Slow Dynamics of Ring Polymer Melts by Asymmetric Interaction of Threading Configuration: Monte Carlo Study of a Dynamically Constrained Lattice Model

Coupling Effect of LDPE Molecular Chain Structure and Additives on the Rheological Behaviors of Cable Insulating Materials

The rheological behaviors of low-density polyethylene doped with additives (PEDA) determine the dynamic extrusion molding and structure of high-voltage cable insulation. However, the coupling effect of additives and molecular chain structure of LDPE on the rheological behaviors of PEDA is still unclear. Here, for the first time, the rheological behaviors of PEDA under uncross-linked conditions are revealed by experiment and simulation analysis, as well as rheology models. The rheology experiment and molecular simulation results indicate that additives can reduce the shear viscosity of PEDA, but the effect degree of different additives on rheological behaviors is determined by both chemical composition and topological structure. Combined with experiment analysis and the Doi-Edwards model, it demonstrates that the zero-shear viscosity is only determined by LDPE molecular chain structure. Nevertheless, different molecular chain structures of LDPE have different coupling effects with additives on the shear viscosity and non-Newtonian feature. Given this, the rheological behaviors of PEDA are predominant by the molecular chain structure of LDPE and are also affected by additives. This work can provide an important theoretical basis for the optimization and regulation of rheological behaviors of PEDA materials used for high-voltage cable insulation.

To thread or not to thread? Effective potentials and threading interactions between asymmetric ring polymers

We use computer simulations to study a system of two unlinked ring polymers, whose length and bending stiffness are systematically varied. We derive the effective potentials between the rings, calculate the areas of minimal surfaces of the same, and characterize the threading between them. When the two rings are of the same kind, threading of a one ring through the surface of the other is immanent for small ring-ring separations. Flexible rings pierce the surface of the other ring several times but only shallowly, as compared to the stiff rings which pierce less frequently but deeply. Typically, the ring that is being threaded swells and flattens up into an oblate-like conformation, while the ring that is threading the other takes a shape of an elongated prolate. The roles of the threader and the threaded ring are being dynamically exchanged. If, on the other hand, the rings are of different kinds, the symmetry is broken and the rings tend to take up roles of the threader and the threaded ring with unequal probabilities. We propose a method how to predict these probabilities based on the parameters of the individual rings. Ultimately, our work captures the interactions between ring polymers in a coarse-grained fashion, opening the way to large-scale modelling of materials such as kinetoplasts, catenanes or topological brushes.

Effect of ring stiffness and ambient pressure on the dynamical slowdown in ring polymers

Using extensive molecular dynamics simulations, we investigate the slowdown of dynamics in a 3D system of ring polymers by varying the ambient pressure and the stiffness of the rings. Our study demonstrates that the stiffness of the rings determines the dynamics of the ring polymers, leading to glassiness at lower pressures for stiffer rings. The threading of the ring polymers, a unique feature that emerges only due to the topological nature of such polymers in three dimensions, is shown to be the determinant feature of dynamical slowdown, albeit only in a certain stiffness range. Our results suggest a possible framework for exploring the phase space spanned by ring stiffness and pressure to obtain spontaneously emerging topologically constrained polymer glasses.

Computer simulations of melts of ring polymers with nonconserved topology: A dynamic Monte Carlo lattice model

We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on a fcc lattice which explicitly takes into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer strands may cross through each other. By applying the method to systems of interacting ring polymers at melt conditions, we characterize their structure and dynamics by measuring, in particular, the amounts of knots and links which are formed during the relaxation process. In comparison with standard melts of unknotted and unconcatenated rings, our simulations demonstrate that the mechanism of strand crossing makes polymer dynamics faster provided the characteristic timescale of the process is smaller than the typical timescale for chain relaxation in the unperturbed state, in agreement with recent experiments employing solutions of DNA rings in the presence of the type II topoisomerase enzyme. In the opposite case of slow rates the melt is shown to become slower, and this prediction may be easily validated experimentally.

Effects of chain length on Rouse modes and non-Gaussianity in linear and ring polymer melts

The dynamics of ring polymer melts are studied via molecular dynamics simulations of the Kremer-Grest bead-spring model. Rouse mode analysis is performed in comparison with linear polymers by changing the chain length. Rouse-like behavior is observed in ring polymers by quantifying the chain length dependence of the Rouse relaxation time, whereas a crossover from Rouse to reptation behavior is observed in linear polymers. Furthermore, the non-Gaussian parameters of the monomer bead displacement and chain center-of-mass displacement are analyzed. It is found that the non-Gaussianity of ring polymers is remarkably suppressed with slight growth for the center-of-mass dynamics at long chain length, which is in contrast to the growth in linear polymers for both the monomer bead and center-of-mass dynamics.

The Longitudinal Superdiffusive Motion of Block Copolymer in a Tight Nanopore

The structure and dynamic properties of polymer chains in a confined environment were studied by means of the Monte Carlo method. The studied chains were represented by coarse-grained models and embedded into a simple 3D cubic lattice. The chains stood for two-block linear copolymers of different energy of bead-bead interactions. Their behavior was studied in a nanotube formed by four impenetrable surfaces. The long-time unidirectional motion of the chain in the tight nanopore was found to be correlated with the orientation of both parts of the copolymer along the length of the nanopore. A possible mechanism of the anomalous diffusion was proposed on the basis of thermodynamics of the system, more precisely on the free energy barrier of the swapping of positions of both parts of the chain and the impulse of temporary forces induced by variation of the chain conformation. The mean bead and the mass center autocorrelation functions were examined. While the former function behaves classically, the latter indicates the period of time of superdiffusive motion similar to the ballistic motion with the autocorrelation function scaling with the exponent t^5/3. A distribution of periods of time of chain diffusion between swapping events was found and discussed. The influence of the nanotube width and the chain length on the polymer diffusivity was studied.

Breakdown of the Stokes-Einstein Equation for Solutions of Water in Oil Reverse Micelles

An experimental study is presented for the reverse micellar system of 15% by mass polydisperse hexaethylene glycol monodecylether (C₁₀E₆) in cyclohexane with varying amounts of added water up to 4% by mass. Measurements of viscosity and self-diffusion coefficients were taken as a function of temperature between 10 and 45 °C at varying sample water loads but fixed C₁₀E₆/cyclohexane composition. The results were used to inspect the validity of the Stokes-Einstein equation for this system. Unreasonably small reverse average micelle radii and aggregation numbers were obtained with the Stokes-Einstein equation, but reasonable values for these quantities were obtained using the ratio of surfactant-to-cyclohexane self-diffusion coefficients. While bulk viscosity increased with increasing water load, a concurrent expected decrease of self-diffusion coefficient was only observed for the surfactant and water but not for cyclohexane, which showed independence of water load. Moreover, a spread of self-diffusion coefficients was observed for the protons associated with the ethylene oxide repeat unit in samples with polydisperse C₁₀E₆ but not in a sample with monodisperse C₁₀E₆. These findings were interpreted by the presence of reverse micelle to reverse micelle hopping motions that with higher water load become increasingly selective toward C₁₀E₆ molecules with short ethylene oxide repeat units, while those with long ethylene oxide repeat units remain trapped within the reverse micelle because of the increased hydrogen bonding interactions with the water inside the growing core of the reverse micelle. Despite the observed breakdown of the Stokes-Einstein equation, the temperature dependence of the viscosities and self-diffusion coefficients was found to follow Arrhenius behavior over the investigated range of temperatures.

Morphology and thermodynamics of polymers with monofunctional hydrogen bonding ends in dilute and semidilute concentration

Rheological properties of supramolecular polymers (SMPs) depend on their equilibrium structure including the size, the number, and the topology of aggregates. A polymer with a hydrogen bonding (H-bonding) motif at both ends is one widely used precursor to build SMPs. Due to the complex interplay between chain stiffness, H-bonding interaction, polarity along a chain, and polymer conformational entropy, it is difficult to theoretically predict the structure of SMPs. In this work we investigate thermodynamics of SMPs with H-bonding ends in a wide range of densities. A replica exchange stochastic approximation Monte Carlo method with coarse-grained models for polyethylene and polybuthylene glycols is used. Our simulation shows that SMPs have two morphological transition lines with increasing temperature, a ring-linear transition, and a linear-free chain transition. The latter is a thermodynamic transition and turns out to be continuous. Comparing the two different spacers, we find that ring-linear transition temperatures differ from each other at the constant volume fraction due to different looping probabilities, which can be calculated from the average polymer size by mean field. However, the linear-free chain transition temperatures are similar because the entropic penalty to form a hydrogen bond mainly depends on the probability of finding H-bonding groups in a system, which is the same for both systems at a given volume fraction.