Tube Diameter of Stretched and Compressed Permanently Entangled Polymers

Qin, Jian; So, J.; Milner, Scott T.

doi:10.1021/ma301830w

Cited by 10 publications

(20 citation statements)

References 22 publications

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“…Such processes, leading to low effective orientation, are well in line with computer simulations of topologically realistic networks 64 and "olympic gels," i.e., permanently entangled ring polymers. 47…”

Section: λ = ×mentioning

confidence: 99%

“…24 More recent computer simulations also suggest even weaker than predicted local deformation of the entanglement tube in gels made from entangled rings. 47 Therefore, herein we use MQ NMR to investigate microscopic stretching of polymer chains during anisotropic swelling and different modes of deformation of dry as well as swollen polymer networks of different chemical makeup. The main focus is on a comparison of chain deformation in the dry and partially swollen states, where for the latter affine behavior was found upon isotropic dilation by approaching swelling equilibrium.…”

Section: Introductionmentioning

confidence: 99%

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Microscopic State of Polymer Network Chains upon Swelling and Deformation

et al. 2019

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We use low-resolution proton NMR to probe the chain deformation in swollen and nonlinearly deformed vulcanized rubber and end-linked PDMS networks on a microscopic level, extending earlier work focusing on uniaxial stretching and isotropic dilation upon swelling toward biaxial deformation and deformation of swollen samples. Previous studies have revealed that chain deformation in bulk samples is best described by tube models, and that chains in swollen samples deform affinely after an initial desinterspersion stage, upon which entanglement-related packing effects are relieved. We test whether a subsequent deformation may also be closer to affine, and find that this is not the case. Unexpectedly, nonisotropic deformation of swollen samples also follows tube-model predictions, which is explained by a dominance of structural inhomogeneities and significant reorganization of the topological constraints active in the swollen and possibly even the bulk state.

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Section: λ = ×mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Microscopic State of Polymer Network Chains upon Swelling and Deformation

et al. 2019

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“…Thus, according to the affine deformation assumption, we can calculate the deformed contour length of PPs as [6,336]:…”

Section: Finite Viscoelasticity Modelingmentioning

confidence: 99%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

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The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale geometric mapping matrix between all-atomistic and coarse-grained models N number of monomers per chain N e entanglement length, which is the number of monomers between two entanglements n v number of polymer chains per unit volume n ij (n 0 (r ij )) entanglement number (at equilibrium) between particle pairs i and j p r , P R configurational probability distributions in all-atomistic and coarse-grained models, respectively R ee end-to-end distance of polymer chain R G radius of gyration of polymer chain s segment index/contour length variable along primitive chain S(q) single chain coherent dynamic scattering function Z number of entanglements per chain, defined as Z = N/N e α exponent in standard Mittag-Leffler function σ

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“…The latter discredited approaches centered on restricted junction or chain fluctuations [9,10]. Very recently, the deformation dependence was revisited by Milner and co-workers from simulations of stretched rings [11]. There, the tube deforms, but to a lesser extent than the square-root law dictates.…”

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confidence: 99%

Direct Observation of Nonaffine Tube Deformation in Strained Polymer Networks

et al. 2013

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We present a one-to-one comparison of polymer segmental fluctuations as measured by small angle neutron scattering in a network under deformation with those obtained by neutron spin echo spectroscopy. This allows an independent proof of the strain dependence of the chain entanglement length. The experimentally observed nonaffine square-root dependence of the tube channel on strain is in excellent agreement with theoretical predictions and permits us to exclude an often invoked nondeformed as well as affinely deformed tube.

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Tube Diameter of Stretched and Compressed Permanently Entangled Polymers

Cited by 10 publications

References 22 publications

Microscopic State of Polymer Network Chains upon Swelling and Deformation

Microscopic State of Polymer Network Chains upon Swelling and Deformation

Challenges in Multiscale Modeling of Polymer Dynamics

Direct Observation of Nonaffine Tube Deformation in Strained Polymer Networks

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