Polymer Viscoelasticity - Basics, Molecular Theories and Experiments

Lin, Yn-Hwang

doi:10.1142/9789812795144

Cited by 39 publications

(159 citation statements)

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“…2B, one can extract a neo-Hookean modulus, G p . This modulus, also known as the Gaussian modulus derived by Mooney (27), was used by Hawards (28) to model cross-linked polymer composite networks as a rubbery spring in parallel with a Eyring dashpot (fillers), and another Hookean spring (fillers) (13,14,(29)(30)(31). In this model, randomly cross-linked (vulcanized) NBR chains create a network made up of Gaussian chains (5,21,22),…”

Section: Significancementioning

confidence: 99%

Nanoparticle amount, and not size, determines chain alignment and nonlinear hardening in polymer nanocomposites

Varol

Meng

Hosseinkhani

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Polymer nanocomposites-materials in which a polymer matrix is blended with nanoparticles (or fillers)-strengthen under sufficiently large strains. Such strain hardening is critical to their function, especially for materials that bear large cyclic loads such as car tires or bearing sealants. Although the reinforcement (i.e., the increase in the linear elasticity) by the addition of filler particles is phenomenologically understood, considerably less is known about strain hardening (the nonlinear elasticity). Here, we elucidate the molecular origin of strain hardening using uniaxial tensile loading, microspectroscopy of polymer chain alignment, and theory. The strain-hardening behavior and chain alignment are found to depend on the volume fraction, but not on the size of nanofillers. This contrasts with reinforcement, which depends on both volume fraction and size of nanofillers, potentially allowing linear and nonlinear elasticity of nanocomposites to be tuned independently.nanocomposites | nonlinear elasticity | strain stiffening | polymer bridging | polymer chain alignment M any synthetic and natural materials around us increase their elastic modulus upon large deformation after initial softening-a phenomenon that is known as work or strain hardening, which is critical to their function. In ductile polymer materials, the strain-hardening behavior is essential for their functional lifetime, resilience, and toughness-all key parameters of their practical uses-because these materials repetitively bear large loads (1, 2). Many industrial and consumer polymeric materials are composites, in which (hard) nanoscale inorganic particles, or fillers, are blended with polymer matrices to tailor their mechanical properties. In preparing such nanocomposites, filler−filler and filler−matrix interaction, filler dispersion, and polymer properties all affect the linear (low strain) and nonlinear (high strain) mechanical response in nontrivial ways (3). Although a massive volume of work has attempted to clarify the mechanism of reinforcement (increased linear elasticity) at low strain and of nonlinear strain softening (the Payne and Mullins effects) at medium strain, a comparatively much smaller body of work exists that focuses on the mechanism of strain hardening in polymer composite materials.In analogy to rubber elasticity at large deformations, strain hardening in polymer composites is typically attributed to the increasing resistance to deformation of extended and oriented polymer chains (4-7). However, it has been shown that polymer chain alignment during strain hardening is strongly affected by dispersing fillers within the host polymer matrix (8-10). To account for these observations, one needs to establish the relation between the macroscopically observed strain hardening and the microscopic chain alignment that is affected by the presence of fillers.The connection between chain alignment and strain hardening in glassy polymer composites is purported to occur because the fillers act as "entanglement attractors." In this...

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Section: Significancementioning

confidence: 99%

Nanoparticle amount, and not size, determines chain alignment and nonlinear hardening in polymer nanocomposites

Varol

Meng

Hosseinkhani

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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“…approximation is actually quite popular in the rheology literature (see e.g., [22,23,26]) since the corresponding configurational equation for K can be explicitly solved using the Fourier series. The stress tensor σ is then more simply given by (see [14,Equation 7.195]):…”

Section: Constitutive Equationmentioning

confidence: 99%

Mathematical Existence Results for the Doi–Edwards Polymer Model

Chupin

2016

Arch Rational Mech Anal

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CHUPINÅbstract. In this paper, we present some mathematical results on the Doi-Edwards model describing the dynamics of flexible polymers in melts and concentrated solutions. This model, developed in the late 1970s, has been used and tested extensively in modeling and simulation of polymer flows. From a mathematical point of view, the Doi-Edwards model consists in a strong coupling between the Navier-Stokes equations and a highly nonlinear constitutive law. The aim of this article is to provide a rigorous proof of the well-posedness of the Doi-Edwards model, namely it has a unique regular solution. We also prove, which is generally much more difficult for flows of viscoelastic type, that the solution is global in time in the two dimensional case, without any restriction on the smallness of the data.

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“…This section follows the monograph of Lin [70]. For more informations the reader could also refer to Bird et al [8], Larson [63] or Fiétier [33].…”

Section: Viscoelastic Fluidsmentioning

confidence: 99%

“…With these assumptions one can show (see Lin [70]) that the time evolution of ψ is given by a Smoluchowski equation…”

Section: Action Of the Solvent On The Polymersmentioning

confidence: 99%

“…The viscoelastic fluids are very challenging from the theoretical as well as from the numerical point of view. There exist numerous very different models, that range from molecular descriptions which consider all the microscopic interactions between particles, to macroscopic continuum mechanics models that ignore the small constitutive elements of the fluids (see the books by Bird et al [8,9], Larson [64] and Lin [70] for example). The continuum based theories, like the Oldroyd-B model, are based on invariance properties of the deformation of continuous media that have been investigated in many details by classical methods, from finite differences to spectral element methods (see Tomé et al [96], Bonito et al [12], Keunings [59], Fiétier [33] for example).…”

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confidence: 99%

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