Semiflexible Polymer Chains Research Articles

Electrostatic stiffening and induced persistence length for coassembled molecular bottlebrushes.

A self-consistent field analysis for tunable contributions to the persistence length of isolated semiflexible polymer chains including electrostatically driven coassembled deoxyribonucleic acid (DNA) bottlebrushes is presented. When a chain is charged, i.e., for polyelectrolytes, there is, in addition to an intrinsic rigidity, an electrostatic stiffening effect, because the electric double layer resists bending. For molecular bottlebrushes, there is an induced contribution due to the grafts. We explore cases beyond the classical phantom main-chain approximation and elaborate molecularly more realistic models where the backbone has a finite volume, which is necessary for treating coassembled bottlebrushes. We find that the way in which the linear charge density or the grafting density is regulated is important. Typically, the stiffening effect is reduced when there is freedom for these quantities to adapt to the curvature stresses. Electrostatically driven coassembled bottlebrushes, however, are relatively stiff because the chains have a low tendency to escape from the compressed regions and the electrostatic binding force is largest in the convex part. For coassembled bottlebrushes, the induced persistence length is a nonmonotonic function of the polymer concentration: For low polymer concentrations, the stiffening grows quadratically with coverage; for semidilute polymer concentrations, the brush chains retract and regain their Gaussian size. When doing so, they lose their induced persistence length contribution. Our results correlate well with observed physical characteristics of electrostatically driven coassembled DNA-bioengineered protein-polymer bottlebrushes.

Form factor for distorted semi-flexible polymer chains.

The statistical presence of kinks which form defects in semi-flexible polymer chains leads to a polydispersity in the effective persistence length. The form factor of a distorted semi-flexible polymer results as an average over this persistence polydispersity. It turns out that the scattering behavior of an ensemble of distorted semi-flexible polymer chains is quite well approximated by a form factor of an undistorted chain with a Rg-equivalent persistence length. An apparent length polydispersity is observed for short distorted chains. The Rg-equivalent persistence length is significantly smaller than the innate persistence length multiplied by the fraction of regular monomers. The results are compared to related work on DNA from the literature.

Monte Carlo simulation on the dynamics of a semi-flexible polymer in the presence of nanoparticles.

The dynamics of a semi-flexible polymer chain in the presence of periodically distributed nanoparticles is simulated by using off-lattice Monte Carlo simulations. For repulsive or weak attractive nanoparticles, the dynamics are slowed down monotonically by increasing the chain stiffness kθ or decreasing the inter-particle distance d. For strong attractive nanoparticles, however, the dynamics show nonmonotonic behaviors with kθ and d. An interesting result is that a stiff polymer may move faster than a flexible one. The underlying mechanism is that the nanoparticle's attraction is weakened by the chain stiffness. The nonmonotonic behavior of the polymer's dynamics with kθ is explained by the competition between the weakening effect of the chain stiffness on the nanoparticle's attraction and the intrinsic effect of chain stiffness which reduces the dynamics of the polymer. In addition, the nonmonotonic behavior of the polymer's dynamics with d is explained by the competition between the nanoparticle-exchange motion of the polymer dominated at small d and the desorption-and-adsorption motion at large d. The excluded volume effect of the nanoparticles plays a more important role for stiffer polymers as the attraction of the nanoparticles is weakened by the chain stiffness.

Supramolecular Organization in Calf-Thymus DNA Solutions under Flow in Dependence with DNA Concentration

DNA dynamics and flow properties are of great importance for understanding its functions. DNA is a semiflexible polymer chain characterized by having a large persistence length of around 50 nm and high charge density; DNA chains are interacting efficiently at high concentrations, in dependence of the ionic concentration. In relation with DNA molecular characteristics, it is also known that DNA solutions are able to form liquid crystalline phases over a critical polymer concentration. In this work, the supramolecular organization in calf-thymus DNA solution, with low degree of entanglement, appearing under flow was studied in a wide DNA concentration range from 2 to 10 mg/mL, at a pH of 7.3 and 20 °C. The rheological behavior of the system was studied using steady state flow and oscillatory measurements. Transient regimes were also tested by imposing controlled shear rates on a short time up to steady state. Furthermore, a combination of visual observations and flow birefringence measurements was proposed to reach a better understanding of the obtained rheological behavior. The presence of a shear-induced texture is revealed under flow for the calf-thymus DNA solutions at CDNA> 5 mg/mL and attributed to organized domains of DNA molecules, named in the text as crystalline parts, which are progressively oriented under shear. Finally, at high shear rates (over 100 s–1), it is shown that for the DNA solutions the orientation of these organized DNA domains and connecting chains under flow goes to an anisotropic monodomain.

Toroidal Condensates by Semiflexible Polymer Chains: Insights into Nucleation, Growth and Packing Defects.

Deciphering the principles of DNA condensation is important to understand problems such as genome packing and DNA compaction for delivery in gene therapy. DNA molecules condense into toroids and spindles upon the addition of multivalent ions. Nucleation of a loop in the semiflexible DNA chain is critical for both the toroid and spindle formation. To understand the structural differences in the nucleated loop, which cause bifurcation in the condensation pathways leading to toroid or spindle formation, we performed molecular dynamics simulations using a coarse-grained bead-spring polymer model. We find that the formation of a toroid or a spindle is correlated with the orientation of the chain segments close to the loop closure in the nucleated loop. Simulations show that toroids grow in size when spindles in solution interact with a pre-existing toroid and merge into it by spooling around the circumference of the toroid, forming multimolecular toroidal condensates. The merging of spindles with toroids is facile, indicating that this should be the dominant pathway through which the toroids grow in size. The Steinhardt bond order parameter analysis of the toroid cross section shows that the chains pack in a hexagonal fashion. In agreement with the experiments there are regions in the toroid with good hexagonal packing and also with considerable disorder. The disorder in packing is due to the defects, which are propagated during the growth of toroids. In addition to the well-known crossover defect, we have identified three other forms of defects, which perturb hexagonal packing. The new defects identified in the simulations are amenable to experimental verification.

Structural Behavior of a Semiflexible Polymer Chain in an Array of Nanoposts.

The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs was also carried out. In the interpretation of the chain structural properties, the geometry of the post array is considered as a combination of a channel approximating the interstitial volume with the diameter dc and a slit approximating the passage aperture with the width wp. The number of interstitial volumes occupied by a chain monotonically increases with the decreasing ratio dc/wp regardless of the way the geometry of the post array is varied. However, depending on how the array geometry is modified, the chain span along the posts displays a monotonic (constant post separation) or a non-monotonic behavior (constant passage width) when plotted as a function of the post diameter. In the case of monotonic trend, the width of interstitial spaces increases with the increasing chain occupation number, while, in the case of non-monotonic trend, the width of interstitial spaces decreases with the increasing chain occupation number. In comparison with linear topology, for circular topology, the stiffness affects more significantly the relative chain extension along the posts and less significantly the occupation number. The geometrical parameters of the post arrays are stored in the single-chain structure factors. The characteristic humps are recognized in the structure factor which ensue from the local increase in the density of segments in the circular chains presented in an interstitial volume or from the correlation of parallel chain fragments separated by a row of posts. Although the orientation correlations provide qualitative information about the chain topology and the character of confinement within a single interstitial volume, information about the array periodicity is missing.

Unfolding Kinetics of a Wormlike Chain under Elongational Flow.

A simple theory of the unfolding kinetics of a semi-flexible polymer chain is presented in terms of a Kramers type picture for the energy of elongation. The hydrodynamic interactions are discussed in terms of slender body theory. It turns out that the elongation of the chain is basically linear in time and independent of the viscosity. The former prediction agrees with experiments on the stretching dynamics of DNA under planar elongational flow. Nevertheless, the theory overestimates the experimental rate by a significant amount for reasons that are unclear.

Event-chain Monte Carlo algorithms for three- and many-particle interactions

We generalize the rejection-free event-chain Monte Carlo algorithm from many-particle systems with pairwise interactions to systems with arbitrary three- or many-particle interactions. We introduce generalized lifting probabilities between particles and obtain a general set of equations for lifting probabilities, the solution of which guarantees maximal global balance. We validate the resulting three-particle event-chain Monte Carlo algorithms on three different systems by comparison with conventional local Monte Carlo simulations: i) a test system of three particles with a three-particle interaction that depends on the enclosed triangle area; ii) a hard-needle system in two dimensions, where needle interactions constitute three-particle interactions of the needle end points; iii) a semiflexible polymer chain with a bending energy, which constitutes a three-particle interaction of neighboring chain beads. The examples demonstrate that the generalization to many-particle interactions broadens the applicability of event-chain algorithms considerably.

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study.

Local stiffness of polymer chains is instrumental in all structure formation processes of polymers, from crystallization of synthetic polymers to protein folding and DNA compactification. We present Stochastic Approximation Monte Carlo simulations—a type of flat-histogram Monte Carlo method—determining the density of states of a model class of single semi-flexible polymer chains, and, from this, their complete thermodynamic behavior. The chains possess a rich pseudo phase diagram as a function of stiffness and temperature, displaying non-trivial ground-state morphologies. This pseudo phase diagram also depends on chain length. Differences to existing pseudo phase diagrams of semi-flexible chains in the literature emphasize the fact that the mechanism of stiffness creation matters.

Effect of polymer rigidity on the phase behaviour of polymer adsorption on to planar surface.

We study the process of a semiflexible polymer chain adsorption on to planar surface by the dynamic Monte Carlo (DMC) method, based on the 3D off-lattice model. Both the strength of attractive monomer–surface interaction (εa) and bending energy (b) have pronounced effect on the adsorption and shape of semiflexible polymer chain. The semiflexible polymer can just fully adsorb on to the surface at certain εa, which is defined as critical εa. The essential features of the semiflexible polymer adsorption on to surface are that (i) the critical εa increases with increase in b; (ii) the shape of the fully adsorbed semiflexible polymer chain is film-like toroid, and the toroid becomes more and more perfect with increase in b. In addition, the size of toroid and the number of turns of toroid can be controlled by the b and εa.

Stretching a Semiflexible Polymer in a Tube.

How the statistical behavior of semiflexible polymer chains may be affected by force stretching and tube confinement is a classical unsolved problem in polymer physics. Based on the Odijk deflection theory and normal mode decomposition in terms of Fourier expansion, we have derived a new compact formula for the extension of a wormlike chain of finite length strongly confined in a tube and simultaneously stretched by an external force. We have also suggested a new deflection length, which together with the force-extension relation is valid for a very extended range of the tube-diameter/persistence-length ratio comparing to the classic Odijk theory. The newly derived formula has no adjustable fitting parameters for the whole deflection regime; in contrast, the classic Odijk length needs different prefactors to fit the free energy and average extension, respectively. Brownian dynamics simulations based on the Generalized Bead-Rod (GBR) model were extensively performed, which justified the theoretical predictions.

Stable knots in the phase diagram of semiflexible polymers: A topological order parameter?

We report a recent computer simulation study of the phase diagram of a single semiflexible polymer chain using a generic coarse-grained bead-stick model. The results are obtained with a combination of multicanonical and replica-exchange simulations. Interestingly, we find in the temperature-stiffness plane well-defined phases that can be characterized by stable knots of various types. We discuss how the knots can be observed and to what extent they can be interpreted as “topological order parameter”. Another surprising observation concerns the peculiar transitions into these stable knot phases which will be also explained.

Flexible star polymer chain adsorption by a flat surface: a molecular dynamics simulation

In this work, we have studied the adsorption of a single flexible star polymer chain by a flat surface. The molecular dynamics simulation has been validated for the case of a free star polymer chain using the diffusion experiment. The scaling laws found are in agreement with the Flory theory predictions and the Rouse model. For the adsorption, preliminary results were obtained for chains of different sizes N=31 to N=199 and different functionalities (f=3,4,6,8,10). For the case of semi-flexible star polymer chains, further investigation is needed to locate the critical point of adsorption when varying the potential interaction strength between the chain and the surface.

Helix-like structure formation of a semi-flexible chain confined in a cylinder channel**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504033 and 11404290) and the General Research Fund of Hong Kong Research Council of China (Grant No. 15301014).

Molecular dynamics method is used to study the conformation behavior of a semi-flexible polymer chain confined in a cylinder channel. A novel helix-like structure is found to form during the simulation. Moreover, the detailed characteristic parameters and formation probability of these helix-like structures under moderate conditions are investigated. We find that the structure is not a perfect helix, but a bundle of elliptical turns. In addition, we conduct a statistical analysis for the chain monomer distribution along the radial direction. This research contributes to our understanding of the microscopic conformation of polymer chains in confined environments filled with a solvent.

A Simple Analytical Model for Predicting the Collapsed State of Self-Attractive Semiflexible Polymers.

We develop an analytical model to predict the collapse conformation for a single semiflexible polymer chain in solution, given its length, diameter, stiffness, and self-attractiveness. We construct conformational phase diagrams containing three collapsed states, namely torus, bundle, and globule over a range of dimensionless ratios of the three energy parameters, namely solvent-water surface energy (), energy of bundle end folds (), and bending energy per unit length in a torus (). Our phase diagram captures the general phase behavior of a single long chain (>10 Kuhn lengths) at moderately high (order unity) dimensionless temperature, which is the ratio of thermal energy to the attractive interaction between neighboring monomers. We find that the phase behavior approaches an asymptotic limit when the dimensionless chain length to diameter ratio (L*) exceeds 300. We successfully validate our analytical results with Brownian Dynamics (BD) simulations, using a mapping of the simulation parameters to those used in the phase diagram. We evaluate the effect of three different bending potentials in the range of moderately high dimensionless temperature, a regime not been previously explored by simulations, and find qualitative agreement between the model and simulation results. We, thus, demonstrate that a rather simplified analytical model can be used to qualitatively predict the final collapsed state of a given polymer chain.

Spatial Rearrangement and Mobility Heterogeneity of an Anionic Lipid Monolayer Induced by the Anchoring of Cationic Semiflexible Polymer Chains.

We use Monte Carlo simulations to investigate the interactions between cationic semiflexible polymer chains and a model fluid lipid monolayer composed of charge-neutral phosphatidyl-choline (PC), tetravalent anionic phosphatidylinositol 4,5-bisphosphate (PIP2), and univalent anionic phosphatidylserine (PS) lipids. In particular, we explore how chain rigidity and polymer concentration influence the spatial rearrangement and mobility heterogeneity of the monolayer under the conditions where the cationic polymers anchor on the monolayer. We find that the anchored cationic polymers only sequester the tetravalent PIP2 lipids at low polymer concentrations, where the interaction strength between the polymers and the monolayer exhibits a non-monotonic dependence on the degree of chain rigidity. Specifically, maximal anchoring occurs at low polymer concentrations, when the polymer chains have an intermediate degree of rigidity, for which the PIP2 clustering becomes most enhanced and the mobility of the polymer/PIP2 complexes becomes most reduced. On the other hand, at sufficiently high polymer concentrations, the anchoring strength decreases monotonically as the chains stiffen—a result that arises from the pronounced competitions among polymer chains. In this case, the flexible polymers can confine all PIP2 lipids and further sequester the univalent PS lipids, whereas the stiffer polymers tend to partially dissociate from the monolayer and only sequester smaller PIP2 clusters with greater mobilities. We further illustrate that the mobility gradient of the single PIP2 lipids in the sequestered clusters is sensitively modulated by the cooperative effects between anchored segments of the polymers with different rigidities. Our work thus demonstrates that the rigidity and concentration of anchored polymers are both important parameters for tuning the regulation of anionic lipids.

Static and dynamic properties of large polymer melts in equilibrium.

We present a detailed study of the static and dynamic behaviors of long semiflexible polymer chains in a melt. Starting from previously obtained fully equilibrated high molecular weight polymer melts [G. Zhang et al., ACS Macro Lett. 3, 198 (2014)], we investigate their static and dynamic scaling behaviors as predicted by theory. We find that for semiflexible chains in a melt, results of the mean square internal distance, the probability distributions of the end-to-end distance, and the chain structure factor are well described by theoretical predictions for ideal chains. We examine the motion of monomers and chains by molecular dynamics simulations using the ESPResSo++ package. The scaling predictions of the mean squared displacement of inner monomers, center of mass, and relations between them based on the Rouse and the reptation theory are verified, and related characteristic relaxation times are determined. Finally, we give evidence that the entanglement length Ne,PPA as determined by a primitive path analysis (PPA) predicts a plateau modulus,GN (0)=45(ρkBT/Ne), consistent with stresses obtained from the Green-Kubo relation. These comprehensively characterized equilibrium structures, which offer a good compromise between flexibility, small Ne, computational efficiency, and small deviations from ideality, provide ideal starting states for future non-equilibrium studies.

Particle-directed assembly of semiflexible polymer chains.

We use Langevin dynamics simulations to study aggregation of semiflexible polymers driven by attractions between polymers and spherical particles. We consider a simple model with purely repulsive polymer/polymer and particle/particle interactions but attractive polymer/particle interactions. We find a rich "phase diagram" that contains several different types of globular and rod-like aggregates with either liquid-like or crystalline structure for the particle positions. Systems that exhibit rod-like aggregates with crystalline internal order exhibit a discontinuous rod-globule transition, while systems with liquid-like internal order exhibit a smooth crossover between isotropic and elongated aggregates with increasing chain stiffness. Polymers in elongated liquid-like aggregates often adopt helical configurations that wind around the axis of the aggregate.

Semiflexible crossing-avoiding trails on plane-filling fractals

We have studied the statistics of semiflexible polymer chains modeled by crossing-avoiding trails (CAT) situated on the family of plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension df is equal to 2 for all members of the fractal family. By applying the exact and Monte Carlo real-space renormalization group method we have calculated the critical exponent ν, which governs the scaling behavior of the end-to-end distance of the polymer, as well as the entropic critical exponent γ, for a large set of fractals, and various values of polymer flexibility. Our results, obtained for CAT model on PF fractals, show that both critical exponents depend on the polymer flexibility, in such a way that less flexible polymer chains display enlarged values of ν, and diminished values of γ. We have compared the obtained results for CAT model with the known results for the self-avoiding walk and self-avoiding trail models and discussed the influence of excluded volume effect on the values of semiflexible polymer critical exponents, for a large set of studied compact fractals.

Molecular Dynamics Insights into Behavior of Poly(ethylene succinate) Single Chain on Carbon Nanotube Surface

The conformational properties of semiflexible polymer chains at their interface with nanoscale organic fillers are classified as a challenging subject due to the vast complexities involved, apart from being the most critical phase of transcrystallization. An extensive computational effort based on atomistic molecular dynamics has been undertaken in this study in order to elucidate the behavior of a single chain of a model aliphatic polyester, poly(ethylene succinate), in the vicinity of a single-walled carbon nanotube to gain new physical insights into the conformational characteristics of this type of polymer. The core finding is that the polymer chain transits from a coiled to a folded shape in the process of adsorption on the nanotube surface being a compromise of the dominant van der Waals interactions and the chain configurational entropy. Varying temperature and chain length, as well as the nanotube curvature, has been highlighted to be influential on chain order parameter and spatial arrangement. C...