as a function of the polymer chain stiffness. We found that the critical nucleus in Model M is easier to occur than in Model S because, for semi-flexible chains, the nucleus in Model M can grow by adding a new polymer chain into the nucleus rather than to diminish the loop and tail parts as in the case of Model S.

Effect of the Fraction and Size of Polar Groups on the Formation of Compact Conformations of a Polymer Chain with Variable Stiffness in Low-Polar Media

The conformational behavior of a single semiflexible polymer chain with a variable fraction of polar groups (dipoles) is studied by the molecular dynamics method. Dipoles of the chain are simulated as two oppositely charged beads, one of which belongs to the backbone and another bead is a side group. The charged bead of the side group may freely rotate around the backbone, and the size of the side bead and the distance between oppositely charged groups (dipole length) are varied. The main attention is focused on studying the effect of backbone stiffness and an interplay of excluded volume and electrostatic interactions on the conformational behavior of a chain and the structure of multiplets formed due to a strong electrostatic attraction in low-polar media.

Lattice theory for binding of linear polymers to a solid substrate from polymer melts: I. Influence of chain connectivity on molecular binding and adsorption.

Most theories of the binding of molecules to surfaces or for the association between molecules treat the binding species as structureless entities and neglect their rigidity and the changes in their stiffness induced by the binding process. The binding species are also taken to be "ideal," meaning that the existence of van der Waals interactions and changes in these interactions upon molecular binding are also neglected. An understanding of the thermodynamics of these multifunctional molecular binding processes has recently come into focus in the context of the molecular binding of complex molecules, such as dendrimers and DNA grafted nanoparticles, to surfaces where the degree of binding cooperativity and selectivity, as well as the location of the binding transition, are found to be sensitive to the number of binding units constrained to a larger scale polymeric scaffold. We address the fundamental problem of molecular binding by extending classical Langmuir theory to describe the particular example of the reversible binding of semiflexible polymer chains to a solid substrate under melt conditions. The polymer chains are assumed to have a variable number N of binding units (segments) and to exhibit variable bending energies and van der Waals interactions in the bulk and on the surface, in addition to strong directional interactions with the surface. The resulting generalized Langmuir theory is applied to the examination of the influence of the chain connectivity of ideal polymers on the surface coverage Θ, transition binding temperature T1/2 at which Θ = 1/2, and on the derivative |dΘ/dT|T=T1/2 and the constant volume specific heat of binding, Cv bind, measures of the cooperativity and "sharpness" of the binding transition, respectively. Paper II is devoted to the impact of the van der Waals attractive interactions and chain stiffness on the reversible binding of nonideal polymer chains to a solid surface, including the enthalpy-entropy compensation phenomenon observed experimentally in many molecular and particle binding processes.

Linear Dimensions of Adsorbed Semiflexible Polymers: What Can Be Learned about Their Persistence Length?

Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length L, chain stiffness, κ, and the strength of the adsorption potential over a wide range. Molecular dynamics simulations show that partially adsorbed chains (with "tails," surface attached "trains," and "loops") are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value (ℓ_{p}) to the enhanced value in two dimensions (2ℓ_{p}) is analyzed, and excluded volume effects are identified for L≫ℓ_{p}. Consequences for the interpretation of experiments are suggested. We verify the prediction that the adsorption threshold scales as ℓ_{p}^{-1/3}.

Spontaneous Tilting Transition in Liquid-Crystalline Polymer Brushes

The equilibrium phase behavior of main-chain liquid-crystalline polymer brushes in good solvent is investigated using self-consistent field theory. The calculation assumes semidilute brushes, where the grafting density is sufficient to cause overlap among the polymers but low enough to allow the solvent to be treated implicitly. The polymers are modeled as semiflexible wormlike chains with Maier–Saupe interactions. Previous calculations based on freely jointed chains have predicted that extended brushes collapse into folded nematic brushes, as the liquid-crystalline interaction strength is increased. For the more sophisticated model of wormlike chains, which penalizes hairpin folds, we find that extended brushes become unstable with respect to tilting prior to the onset of folding. This implies that the brushes spontaneously collapse by a symmetry-breaking transition, where the chains tilt rather than fold.

Simulation of the Critical Adsorption of Semi-Flexible Polymers**Supported by the National Natural Science Foundation of China under Grant Nos 11674277, 11704210 and 21574117.

The critical adsorption of semi-flexible polymer chains on attractive surfaces is studied using Monte Carlo simulations. The results reveal that the critical adsorption point of a free polymer chain is the same as that of an end-grafted one. For the end-grafted polymer, we find that the finite-size scaling relation and the maximum fluctuation of adsorbed monomers are equivalent in estimating the critical adsorption point. The effect of chain stiffness on the critical adsorption is also investigated. The surface attraction strength for the critical adsorption of semi-flexible polymer chain decreases exponentially with an increase in the chain stiffness; In other words, lower adsorption energy is needed to adsorb a stiffer polymer chain. The result is explained from the viewpoint of the free energy profile for the adsorption.

Crystallisation in Melts of Short, Semi-Flexible Hard-Sphere Polymer Chains: The Role of the Non-Bonded Interaction Range

A melt of short semi-flexible polymers with hard-sphere-type non-bonded interaction undergoes a first-order crystallisation transition at lower density than a melt of hard-sphere monomers or a flexible hard-sphere chain. In contrast to the flexible hard-sphere chains, the semi-flexible ones have an intrinsic stiffness energy scale, which determines the natural temperature scale of the system. In this paper, we investigate the effect of weak additional non-bonded interaction on the phase transition temperature. We study the system using the stochastic approximation Monte Carlo (SAMC) method to estimate the micro-canonical entropy of the system. Since the density of states in the purely hard-sphere non-bonded interaction case already covers 5600 orders of magnitude, we consider the effect of weak interactions as a perturbation. In this case, the system undergoes the same ordering transition with a temperature shift non-uniformly depending on the additional interaction. Short-range attractions impede ordering of the melt of semi-flexible polymers and decrease the transition temperature, whereas relatively long-range attractions assist ordering and shift the transition temperature to higher values, whereas weak repulsive interactions demonstrate an opposite effect on the transition temperature.

Flow-Induced Translocation of Star Polymers through a Nanopore.

The flow-induced translocation of star polymers through a cylindrical nanopore has been studied using dissipative particle dynamics (DPD) simulations. The number of arms, f, was varied with the total number of monomers, N, kept constant. The effect of simulating the capture of the polymer into the pore upon the mean translocation time, <τt>, has been investigated by varying the chain's initial location. The results indicate that the incorporation of the capture process results in a reduction of <τt> by up to 15%. This is because the chain's initial location affects the extent of its stretching along the flow direction during translocation. <τt> exhibits nonmonotonic variation with f, in agreement with recently reported results for electric field-driven translocation of star polymers. Its value is larger and shows greater variation with f when the solvent quality is better. For the same value of f, the capture occurs faster in a good solvent. In addition, <τt> is greater for a semiflexible chain than its flexible counterpart as the time required for the branch point to enter the nanopore is longer in the former case.

Theory of self-assembly-driven nematic liquid crystals revised

ABSTRACTConcentrated solutions of short blunt-ended DNA duplexes at room temperature can form liquid crystal phases due to stacking interactions between duplex terminals which induce the aggregation of the duplexes into semi-flexible linear chains. Mesophases observed in these systems include nematic, columnar and cholesteric ones. This experimental system is just one of many examples, where liquid crystals ordering emerges as a result of molecular self-assembly into linear chains. In the attempt to go beyond a simple Onsager theoretical approach to understand the thermodynamic behavior of this system, we introduced some years ago a general theoretical description, which models the isotropic-nematic transition by properly taking into account molecular self-assembly, and we carefully verified the theoretical predictions against numerical simulations of patchy hard cylinders. Here, we provide a revised version of the theory in the attempt of understanding which assumptions are worth to be improved. In particular, we focus on the Parsons-Lee approximation and the modeling of orientational entropy. We compare the results from the revised version of the theory against original ones, showing that the present version of the theory is able to capture more accurately the phase boundaries of the isotropic-nematic transition.

Emerging Two-Dimensional Crystallization of Cucurbit[8]uril Complexes: From Supramolecular Polymers to Nanofibers.

The binding of imidazolium salts to cucurbit[8]uril, CB[8], triggers a stepwise self-assembly process with semiflexible polymer chains and crystalline nanostructures as early- and late-stage species, respectively. In such a process, which involves the crystallization of the host–guest complexes, the guest plays a critical role in directing self-assembly toward desirable morphologies. These include platelet-like aggregates and two-dimensional (2D) fibers, which, moreover, exhibit viscoelastic and lyotropic properties. Our observations provide a deeper understanding of the self-assembly of CB[8] complexes, with fundamental implications in the design of functional 2D systems and crystalline materials.

Simulation Study on the Extension of Semi-flexible Polymer Chains in Cylindrical Channel

The scaling relations among the mean end-to-end distance of polymer along the channel , the polymer length N, and the effective diameter of channel De were investigated for flexible and semi-flexible polymer chains confined in long cylindrical channels. For the flexible polymer chain, scaling relation ∼ NDe-0.7 was found in the classic de Gennes regime at lp2/b ∼ NDe-1 in the transition regime lp 1) and ∼ De-0.7 in the classic de Gennes regime at larger De > xlp were observed. The simulation results revealed that the scaling relation in the transition regime was due to the rod-like behavior of the semi-flexible polymer in the small regime lp < De < xlp.

Effect of ultrasonic intensity on the conformational changes in citrus pectin under ultrasonic processing

In this study, the effects of ultrasonic intensity on conformational changes in aqueous citrus pectin solution under ultrasonic processing and its possible transition mechanism were investigated. The results demonstrated that higher ultrasonic intensity (104.7 W/cm2) caused larger alterations in the molecular and conformational parameters of the semiflexible pectin (Mark–Houwink relation exponent a: 0.820, conformational parameter α: 0.607, structural parameter ρ: 2.22) in aqueous solution. Meanwhile, the semiflexible chain of pectin became more flexible (a: 0.804, α: 0.601, ρ: 1.75) at higher ultrasonic intensity in aqueous solution, as was verified by atomic force microscopy. Moreover, conformational changes in pectin from semiflexible chains to flexible chains or even flexible coils (a: 0.791, α: 0.597, ρ: 1.70) could be attributed to the decreased degree of methoxylation and neutral sugars in side chains and the destruction of inter- and intramolecular hydrogen bonds under ultrasonic processing. Therefore, these results have important implications for understanding the ultrasonic modification of pectin.

Crowding-Activity Coupling Effect on Conformational Change of a Semi-Flexible Polymer.

The behavior of a polymer in a passive crowded medium or in a very dilute active bath has been well studied, while a polymer immersed in an environment featured by both crowding and activity remains an open problem. In this paper, a systematic Langevin simulation is performed to investigate the conformational change of a semi-flexible chain in a concentrated solution packed with spherical active crowders. A very novel shrinkage-to-swelling transition is observed for a polymer with small rigidity. The underlying phase diagram is constructed in the parameter space of active force and crowder size. Moreover, the variation of the polymer gyration radius demonstrates a non-monotonic dependence on the dynamical persistence length of the active particle. Lastly, the activity-crowding coupling effect in different crowder size baths is clarified. In the case of small crowders, activity strengthens the crowding-induced shrinkage to the chain. As crowder size increases, activity turns out to be a contrasting factor to crowding, resulting in a competitive shrinkage and swelling. In the large size situation, the swelling effect arising from activity eventually becomes dominant. The present study provides a deeper understanding of the unusual behavior of a semi-flexible polymer in an active and crowded medium, associated with the nontrivial activity-crowding coupling and the cooperative crowder size effect.

Driven translocation of semiflexible polyelectrolyte through a nanopore

ABSTRACTThe influence of the chain stiffness on the translocation of semiflexible polyelectrolyte through a nanopore is investigated using Langevin dynamics simulations. Results show that the translocation time τ increases with the bending modulus kθ because of the increase of viscous drag forces with kθ. We find that the relation between τ and kθ, the asymptotic behavior of τ on the polyelectrolyte length N, and the scaling relation between τ and the driving force f are dependent on kθ and N. Our simulation results show that the semiflexible polyelectrolyte chain can be regarded as either a flexible polyelectrolyte at small kθ or large N where its radius of gyration RG is larger than the persistence length Lp or a stiff polyelectrolyte at large kθ or short N where RG &lt; Lp. Results also show that the out‐of‐equilibrium effect during the translocation becomes weak with increasing kθ. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 912–921

Modeling the mechanical behavior of semi-flexible polymer chains using a surrogate model based on a finite-element approach to Brownian polymer dynamics

The micromechanical behavior of single polymer chains determines the macroscopic mechanics of a large number of synthetic and biological materials. An important tool for the study of polymers are Brownian dynamics simulations, classically based on bead-rod models. In a recent work by Cyron and Wall (2009), an advantageous approach in the finite-element framework was presented, where Brownian polymer dynamics have been described by a white noise driven stochastic partial differential equation (SPDE). In the present contribution, the SPDE is solved using a geometrically-exact Kirchhoff–Love beam element and a piecewise constant white noise approximation in time and space. The resulting numerical method is used to obtain mean force-extension data, to set up a surrogate model based on a Gaussian process, and to identify parameters through a fit to experimental data in a Bayesian framework.

Filament flexibility enhances power transduction of F-actin bundles.

The dynamic behavior of bundles of actin filaments growing against a loaded obstacle is investigated through a generalized version of the standard multifilament Brownian Ratchet model in which the (de)polymerizing filaments are treated not as rigid rods but as semiflexible discrete wormlike chains with a realistic value of the persistence length. By stochastic dynamic simulations, we study the relaxation of a bundle of Nf filaments with a staggered seed arrangement against a harmonic trap load in supercritical conditions. Thanks to the time scale separation between the wall motion and the filament size relaxation, mimicking realistic conditions, this setup allows us to extract a full load-velocity curve from a single experiment over the trap force/size range explored. We observe a systematic evolution of steady nonequilibrium states over three regimes of bundle lengths L. A first threshold length Λ marks the transition between the rigid dynamic regime (L < Λ), characterized by the usual rigid filament load-velocity relationship V(F), and the flexible dynamic regime (L > Λ), where the velocity V(F, L) is an increasing function of the bundle length L at a fixed load F, the enhancement being the result of an improved level of work sharing among the filaments induced by flexibility. A second critical length corresponds to the beginning of an unstable regime characterized by a high probability to develop escaping filaments which start growing laterally and thus do not participate anymore in the generation of the polymerization force. This phenomenon prevents the bundle from reaching at this critical length the limit behavior corresponding to perfect load sharing.

The Effect of Bending Rigidity on Polymers

Front Cover: The figure is one conformation of a semiflexible chain with 160 monomers in a cubic box with side length a=16. Due to the interaction of bending energy and the confinement, the chain forms spirals. The persistence length of this chain is about 5.4, small than the box size. Therefore these spirals are small and randomly ordered. This is reported by Jiying Jia, Kunhe Li, Andreas Hofmann, Dieter W. Heermann in the article 1800071.

A complete integral equation theory for accurate thermodynamics of chain molecules

An integral equation theory is developed for n-alkane chains ranging in carbon number from eight to infinity through an adaptation of the polymer referenced interaction site model (PRISM). Thermodynamic perturbation theory (TPT) is adapted as the basis for expressing the equation of state through the coupling parameter expansion (CPE) as an extension of the theory developed by Ramana et al. for spherical molecules. The key feature of PRISM theory is the assumption that all pair correlations for a given site type are equivalent, regardless of whether they appear at the end of the chain or in the middle. The present analysis assumes that the PRISM result represents the average over all sites in the chain. The site-site interaction energies are then implemented through a weighted average based on their frequency of occurrence. The CPE is demonstrated through the fourth order in temperature, although higher order terms are accessible in principle. An advantage of the TPT representation is that convergence need be achieved only once for each chain length and density, then the TPT coefficients can be tabulated and interpolated for future reference. This approach moderates difficulties with molecular simulation of fully equilibrated long chains and uncertainty in the estimation of higher order TPT coefficients. Step potentials are used as the basis for validating and refining the theory using published simulation results for n-alkanes through 80 carbons. We find that the first order TPT contribution is fairly accurate regardless of conformational details but the second order TPT contribution is remarkably sensitive to conformation. We can obtain accurate characterization of the second order contribution by varying the stiffness parameter of the semi-flexible chain model. Higher order TPT contributions follow from the second order result. The theory would not be “complete,” however, without accurate characterization of the TPT reference contribution, which simultaneously impacts the first order contribution. We combine the compressibility route with a Yukawa closure to accurately characterize the reference fluid thermodynamics as a function of density, chain length, and bond length. Altogether, the result is an accurate model of all contributions to chain molecular thermodynamics, including the underlying fluid structure. A sample application is demonstrated by generating the phase diagrams through 80 carbons. It is observed that the flatness near the critical region is reproduced by including the higher order TPT contributions, but the impact of higher order contributions in the critical region is diminished for 80 carbon chains.