Tube theory of entangled polymer dynamics

McLeish, Tom

doi:10.1080/00018730210153216

Cited by 827 publications

(1,178 citation statements)

References 279 publications

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“…[36][37][38][39][40][41][42][43][44] However, the impacts of grafting density on block polymer self-assembly have not been explored. [45][46][47][48] Elucidating these physical principles is not only of fundamental importance but should also guide material design.…”

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confidence: 99%

Effects of Grafting Density on Block Polymer Self-Assembly: From Linear to Bottlebrush

et al. 2017

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Grafting density is an important structural parameter that exerts significant influences over the physical properties of architecturally complex polymers. In this report, the physical consequences of varying the grafting density (z) were studied in the context of block polymer self-assembly. Well-defined block polymers spanning the linear, comb, and bottlebrush regimes (0 ≤ z ≤ 1) were prepared via grafting-through ring-opening-metathesis polymerization. ω-Norbornenyl poly(d,l-lactide) and polystyrene macromonomers were copolymerized with discrete comonomers in different feed ratios, enabling precise control over both the grafting density and molecular weight. Small-angle X-ray scattering experiments demonstrate that these graft block polymers self-assemble into long-range-ordered lamellar structures. For 17 series of block polymers with variable z, the scaling of the lamellar period with the total backbone degree of polymerization (d* ∼ N bb α) was studied. The scaling exponent α monotonically decreases with decreasing z and exhibits an apparent transition at z ≈ 0.2, suggesting significant changes in the chain conformations. Comparison of two block polymer systems, one that is strongly segregated for all z (System I) and one that experiences weak segregation at low z (System II), indicates that the observed trends are primarily caused by the polymer architectures, not segregation effects. A model is proposed in which the characteristic ratio (C ∞), a proxy for the backbone stiffness, scales with N bb as a function of the grafting density: C ∞ ∼ N bb f(z). The scaling behavior disclosed herein provides valuable insights into conformational changes with grafting density, thus introducing opportunities for block polymer and material design.

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Effects of Grafting Density on Block Polymer Self-Assembly: From Linear to Bottlebrush

et al. 2017

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“…The tube model has enabled us to understand the relationship between molecular structure and linear rheology in an entangled system. 5 Alternatively, Ball et al 6 proposed a slip-link model, in which the chain can slip at a trapped entanglement. The slip-link model is widely used in computer simulations of viscoelastic behavior in uncrosslinked and crosslinked polymeric materials.…”

Section: Introductionmentioning

confidence: 99%

Novel entropic elasticity of polymeric materials: why is slide-ring gel so soft?

Ito

2011

Polym J

114

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We have recently developed a slide-ring gel that is different from physical and chemical gels by crosslinking polyrotaxane, a necklace-like supramolecule. Slide-ring gel, consisting of movable crosslinks and free uncrosslinked cyclic molecules, shows peculiar mechanical properties, different from conventional chemical gels. For instance, slide-ring gel shows quite a low Young's modulus, which is not proportional to crosslinking density and is much lower than that of chemical gels with the same density. This low modulus arises from differences in the molecular mechanism of entropic elasticity; whereas conformational entropy is mainly responsible for elasticity in typical chemical gels and rubbers, the mechanical properties of slide-ring gel are inherently governed by the arrangement entropy of free cyclic molecules in polyrotaxane, as well as the conformational entropy of the axis polymer. This means that the softness of slide-ring gel is due to novel entropic elasticity, which is also expected to provide a sliding state and a sliding transition. Polymer Journal (2012) 44, 38-41; doi:10.1038/pj.2011.85; published online 14 September 2011 Keywords: crosslink; entanglement effect; entropic elasticity; polyrotaxane; pulley effect; slide-ring gel; sliding state INTRODUCTIONSince the discovery of crosslinking in natural rubber with sulfur in 1839 by Goodyear, crosslinking of polymeric materials has been one of the most important topics in polymer science and technology. 1,2 Uncrosslinked natural rubbers inherently resemble liquids with regard to their flow behavior, although they show viscoelastic properties due to the entanglement of polymer chains. Once crosslinked, however, they behave like solids, in that they maintain their shape against deformation above the glass temperature. Thus far, the unique mechanical behavior of crosslinked polymeric materials has been investigated intensively. 1,2 The elasticity of crosslinked rubbers and elastomers arises mainly from the conformational entropy of polymer chains between crosslinking junctions, with Young's modulus increasing proportionally with crosslinking density. Entropic elasticity also gives a stable rubber state characteristic of crosslinked polymeric materials.Polymer entanglement is also one of the most important features of polymers. It behaves like crosslinking over short time scales, but entangled chains are eventually released by reptation or one-dimensional diffusion along a polymer chain. Accordingly, reptation of uncrosslinked chains relaxes the rubber elasticity of the entangled polymer system over a relaxation time. The entanglement effect is described effectively by the tube or reptation model, developed by de Gennes 3 and Edwards and Doi 4 in the 1970s, in which each chain is assumed to move along a tube, due to constraints imposed by surrounding chains. The tube model has enabled us to understand the relationship between molecular structure and linear rheology in an

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“…Apart from linear and nonlinear rheology of different molecular architectures, such experiments include neutron scattering, neutron spin-echo (NSE), dielectric spectroscopy, NMR, and self-diffusion measurements. 4,5 There are also significant advances in molecular dynamics simulations, [6][7][8] which can potentially provide very detailed confirmation of any theory.…”

Section: Introductionmentioning

confidence: 99%

Single-Chain Slip-Link Model of Entangled Polymers: Simultaneous Description of Neutron Spin−Echo, Rheology, and Diffusion

2005

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The model presented in this paper describes simultaneously three different experimental techniques applied to different monodisperse polymer melts: neutron spin-echo (NSE), linear rheology, and diffusion. First, it shows that the standard tube model cannot be applied to NSE because the statistics of a one-dimensional (1D) chain in a three-dimensional (3D) random-walk tube become wrong on the length scale of the tube diameter, whereas all available NSE data are for scattering vectors in this range. Then a new single-chain dynamic slip-link model on the basis of a recent network model by Rubinstein and Panyukov is introduced. Instead of solving the model analytically, which would require uncontrolled approximations, the model is formulated in terms of stochastic differential equations, suitable for Brownian dynamics simulations. I perform these simple simulations, demonstrate that the model describes individual experiments well, and then compare the results with experiments on monodisperse polyethylene, polyethylene-propylene, polyisoprene, polybutadiene, and polystyrene. For all polymers, model parameters from one experiment are obtained, and the others are predicted without fitting. The results show some systematic discrepancies, suggesting possible inadequacy of the Gaussian chain model for some of the polymers, and possible inadequacy of time-temperature superposition.

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Tube theory of entangled polymer dynamics

Cited by 827 publications

References 279 publications

Effects of Grafting Density on Block Polymer Self-Assembly: From Linear to Bottlebrush

Effects of Grafting Density on Block Polymer Self-Assembly: From Linear to Bottlebrush

Novel entropic elasticity of polymeric materials: why is slide-ring gel so soft?

Single-Chain Slip-Link Model of Entangled Polymers: Simultaneous Description of Neutron Spin−Echo, Rheology, and Diffusion

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