Entangled polymer systems (original) (raw)
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Identifying the primitive path mesh in entangled polymer liquids
Journal of Polymer Science Part B: Polymer Physics, 2005
Similar to entangled ropes, polymer chains cannot slide through each other. These topological constraints, the so-called entanglements, dominate the viscoelastic behavior of high-molecular-weight polymeric liquids. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path which follows the coarse-grained chain contour. To establish the microscopic foundation for these highly successful phenomenological models, we have recently introduced a method for identifying the primitive path mesh that characterizes the microscopic topological state of computer-generated conformations of long-chain polymer melts and solutions. Here we give a more detailed account of the algorithm and discuss several key aspects of the analysis that are pertinent for its successful use in analyzing the topology of the polymer configurations. We also present a slight modification of the algorithm that preserves the previously neglected self-entanglements and allows us to distinguish between local self-knots and entanglements between distant sections of the same chain. Our results indicate that the latter make a negligible contribution to the tube and that the contour length between local self-knots, N lk is significantly larger than the entanglement length N e . c 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: [917][918][919][920][921][922][923][924][925][926][927][928][929][930][931][932][933] 2005
Polymers
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees–Edwards boundary conditions. We show how our topological characteristics can be used to capture key features of the polymer entanglements related to the viscoelastic responses. We find there is a linear relation over a significant range of frequencies between the mean absolute Writhe W r and the Loss Tangent tan ( δ ) . We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number L K P and the Loss Tangent tan ( δ ) . Our results show some of th...
INTERNATIONAL JOURNAL OF MOLECULAR SCIENCES, 2009
We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature.
The Journal of Chemical Physics, 2010
The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static ͑statistical͒ properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics ͑MD͒ trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability ͑s , t͒ that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time.
Writhe versus mutual entanglement of linear polymer chains in a melt
One of the reasons why the notion of entanglement in polymer melts is elusive is because it refers to both local and global characteristics of the conformations of the chains that compose it. Here we propose to use a combination of topological and geometrical measures of entanglement. Both the writhe and number of kinks (entanglements) of the primitive path of linear polymer chains in a melt are analysed over a range of molecular weights. Our numerical results show that the mean absolute writhe of linear semiflexible chains follows a scaling with respect to chain length and stiffness that is similar to the one known for semiflexible ring polymers. Focusing on linear finitely extendable chains, we find that the writhe of the corresponding primitive paths does not exhibit similar scaling behavior. Using the number of kinks in a chain and the writhe of both the original and primitive chains, we calculate the mean writhe and the mean squared writhe of an entanglement strand. Following this analysis, a new method to estimate the number of monomers in an entanglement strand, Ne, is presented and compared to existing Ne-estimators.
Polymer Science, Series C, 2023
The main models of phantom and topologically entangled polymer networks are surveyed. A theory of anisotropic and nonaffine deformation of both swollen and deswollen (with partial solvent removal) strongly entangled polymer networks in athermal and θ-solvents has been developed. It is shown that under weak anisotropic deformations of the deswollen network, the entanglement tube consists of fractal loopy globules. In a θ-solvent, slight deformations of the network lead to a decrease in the overlap of loopy globules without changing their sizes. Deformations of swollen networks, as well as strong deformations of deswollen networks, are described in terms of the slip-tube model. An effective Hamiltonian has been derived that determines the entropy of fractal loopy globules. Based on the Hamiltonian, it is shown that topological constraints can be described using the polymer-quantum diffusion analogy. The connection between topological and quantum entanglements is demonstrated.
Hierarchical Modelling of Entangled Polymer Melts: Structure and Rheology
2018
We describe the extension of a novel hierarchical backmapping strategy to equilibrating highmolecular-weight homopolymer melts described with chemistry-specific microscopic models. The method has been initially developed in the framework of highly entangled melts, described through generic microscopic (bead-spring) models. The systems are first efficiently equilibrated on the mesoscopic level, based on a model describing polymers as chains of soft spheres. Each sphere represents a large number of microscopic repeat units. After the mesoscopic configuration is generated, microscopic details are reinserted through Molecular Dynamics simulations. Here we demonstrate that the method can be indeed implemented to generate equilibrated configurations of actual molten polymers, considering the case of polystyrene. We illustrate how the backmapping strategy facilitates fundamental computational studies in polymer physics, focusing on two questions from the area of polymer dynamics and rheology. The highly-entangled samples described with a generic microscopic model are first employed to verify basic predictions of tube theories at equilibrium. Subsequently we address the intriguing question of how topological constraints evolve during relaxation after strong deformation.
Microscopic Definition of Polymer Entanglements
Macromolecules, 2014
The dynamics of polymer melts and concentrated solutions is notoriously slow due to the fact that long polymer chains can not cross each other and therefore …nd themselves entangled. This popular belief is very di¢ cult to quantify and convert into mathematical model because there is still no clear de…nition of what entanglement really is. In this paper we propose to de…ne entanglement as a persistent contact between mean paths of the chains. In molecular dynamics (MD) simulations of well-entangled linear chains we discovered that such very tight and longlived contacts exist in signi…cant numbers. Moreover, once such contact is formed, it exists at every time step of the simulation until its destruction, which allows one to de…ne its life time. We study several properties of individual entanglements and discover several unexpected features not taken into account in the tube theory or slip-links models. We believe that our simple and versatile de…nition opens the way to the truly microscopic understanding of polymer dynamics.
Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts
Polymers
We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric ...