Ring Polymers Research Articles

Comment on "Effects of topological constraints on linked ring polymers in solvents of varying quality" by Z. A. Dehaghani, I. Chubak, C. N. Likos and M. R. Ejtehadi, Soft Matter, 2020, 16, 3029.

This comment critically evaluates the work of Dehaghani et al., who investigated the conformational behavior of catenated polymers under diverse solvent conditions using coarse-grained molecular dynamics simulations. While their study provides valuable insights into the scaling behavior of poly[n]catenane's radius of gyration in a good solvent, significant discrepancies arise, particularly concerning the reported θ-temperature trends. The validity of their methodology in determining θ-temperatures for linear and ring polymers is questioned, given observed disparities in chosen number of bead ranges that imply varying molecular weights. This comment underscores the need for a meticulous reassessment of the methodologies and interpretations presented in Dehaghani et al.'s study, emphasizing the importance of rigorous considerations in the investigation of the physical properties of catenated polymers.

Reply to the 'Comment on "Effects of topological constraints on linked ring polymers in solvents of varying quality"' by M. Tsige and H. Guo, Soft Matter, 2024, 20, DOI: 10.1039/D3SM01614E.

In the preceding Comment, Drs Tsige and Guo compare their findings about the θ-temperatures of linear chains, ring polymers and poly[n]catenanes with those of previous work by us [Z. A. Dehaghani, I. Chubak, C. N. Likos and M. R. Ejtehadi, Soft Matter, 2020, 16, 3029-3038] and point out that the ordering they obtain for these three quantities is, for large degrees of polymerisation, the reverse of the one we had found in our own investigations. We thank the authors of the Comment for their remarks and we appreciate their detailed investigations, which emphasise the importance of understanding the properties of topological polymers and their behaviour under varying solvent quality. We point out, however, that the discrepancy found by Tsige and Guo is only apparent because it pertains to the Θ-temperature of rings and poly[n]catenanes with the same overall molecular weight, whereas in our work we compared the Θ-temperature of a constituent ring of the poly[n]catenane with that of the entire mechanically linked macromulecule.

Mapping deformation dynamics to composition of topologically-active DNA blends.

Blends of circular and linear polymers have fascinated researchers for decades, and the role of topology on their stress response and dynamics remains fervently debated. While linear polymers adopt larger coil sizes and form stronger, more pervasive entanglements than their circular counterparts, threading of circular polymers by linear chains can introduce persistent constraints that dramatically decrease mobility, leading to emergent rheological properties in blends. However, the complex interplay between topology-dependent polymer overlap and threading propensity, along with the large amounts of material required to sample many compositions, has limited the ability to experimentally map stress response to composition with high resolution. Moreover, the role of supercoiling on the response of circular-linear blends remains poorly understood. Here, we leverage in situ enzymatic topological conversion to map the deformation dynamics of DNA blends with over 70 fractions of linear, ring and supercoiled molecules that span the phase space of possible topological compositions. We use OpTiDDM (optical tweezers integrating differential dynamic microscopy) to map strain-induced deformation dynamics to composition, revealing that strain-coupling, quantified by superdiffusive dynamics that are aligned with the strain, is maximized for blends with comparable fractions of ring and linear polymers. Increasing the supercoiled fraction dramatically reduces strain-coupling, while converting rings to linear chains offers more modest coupling reduction. We demonstrate that these results are a direct consequence of the interplay between increasing polymer overlap and decreasing threading probability as circular molecules are converted to linear chains, with a careful balance achieved for blends with ample ring fractions but devoid of supercoiled molecules.

Supercoiled ring polymers under shear flow.

We apply monomer-resolved computer simulations of supercoiled ring polymers under shear, taking full account of the hydrodynamic interactions, accompanied, in parallel, by simulations in which these are switched off. The combination of bending and torsional rigidities inherent in these polymers, in conjunction with hydrodynamics, has a profound impact on their flow properties. In contrast to their flexible counterparts, which dramatically deform and inflate under shear [Liebetreu et al., Commun. Mater. 2020, 1, 4], supercoiled rings undergo only weak changes in their overall shape and they display both a reduced propensity to tumbling (at fixed Weissenberg number) and a much stronger orientational resistance with respect to their flexible counterparts. In the presence of hydrodynamic interactions, the coupling of the polymer to solvent flow is capable of bringing about a topological transformation of writhe to twist at strong shear upon conservation of the overall linking number.

Shape and size tunability of sheets of interlocked ring copolymers.

Mechanically bonded membranes of interlocked ring polymers are a significant generalization of conventional elastic sheets, where connectivity is provided by covalent bonding, and represent a promising class of topological meta-materials. In this context, two open questions regard the large-scale reverberations of the heterogeneous composition of the rings and the inequivalent modes of interlocking neighboring rings. We address these questions with Langevin dynamics simulations of chainmails with honeycomb-lattice connectivity, where the rings are block copolymers with two segments of different rigidity. We considered various combinations of the relative lengths of the two segments and the patterns of the over- and under-passes linking neighboring rings. We find that varying ring composition and linking patterns have independent and complementary effects. While the former sets the overall size of the chainmail, the latter defines the shape, enabling the selection of starkly different conformation types. Notably, one of the considered linking patterns favors saddle-shaped membranes, providing a first example of spontaneous negative Gaussian curvature in mechanically bonded sheets. The results help establish the extent to which mechanically bonded membranes can differ from conventional elastic ones, particularly for the achievable shape and size tunability.

Escape dynamics of active ring polymers in a cylindrical nanochannel.

We explore the escape dynamics of active ring polymers confined in a cylindrical nanochannel using Brownian dynamics. Our simulation results show that the escape time decreases with the increase of the Péclet number, which is not noticeable between the two stages of the escape process, based on whether the center of mass of the polymer is inside or outside the nanochannel. However, the monomer motion trajectory of the active polymer is very different from that of the passive polymer, similar to the snake-like motion with uniform velocity. The passive polymer, however, is in constant fugitive motion with increased velocity at the tail end of the escape. Our work is vital for understanding the escape dynamics of active ring polymers in the confined nanochannel, which provides new perspectives on their characterization and analysis.

Rate coefficients for the O + H2 and O + D2 reactions: how well ring polymer molecular dynamics accounts for tunelling.

We present here extensive calculations of the O(3P) + H2 and O(3P) + D2 reaction dynamics spanning the temperature range from 200 K to 2500 K. The calculations have been carried out using fully converged time-independent quantum mechanics (TI QM), quasiclassical trajectories (QCT) and ring polymer molecular dynamics (RPMD) on the two lowest lying adiabatic potential energy surfaces (PESs), 13A' and 13A'', calculated by Zanchet et al. [J. Chem. Phys., 2019, 151, 094307]. TI QM rate coefficients were determined using the cumulative reaction probability formalism on each PES including all of the total angular momenta and the Coriolis coupling and can be considered to be essentially exact within the Born-Oppenheimer approximation. The agreement between the rate coefficients calculated by using QM and RPMD is excellent for the reaction with D2 in almost the whole temperature range. For the reaction with H2, although the agreement is very good above 500 K, the deviations are significant at lower temperatures. In contrast, the QCT calculations largely underestimate the rate coefficients for the two isotopic variants due to their inability to account for tunelling. The differences found in the disagreements between RPMD and QM rate coefficients for the reactions for both the isotopologues are indicative of the ability of the RPMD method to accurately describe systems where tunelling plays a relevant role. Considering that both reactions are dominated by tunelling below 500 K, the present results show that RPMD is a very powerful tool for determining rate coefficients. The present QM rate coefficients calculated on adiabatic PESs slightly underestimate the best global fits of the experimental measurements, which we attribute to the intersystem crossing with the singlet 11A' PES.

Self-Organized States from Solutions of Active Ring Polymers in Bulk and under Confinement.

In the present work, we study, by means of numerical simulations, the structural and dynamical behavior of a suspension of active ring polymers in bulk and under lateral confinement. At high activity, when changing the distance between the confining planes and the polymers' density, we identify the emergence of a self-organized dynamical state, characterized by the coexistence of slowly diffusing clusters of rotating disks and faster rings moving in between them. We further assess that self-organization is robust in a range of polymer sizes, and we identify a critical value of the activity, necessary to trigger cluster formation. This system has distinctive features resembling at the same time polymers, liquid crystals, and active systems, where the interplay between activity, topology, and confinement leads to a spontaneous segregation in an initially one-component solution.

Effect of threading on static and dynamic properties of polymer chains in entangled linear-ring blend systems with different stiffness

Threading is a unique topological state in linear/ring polymer blends (LRB), which is considered to be essential for evaluating both the static and dynamic properties of ring polymer (RP)-containing polymer melts. In the present work, we use molecular dynamics simulations with the Kremer-Grest model to systematically investigate the threading event and its effect on the properties of RP in linear polymer (LP) dominated LRB. The chain stiffness is also considered in the simulation to represent a wider range of polymer systems. To obtain the exact number of threads for each RP chain, the inner minimal surface (IMS) technique is applied. We find that for a wide range of chain lengths, the number of threads can be roughly estimated using the predetermined entanglement number for RP chains with different stiffness. The number of threads follows a Gaussian distribution, and the width increases monotonically for longer and stiffer chains. The effect of threading on both the size and shape of RP chains is investigated. We find that for RP chains of different chain lengths, the effect of threading on polymer size is more pronounced for more flexible chains. The effect of threading on shape of RP is also enhanced for longer chains, but the sensitivity of the shape to threading is indistinguishable for RP chains of different stiffness. The dynamics of threading is also studied in this work, and a much slower relaxation time is found for more flexible chains. In conclusion, we have developed a method that can directly detect the threading events in LRB, which allows us to quantitatively study the effect of threading. The result obtained by this method is also expected to be integrated into the viscoelastic theory to better estimate the rheological properties of LRB systems.

Low-Cost Fully Non-fused Ring Acceptor Enables Efficient Organic Photovoltaic Modules for Multi-Scene Applications.

Organic photovoltaic (OPV) cells, with highly tunable light-response ranges, offer significant potential for use in driving low-power consumption off-grid electronics in multi-scenarios. However, development of photoactive layer materials that can meet simultaneously the requirements of diverse irradiation conditions is a still challenging task. Herein, a low-cost fully non-fused acceptor (denoted as GS60) featuring well-matched absorption spectra with solar, scattered light and artificial light radiation was designed and synthesized. Systematic characterizations revealed that GS60 possessed outstanding photoelectron properties and ideal morphology, which resulted in reduced voltage loss and suppressed charge recombination. By blending with a non-fused ring polymer PTVT-T, the as-obtained GS60 based OPV cells achieved a good power conversion efficiency (PCE) of 14.1 %, a high value for the cells based on non-fused ring bulk heterojunction. Besides, manufactured large-area OPV modules based on PTVT-T:GS60 yielded PCEs of 11.2 %, 11.8 %, 12.1 %, 23.1 %, and 20.3 % under irradiation of AM 1.5G, natural light of cloudy weather, natural light in shadow, laser and indoor, respectively. The PTVT-T:GS60 devices exhibited considerable potential in terms of improving photostability and reducing material cost. Overall, this work provides novel insight into the molecular design of low-cost non-fused ring acceptors, and extended potential of medium band gap acceptors based OPV cells used in various application scenarios.

Low‐Cost Fully Non‐fused Ring Acceptor Enables Efficient Organic Photovoltaic Modules for Multi‐Scene Applications

AbstractOrganic photovoltaic (OPV) cells, with highly tunable light‐response ranges, offer significant potential for use in driving low‐power consumption off‐grid electronics in multi‐scenarios. However, development of photoactive layer materials that can meet simultaneously the requirements of diverse irradiation conditions is a still challenging task. Herein, a low‐cost fully non‐fused acceptor (denoted as GS60) featuring well‐matched absorption spectra with solar, scattered light and artificial light radiation was designed and synthesized. Systematic characterizations revealed that GS60 possessed outstanding photoelectron properties and ideal morphology, which resulted in reduced voltage loss and suppressed charge recombination. By blending with a non‐fused ring polymer PTVT−T, the as‐obtained GS60 based OPV cells achieved a good power conversion efficiency (PCE) of 14.1 %, a high value for the cells based on non‐fused ring bulk heterojunction. Besides, manufactured large‐area OPV modules based on PTVT−T:GS60 yielded PCEs of 11.2 %, 11.8 %, 12.1 %, 23.1 %, and 20.3 % under irradiation of AM 1.5G, natural light of cloudy weather, natural light in shadow, laser and indoor, respectively. The PTVT−T:GS60 devices exhibited considerable potential in terms of improving photostability and reducing material cost. Overall, this work provides novel insight into the molecular design of low‐cost non‐fused ring acceptors, and extended potential of medium band gap acceptors based OPV cells used in various application scenarios.

Quantum-inspired encoding enhances stochastic sampling of soft matter systems.

Quantum advantage in solving physical problems is still hard to assess due to hardware limitations. However, algorithms designed for quantum computers may engender transformative frameworks for modeling and simulating paradigmatically hard systems. Here, we show that the quadratic unconstrained binary optimization encoding enables tackling classical many-body systems that are challenging for conventional Monte Carlo. Specifically, in self-assembled melts of rigid lattice ring polymers, the combination of high density, chain stiffness, and topological constraints results in divergent autocorrelation times for real-space Monte Carlo. Our quantum-inspired encoding overcomes this problem and enables sampling melts of lattice rings with fixed curvature and compactness, unveiling counterintuitive topological effects. Tackling the same problems with the D-Wave quantum annealer leads to substantial performance improvements and advantageous scaling of sampling computational cost with the size of the self-assembled ring melts.

Intrinsic viscosity and dielectric relaxation of ring polymers in dilute solutions.

The absence of chain ends makes ring polymers distinctly different from their linear analogues. The intrinsic viscosity, complex viscosity and the dielectric relaxation of ring polymers are investigated within the tenets of the optimized Rouse-Zimm theory. The distance dependent excluded volume interactions (EVIs) are obtained from Flory's mean field theory. The hydrodynamic interactions (HIs) between the pairs of monomers are estimated using the preaveraged Oseen tensor. The intrinsic viscosity of linear and ring polymers both with and without EVI are compared as a function of ring size. A monotonically increasing trend of the intrinsic viscosity is observed in both cases. The intrinsic viscosity of both linear and ring polymers both with and without EVI show a very good agreement with the experimental results of polystyrene over a wide range of molecular weights in both good and theta solvents, respectively. The fractal dimensions of the ring polymers with EVI lie between that of a random walk and a self-avoiding walk model of linear polymers in three dimensions. The ring size increases with EVI and the effect of EVI is stronger on larger rings than that on smaller rings. The dielectric relaxation follow a connectivity independent universal scaling behavior at low and high frequency regions. The imaginary part of the complex dielectric susceptibility displays a local maxima in the intermediate frequency region, which reveals a structure dependent behavior of the rings. The theoretically calculated dielectric loss of ring polymers with HI matches well with those obtained from experiments.

Mixing Linear Polymers with Rings and Catenanes: Bulk and Interfacial Behavior.

We derive and parameterize effective interaction potentials between a multitude of different types of ring polymers and linear chains, varying the bending rigidity and solvent quality for the former species. We further develop and apply a density functional treatment for mixtures of both disconnected (chain-ring) and connected (chain-polycatenane) mixtures of the same, drawing coexistence binodals and exploring the ensuing response functions as well as the interface and wetting behavior of the mixtures. We show that worsening of the solvent quality for the rings brings about a stronger propensity for macroscopic phase separation in the linear-polycatenane mixtures, which is predominantly of the demixing type between phases of similar overall particle density. We formulate a simple criterion based on the effective interactions, allowing us to determine whether any specific linear-ring mixture will undergo a demixing phase separation.

Spatial Organization of Slit-Confined Melts of Ring Polymers with Nonconserved Topology: A Lattice Monte Carlo Study.

We present Monte Carlo computer simulations for melts of semiflexible randomly knotted and randomly concatenated ring polymers on the fcc lattice and in slit confinement. Through systematic variation of the slit width at fixed melt density, we explore the influence of confinement on single-chain conformations and interchain interactions. We demonstrate that confinement makes chains globally larger and more elongated while enhancing both contacts and knottedness propensities. As for multichain properties, we show that ring-ring contacts decrease with the confinement, yet neighboring rings overlap more as confinement grows. These aspects are accompanied by a marked decrease in the links formed between pairs of neighboring rings. In connection with the quantitative relation between links and entanglements in polymer melts recently established by us [Ubertini M. A.; Rosa A.Macromolecules2023, 56, 3354-3362], we propose that confinement can be used to set polymer networks that act softer under mechanical stress and suggest a viable experimental setup to validate our results.

Real-Time Dynamics and Detailed Balance in Ring Polymer Surface Hopping: The Impact of Frustrated Hops.

Ring polymer surface hopping (RPSH) has been recently introduced as a well-tailored method for incorporating nuclear quantum effects, such as zero-point energy and tunneling, into nonadiabatic molecular dynamics simulations. The practical widespread usage of RPSH demands a comprehensive benchmarking of different reaction regimes and conditions with equal emphasis on demonstrating both the cons and the pros of the method. Here, we investigate the fundamental questions related to the conservation of energy and detailed balance in the context of RPSH. Using Tully's avoided crossing model as well as a 2-state quantum system coupled to a classical bath undergoing Langevin dynamics, we probe the critical problem of the proper treatment of the classically forbidden transitions stemming from the surface hopping algorithm. We show that proper treatment of these frustrated hops is key to the accurate description of real-time dynamics as well as reproducing the correct quantum Boltzmann populations.

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.

Multi-particle collision dynamics for a coarse-grained model of soft colloids applied to ring polymers.

The simulation of polymer solutions often requires the development of methods that accurately include hydrodynamic interactions. Resolution on the atomistic scale is too computationally expensive to cover mesoscopic time and length scales on which the interesting polymer phenomena are observed. Therefore, coarse-graining methods have to be applied. In this work, the solvent is simulated using the well-established multi-particle collision dynamics scheme, and for the polymer, different coarse-graining methods are employed and compared against the monomer resolved Kremer-Grest model by their resulting diffusion coefficients. This research builds on previous work [Ruiz-Franco et al., J. Chem. Phys. 151, 074902 (2019)], in which star polymers and linear chains in a solvent were simulated and two different coarse-graining methods were developed, in order to increase computational efficiency. The present work extends this approach to ring polymers and seeks to refine one of the authors' proposed model: the penetrable soft colloid model. It was found that both proposed models are not well suited to ring polymers; however, the introduction of a factor to the PSC model delivers satisfying results for the diffusion behavior by regulating the interaction intensity with the solvent.

Topology Matters: Conformation and Microscopic Dynamics of Ring Polymers

Topology Matters: Conformation and Microscopic Dynamics of Ring Polymers

Comparison of Linear and Ring Polymers Partitioning into Pores Using Random Walks and Self‐Avoiding Walks Models

AbstractMonte Carlo simulations that examine the partitioning of dilute solutions of ring or linear chains into a slit pore using two chain models, the random‐walk (RW) model and the self‐avoiding walk (SAW) model are presented. The partitioning coefficients K for the ring and the linear chains at the surface interaction both under the critical adsorption point (CAP) and above the CAP are compared. In both chain models, K for the ring remains larger than K for the linear chains. The ring chain crosses over the point K = 1 at a weaker surface interaction than the linear chain. When extrapolated to infinite chain length, the cross‐over point for the ring and linear chain becomes the same (within statistical errors) for the RW model but remains different for the SAW model. The density profiles of the ring within the pore reveal the development of humps near the wall as the surface interaction crosses over the CAP. The excluded volume interaction in the SAW model additionally impacts the partitioning of chains in a solution consisting of a binary mixture of ring and linear chains and makes the K values in a binary mixture differ from the monodispersed solutions.