Tom McLeish - Profile on Academia.edu (original) (raw)
Papers by Tom McLeish
…, 2010
Using SANS to map the deformation of individual polymer chains in the vicinity of re-entrant corn... more Using SANS to map the deformation of individual polymer chains in the vicinity of re-entrant corners in a contraction-expansion flow, we show that stress singularities at such corners, predicted by formulations of fluid dynamics that lack a molecular basis, do not cause extreme deformation of the chains. Multiscale modeling based on a nonlinear tube theory incorporating appropriate relaxation processes quantitatively reproduces the observed scattering, thus providing further evidence for the universality of the tube model for polymer flow.
Theology, 1999
'Real Presences' is Steiner's personal manifesto against the de- construction movement in modern ... more 'Real Presences' is Steiner's personal manifesto against the de- construction movement in modern literature (and art and music). It is not a book that many scientists would read, let alone re-read. And yet we have read and re-read the book; it has made us laugh and cry. Why? This essay is a first attempt at articulating the shock of relevance two scientists felt after their encounter with this remarkable book.
Neutron flow-mapping: Multiscale modelling opens a new experimental window
Soft Matter, 2009
... 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 ...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2014
In his treatise on light, written in about 1225, Robert Grosseteste describes a cosmological mode... more In his treatise on light, written in about 1225, Robert Grosseteste describes a cosmological model in which the Universe is created in a big-bang like explosion and subsequent condensation. He postulates that the fundamental coupling of light and matter gives rises to the material body of the entire cosmos. Expansion is arrested when matter reaches a minimum density and subsequent emission of light from the outer region leads to compression and rarefaction of the inner bodily mass so as to create nine celestial spheres, with an imperfect residual core. In this paper we reformulate the Latin description in terms of a modern mathematical model. The equations which describe the coupling of light and matter are solved numerically, subject to initial conditions and critical criteria consistent with the text. Formation of a universe with a non-infinite number of perfected spheres is extremely sensitive to the initial conditions, the intensity of the light and the transparency of these spheres. In this "medieval multiverse", only a small range of opacity and initial density profiles lead to a stable universe with nine perfected spheres. As in current cosmological thinking, the existence of Grosseteste's universe relies on a very special combination of fundamental parameters.
Color-coordinate system from a 13th-century account of rainbows
Journal of the Optical Society of America A, 2014
We present a new analysis of Robert Grosseteste&a... more We present a new analysis of Robert Grosseteste's account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste's De colore [see J. Opt. Soc. Am. A29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste's key terms.
Macromolecules, 2006
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.
Neutron Flow-Mapping of Controlled-Architecture Polymer Melts
We report on results of a new method for probing complex flows of entangled polymer melts that is... more We report on results of a new method for probing complex flows of entangled polymer melts that is able to compare simultaneously chain configurations on different length scales and stress distribution in the flow with the predictions of molecular models. Controlled-architecture melts synthesised by anionic polymerisation and selectively deuterated are made in sufficient quantities to fill a recirculating flow device
Journal of the Optical Society of America (JOSA A) Vol. 29, Iss. 2 (2012), pp. A349-355.
Journal of the Optical Society of America (JOSA A) Vol. 31, no. 4, pp. A341-A349. , Apr 2014
We present a new analysis of Robert Grosseteste's account of color in his treatise De iride (On t... more We present a new analysis of Robert Grosseteste's account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste's De colore [see J. Opt. Soc. Am. A 29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste's key terms.
Anomalous Difference in the Order-Disorder Transition Temperature of Symmetric AB Diblock Compared to A2B2 Star Block Copolymer
The order-disorder transition temperature (T_ODT) of symmetric styrene-isoprene diblock copolymer... more The order-disorder transition temperature (T_ODT) of symmetric styrene-isoprene diblock copolymers (AB) and its hetero-four-arm star analog (A2 B_2) was measured using dynamic mechanical spectroscopy and small angle X-ray scattering (SAXS). Care was taken to ensure that the arm molecular weights of both AB and A2 B2 were matched. Contrary to mean-field theory predictions, a significant difference in T_ODT, approx. 30degC, is found between the two systems (the arm molecular weight for both the styrene and isoprene is about 10 kg/mol). We show that this difference is too large to be explained by polydispersity, segmental asymmetry or the Fredrickson-Helfand theory of compositional fluctuations (which assumes that the polymer chains are Gaussian). Instead, we suggest that one needs to incorporate the differing degrees of non-Gaussian chain stretching in the two systems at the order-disorder transition (as confirmed by SAXS) into the fluctuation theory for a proper understanding of the effect. We demonstrate that a simple model calculation that incorporates sufficient chain stretching to match the experimentally determined shifts in the SAXS peak for the two systems also reproduces a difference in the T_ODT which is comparable to what is measured experimentally.
Molecular Drag-Strain Coupling in Branched Polymer Melts
Journal of Rheology, 2000
The ``pom-pom&amp... more The ``pom-pom'' model of McLeish and Larson (J. Rheol. 42(1):81--110, 1998) provides a simple molecular theory for the nonlinear rheology of long chain branched polymer melts. The Edwards-de Gennes tube concept is used to derive a constitutive equation for a simple branched molecule composed of two star polymers linked by a single "backbone" chain. A feature of this model is
A Lagrangian flow solver for complex flows in polymers
The transient flow of a branched polymer melt through various contraction geometries has been mod... more The transient flow of a branched polymer melt through various contraction geometries has been modelled using a molecularly based constitutive equation together with a Lagrangian finite element method and compared to experimental data. The constitutive equation models the polymer as a multi-mode suspension of idealised "pom-pom" molecules each consisting of a cross-bar connecting two identical stars. The constitutive parameters directly relate to features in this structure. These parameters can be obtained by a simultaneous fit to transient shear and extension experimental rheological data. The flow of the polymer was calculated using a finite element method with a moving triangular grid. At each time step the velocity and pressure were calculated from the current values of the constitutive parameters. The constitutive parameters, and positions of the grid vertices were then updated using the calculated data. Geometries considered include flow through a contraction, die swell upon emerging from a die, and flow through a constriction. In each case a comparison can be made with experimental observations of the polymers parameterised.
Fluctuation power spectra reveal dynamical heterogeneity of peptides
Chemical Physics, 2010
Characterizing the conformational properties and dynamics of biopolymers and their relation to bi... more Characterizing the conformational properties and dynamics of biopolymers and their relation to biological activity and function is an ongoing challenge. Single molecule techniques have provided a rich experimental window on these properties, yet they have often relied on simple one-dimensional projections of a multidimensional free energy landscape for a practical interpretation of the results. Here, we study three short peptides with different structural propensity (α helical, β hairpin, and random coil) in the presence (or absence) of a force applied to their ends using Langevin dynamics simulation and an all-atom model with implicit solvation. Each peptide produces fluctuation power spectra with a characteristic dynamic fingerprint consistent with persistent structural motifs of helices, hairpins, and random coils. The spectra for helix formation shows two well-defined relaxation modes, corresponding to local relaxation and cooperative coil to uncoil interconversion. In contrast, both the hairpin and random coil are polymerlike, showing a broad and continuous range of relaxation modes giving characteristic power laws of ω-5/4 and ω-3/2, respectively; the -5/4 power law for hairpins is robust and has not been previously observed. Langevin dynamics simulations of diffusers on a potential of mean force derived from the atomistic simulations fail to reproduce the fingerprints of each peptide motif in the power spectral density, demonstrating explicitly that such information is lacking in such one-dimensional projections. Our results demonstrate the yet unexploited potential of single molecule fluctuation spectroscopy to probe more fine scaled properties of proteins and biological macromolecules and how low dimensional projections may cause the loss of relevant information.
Physical Review Letters, 2008
The unfolding of a protein by the application of an external force pulling two atoms of the prote... more The unfolding of a protein by the application of an external force pulling two atoms of the protein can be detected by atomic force and optical tweezers technologies as have been broadly demonstrated in the past decade. Variation of the applied force results in a modulation of the free-energy barrier to unfolding and thus, the rate of the process, which is often assumed to have single exponential kinetics. It has been recently shown that it is experimentally feasible, through the use of force clamps, to estimate the distribution of unfolding times for a population of proteins initially in the native state. In this Letter we show how the analysis of such distributions under a range of forces can provide unique information about the underlying free-energy surface such as the height of the free-energy barrier, the preexponential factor and the force dependence of the unfolding kinetics without resorting to ad hoc kinetic models.
Neutron Flow-Mapping of Controlled-Architecture Polymer Melts
We report on results of a new method for probing complex flows of entangled polymer melts that is... more We report on results of a new method for probing complex flows of entangled polymer melts that is able to compare simultaneously chain configurations on different length scales and stress distribution in the flow with the predictions of molecular models. Controlled-architecture melts synthesised by anionic polymerisation and selectively deuterated are made in sufficient quantities to fill a recirculating flow device that contains a windowed processing zone. This may take the form of a constriction or a cross-slot. The whole processing rig is scanned across a narrow neutron beam before a small-angle detector that reports on the structure factor of labelled chains (this sometimes requires the subtraction of two differently-labelled experiments). The same flow is probed in birefringence, measuring the independent orientation at the bond level of the chains.
Neutron Flow-Mapping of Controlled-Architecture Polymer Melts
We report on results of a new method for probing complex flows of entangled polymer melts that is... more We report on results of a new method for probing complex flows of entangled polymer melts that is able to compare simultaneously chain configurations on different length scales and stress distribution in the flow with the predictions of molecular models via multiscale ...
Predicting non-linear rheology of randomly branched entangled polymer melts
We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (20... more We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (2006)] for predicting the linear rheology of arbitrarily branched polymer melts, which was successfully used for well defined architectures (stars, combs, Cayley trees etc.) and well-characterised industrial resins. We now discuss an extension to the non-linear regime, via a mapping onto a multi-mode ``pom-pom" ensemble. There is, in principle, sufficient information in the algorithm to do this without additional free parameters. However, the procedure is not exact and one must consider the most important physics to represent. In particular, we highlight the need to distinguish between stress relaxation via constraint release and via tube escape. We also discuss the topological ``priority" variable (which limits the stress in extension) and the considerations needed when assigning this to each polymer strand (which polymer segments should one count as relaxed?) In doing this, and as a result of tube advection, we find we need to introduce a new variable (``altitude") related to the topological distance of a strand from the molecule centre.
Physical Review Letters, 2009
- 'Elongational flow of blends of long and short polymers : effective stretch relaxation time... more 2009) 'Elongational flow of blends of long and short polymers : effective stretch relaxation time.', Physical review letters., 103 (13).
…, 2010
Using SANS to map the deformation of individual polymer chains in the vicinity of re-entrant corn... more Using SANS to map the deformation of individual polymer chains in the vicinity of re-entrant corners in a contraction-expansion flow, we show that stress singularities at such corners, predicted by formulations of fluid dynamics that lack a molecular basis, do not cause extreme deformation of the chains. Multiscale modeling based on a nonlinear tube theory incorporating appropriate relaxation processes quantitatively reproduces the observed scattering, thus providing further evidence for the universality of the tube model for polymer flow.
Theology, 1999
'Real Presences' is Steiner's personal manifesto against the de- construction movement in modern ... more 'Real Presences' is Steiner's personal manifesto against the de- construction movement in modern literature (and art and music). It is not a book that many scientists would read, let alone re-read. And yet we have read and re-read the book; it has made us laugh and cry. Why? This essay is a first attempt at articulating the shock of relevance two scientists felt after their encounter with this remarkable book.
Neutron flow-mapping: Multiscale modelling opens a new experimental window
Soft Matter, 2009
... 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 ...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2014
In his treatise on light, written in about 1225, Robert Grosseteste describes a cosmological mode... more In his treatise on light, written in about 1225, Robert Grosseteste describes a cosmological model in which the Universe is created in a big-bang like explosion and subsequent condensation. He postulates that the fundamental coupling of light and matter gives rises to the material body of the entire cosmos. Expansion is arrested when matter reaches a minimum density and subsequent emission of light from the outer region leads to compression and rarefaction of the inner bodily mass so as to create nine celestial spheres, with an imperfect residual core. In this paper we reformulate the Latin description in terms of a modern mathematical model. The equations which describe the coupling of light and matter are solved numerically, subject to initial conditions and critical criteria consistent with the text. Formation of a universe with a non-infinite number of perfected spheres is extremely sensitive to the initial conditions, the intensity of the light and the transparency of these spheres. In this "medieval multiverse", only a small range of opacity and initial density profiles lead to a stable universe with nine perfected spheres. As in current cosmological thinking, the existence of Grosseteste's universe relies on a very special combination of fundamental parameters.
Color-coordinate system from a 13th-century account of rainbows
Journal of the Optical Society of America A, 2014
We present a new analysis of Robert Grosseteste&a... more We present a new analysis of Robert Grosseteste's account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste's De colore [see J. Opt. Soc. Am. A29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste's key terms.
Macromolecules, 2006
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.
Neutron Flow-Mapping of Controlled-Architecture Polymer Melts
We report on results of a new method for probing complex flows of entangled polymer melts that is... more We report on results of a new method for probing complex flows of entangled polymer melts that is able to compare simultaneously chain configurations on different length scales and stress distribution in the flow with the predictions of molecular models. Controlled-architecture melts synthesised by anionic polymerisation and selectively deuterated are made in sufficient quantities to fill a recirculating flow device
Journal of the Optical Society of America (JOSA A) Vol. 29, Iss. 2 (2012), pp. A349-355.
Journal of the Optical Society of America (JOSA A) Vol. 31, no. 4, pp. A341-A349. , Apr 2014
We present a new analysis of Robert Grosseteste's account of color in his treatise De iride (On t... more We present a new analysis of Robert Grosseteste's account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste's De colore [see J. Opt. Soc. Am. A 29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste's key terms.
Anomalous Difference in the Order-Disorder Transition Temperature of Symmetric AB Diblock Compared to A2B2 Star Block Copolymer
The order-disorder transition temperature (T_ODT) of symmetric styrene-isoprene diblock copolymer... more The order-disorder transition temperature (T_ODT) of symmetric styrene-isoprene diblock copolymers (AB) and its hetero-four-arm star analog (A2 B_2) was measured using dynamic mechanical spectroscopy and small angle X-ray scattering (SAXS). Care was taken to ensure that the arm molecular weights of both AB and A2 B2 were matched. Contrary to mean-field theory predictions, a significant difference in T_ODT, approx. 30degC, is found between the two systems (the arm molecular weight for both the styrene and isoprene is about 10 kg/mol). We show that this difference is too large to be explained by polydispersity, segmental asymmetry or the Fredrickson-Helfand theory of compositional fluctuations (which assumes that the polymer chains are Gaussian). Instead, we suggest that one needs to incorporate the differing degrees of non-Gaussian chain stretching in the two systems at the order-disorder transition (as confirmed by SAXS) into the fluctuation theory for a proper understanding of the effect. We demonstrate that a simple model calculation that incorporates sufficient chain stretching to match the experimentally determined shifts in the SAXS peak for the two systems also reproduces a difference in the T_ODT which is comparable to what is measured experimentally.
Molecular Drag-Strain Coupling in Branched Polymer Melts
Journal of Rheology, 2000
The ``pom-pom&amp... more The ``pom-pom'' model of McLeish and Larson (J. Rheol. 42(1):81--110, 1998) provides a simple molecular theory for the nonlinear rheology of long chain branched polymer melts. The Edwards-de Gennes tube concept is used to derive a constitutive equation for a simple branched molecule composed of two star polymers linked by a single "backbone" chain. A feature of this model is
A Lagrangian flow solver for complex flows in polymers
The transient flow of a branched polymer melt through various contraction geometries has been mod... more The transient flow of a branched polymer melt through various contraction geometries has been modelled using a molecularly based constitutive equation together with a Lagrangian finite element method and compared to experimental data. The constitutive equation models the polymer as a multi-mode suspension of idealised "pom-pom" molecules each consisting of a cross-bar connecting two identical stars. The constitutive parameters directly relate to features in this structure. These parameters can be obtained by a simultaneous fit to transient shear and extension experimental rheological data. The flow of the polymer was calculated using a finite element method with a moving triangular grid. At each time step the velocity and pressure were calculated from the current values of the constitutive parameters. The constitutive parameters, and positions of the grid vertices were then updated using the calculated data. Geometries considered include flow through a contraction, die swell upon emerging from a die, and flow through a constriction. In each case a comparison can be made with experimental observations of the polymers parameterised.
Fluctuation power spectra reveal dynamical heterogeneity of peptides
Chemical Physics, 2010
Characterizing the conformational properties and dynamics of biopolymers and their relation to bi... more Characterizing the conformational properties and dynamics of biopolymers and their relation to biological activity and function is an ongoing challenge. Single molecule techniques have provided a rich experimental window on these properties, yet they have often relied on simple one-dimensional projections of a multidimensional free energy landscape for a practical interpretation of the results. Here, we study three short peptides with different structural propensity (α helical, β hairpin, and random coil) in the presence (or absence) of a force applied to their ends using Langevin dynamics simulation and an all-atom model with implicit solvation. Each peptide produces fluctuation power spectra with a characteristic dynamic fingerprint consistent with persistent structural motifs of helices, hairpins, and random coils. The spectra for helix formation shows two well-defined relaxation modes, corresponding to local relaxation and cooperative coil to uncoil interconversion. In contrast, both the hairpin and random coil are polymerlike, showing a broad and continuous range of relaxation modes giving characteristic power laws of ω-5/4 and ω-3/2, respectively; the -5/4 power law for hairpins is robust and has not been previously observed. Langevin dynamics simulations of diffusers on a potential of mean force derived from the atomistic simulations fail to reproduce the fingerprints of each peptide motif in the power spectral density, demonstrating explicitly that such information is lacking in such one-dimensional projections. Our results demonstrate the yet unexploited potential of single molecule fluctuation spectroscopy to probe more fine scaled properties of proteins and biological macromolecules and how low dimensional projections may cause the loss of relevant information.
Physical Review Letters, 2008
The unfolding of a protein by the application of an external force pulling two atoms of the prote... more The unfolding of a protein by the application of an external force pulling two atoms of the protein can be detected by atomic force and optical tweezers technologies as have been broadly demonstrated in the past decade. Variation of the applied force results in a modulation of the free-energy barrier to unfolding and thus, the rate of the process, which is often assumed to have single exponential kinetics. It has been recently shown that it is experimentally feasible, through the use of force clamps, to estimate the distribution of unfolding times for a population of proteins initially in the native state. In this Letter we show how the analysis of such distributions under a range of forces can provide unique information about the underlying free-energy surface such as the height of the free-energy barrier, the preexponential factor and the force dependence of the unfolding kinetics without resorting to ad hoc kinetic models.
Neutron Flow-Mapping of Controlled-Architecture Polymer Melts
We report on results of a new method for probing complex flows of entangled polymer melts that is... more We report on results of a new method for probing complex flows of entangled polymer melts that is able to compare simultaneously chain configurations on different length scales and stress distribution in the flow with the predictions of molecular models. Controlled-architecture melts synthesised by anionic polymerisation and selectively deuterated are made in sufficient quantities to fill a recirculating flow device that contains a windowed processing zone. This may take the form of a constriction or a cross-slot. The whole processing rig is scanned across a narrow neutron beam before a small-angle detector that reports on the structure factor of labelled chains (this sometimes requires the subtraction of two differently-labelled experiments). The same flow is probed in birefringence, measuring the independent orientation at the bond level of the chains.
Neutron Flow-Mapping of Controlled-Architecture Polymer Melts
We report on results of a new method for probing complex flows of entangled polymer melts that is... more We report on results of a new method for probing complex flows of entangled polymer melts that is able to compare simultaneously chain configurations on different length scales and stress distribution in the flow with the predictions of molecular models via multiscale ...
Predicting non-linear rheology of randomly branched entangled polymer melts
We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (20... more We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (2006)] for predicting the linear rheology of arbitrarily branched polymer melts, which was successfully used for well defined architectures (stars, combs, Cayley trees etc.) and well-characterised industrial resins. We now discuss an extension to the non-linear regime, via a mapping onto a multi-mode ``pom-pom" ensemble. There is, in principle, sufficient information in the algorithm to do this without additional free parameters. However, the procedure is not exact and one must consider the most important physics to represent. In particular, we highlight the need to distinguish between stress relaxation via constraint release and via tube escape. We also discuss the topological ``priority" variable (which limits the stress in extension) and the considerations needed when assigning this to each polymer strand (which polymer segments should one count as relaxed?) In doing this, and as a result of tube advection, we find we need to introduce a new variable (``altitude") related to the topological distance of a strand from the molecule centre.
Physical Review Letters, 2009
- 'Elongational flow of blends of long and short polymers : effective stretch relaxation time... more 2009) 'Elongational flow of blends of long and short polymers : effective stretch relaxation time.', Physical review letters., 103 (13).