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Theory and Simulations of Entangled Polymers

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A special issue of Polymers (ISSN 2073-4360). This special issue belongs to the section "Polymer Physics and Theory".

Deadline for manuscript submissions: closed (31 January 2019) | Viewed by 74083

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Special Issue Editors

Prof. Dr. Vlasis Mavrantzas

E-Mail Website1 Website2
Guest Editor

1. Department of Chemical Engineering, University of Patras & FORTH-ICE/HT, GR 26504 Patras, Greece
2. Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH-Z, CH-8093 Zürich, Switzerland
Interests: polymer physics; polymer rheology; molecular simulations; statistical mechanics; nonequilibrium thermodynamics; constitutive modelling; dissipative quantum field theory
Special Issues, Collections and Topics in MDPI journals

Dr. Pavlos Stephanou

E-Mail Website1 Website2
Guest Editor

Department of Chemical Engineering, Cyprus University of Technology, Limassol, Cyprus
Interests: equilibrium thermodynamics; statistical thermodynamics; non-equilibrium thermodynamics; statistical mechanics; physical and chemical processes; statistical mechanics of polymers; polymer mechanics and physics; nanomaterials; dynamics of polymeric liquids; polymer rheology; fluid mechanics; polymer physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleague,

Polymers continue to fascinate people with their intriguing properties and continuous application in new fields in all aspects of our life. Most of these properties have their origin in the macromolecular nature of the constituent molecules. Chain connectivity and chain uncrossability give rise to the development of topological constraints in macromolecular systems, collectively known as entanglements, which govern to a large extent the relation between structure, properties, processing, and performance of the corresponding materials. The last years have witnessed a tremendous progress in the field, driven mostly by new applications of polymers. We mention, for example, the renewed interest in polymer nanocomposites, polymer networks, associating polymers, polymer blends, and ring polymers. Understanding the behaviour of entangled polymer chains, both under equilibrium and under flow conditions at several levels (ranging from the microscopic to the macroscopic level), forms the basis for a more efficient, rational, and economical design of new products and processes for specific applications in several new technologies where polymers are used.

Recognizing the importance of theory and simulations in understanding the properties of polymers across scales and under a variety of conditions, this Special Issue of Polymers invites contributions addressing several aspects of entangled macromolecular systems, such as the formulation of new constitutive modelling, the study of entanglement dynamics under flow, the development of new hierarchical or multi-scale strategies to address more complicated systems than pure homopolymers, such as nanocomposites, associating polymers, and self-assembled systems, nonequilibrium simulation methodologies satisfying the fundamental laws of nonequilibrium thermodynamics and statistical mechanics, well-founded coarse-graining schemes for speeding up the simulations under both equilibrium and nonequilibrium conditions, new theoretical developments and simulations advancing our knowledge of ring polymers, new methods for computing rare events, approaches for predicting chain organization and morphology or self-assembly in nanostructured polymers, etc.. The above list is only indicative and by no means exhaustive; any original theoretical or simulation work or review article on the role of entanglements in polymer dynamics is welcome. We hope that these contributions will address a variety of systems, including linear and nonlinear polymer architectures, polymer solutions, polymer blends, copolymers, semi-conductive conjugate polymers, polymeric networks, polymer hydrogels, polymer nanocomposites, multicomponent polymeric systems, and polymers for biological or medical applications.

Prof. Vlasis Mavrantzas
Dr. Pavlos Pavlos Stephanou
Guest Editors

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Keywords

entangled polymer melts, solutions, blends, nanocomposites
linear and branched polymers, ring polymers
theory and constitutive modelling
simulations (molecular, coarse-grained, Brownian, slip-link models)

Published Papers (17 papers)

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Research

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8 pages, 332 KiB

Open AccessArticle

Determine Mesh Size through Monomer Mean-Square Displacement

by Ji-Xuan Hou

Polymers 2019, 11(9), 1405; https://doi.org/10.3390/polym11091405 - 27 Aug 2019

Cited by 9 | Viewed by 3867

Abstract

A dynamic method to determine the main parameter of the tube theory through monomer mean-square displacement is discussed in this paper. The tube step length can be measured from the intersection of the slope-

\frac{1}{2}

line and the slope-

\frac{1}{4}

line [...] Read more.

\frac{1}{2}

line and the slope-

\frac{1}{4}

line in log-log plot, and the tube diameter can be obtained by recording the time at which

g_{1}

data start to leave the slope-

\frac{1}{2}

regime. According to recent simulation data, the ratio of the tube step length to the tube diameter was found to be about 2 for different entangled polymer systems. Since measuring the tube diameter does not require

g_{1}

data to reach the slope-

\frac{1}{4}

regime, this could be the best way to find the entanglement length from microscopic consideration. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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26 pages, 15101 KiB

Open AccessArticle

Shear Rheology of Unentangled and Marginally Entangled Ring Polymer Melts from Large-Scale Nonequilibrium Molecular Dynamics Simulations

by Alexandros J. Tsamopoulos, Anna F. Katsarou, Dimitrios G. Tsalikis and Vlasis G. Mavrantzas

Polymers 2019, 11(7), 1194; https://doi.org/10.3390/polym11071194 - 17 Jul 2019

Cited by 23 | Viewed by 4606

Abstract

We present results for the steady state shear rheology of non-concatenated, unentangled and marginally entangled ring poly(ethylene oxide) (PEO) melts from detailed, atomistic nonequilibrium molecular dynamics (NEMD) simulations, and compare them to the behavior of the corresponding linear melts. The applied flow field spans a wide range of shear rates, from the linear (Newtonian) to the highly non-linear (described by a power law) regime. For all melts studied, rings are found to exhibit shear thinning but to a lesser degree compared to linear counterparts, mostly due to their reduced deformability and stronger resistance to alignment in the direction of flow. These features are attributed to the more compact structure of ring molecules compared to linear chains; the latter are capable of adopting wider and more open conformations even under shear due to the freedom provided by the free ends. Similar to linear melts, rings also exhibit a first and a second normal stress coefficient; the latter is negative. The ratio of the magnitude of the two coefficients remains practically constant with shear rate and is systematically higher than the corresponding one for linear melts. Emphasis was also given to the statistics of terminal (re-orientational) relaxation times which we computed by analyzing all chains in the simulated systems one by one; it was demonstrated that long time dynamics are strongly heterogeneous both for rings and (especially) linears. Repeating the analysis under flow conditions, and as expected, we found that the applied flow field significantly suppresses dynamic heterogeneity, especially for high shear rates well beyond the Newtonian plateau. Finally, a detailed geometrical analysis revealed that the average population of ring–ring threading events in the longest melt studied here (the PEO-5k ring) remains practically unaffected by the imposed flow rate even at strong shear rates, except for multi-threadings which disappear. To further analyze this peculiar and rather unexpected effect, we computed the corresponding survival times and penetration lengths, and found that the overwhelming majority of threadings under shear are extremely weak constraints, as they are characterized by very small penetration lengths, thus also by short survival times. They are expected therefore to play only a minor (if any) role on chain dynamics. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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15 pages, 1286 KiB

Open AccessArticle

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

by Alexandros Chremos and Jack F. Douglas

Polymers 2019, 11(6), 1045; https://doi.org/10.3390/polym11061045 - 14 Jun 2019

Cited by 14 | Viewed by 4426

Abstract

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 [...] Read more.

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 glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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30 pages, 1270 KiB

Open AccessArticle

Comparative Analysis of Different Tube Models for Linear Rheology of Monodisperse Linear Entangled Polymers

by Volha Shchetnikava, Johan Slot and Evelyne van Ruymbeke

Polymers 2019, 11(5), 754; https://doi.org/10.3390/polym11050754 - 28 Apr 2019

Cited by 14 | Viewed by 3986

Abstract

The aim of the present paper is to analyse the differences between tube-based models which are widely used for predicting the linear viscoelasticity of monodisperse linear polymers, in comparison to a large set of experimental data. The following models are examined: Milner–McLeish, Likhtman–McLeish, the Hierarchical model proposed by the group of Larson, the BoB model of Das and Read, and the TMA model proposed by the group of van Ruymbeke. This comparison allows us to highlight and discuss important questions related to the relaxation of entangled polymers, such as the importance of the contour-length fluctuations (CLF) process and how it affects the reptation mechanism, or the contribution of the constraint release (CR) process on the motion of the chains. In particular, it allows us to point out important approximations, inherent in some models, which result in an overestimation of the effect of CLF on the reptation time. On the contrary, by validating the TMA model against experimental data, we show that this effect is underestimated in TMA. Therefore, in order to obtain accurate predictions, a novel modification to the TMA model is proposed. Our current work is a continuation of earlier research (Shchetnikava et al., 2014), where a similar analysis is performed on well-defined star polymers. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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17 pages, 6217 KiB

Open AccessArticle

Statistical Properties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function

by Pawel Dabrowski-Tumanski, Bartosz Gren and Joanna I. Sulkowska

Polymers 2019, 11(4), 707; https://doi.org/10.3390/polym11040707 - 17 Apr 2019

Cited by 8 | Viewed by 4635

Abstract

The shape and properties of closed loops depend on various topological factors. One of them is loop-threading, which is present in complex lasso proteins. In this work, we analyze the probability of loop-threading by the tail and its influence on the shape of the loop measured by the radius of gyration, distention, asphericity, and prolateness. In particular, we show that the probability of a trivial lasso for phantom polymer is non-zero even for an infinite structure, as well as that the threading flattens the loop by restricting its motion in one dimension. These results are further used to show that there are fewer non-trivial protein lassos than expected and select potentially functional complex lasso proteins. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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17 pages, 4865 KiB

Open AccessArticle

Scaling and Interactions of Linear and Ring Polymer Brushes via DPD Simulations

by Martin Jehser, Gerhard Zifferer and Christos N. Likos

Polymers 2019, 11(3), 541; https://doi.org/10.3390/polym11030541 - 22 Mar 2019

Cited by 14 | Viewed by 4414

Abstract

Single and double layers of polymer coated surfaces are investigated by means of Dissipative Particle Dynamics (DPD), focusing on the difference between grafted ring and linear chains. Several different surface coverages

σ

, as well as chain lengths N and brush separations D [...] Read more.

σ

, as well as chain lengths N and brush separations D, are analyzed for athermal, i.e., good solvent, conditions. The size in the form of the radius of gyration

R_{g}

, the shape as asphericity

δ^{*}

, and orientation

β^{*}

, as well as density profiles as functions of distance from grafting plane

ρ (z)

, are studied. The effect of an added bond repulsion potential to suppress bond crossing in DPD is analyzed. Scaling laws of

R_{g}

and its components

R_{g ⊥}

and

R_{g ∥}

are investigated. We find

R_{g} \propto N^{ν}, ν = 0.588

for surface coverages below the overlap surface concentration

σ_{*}

. For

σ > σ_{*}

we find

R_{g ⊥} \propto N^{ν_{⊥}}, ν_{⊥} ≅ 1

and

R_{g ∥} \propto N^{ν_{∥}}, ν_{∥} = 1 / 2

of ring brushes with the standard DPD model and

ν_{∥} ≅ 2 / 5

with added bond repulsion. The

σ

dependence of the radius of gyration was found to be

R_{g} \propto σ^{μ}

with

μ = 1 / 3

for surface coverages grater than

σ_{*}

. The perpendicular component

R_{g ⊥}

scales independent of the bond repulsion potential as

R_{g ⊥} \propto σ^{μ_{⊥}}, μ_{⊥} = 1 / 3

, whereas the scaling of the parallel component exhibits a topological repulsion dependence

R_{g ∥} \propto σ^{μ_{∥}}, μ_{∥} = - 1 / 12

for standard DPD and

μ_{∥} = - 1 / 6

for bond repulsion. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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14 pages, 1621 KiB

Open AccessArticle

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

by Eunsang Lee and YounJoon Jung

Polymers 2019, 11(3), 516; https://doi.org/10.3390/polym11030516 - 19 Mar 2019

Cited by 16 | Viewed by 3562

Abstract

Abnormally slower diffusional processes than its internal structure relaxation have been observed in ring polymeric melt systems recently. A key structural feature in ring polymer melts is topological constraints which allow rings to assume a threading configuration in the melt phase. In this work, we constructed a lattice model under the assumption of asymmetric diffusivity between two threading rings, and investigated a link between the structural correlation and its dynamic behavior via Monte Carlo simulations. We discovered that the hierarchical threading configurations render the whole system to exhibit abnormally slow dynamics. By analyzing statistical distributions of timescales of threading configurations, we found that the decoupling between internal structure relaxation and diffusion is crucial to understand the threading effects on the dynamics of a ring melt. In particular, in the limit of small but threaded rings, scaling exponents of the diffusion coefficient D and timescale

τ_{diff}

with respect to the degree of polymerization N agree well with that of the annealed tree model as well as our mean-field analysis. As N increases, however, the ring diffusion abruptly slows down to the glassy behavior, which is supported by a breakdown of the Stokes–Einstein relation. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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27 pages, 2277 KiB

Open AccessArticle

Determining Tube Theory Parameters by Slip-Spring Model Simulations of Entangled Star Polymers in Fixed Networks

by Jing Cao, Zuowei Wang and Alexei E. Likhtman

Polymers 2019, 11(3), 496; https://doi.org/10.3390/polym11030496 - 14 Mar 2019

Cited by 3 | Viewed by 3538

Abstract

Dynamical properties of branched polymer melts are determined by the polymer molecular weights and architectures containing junction points. Relaxation of entangled symmetric star polymers proceeds via arm-retraction and constraint release (CR). In this work, we investigate arm-retraction dynamics in the framework of a single-chain slip-spring model without CR effect where entanglements are treated as binary contacts, conveniently modeled as virtual “slip-links”, each involving two neighboring strands. The model systems are analogous to isolated star polymers confined in a permanent network or a melt of very long linear polymers. We find that the distributions of the effective primitive path lengths are Gaussian, from which the entanglement molecular weight

N_{e}

, a key tube theory parameter, can be extracted. The procured

N_{e}

value is in good agreement with that obtained from mapping the middle monomer mean-square displacements of entangled linear chains in slip-spring model to the tube model prediction. Furthermore, the mean first-passage (FP) times of destruction of original tube segments by the retracting arm end are collected in simulations and examined quantitatively using a theory recently developed in our group for describing FP problems of one-dimensional Rouse chains with improbable extensions. The asymptotic values of

N_{e}

as obtained from the static (primitive path length) and dynamical (FP time) analysis are consistent with each other. Additionally, we manage to determine the tube survival function of star arms

μ (t)

, or equivalently arm end-to-end vector relaxation function

ϕ (t)

, through the mean FP time spectrum

τ (s)

of the tube segments after careful consideration of the inner-most entanglements, which shows reasonably good agreement with experimental data on dielectric relaxation. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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25 pages, 7605 KiB

Open AccessEditor’s ChoiceArticle

Individual Molecular Dynamics of an Entangled Polyethylene Melt Undergoing Steady Shear Flow: Steady-State and Transient Dynamics

by Mohammad Hadi Nafar Sefiddashti, Brian J. Edwards and Bamin Khomami

Polymers 2019, 11(3), 476; https://doi.org/10.3390/polym11030476 - 12 Mar 2019

Cited by 40 | Viewed by 4037

Abstract

The startup and steady shear flow properties of an entangled, monodisperse polyethylene liquid (C₁₀₀₀H₂₀₀₂) were investigated via virtual experimentation using nonequilibrium molecular dynamics. The simulations revealed a multifaceted dynamical response of the liquid to the imposed flow field in which entanglement loss leading to individual molecular rotation plays a dominant role in dictating the bulk rheological response at intermediate and high shear rates. Under steady shear conditions, four regimes of flow behavior were evident. In the linear viscoelastic regime (

\dot{γ} < τ_{d}^{- 1}

), orientation of the reptation tube network dictates the rheological response. Within the second regime (

τ_{d}^{- 1} < \dot{γ} < τ_{R}^{- 1}

), the tube segments begin to stretch mildly and the molecular entanglement network begins to relax as flow strength increases; however, the dominant relaxation mechanism in this region remains the orientation of the tube segments. In the third regime (

τ_{R}^{- 1} < \dot{γ} < τ_{e}^{- 1}

), molecular disentangling accelerates and tube stretching dominates the response. Additionally, the rotation of molecules become a significant source of the overall dynamic response. In the fourth regime (

\dot{γ} > τ_{e}^{- 1}

), the entanglement network deteriorates such that some molecules become almost completely unraveled, and molecular tumbling becomes the dominant relaxation mechanism. The comparison of transient shear viscosity,

η^{+}

, with the dynamic responses of key variables of the tube model, including the tube segmental orientation,

S

, and tube stretch,

λ

, revealed that the stress overshoot and undershoot in steady shear flow of entangled liquids are essentially originated and dynamically controlled by the

S_{x y}

component of the tube orientation tensor, rather than the tube stretch, over a wide range of flow strengths. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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32 pages, 8372 KiB

Open AccessArticle

Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids

by Soroush Moghadam, Indranil Saha Dalal and Ronald G. Larson

Polymers 2019, 11(3), 465; https://doi.org/10.3390/polym11030465 - 11 Mar 2019

Cited by 8 | Viewed by 3317

Abstract

We combine a slip-spring model with an ‘entangled kink dynamics’ (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number

W i_{R} ≫ 1

) of long (

M_{w} > 1 Mkg / mol

for polystyrene) entangled polymers in [...] Read more.

We combine a slip-spring model with an ‘entangled kink dynamics’ (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number

W i_{R} ≫ 1

) of long (

M_{w} > 1 Mkg / mol

for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a ‘kinked’ or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of

ζ^{'} \dot{ϵ} L^{2} / 8

where

ζ^{'}

\dot{ϵ}

and

L

are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight (

M_{w} > 1 Mkg / mol

) polymers in fast flows (

W i_{R} ≫ 1

), where conventional simulation techniques are less applicable due to computational cost. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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20 pages, 10421 KiB

Open AccessArticle

Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

by Eleni Panagiotou, Kenneth C. Millett and Paul J. Atzberger

Polymers 2019, 11(3), 437; https://doi.org/10.3390/polym11030437 - 06 Mar 2019

Cited by 21 | Viewed by 5099

Abstract

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 the ways topological methods can be used to characterize chain entanglements to better understand the origins of mechanical responses in polymeric materials. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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16 pages, 1190 KiB

Open AccessArticle

Shear Banding in 4:1 Planar Contraction

by Soroush Hooshyar and Natalie Germann

Polymers 2019, 11(3), 417; https://doi.org/10.3390/polym11030417 - 04 Mar 2019

Cited by 15 | Viewed by 2898

Abstract

We study shear banding in a planar 4:1 contraction flow using our recently developed two-fluid model for semidilute entangled polymer solutions derived from the generalized bracket approach of nonequilibrium thermodynamics. In our model, the differential velocity between the constituents of the solution allows for coupling between the viscoelastic stress and the polymer concentration. Stress-induced migration is assumed to be the triggering mechanism of shear banding. To solve the benchmark problem, we used the OpenFOAM software package with the viscoelastic solver RheoTool v.2.0. The convection terms are discretized using the high-resolution scheme CUBISTA, and the governing equations are solved using the SIMPLEC algorithm. To enter into the shear banding regime, the uniform velocity at the inlet was gradually increased. The velocity increases after the contraction due to the mass conservation; therefore, shear banding is first observed at the downstream. While the velocity profile in the upstream channel is still parabolic, the corresponding profile changes to plug-like after the contraction. In agreement with experimental data, we found that shear banding competes with flow recirculation. Finally, the profile of the polymer concentration shows a peak in the shear banding regime, which is closer to the center of the channel for larger inlet velocities. Nevertheless, the increase in the polymer concentration in the region of flow recirculation was significantly larger for the inlet velocities studied in this work. With our two-fluid finite-volume solver, localized shear bands in industrial applications can be simulated. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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19 pages, 3338 KiB

Open AccessArticle

Assessment of the Tumbling-Snake Model against Linear and Nonlinear Rheological Data of Bidisperse Polymer Blends

by Pavlos S. Stephanou and Martin Kröger

Polymers 2019, 11(2), 376; https://doi.org/10.3390/polym11020376 - 20 Feb 2019

Cited by 6 | Viewed by 3672

Abstract

We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the academic case of a monodisperse sample. Here, we extend these studies and provide the stationary solutions of the tumbling-snake model both analytically, for small shear rates, and via Brownian dynamics simulations, for a bidisperse sample over a wide range of shear rates and model parameters. We further show that the tumbling-snake model bears the necessary capacity to compare well with available linear and non-linear rheological data for bidisperse systems. This capacity is added to the already documented ability of the model to accurately predict the shear rheology of monodisperse systems. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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9 pages, 1540 KiB

Open AccessArticle

Contraction of Entangled Polymers After Large Step Shear Deformations in Slip-Link Simulations

by Yuichi Masubuchi

Polymers 2019, 11(2), 370; https://doi.org/10.3390/polym11020370 - 20 Feb 2019

Cited by 7 | Viewed by 3332

Abstract

Although the tube framework has achieved remarkable success to describe entangled polymer dynamics, the chain motion assumed in tube theories is still a matter of discussion. Recently, Xu et al. [ACS Macro Lett. 2018, 7, 190–195] performed a molecular dynamics simulation for entangled bead-spring chains under a step uniaxial deformation and reported that the relaxation of gyration radii cannot be reproduced by the elaborated single-chain tube model called GLaMM. On the basis of this result, they criticized the tube framework, in which it is assumed that the chain contraction occurs after the deformation before the orientational relaxation. In the present study, as a test of their argument, two different slip-link simulations developed by Doi and Takimoto and by Masubuchi et al. were performed and compared to the results of Xu et al. In spite of the modeling being based on the tube framework, the slip-link simulations excellently reproduced the bead-spring simulation result. Besides, the chain contraction was observed in the simulations as with the tube picture. The obtained results imply that the bead-spring results are within the scope of the tube framework whereas the failure of the GLaMM model is possibly due to the homogeneous assumption along the chain for the fluctuations induced by convective constraint release. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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14 pages, 4009 KiB

Open AccessArticle

Effect of Bidispersity on Dynamics of Confined Polymer Films

by Sijia Li, Qiaoyue Chen, Mingming Ding and Tongfei Shi

Polymers 2018, 10(12), 1327; https://doi.org/10.3390/polym10121327 - 30 Nov 2018

Cited by 2 | Viewed by 2058

Abstract

Using Monte Carlo simulations, we studied the effect of bidispersity on the dynamics of polymer films capped between two neutral walls, where we chose three representative compositions for bidispersed polymer films. Our results demonstrate that the characteristic entanglement length is an important parameter to clarify the effect of the bidispersity on the dynamics of polymer films. For the short chains, shorter than the characteristic entanglement length, the average number of near-neighboring particles increases with the decrease of the film thickness and limits the diffusivity of the short chains, which is independent of the film compositions. However, the dynamics of the long chains, of which is above the characteristic entanglement length, is determined by the film’s composition. In our previous paper, we inferred from the structures and entanglements of the bidisperse system with short and long chains that the constraint release contributes significantly to the relaxation mechanism of long chains. By calculating the self-diffusion coefficient of long chains, we confirmed this prediction that, with a lower weight fraction of long chains, the self-diffusion coefficient of long chains decreases slowly with the decrease of the film thickness, which is similar to that of short chains. With a higher weight fraction of long chains, the competition between the disentanglement and the increased in the local degree of confinement which resulted in the self-diffusion coefficient of long chains varying non-monotonically with the film thickness. Furthermore, for the bidisperse system with long and long chains, the diffusivity of long chains was not affected by the constraint release, which varied nonmonotonically with the decrease of the film thickness due to the competition between the disentanglement and the enhanced confinement. Herein, compared with the previous work, we completely clarified the relationship between the structures and dynamics for three representative compositions of bidisperse polymer films, which contains all possible cases for bidisperse systems. Our work not only establishes a unified understanding of the dependency of dynamics on the bidispersity of polymer films, but also helps to understand the case of polydispersity, which can provide computational supports for various applications for polymer films. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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26 pages, 3264 KiB

Open AccessArticle

Slip Spring-Based Mesoscopic Simulations of Polymer Networks: Methodology and the Corresponding Computational Code

by Grigorios Megariotis, Georgios G. Vogiatzis, Aristotelis P. Sgouros and Doros N. Theodorou

Polymers 2018, 10(10), 1156; https://doi.org/10.3390/polym10101156 - 16 Oct 2018

Cited by 21 | Viewed by 6291

Abstract

In previous work by the authors, a new methodology was developed for Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of polymer melts. In this study, this methodology is extended for dynamical simulations of crosslinked polymer networks in a coarse-grained representation, wherein chains are modeled as sequences of beads, each bead encompassing a few Kuhn segments. In addition, the C++ code embodying these simulations, entitled Engine for Mesoscopic Simulations for Polymer Networks (EMSIPON) is described in detail. A crosslinked network of cis-1,4-polyisoprene is chosen as a test system. From the thermodynamic point of view, the system is fully described by a Helmholtz energy consisting of three explicit contributions: entropic springs, slip springs and non-bonded interactions. Entanglements between subchains in the network are represented by slip springs. The ends of the slip springs undergo thermally activated hops between adjacent beads along the chain backbones, which are tracked by kinetic Monte Carlo simulation. In addition, creation/destruction processes are included for the slip springs at dangling subchain ends. The Helmholtz energy of non-bonded interactions is derived from the Sanchez–Lacombe equation of state. The isothermal compressibility of the polymer network is predicted from equilibrium density fluctuations in very good agreement with the underlying equation of state and with experiment. Moreover, the methodology and the corresponding C++ code are applied to simulate elongational deformations of polymer rubbers. The shear stress relaxation modulus is predicted from equilibrium simulations of several microseconds of physical time in the undeformed state, as well as from stress-strain curves of the crosslinked polymer networks under deformation. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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29 pages, 5307 KiB

Open AccessEditor’s ChoiceReview

Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

by Argyrios Karatrantos, Russell J. Composto, Karen I. Winey, Martin Kröger and Nigel Clarke

Polymers 2019, 11(5), 876; https://doi.org/10.3390/polym11050876 - 14 May 2019

Cited by 48 | Viewed by 8429

Abstract

This review concerns modeling studies of the fundamental problem of entangled (reptational) homopolymer diffusion in melts and nanocomposite materials in comparison to experiments. In polymer melts, the developed united atom and multibead spring models predict an exponent of the molecular weight dependence to the polymer diffusion very similar to experiments and the tube reptation model. There are rather unexplored parameters that can influence polymer diffusion such as polymer semiflexibility or polydispersity, leading to a different exponent. Models with soft potentials or slip-springs can estimate accurately the tube model predictions in polymer melts enabling us to reach larger length scales and simulate well entangled polymers. However, in polymer nanocomposites, reptational polymer diffusion is more complicated due to nanoparticle fillers size, loading, geometry and polymer-nanoparticle interactions. Full article

(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)

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