Dynamics Of Ring Polymers Research Articles

From Bioreactor to Bulk Rheology: Achieving Scalable Production of Highly Concentrated Circular DNA.

DNA serves as a model system in polymer physics due to its ability to be obtained as a uniform polymer with controllable topology and nonequilibrium behavior. Currently, a major obstacle in the widespread adoption of DNA is obtaining it on a scale and cost basis that accommodates bulk rheology and high-throughput screening. To address this, recent advancements in bioreactor-based plasmid DNA production is coupled with anion exchange chromatography producing a unified approach to generating gram-scale quantities of monodisperse DNA. With this method, 1.1 grams of DNA is obtained per batch to generate solutions with concentrations up to 116mg mL-1. This solution of uniform supercoiled and relaxed circular plasmid DNA, is roughly 69 times greater than the overlap concentration. The utility of this method is demonstrated by performing bulk rheology measurements at sample volumes up to 1 mL on DNA of different lengths, topologies, and concentrations. The measured elastic moduli are orders of magnitude larger than those previously reported for DNA and allowed for the construction of a time-concentration superposition curve that spans 12 decades of frequency. Ultimately, these results can provide important insights into the dynamics of ring polymers and the nature of highly condensed DNA dynamics.

Topology Matters: Conformation and Microscopic Dynamics of Ring Polymers

Topology Matters: Conformation and Microscopic Dynamics of Ring Polymers

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.

Size and Dynamics of Ring Polymers under Different Topological Constraints

Size and Dynamics of Ring Polymers under Different Topological Constraints

Conformation and dynamics of ring polymers under symmetric thin film confinement.

Understanding the structure and dynamics of polymers under confinement has been of widespread interest, and one class of polymers that have received comparatively little attention under confinement is that of ring polymers. The properties of non-concatenated ring polymers can also be important in biological fields because ring polymers have been proven to be a good model to study DNA organization in the cell nucleus. From our previous study, linear polymers in a cylindrically confined polymer melt were found to segregate from each other as a result of the strong correlation hole effect that is enhanced by the confining surfaces. By comparison, our subsequent study of linear polymers in confined thin films at similar levels of confinements found only the onset of segregation. In this study, we use molecular dynamics simulation to investigate the chain conformations and dynamics of ring polymers under planar (1D) confinement as a function of film thickness. Our results show that conformations of ring polymers are similar to the linear polymers under planar confinement, except that ring polymers are less compressed in the direction normal to the walls. While we find that the correlation hole effect is enhanced under confinement, it is not as pronounced as the linear polymers under 2D confinement. Finally, we show that chain dynamics far above Tg are primarily affected by the friction from walls based on the monomeric friction coefficient we get from the Rouse mode analysis.

Threading-Induced Dynamical Transition in Tadpole-Shaped Polymers.

The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring–linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in “chimeric” architectures. The simplest example of this family is a “tadpole”-shaped polymer, a single ring fused to the end of a single linear chain. We show that polymers with this architecture display a threading-induced dynamical transition that substantially slows chain relaxation. Our findings shed light on how threadings control dynamics and may inform design principles for chimeric polymers with topologically tunable bulk rheological properties.

Effect of molecular architecture on ring polymer dynamics in semidilute linear polymer solutions

Understanding the dynamics of ring polymers is a particularly challenging yet interesting problem in soft materials. Despite recent progress, a complete understanding of the nonequilibrium behavior of ring polymers has not yet been achieved. In this work, we directly observe the flow dynamics of DNA-based rings in semidilute linear polymer solutions using single molecule techniques. Our results reveal strikingly large conformational fluctuations of rings in extensional flow long after the initial transient stretching process has terminated, which is observed even at extremely low concentrations (0.025 c*) of linear polymers in the background solution. The magnitudes and characteristic timescales of ring conformational fluctuations are determined as functions of flow strength and polymer concentration. Our results suggest that ring conformational fluctuations arise due to transient threading of linear polymers through open ring chains stretching in flow.

Orientational relaxation of ring polymers in dilute solutions.

The segmental relaxation dynamics of ring polymers in dilute solutions is investigated via optimized Rouse-Zimm theory. To the best of our knowledge, this is the first study that characterizes the orientational relaxation dynamics of ring polymers in dilute solutions. The orientational time autocorrelation functions are governed by two major processes that span a broad range of timescales: (i) local segmental motion at short times, independent of the ring size, and (ii) overall motion of the ring at long times that depends on the limiting ring size. Smaller rings relax faster than larger rings and their respective linear analogues. The hydrodynamic interactions decrease the higher relaxation rates corresponding to the local relaxation modes and increase the smaller relaxation rates which correspond to the collective relaxation modes. The spectral density is independent of frequency in the low frequency regime while it decreases with increasing frequency. Regardless of the ring size, the spin-lattice relaxation rate exhibits a single characteristic maximum as a function of frequency that shifts to a lower value with increasing strength of hydrodynamic interactions.

A Study of the Morphology, Dynamics, and Folding Pathways of Ring Polymers with Supramolecular Topological Constraints Using Molecular Simulation and Nonlinear Manifold Learning

Ring polymers are prevalent in natural and engineered systems, including circular bacterial DNA, crown ethers for cation chelation, and mechanical nanoswitches. The morphology and dynamics of ring polymers are governed by the chemistry and degree of polymerization of the ring, and intramolecular and supramolecular topological constraints such as knots or mechanically-interlocked rings. In this study, we perform molecular dynamics simulations of polyethylene ring polymers at two different degrees of polymerization and in different topological states, including a trefoil knot, catenane state (two interlocked rings), and Borromean state (three interlocked rings). We employ nonlinear manifold learning to extract the low-dimensional free energy surface to which the structure and dynamics of the polymer chain are effectively restrained. The free energy surfaces reveal how degree of polymerization and topological constraints affect the thermally accessible conformations, chiral symmetry breaking, and folding and collapse pathways of the rings, and present a means to rationally engineer ring size and topology to stabilize particular conformational states and folding pathways. We compute the rotational diffusion of the ring in these various states as a crucial property required for the design of engineered devices containing ring polymer components.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers.

The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a and is related to the hopping diffusion of NPs in the entanglement network. In contrast to the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled nonconcatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.

Ring Polymer Dynamics Are Governed by a Coupling between Architecture and Hydrodynamic Interactions

The behavior of linear polymer chains in dilute solution flows has an established history. Polymers often possess more complex architectures, however, such as branched, dendritic, or ring structures. A major challenge lies in understanding how these nonlinear chain topologies affect the dynamic properties in nonequilibrium conditions, in both dilute and entangled solutions. In this work, we interrogate the single-chain dynamics of ring polymers using a combination of simulation, theory, and experiment. Inspired by recent experimental results by Li et al., we demonstrate that the presence of architectural constraints has surprising and pronounced effects on the dynamic properties of polymers as they are driven out of equilibrium. Ring constraints lead to two behaviors that contrast from linear chains. First, the coil–stretch transition occurs at larger values of the dimensionless flow strength (Weissenberg number) compared to linear chains, which is driven by coupling between intramolecular hydrodynamic in...

Slowing down of ring polymer diffusion caused by inter-ring threading.

Diffusion of long ring polymers in a melt is much slower than the reorganization of their internal structures. While direct evidence for entanglements has not been observed in the long ring polymers unlike linear polymer melts, threading between the rings is suspected to be the main reason for slowing down of ring polymer diffusion. It is, however, difficult to define the threading configuration between two rings because the rings have no chain end. In this work, evidence for threading dynamics of ring polymers is presented by using molecular dynamics simulation and applying a novel analysis method. The simulation results are analyzed in terms of the statistics of persistence and exchange times that have proved useful in studying heterogeneous dynamics of glassy systems. It is found that the threading time of ring polymer melts increases more rapidly with the degree of polymerization than that of linear polymer melts. This indicates that threaded ring polymers cannot diffuse until an unthreading event occurs, which results in the slowing down of ring polymer diffusion.

Conformations and dynamics of single flexible ring polymers in simple shear flow

The conformational, orientational and dynamical properties of single flexible ring polymers under simple shear flow are studied by a hybrid multiparticle collision dynamics simulation method. We found that contributing to the continuous stretching and constant alignment in the tank-treading motion, ring polymers undergo weaker deformation and orientation in the gradient direction, and show similar behaviors in the vorticity direction compared with their linear analogues. We also present the mechanisms of both tumbling and tank-treading motions based on the time trajectories of relative deformation and orientation. Furthermore, the simulation results reveal that the special structures and unique dynamics of ring polymers in simple shear flow have an obvious influence on rheological properties, which are qualitatively different from the properties of linear polymers.

Celebrating Soft Matter's 10th Anniversary: Topology matters: structure and dynamics of ring polymers.

Considering topology among all polymer architectures polymer rings are unique, as they are the simplest closed structures without ends. In this review we present recent experimental advances addressing the structure and dynamics of rings. We focus mainly on neutron scattering results that reveal experimental insight on a molecular scale. We first briefly reflect on the progress in ring chemistry that made the experimental access possible. Structural investigations characterizing rings as compact objects in the melts are put into theoretical context. In contrast to the plateau regime common for all other high molecular weight polymer systems, the dynamic modulus of pure ring systems is characterized by a power law decay, while the viscosity displays a much weaker molecular weight dependence as a corresponding linear melt. The dynamics of ring melts is uniquely addressed by neutron spin-echo spectroscopy. The sub-diffusive center of mass motion at short times agrees well with simulation as well as theoretical concepts. In the internal dynamics the basic length scale of the ring molecule, the loop size, manifests itself clearly. The experiments reveal strong evidence for loop motions and call for further theoretical work describing them. Finally, small fractions of ring molecules in linear melts turn out to be very sensitive probes in order to scrutinize the dynamics of the host with the potential to reveal fundamental aspects of the dynamics of branched polymer systems.

Threading Dynamics of Ring Polymers in a Gel.

We perform large scale three-dimensional molecular dynamics simulations of unlinked and unknotted ring polymers diffusing through a background gel, here a three-dimensional cubic lattice. Taking advantage of this architecture, we propose a new method to unambiguously identify and quantify inter-ring threadings (penetrations) and to relate these to the dynamics of the ring polymers. We find that both the number and the persistence time of the threadings increase with the length of the chains, ultimately leading to a percolating network of inter-ring penetrations. We discuss the implications of these findings for the possible emergence of a topological jammed state of very long rings.

Dynamics of self-threading ring polymers in a gel.

We study the dynamics of ring polymers confined to diffuse in a background gel at low concentrations. We do this in order to probe the inter-play between topology and dynamics in ring polymers. We develop an algorithm that takes into account the possibility that the rings hinder their own motion by passing through themselves, i.e. "self-threading". Our results suggest that the number of self-threadings scales extensively with the length of the rings and that this is substantially independent of the details of the model. The slowing down of the rings' dynamics is found to be related to the fraction of segments that can contribute to the motion. Our results give a novel perspective on the motion of ring polymers in a gel, for which a complete theory is still lacking, and may help us to understand the irreversible trapping of ring polymers in gel electrophoresis experiments.

Tumbling and tank-treading dynamics of individual ring polymers in shear flow

The dynamics of individual ring polymers in a shear flow is studied by a hybrid mesoscale simulation approach. New insight into the dynamics of ring polymers is provided: ring polymers exhibit both tumbling and tank-treading motions. A novel angle autocorrelation function is proposed to analyze the tank-treading motion that usually coexists with tumbling and may be applied to other highly deformable soft objects such as vesicles. The shear dependence of the average gyration tensor, the orientation angle, the tumbling and the tank-treading frequencies is determined quantitatively. The simulations also reveal that the existence of the tank-treading motion apparently increases the intrinsic viscosity of ring polymers under shear flow.

Structure and Dynamics of Ring Polymers: Entanglement Effects Because of Solution Density and Ring Topology

The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed solution density. Here, we use a different approach to investigate numerically the equilibrium and kinetic properties of solutions of model ring polymers. Specifically, the ring contour length is maintained fixed, while the interplay of inter- and intra-chain entanglement is modulated by varying both solution density (from infinite dilution up to \approx 40 % volume occupancy) and ring topology (by considering unknotted and trefoil-knotted chains). The equilibrium metric properties of rings with either topology are found to be only weakly affected by the increase of solution density. Even at the highest density, the average ring size, shape anisotropy and length of the knotted region differ at most by 40% from those of isolated rings. Conversely, kinetics are strongly affected by the degree of inter-chain entanglement: for both unknots and trefoils the characteristic times of ring size relaxation, reorientation and diffusion change by one order of magnitude across the considered range of concentrations. Yet, significant topology-dependent differences in kinetics are observed only for very dilute solutions (much below the ring overlap threshold). For knotted rings, the slowest kinetic process is found to correspond to the diffusion of the knotted region along the ring backbone.

Self-Similar Dynamics of a Flexible Ring Polymer in a Fixed Obstacle Environment: A Coarse-Grained Molecular Model

In this contribution we concern ourselves with an interesting problem, namely, the dynamics of ideal flexible ring polymers constrained in an array of fixed obstacles. The fundamental issue in this problem is to understand how a topologically constrained polymer chain is able to relax its conformation in the absence of chain ends. The key physics was provided in an elegant scaling theory by Rubinstein and co-workers (Obukhov, S. P.; Rubinstein, M.; Duke, T. Dynamics of a Ring Polymer in a Gel. Phys. Rev. Lett. 1994, 73, 1263-1267). In this work we develop a coarse-grained mean-field model based on the physical arguments of the scaling theory and derive constitutive relations for rings in fixed obstacle and melt environments. The model is composed of three distinct steps. In the first step the dynamics of an arbitrary section of a ring chain is worked out based on fractal Blob-Spring (BS) dynamics, and the center of mass diffusion and the relaxation spectrum of this section are determined. In the second step the center of mass diffusion obtained using the BS dynamics is used to model the one-dimensional diffusion of the section in a topologically constrained environment. In the final step we invoke the idea of dynamic self-similarity and argue that the dynamics described in the first and the second step, for any arbitrary section of the chain, applies to all sections of the chain. The constitutive relation is obtained consequently as the superposition of dynamic response of all sections of the ring chain.

Influence of topological constraints on the statics and dynamics of ring polymers.

We report a computer simulation study of the influence of topological constraints on the statics and dynamics of single ring polymers and ring polymers in the melt. We show that single rings have identical static and dynamic scaling behavior regardless of the presence of topological constraints. For rings in the melt we find that the scaling behavior is significantly influenced by the presence of topological constraints.