The experimentally determined zero-shear viscosity of entangled branched polymers shows dramatic ... more The experimentally determined zero-shear viscosity of entangled branched polymers shows dramatic variation due to the topological arrangements of the branches in branched polymer melts. The position of the branch points, the arm length, and number of the arms are essential to defining the rheological behavior. Recent advances in molecular tube models have led to a much greater understanding of the linear rheology of linear, star, H-shaped, pom-pom, and comb polymers. We correct and extend existing molecular theories for the linear viscoelasticity of comb polymer melts, especially in accounting for (1) polydispersity and (2) the path length of backbone extremities. We compare the predictions with linear rheological data of nearly monodisperse polybutadiene combs. We then predict the zero-shear viscosity for monodisperse comb polyethylenes with varying arm lengths, backbone lengths, and number of arms. For a fixed molecular weight, we find that combs with the longest arms but few branch points give the highest predicted zero-shear viscosities and that they obey an exponential dependence on the length of the arms in the same way as star polymers. We find that combs with short arms, under four entanglements, lie below the 3.4 power law obeyed by linear polymers. All other comb topologies are bounded by these extremes.
Soft Matter, 2009, 5, 2383-2389 DOI:10.1039/B817440G (Paper). The long-chain dynamics in a model ... more Soft Matter, 2009, 5, 2383-2389 DOI:10.1039/B817440G (Paper). The long-chain dynamics in a model homopolymer blend under strong flow: small-angle neutron scattering and theory. Richard S. Graham*a, Julian Bentb, Nigel ...
Small-angle neutron scattering measurements on a series of monodisperse linear entangled polystyr... more Small-angle neutron scattering measurements on a series of monodisperse linear entangled polystyrene melts in nonlinear flow through an abrupt 4:1 contraction have been made. Clear signatures of melt deformation and subsequent relaxation can be observed in the scattering patterns, which were taken along the centerline. These data are compared with the predictions of a recently derived molecular theory. Two levels of molecular theory are used: a detailed equation describing the evolution of molecular structure over all length scales relevant to the scattering data and a simplified version of the model, which is suitable for finite element computations. The velocity field for the complex melt flow is computed using the simplified model and scattering predictions are made by feeding these flow histories into the detailed model. The modeling quantitatively captures the full scattering intensity patterns over a broad range of data with independent variation of position within the contraction geometry, bulk flow rate and melt molecular weight. The study provides a strong, quantitative validation of current theoretical ideas concerning the microscopic dynamics of entangled polymers which builds upon existing comparisons with nonlinear mechanical stress data. Furthermore, we are able to confirm the appreciable length scale dependence of relaxation in polymer melts and highlight some wider implications of this phenomenon.
... The nonlinear tube model, GLaMM,(18) has been used to predict the SANS patterns from entangle... more ... The nonlinear tube model, GLaMM,(18) has been used to predict the SANS patterns from entangled polymers under strong flow.(8, 14, 19) In the model, the relaxation mechanisms of reptation, contour length fluctuations, retraction, and constraint release are formulated into a ...
... Tom CB McLeish*a, Nigel Clarkea, Eduardo de Lucaa, Lian R. Hutchingsa, Richard S. Grahamb, Ti... more ... Tom CB McLeish*a, Nigel Clarkea, Eduardo de Lucaa, Lian R. Hutchingsa, Richard S. Grahamb, Tim Goughc, Isabelle Grillod, Christine M ... 18, TCB McLeish, J. Allgaier, DK Bick, G. Bishko, P. Biswas, R. Blackwell, B. Blottière, N. Clarke, B. Gibbs, DJ Groves, A. Hakiki, R. Heenan ...
The experimentally determined zero-shear viscosity of entangled branched polymers shows dramatic ... more The experimentally determined zero-shear viscosity of entangled branched polymers shows dramatic variation due to the topological arrangements of the branches in branched polymer melts. The position of the branch points, the arm length, and number of the arms are essential to defining the rheological behavior. Recent advances in molecular tube models have led to a much greater understanding of the linear rheology of linear, star, H-shaped, pom-pom, and comb polymers. We correct and extend existing molecular theories for the linear viscoelasticity of comb polymer melts, especially in accounting for (1) polydispersity and (2) the path length of backbone extremities. We compare the predictions with linear rheological data of nearly monodisperse polybutadiene combs. We then predict the zero-shear viscosity for monodisperse comb polyethylenes with varying arm lengths, backbone lengths, and number of arms. For a fixed molecular weight, we find that combs with the longest arms but few branch points give the highest predicted zero-shear viscosities and that they obey an exponential dependence on the length of the arms in the same way as star polymers. We find that combs with short arms, under four entanglements, lie below the 3.4 power law obeyed by linear polymers. All other comb topologies are bounded by these extremes.
Soft Matter, 2009, 5, 2383-2389 DOI:10.1039/B817440G (Paper). The long-chain dynamics in a model ... more Soft Matter, 2009, 5, 2383-2389 DOI:10.1039/B817440G (Paper). The long-chain dynamics in a model homopolymer blend under strong flow: small-angle neutron scattering and theory. Richard S. Graham*a, Julian Bentb, Nigel ...
Small-angle neutron scattering measurements on a series of monodisperse linear entangled polystyr... more Small-angle neutron scattering measurements on a series of monodisperse linear entangled polystyrene melts in nonlinear flow through an abrupt 4:1 contraction have been made. Clear signatures of melt deformation and subsequent relaxation can be observed in the scattering patterns, which were taken along the centerline. These data are compared with the predictions of a recently derived molecular theory. Two levels of molecular theory are used: a detailed equation describing the evolution of molecular structure over all length scales relevant to the scattering data and a simplified version of the model, which is suitable for finite element computations. The velocity field for the complex melt flow is computed using the simplified model and scattering predictions are made by feeding these flow histories into the detailed model. The modeling quantitatively captures the full scattering intensity patterns over a broad range of data with independent variation of position within the contraction geometry, bulk flow rate and melt molecular weight. The study provides a strong, quantitative validation of current theoretical ideas concerning the microscopic dynamics of entangled polymers which builds upon existing comparisons with nonlinear mechanical stress data. Furthermore, we are able to confirm the appreciable length scale dependence of relaxation in polymer melts and highlight some wider implications of this phenomenon.
... The nonlinear tube model, GLaMM,(18) has been used to predict the SANS patterns from entangle... more ... The nonlinear tube model, GLaMM,(18) has been used to predict the SANS patterns from entangled polymers under strong flow.(8, 14, 19) In the model, the relaxation mechanisms of reptation, contour length fluctuations, retraction, and constraint release are formulated into a ...
... Tom CB McLeish*a, Nigel Clarkea, Eduardo de Lucaa, Lian R. Hutchingsa, Richard S. Grahamb, Ti... more ... Tom CB McLeish*a, Nigel Clarkea, Eduardo de Lucaa, Lian R. Hutchingsa, Richard S. Grahamb, Tim Goughc, Isabelle Grillod, Christine M ... 18, TCB McLeish, J. Allgaier, DK Bick, G. Bishko, P. Biswas, R. Blackwell, B. Blottière, N. Clarke, B. Gibbs, DJ Groves, A. Hakiki, R. Heenan ...
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