Ring Polymers Research Articles

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.

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.

Caracal: A Versatile Ring Polymer Molecular Dynamics Simulation Package.

A new open-source program package named Caracal covering simulations of molecular systems with ring polymer molecular dynamics (RPMD) is presented. It combines a powerful RPMD implementation including chemical reaction rate calculations and biased periodic and nonperiodic samplings with a collection of easy to set up potential energy surface (PES) methodologies, thus delivering an all-inclusive approach. Most implemented PESs are based on the QMDFF and EVB-QMDFF methods. Where the quantum mechanically derived force field (QMDFF) can be set up for an arbitrary molecular system in a black-box fashion, the empirical valence bond (EVB)-QMDFF connects two QMDFFs and is able to represent the PES of a chemical reaction. With our previously published flavors of this composite method, PESs for almost arbitrary gas phase thermal ground state reactions can be set up. Given an optimized reaction path, the mechanism of the reaction can be classified and RPMD rate constants can be obtained via umbrella sampling and recrossing calculations on an EVB-QMDFF PES. Further, QMDFFs can be polymerized for the description of liquid systems. In this paper, the internal structure as well as the handling philosophy of Caracal are outlined. Further, examples of the different possible kinds of calculations are given.

Ring Polymer Molecular Dynamics Approach to Quantum Dissociative Chemisorption Rates.

A ring polymer molecular dynamics (RPMD) method is proposed for the calculation of the dissociative chemisorption rate coefficient on surfaces. The RPMD rate theory is capable of handling quantum effects such as the zero-point energy and tunneling in dissociative chemisorption, while it relies on classical trajectories for the simulation. Applications to H2 dissociative chemisorption are demonstrated. For the highly activated process on Ag(111), strong deviations from Arrhenius behavior are found at low temperatures and attributed to tunneling. On Pt(111), where the dissociation has a barrierless pathway, the RPMD rate coefficient is found to agree with the experimentally derived thermal sticking coefficient within a factor of 2 over a large temperature range. Significant quantum effects are also found.

Ring-linear mixtures of semiflexible rubber bands

During the synthesis of ring polymers, it is quite common to obtain mixtures containing both ring and linear molecules. Recent studies, including experiments and simulations, have shown that even small quantities of linear molecules can significantly influence the shape of ring polymers, ultimately altering their rheological response. To further explore this phenomenon, we investigated blends of semiflexible linear and ring filaments by using disordered assemblies of open and closed rubber bands. We employed x-ray tomography to analyze the structure of these mixtures, focusing on how the length and composition of linear bands influenced the overall mixture. In contrast to the behavior observed in fully-flexible polymers, our findings revealed that increasing the concentration of linear bands could actually decrease the average size of rings within a semiflexible ring-linear mixture. This outcome is attributable to a reduction in inter-ring threading, which naturally occurs as the proportion of rings diminishes. To validate our findings, we conducted molecular dynamics simulations on semiflexible ring-linear polymer mixtures in bulk. These simulations confirmed that our results stem from the semiflexibility of the bands or chains rather than confinement or athermal conditions.

Exact tunneling splittings from symmetrized path integrals.

We develop a new simulation technique based on path-integral molecular dynamics for calculating ground-state tunneling splitting patterns from ratios of symmetrized partition functions. In particular, molecular systems are rigorously projected onto their J = 0 rotational state by an "Eckart spring" that connects two adjacent beads in a ring polymer. Using this procedure, the tunneling splitting can be obtained from thermodynamic integration at just one (sufficiently low) temperature. Converged results are formally identical to the values that would have been obtained by solving the full rovibrational Schrödinger equation on a given Born-Oppenheimer potential energy surface. The new approach is showcased with simulations of hydronium and methanol, which are in good agreement with wavefunction-based calculations and experimental measurements. The method will be of particular use for the study of low-barrier methyl rotations and other floppy modes, where instanton theory is not valid.

Evaluating the Effectiveness of the Original Designs of Immediate-Prostheses after Multiple Tooth Extraction: Clinical Cases

Background. Rehabilitation of patients with chronic periodontal diseases leading to multiple tooth loss can be carried out using the method of immediate prosthetics. However, the likelihood of atrophy of denture-supporting tissues under non-physiological load with removable dental prostheses imposes special requirements for their design features.Case description. Two patients seeking for dental surgical and prosthetic treatment for the diagnosis of chronic generalized periodontitis were treated in the dental clinic of Ryazan State Medical University named after academician I.P. Pavlov. Patient A. was mounted immediate prostheses made using additive technologies with the original design of the drug reservoir. Patient B. was mounted immediate prostheses with bases made of acrylic plastic, border ring of elastic polymer, and a drug reservoir made of polymethyl methacrylate. Patients underwent tooth extraction with immediate prosthetics. Patients were followed for 21 days. Criteria for the effectiveness of treatment included visual and palpatory control of extraction sites with a planimetric wound size analysis, assessment of microcirculation at the extraction site, control of the drug persistence in the reservoirs of prostheses.Conclusion. The observations at the stages of prosthodontic treatment revealed that immediate prostheses made with the help of 3D modeling and printing technologies resulted in a normal course of healing after tooth extraction with the normalization of microcirculatory parameters at the surgical wound sites. When using combined prosthetic structures, healing of postoperative wounds also proceeded favorably, however, congestion in the microcirculatory system was noted.

Local Polar and Long-Range Isotropic Activity Assisted Swelling and Collapse Dynamics of an Active Ring Polymer

Local Polar and Long-Range Isotropic Activity Assisted Swelling and Collapse Dynamics of an Active Ring Polymer

Conformation and Dynamics of Ring Polymer Chains under Cylindrical Confinement

AbstractUsing coarse‐grained molecular dynamics simulations, the conformation and dynamic behavior of ring polymer chains in ring/linear blends confined into cylinders are studied. By changing the particle number density, polymer chain bending energy and length, the spatial distribution of rings in the constrained binary polymer blends is investigated. An ordered tubular structure composed of several quasi‐parallel rings is observed. The mean square displacement of the center‐of‐mass of ring chains and its diffusion coefficient are analyzed. The results indicate that the diffusion behavior of rings is transformed from inhibition to promotion as the increase of linear chain bending energy. This study provides a new way to further understand the special conformation and dynamic behavior of ring polymer chains in constrained systems.

Understanding Mass Dependence of Glass Formation in Ring Polymers

Understanding Mass Dependence of Glass Formation in Ring Polymers

Structure of Polymer Rings in Linear Matrices: SANS Investigation

Structure of Polymer Rings in Linear Matrices: SANS Investigation

The role of dimers in complex forming reactions at low temperature: full dimension potential and dynamics of (H2CO)2 + OH reaction.

The (H2CO)2 + OH and H2CO-OH + H2CO reaction dynamics are studied theoretically for temperatures below 300 K. For this purpose, a full dimension potential energy surface is built, which reproduces well accurate ab initio calculations. The potential presents a submerged reaction barrier, as an example of the catalytic effect induced by the presence of the third molecule. However, quasi-classical and ring polymer molecular dynamics calculations show that the dominant channel is the dimer-exchange mechanism below 200 K, and that the reactive rate constant tends to stabilize at low temperatures, because the effective dipole of either dimer is reduced with respect to that of formaldehyde alone. The reaction complex formed at low temperatures does not live long enough to produce a complete energy relaxation, as assumed in statistical theories. These results show that the reactivity of the dimers cannot explain the large rate constants measured at temperatures below 100 K.

FEM Analysis of Buckled Dielectric Thin-Film Packaging Based on 3D Direct Numerical Simulation.

This paper presents a 3D direct numerical simulation of buckled thin-film packaging based on transferred elastic thin-film wrinkling bonded on a compliant polymer ring. The mode change of the fabricated thin-film cap is found by measuring the thin-film cap shape at different times after Si substrate debonding. The conventional linear and nonlinear buckling simulations are not adequate to understand the behavior of the thin-film buckling mechanism creating such packaging cap mode change. Direct buckling simulation is recently reported as an easy and useful numerical wrinkling simulation method. A novel 3D FEM model of a thin-film package suitable for direct 3D buckling simulation is built to reduce the mode mixture between different buckling modes. Buckling modes of the packaging cap are investigated in terms of elastic moduli of package materials and applied strain due to thermal expansion coefficient difference. Based on the simulation results, it is found that there are two main modes in the fabricated thin-film buckling package determining the shape of the transferred thin-film packaging cover depending on the elasticity ratio between the cap and sealing ring materials. The mode shift from wrinkling cap mode to out-of-plane cap mode due to applied strain along a polymeric sealing ring is found.

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.

Pressure of Linear and Ring Polymers Confined in a Cavity.

Nanoscale confinement of polymers in a cavity is central to a variety of biological and nanotechnology processes. Using the discrete WLC model we simulate the compression of flexible and semiflexible polymers of linear and ring topology in a closed cavity. Simulation reveals that polymer pressure inside the cavity increases with the chain stiffness but is practically unaffected by the chain topology. For flexible polymers, the computed dependence of pressure on the cavity size and polymer concentration is consistent with the scaling behavior expected for bulk polymers in a good solvent. However, the scaling behavior of semiflexible polymers is only in partial agreement with the theory prediction, with discrepancies arising from a continuous transition between regimes in chains of moderate lengths. The computed segment density profiles endorse the propensity of semiflexible polymers to concentrate beneath the cavity surface and thus elevate the pressure. The compaction of polymers by compression into the disordered globule or growing toroidal structure is documented.

Structure and Thermodynamics of Linear, Ring, and Catenane Polymers in Solutions and at Liquid–Liquid Interfaces

In recent decades, advances in the syntheses of mechanically interlocked macromolecules, such as catenanes, have led to much greater interest in the applications of these complexes, from molecular motors and actuators to nanoscale computational memory and nanoswitches. Much remains to be understood, however, regarding how catenated ring compounds behave as a result of the effects of different solvents as well as the effects of solvent/solvent interfaces. In this work, we have investigated, using molecular dynamics simulations, the effects of solvation of poly(ethylene oxide) chains of different topologies─linear, ring, and [2]catenane─in two solvents both considered favorable toward PEO (water, toluene) and at the water/toluene interface. Compared to ring and [2]catenane molecules, the linear PEO chain showed the largest increase in size at the water/toluene interface compared to bulk water or bulk toluene. Perhaps surprisingly, observations indicate that the tendency of all three topologies to extend at the water/toluene interface may have more to do with screening the interaction between the two solvents than with optimizing specific solvent-polymer contacts.