Relaxation of Anisotropic Thermal Diffusivity in a Polymer Melt Following Step Shear Strain

Venerus, David C.; Schieber, Jay D.; Iddir, Hadjira; Guzmán, Job D.; Broerman, A. W.

doi:10.1103/physrevlett.82.366

Cited by 36 publications

(47 citation statements)

References 13 publications

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“…Step strain experiments on polyisobutylene performed in our laboratory for a simpler flow cell (which allowed gratings in the x and z directions after step strains only), agreed with such a linear relation (17). However, the average orientation of the chain segments, as measured by the birefringence extinction angle, is constant for relaxation after a step strain (Lodge-Meissner rule).…”

Section: Resultsmentioning

confidence: 71%

Measurement of anisotropic energy transport in flowing polymers by using a holographic technique

Schieber

Venerus

Bush

et al. 2004

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

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Almost no experimental data exist to test theories for the nonisothermal flow of complex fluids. To provide quantitative tests for newly proposed theories, we have developed a holographic grating technique to study energy transport in an amorphous polymer melt subject to flow. Polyisobutylene with weight-averaged molecular mass of 85 kDa is sheared at a rate of 10 s ؊1 , and all nonzero components of the thermal conductivity tensor are measured as a function of time, after cessation. Our results are consistent with proposed generalizations to the energy balance for microstructural fluids, including a generalized Fourier's law for anisotropic media. The data are also consistent with a proposed stress-thermal rule for amorphous polymer melts. Confirmation of the universality of these results would allow numerical modelers to make quantitative predictions for the nonisothermal flow of polymer melts.N early all biological and advanced synthetic materials can exhibit molecular order or structure spontaneously, or be induced by flow. For example, rod-like molecules can form liquid crystals or membranes at equilibrium, and surfactants can self-assemble into worm-like shapes (1). These materials with microstructure exhibit nonequilibrium behavior much more complex than what is observed for simple, low-molecular-weight liquids. Upon flow, they may orient, crystallize, and show stresses many orders of magnitude larger than water. What is more, these large stresses relax back to equilibrium on time scales from seconds to minutes when the flow is stopped (2).The governing dynamics of simple (low-molecular-weight) f luids are well understood. Their derivation begins with straightforward balance equations for mass, momentum, and energy (and possibly angular momentum conservation) applied to a continuum (3). Mass conservation leads to an evolution equation for density , the continuity equation. The second and third balances, however, are not closed; we have too many unknowns and not enough equations. For closure we need additional equations called constitutive relations. For the momentum balance, we need an equation to relate stress to velocity in the f luid, and, in the case of the energy balance, we require two additional equations: a relationship between energy and measurable quantities, usually temperature T and velocity v; and a relationship between heat f lux and temperature. For simple f luids, these constitutive relations are well known. For the stress tensor we use the Newtonian constitutive equation, which states that the stress is linearly related to the instantaneous velocity gradient ٌv, through the viscosity. The energy density is a sum of internal energy density u, and kinetic energy density 1͞2 v 2 . The third relation is Fourier's law for the heat f lux q, which is linearly related to the temperature gradient by a scalar thermal conductivity.Using these three relations, we then have a closed set of evolution equations for the density , the velocity field v, and the temperature field T. If material parameters, ...

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Section: Resultsmentioning

confidence: 71%

Measurement of anisotropic energy transport in flowing polymers by using a holographic technique

Schieber

Venerus

Bush

et al. 2004

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

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“…Birefringence (anisotropy of the refractive index tensor) measured in the same flow allowed us, using a combination of eqs 2 and 3, to verify indirectly the stress-thermal rule for a polymer melt in shear flow. 20,21 In a similar study on a cross-linked polymer subjected to simple elongation, 22 we reported measurements of the thermal diffusivity tensor and tensile stress that provided direct evidence for the stress-thermal rule. Validity of the stressthermal rule, eq 2, indicates that deformation-induced anisotropies in mechanical and thermal transport in polymers are governed by polymer chain orientation on a common length scale.…”

Section: Introductionmentioning

confidence: 92%

Measurements of Flow-Induced Anisotropic Thermal Conduction in a Polyisobutylene Melt Following Step Shear Flow

et al. 2005

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Flow-induced anisotropic thermal conduction in a polyisobutylene melt subjected to shear deformations is studied experimentally. Time-dependent measurements of the full (four components) thermal diffusivity tensor following step shear strain flow are presented. These data were obtained with a novel experimental setup based on the optical technique of forced Rayleigh scattering. Birefringence and stress measurements are made for the same flow, and the well-known stress-thermal rule is found to be satisfied. Thermal diffusivity data and stress data are used to test directly the stress-thermal rule, which is also satisfied for the two cases considered. Consideration of stress-thermal coefficients from the present and previous studies gives preliminary evidence that flow-induced anisotropic thermal conduction is a universal phenomenon for flexible polymers.

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“…Because most of the heat is generated by shear heating during flow, we expect these effects to be minor while all the polymer is in the molten phase. Moreover, the anisotropy of thermal diffusivity, which can be significantly increased in the direction of flow [105], is not accounted for. Because the thermal gradient in flow direction in our experiments is generally quite small and the thermal diffusivity perpendicular to flow direction is affected much less [105], we trust this is a reasonable approximation.…”

Section: Heat Balancementioning

confidence: 99%

Modeling Flow-Induced Crystallization

Roozemond

Drongelen

Peters

2016

Polymer Crystallization II

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A numerical model is presented that describes all aspects of flow-induced crystallization of isotactic polypropylene at high shear rates and elevated pressures. It incorporates nonlinear viscoelasticity, including viscosity change as a result of formation of oriented fibrillar crystals (shish), compressibility, and nonisothermal process conditions caused by shear heating and heat release as a result of crystallization. In the first part of this chapter, the model is validated with experimental data obtained in a channel flow geometry. Quantitative agreement between experimental results and the numerical model is observed in terms of pressure drop, apparent crystallinity, parent/daughter ratio, Hermans' orientation, and shear layer thickness. In the second part, the focus is on flow-induced crystallization of isotactic polypropylene at elevated pressures, resulting in multiple crystal phases and morphologies. All parameters but one are fixed a priori from the first part of the chapter. One additional parameter, determining the portion of β-crystal spherulites nucleated by flow, is introduced. By doing so, an accurate description of the fraction of β-phase crystals is obtained. The model accurately captures experimental data for fractions of all crystal phases over a wide range of flow conditions (shear rates from 0 to 200 s À1 , pressures from 100 to 1,200 bar, shear temperatures from 130 C to 180 C). Moreover, it is shown that, for high shear rates and pressures, the measured γ-phase fractions can only be matched if γ-crystals can nucleate directly on shish.

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Relaxation of Anisotropic Thermal Diffusivity in a Polymer Melt Following Step Shear Strain

Cited by 36 publications

References 13 publications

Measurement of anisotropic energy transport in flowing polymers by using a holographic technique

Measurement of anisotropic energy transport in flowing polymers by using a holographic technique

Measurements of Flow-Induced Anisotropic Thermal Conduction in a Polyisobutylene Melt Following Step Shear Flow

Modeling Flow-Induced Crystallization

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