Semiflexible Ring Polymers Research Articles

Active polar ring polymer in shear flow-An analytical study.

We theoretically study the conformational and dynamical properties of semiflexible active polar ring polymers under linear shear flow. A ring is described as a continuous semiflexible Gaussian polymer with a tangential active force of a constant density along its contour. The linear but non-Hermitian equation of motion is solved using an eigenfunction expansion, which yields activity-independent, but shear-rate-dependent, relaxation times and activity-dependent frequencies. As a consequence, the ring's stationary-state properties are independent of activity, and its conformations and rheological properties are equal to those of a passive ring under shear. The presence of characteristic time scales by relaxation and the activity-dependent frequencies give rise to a particular dynamical behavior. A tank-treading-like motion emerges for long relaxation times and high activities, specifically for stiff rings. In the case of very flexible polymers, the relaxation behavior dominates over activity contributions suppressing tank-treading. Shear strongly affects the crossover from a tank-treading to a relaxation-dominated dynamics, and the ring polymer exhibits tumbling motion at high shear rates. This is reflected in the tumbling frequency, which displays two shear-rate dependent regimes, with an activity-dependent plateau at low shear rates followed by a power-law regime with increasing tumbling frequency for high shear rates.

Conformational Transition of Semiflexible Ring Polyelectrolyte in Tetravalent Salt Solutions: A Simple Numerical Modeling without the Effect of Twisting.

In this work, the conformational behaviors of ring polyelectrolyte in tetravalent salt solutions are discussed in detail through molecular dynamics simulation. For simplification, here we have neglected the effect of the twisting interaction, although it has been well known that both bending and twisting interactions play a deterministic in the steric conformation of a semiflexible ring polymer. The salt concentration CS and the bending energy b take a decisive role in the conformation of the ring polyelectrolyte (PE). Throughout our calculations, the b varies from b = 0 (freely joint chain) to b = 120. The salt concentration CS changes in the range of 3.56 × 10-4 M ≤ CS ≤ 2.49 × 10-1 M. Upon the addition of salt, ring PE contracts at first, subsequently re-expands. More abundant conformations are observed for a semiflexible ring PE. For b = 10, the conformation of semiflexible ring PE shifts from the loop to two-racquet-head spindle, then it condenses into toroid, finally arranges into coil with the increase of CS. As b increases further, four phase transitions are observed. The latter two phase transitions are different. The semiflexible ring PE experiences transformation from toroid to two racquet head spindle, finally to loop in the latter two phase transitions. Its conformation is determined by the competition among the bending energy, cation-bridge, and entropy. Combined, our findings indicate that the conformations of semiflexible ring PE can be controlled by changing the salt concentration and chain stiffness.

Single-molecule analysis of solvent-responsive mechanically interlocked ring polymers and the effects of nanoconfinement from coarse-grained simulations.

In this study, we simulate mechanically interlocked semiflexible ring polymers inspired by the minicircles of kinetoplast DNA (kDNA) networks. Using coarse-grained molecular dynamics simulations, we investigate the impact of molecular topological linkage and nanoconfinement on the conformational properties of two- and three-ring polymer systems in varying solvent qualities. Under good-quality solvents, for two-ring systems, a higher number of crossing points lead to a more internally constrained structure, reducing their mean radius of gyration. In contrast, three-ring systems, which all had the same crossing number, exhibited more similar sizes. In unfavorable solvents, structures collapse, forming compact configurations with increased contacts. The morphological diversity of structures primarily arises from topological linkage rather than the number of rings. In three-ring systems with different topological conformations, structural uniformity varies based on link types. Extreme confinement induces isotropic and extended conformations for catenated polymers, aligning with experimental results for kDNA networks and influencing the crossing number and overall shape. Finally, the flat-to-collapse transition in extreme confinement occurs earlier (at relatively better solvent conditions) compared to non-confined systems. This study offers valuable insights into the conformational behavior of mechanically interlocked ring polymers, highlighting challenges in extrapolating single-molecule analyses to larger networks such as kDNA.

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.

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.

Dynamics of semiflexible ring polymer in chiral Brownian particles bath

Molecular dynamics simulations are used to investigate the dynamic behavior of ring polymer in a bath containing a high concentration of chiral Brownian particles. The chiral Brownian particles around the chain drive the ring polymer to deform, and torque acting on ring is produced and drive the ring to rotate in one direction. Furthermore, the relationship between the ring's rotation speed and the angular velocity of the surrounding Brownian particles is not monotonically linear. The rotation of the ring chain increases initially, then decreases as the angular velocity of the Brownian particle increases. These findings offer a theoretical framework for investigating the conformation and motion properties of polymer macromolecules in Brownian particle systems.

Molecular Conformation and Intermolecular Interactions of Linear and Cyclic Amylose Derivatives in Solution

AbstractFour kinds of rigid and semiflexible ring polymers are synthesized from flexible cyclic amylose. Their conformational properties in dilute solution are determined from dimensional and hydrodynamic properties in terms of the wormlike ring model. The helix rise per residue h of some ring polymers is larger or smaller than that for the corresponding linear chains, indicating that the local helical structure of the ring polymer is not the same as that for the linear chain. Intermolecular interactions detected by the second virial coefficient and chiral recognition ability of some ring polymers are different from the linear chain, suggesting the local structural change causes the intermolecular interactions. The study also finds that rigid ring polymers can form liquid crystal phase at high concentration. X‐ray diffraction results suggest that the ring chains form pseudo rodlike conformation in the liquid crystal phase, showing that intermolecular excluded volume effects significantly influence the conformation of the polymer chains.

Adherent Moving of Polymers in Spherical Confined Binary Semiflexible Ring Polymer Mixtures

Based on the coarse-grained model, we used molecular dynamics methods to calculate and simulate a semiflexible long ring–semiflexible short ring blended polymer system confined in a hard sphere. We systematically studied the distribution and motion characteristics of the long ring chain. The results show that when the short ring is short enough (Lshort < 20), the long ring (Llong = 50) is separated from the blend system and then distributed against the inner wall. As the length of the short ring increases (Lshort ≥ 20), the long ring can no longer be separated from the blending system. Moreover, we found that the long ring demonstrates a random direction of adherent walking behavior on the inner surface of the hard sphere. The velocity of the long ring decreases with the increase in the short ring length Lshort. Specifically for Lshort ≥ 20, the system does not undergo phase separation and the speed of the long ring decreases sharply along with the long ring distributed inside the confined bulk. This is related to the inner wall layer moving faster than the inside bulk of the restricted system. Our simulation results can help us to understand the distribution of macromolecules in biological systems in confined systems, including the restricted chromosome partitioning distribution and packing structure of circular DNA molecules.

Dynamics of active polar ring polymers.

The conformational and dynamical properties of isolated semiflexible active polar ring polymers are investigated analytically. A ring is modeled as a continuous Gaussian polymer exposed to tangential active forces. The analytical solution of the linear non-Hermitian equationof motion in terms of an eigenfunction expansion shows that ring conformations are independent of activity. In contrast, activity strongly affects the internal ring dynamics and yields characteristic time regimes, which are absent in passive rings. On intermediate timescales, flexible rings show an activity-enhanced diffusive regime, while semiflexible rings exhibit ballistic motion. Moreover, a second active time regime emerges on longer timescales, where rings display a snake-like motion, which is reminiscent to a tank-treading rotational dynamics in shear flow, dominated by the mode with the longest relaxation time.

Piston Compression of Semiflexible Ring Polymers in Channels

AbstractMolecular simulations in nanochannels are used to explore the compression elasticity of ring polymers of stiffness (persistence length) similar to DNA. By combination with the parallel data for linear polymers, the effect of chain topology on their compression behavior is assessed. The results show that the ring polymers are much less bendable at longitudinal compression than the linear analogs. The chain span of linear polymers is continuously reduced at compression, whereas in ring polymers, an abrupt decrease of the span is observed. The simulation data elucidate this phenomenon as the buckling of a ring polymer into the double‐folded hairpin. The shrinking ratio of sizes of the ring and linear chains shows a complex behavior much differing from the existing reports. The force–displacement functions for chains of both topologies at moderate confinement are very well accounted for by the mean‐field Flory scheme. The theory predicts the difference in the mechanical stiffness of the ring and linear polymers in qualitative agreement with the simulation data. These findings are relevant to the compression behavior of semiflexible ring polymers under spatial constraints such as in nanofluidic experiments, disordered media, or cellular environment.

Conformational behavior and self-assembly of disjoint semi-flexible ring polymers adsorbed on solid substrates.

The conformational behavior and spatial organization of self-avoiding semi-flexible ring polymers, that are fully adsorbed on solid substrates, are investigated via systematic coarse-grained molecular dynamics simulations. Our results show that both conformations and spatial organization of the polymers depend strongly on their bending stiffness, κ, and on their areal number density, ρ. For ρ < ρ*, where ρ* is the overlap density, and for low values of κ, thermal fluctuations lead to weakly anisotropic instantaneous conformations of the polymers. The interplay between thermal fluctuations and polymer stiffness leads to a non-monotonic dependence of the polymers elongation on κ with a maximum elongation at some intermediate κ. Regardless of κ, the polymers elongation is almost independent of ρ for ρ ⪅ ρ*, then increases with ρ. At ρ ≈ ρ* and high κ, the almost circularly-shaped polymers self-assemble into a triangular lattice with quasi-long range order. For ρ above ρ* and high κ, crowding of the polymers leads to their self-assembly into liquid-crystalline phases. In particular, for ρ moderately above ρ* and high κ, the polymer conformations are obround and self-assemble into domains with smectic-A-like order. At higher densities, the polymer have a biconcave geometry and self-assemble into domains with smectic-C-like order.

Effects of Topological Constraints on Penetration Structures of Semi-Flexible Ring Polymers.

The effects of topological constraints on penetration structures of semi-flexible ring polymers in a melt are investigated using molecular dynamics simulations, considering simultaneously the effects of the chain stiffness. Three topology types of rings are considered: 01-knot (the unknotted), 31-knot and 61-knot ring polymers, respectively. With the improved algorithm to detect and quantify the inter-ring penetration (or inter-ring threading), the degree of ring threading does not increase monotonously with the chain stiffness, existing a peak value at the intermediate stiffness. It indicates that rings interpenetrate most at intermediate stiffness where there is a balance between coil expansion (favoring penetrations) and stiffness (inhibiting penetrations). Meanwhile, the inter-ring penetration would be suppressed with the knot complexity of the rings. The analysis of effective potential between the rings provides a better understanding for this non-monotonous behavior in inter-ring penetration.

Ordered aggregation of semiflexible ring-linear blends in ellipsoidal confinement

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

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

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

Entropy-induced Separation of Binary Semiflexible Ring Polymer Mixtures in Spherical Confinement.

Coarse-grained molecular dynamics simulations are used to investigate the conformations of binary semiflexible ring polymers (SRPs) of two different lengths confined in a hard sphere. Segregated structures of SRPs in binary mixtures are strongly dependent upon the number density of system (ρ), the bending energy of long SRPs (Kb, long), and the chain length ratio of long to short SRPs (α). With a low ρ or a weak Kb, long at a small ratio α, long SRPs are immersed randomly in the matrix of short SRPs. As ρ and bending energy of long SRPs (Kb, long) are increased up to a certain value for a large ratio α, a nearly complete segregation between long and short SRPs is observed, which can be further characterized by the ratio of tangential and radial components of long SRPs velocity. These explicit segregated structures of the two components in spherical confinement are induced by a delicate competition between the entropic excluded volume (depletion) effects and bending contributions.

Ordered aggregation structures of semiflexible ring polymers in ring-linear blends

Conformations and dynamical properties of semiflexible ring polymers (SRPs) in semiflexible ring-linear blends are investigated by using molecular dynamic simulation. The conformations of SRPs rely mainly on bending energy (Kb,linear) and chain length (Nlinear) of semiflexible linear polymers as well as the fraction of SRPs (φring) in semiflexible ring-linear blends. SRPs are randomly immersed in flexible or short semiflexible linear polymer melts, however, ordered aggregation structures of SRPs are formed in the matrix of semiflexible linear polymers, especially for long semiflexible linear polymers. These ordered aggregation structures are induced by entropy of SRPs, and long semiflexible linear polymers can improve the overlap of SRPs in semiflexible ring-linear blends. In addition, the center-of-mass diffusion coefficient (D) of SRPs first decreases abruptly and then gradually with the bending energy of linear polymers increasing in semiflexible ring-linear blends, and SRPs diffuse very slowly in the blends of long semiflexible linear polymers due to the strong threading by long semiflexible linear polymers. Our results may help us understand special topological conformations and dynamical behaviors of SRPs in semiflexible ring-linear blends.

Active Brownian ring polymers.

The conformational and dynamical properties of semiflexible active Brownian ring polymers are investigated analytically. A ring is described by the Gaussian semiflexible polymer model accounting for the finite contour length. Activity is implemented by a Gaussian, non-Markovian stochastic process resembling either an external nonthermal force or a local self-propulsion velocity as for an active Ornstein-Uhlenbeck particle. Specifically, the fluctuation spectrum of normal-mode amplitudes is analyzed. At elevated activities, flexible (tension) modes dominate over bending modes even for semiflexible rings, corresponding to enhanced conformational fluctuations. The fluctuation spectrum exhibits a crossover from a quadratic to a quartic dependence on the mode number with increasing mode number, originating from intramolecular tension, but the relaxation behavior is either dominated by intra-polymer processes or the active stochastic process. A further increase in activity enhances fluctuations at large length scales at the expense of reduced fluctuations at small scales. Conformationally, the mean square ring diameter exhibits swelling qualitatively comparable to liner polymers. The ring's diffusive dynamics is enhanced, and the mean square displacement shows distinct activity-determined regimes, consecutively, a ballistic, a subdiffusive, and a diffusive regime. The subdiffusive regime disappears gradually with increasing activity.

Unusual conformations of semiflexible ring polymers confined in two parallel surfaces

By employing molecular dynamics simulation, we explore the conformations of semiflexible ring polymers (SRPs) confined in two parallel surfaces. The conformations of confined SRPs rely on the distance between two parallel surfaces D and the chain stiffness as well as the interaction between SRPs and the surface. For strong confinements with the repulsive surface, SRPs are almost parallel to the surface, however, for weak confinements with the attractive surface, some SRPs are perpendicular to the surface owing to the competition between the attractive interactions and the topological constrains of SRPs. For the attractive surface, adsorption ability of SRPs decreases with the increase of chain stiffness Kb because disk-like conformations hinder more monomers to be adsorbed on the attractive surfaces, which is different completely from semiflexible linear polymers. Meanwhile, the shape of SRPs near the repulsive surface is oblate, while most of SRPs are prolate near the attractive surface. Moreover, confinements hinder large stack structures to be formed for SRPs, especially for the attractive surface. Our results can help us understand topological constraints for confined SRPs.

Semiflexible ring polymers in dilute solutions

Our recent theoretical and/or Monte Carlo results for dilute solution properties of semiflexible ring polymers on the basis of the wormlike ring model are briefly summarized. The behavior of the mean-square radius of gyration 〈S2〉, intrinsic viscosity [η], scattering function P(k) with k the magnitude of the scattering vector, and second virial coefficient A2,Θ at the Θ state is examined as a function of the reduced contour length λL, where λ−1 and L are the stiffness parameter and contour length of the wormlike ring, respectively. Effects of the topological constraints on 〈S2〉, [η], P(k), and A2,Θ of semiflexible rings are also examined by comparing the results for the wormlike rings without the topological constraints with those for the wormlike ring of the trivial or trefoil knot.

SEMI-FLEXIBLE COMPACT POLYMERS IN A DISORDERED ENVIRONMENT

Hamiltonian cycles with bending rigidity are studied on the first three members of the fractal family obtained by generalization of the modified rectangular (MR) fractal lattice. This model is proposed to describe conformational and thermodynamic properties of a single semi-flexible ring polymer confined in a poor and disordered (e.g. crowded) solvent. Due to the competition between temperature and polymer stiffness, there is a possibility for the phase transition between molten globule and crystal phase of a polymer to occur. The partition function of the model in the thermodynamic limit is obtained and analyzed as a function of polymer stiffness parameter s (Boltzmann weight), which for semi-flexible polymers can take on values over the interval (0,1). Other quantities, such as persistence length, specific heat and entropy, are obtained numerically and presented graphically as functions of stiffness parameter s .