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Journal of RheologyVolume 47, Issue 1 (January-February 2003) |
Contents
Linear rheology of multiarm star polymers diluted with short linear chainsA. Miros, D. Vlassopoulos A. E. Likhtman J. Roovers AbstractWe present experimental results on the linear rheology of multiarm star / linear polymer mixtures, the latter having molecular weight much smaller than the star arm molecular weight. In such a case the linear chains act as ideal macromolecular solvents, which dilute the entanglements of the arms. Using different star polymers we show that it is possible to account for this dilution and describe the linear rheology of the mixtures using the Milner-McLeish theory for the arm relaxation, complemented by the longitudinal modes of stress relaxation and the high frequency Rouse modes. A universal description of the isofrictional arm relaxation time as function of the number of entanglements is obtained for stars of any functionality and degree of dilution. The slow structural mode, relating to the diluted star's colloidal core, also depends on the number of entanglements, but in a more complex way. On a new strain measure tensor for entangled polymeric liquidsFrancesco Grecoa) AbstractA novel approach to the description of entangled polymeric liquids has recently been presented [Greco, F., Phys. Rev. Lett. 88, 108301/1-4 (2002)], where the mechanical behaviour of any subchain connecting two entanglements is determined through the grand canonical formalism of statistical mechanics, thus properly allowing for exchange of particles (Kuhn segments) among subchains. The deduction of a strain measure tensor within this new approach is here summed up and discussed in detail. It is also shown that the new strain measure tensor fulfills the stress-optical law. Predictions obtained with the new strain measure are compared with data for stepstrain deformations, both in shear and elongation, and good agreement is found. In particular, the normal stress ratio in step shear is found to be better described than with the classical “rigorous” Doi-Edwards strain measure. a) Address for correspondence: Chemical Engineering Department, University of Naples, P. le Tecchio 80 - 80125, Naples, Italy. Phone: +39 081 7682275; Fax: +39 081 2391800; E-mail: fgreco@irc.na.cnr.it
Why, and when, does “Dynamic Tube Dilation” work for stars?T. C. B. McLeish AbstractThe anzatz known as “Dynamic Dilution” or “tube dilation”, introduced by Marrucci and employed by Ball and McLeish in the case of star polymers, has been criticised, in spite of its success, for its apparent lack of controlled renormalisation at different timescales of the effective diffusion constant of the retracting star arm. Here we show that the dynamic dilution hypothesis, and the “Ball-McLeish equation”, may in some circumstances generate a close approximation to a less heuristic approach in which arm retraction procedes by a nested set of constraint-release “supertubes”. This more complex picture, consistent with the current treatment of constraint release in linear entangled polymers, provides a way to understand recent results on diffusion, dielectric relaxation and slip-link simulations of star polymer melts. Nonlinear dynamics of a concentrated system of rigid rods subjected to periodic shear flowsLucia Russo Pier Luca Maffettonea) AbstractPolymers in liquid crystalline nematic phase exhibit a complex rheological behavior. Under steady shear flows, and in homogeneous conditions, different regimes have been theoretically predicted, and in some cases experimentally observed. In particular, periodic and even aperiodic regimes have been theoretically predicted. Sustained periodic stress responses have been recently measured on a lyotropic sample of PBG in m-cresol. The natural oscillating behavior, as the well known tumbling or wagging regimes, can give rise to a number of resonance phenomena when the system is forced with proper periodic flows. It will be shown that frequency-locking phenomena are predicted in such conditions, and that the Arnol'd tongues can be used to discriminate among the unforced periodic behaviors. The nematic polymer is modeled with a simplified equation derived from the rigid rod model. a) Corresponding author. E-mail: maffetto@athena.polito.it A full-chain, temporary network model with sliplinks, chain-length fluctuations, chain connectivity and chain stretchingJay D. Schieber, Jesper Neergaard, and Sachin Gupta AbstractA full-chain, temporary network model is proposed for nonlinear flows of linear, entangled polymeric liquids. The model is inspired by the success of a recent reptation model, but contains no beads or tubes. Instead, each chain uses a different (and smaller) set of dynamic variables: thee location of each entanglement, and the number of Kuhn steps in chain strands between entanglements. As before, the model requires only a single phenomenological parameter that is fit by linear viscoelasticity. The number of Kuhn steps varies stochastically from imbalances in chemical potential, and Brownian forces. In the language of reptation, the model exhibits chain connectivity, chain-length fluctuations, chain stretching, and tube dilation. The current implementation in this framework does not include constraint release, although its addition is possible. The entanglements are assumed to move affinely. Because of the affinity assumption and lack of constraint release, the model should be expected to approximate well a linear chain in a matrix of fixed obstacles, and somewhat less accurately a polymer melt. Straightforward modifications to these assumptions allow us to consider chains of any architecture in concentrated solutions or melts. A simulation algorithm for the model is described in detail. Stress results are encouraging, since the model performs at least as well as a complete tube model without constraint release at much lower computational cost. Finally, we consider possible generalizations of the proposed model, to include additional physics, such as constraint release, branching, and non-affine motion. Dilution exponent in the dynamic dilution theory for polymer meltsSeung Joon Park and Ronald G. Larsona) AbstractTwo values, unity and 4/3, of the dilution exponent a in the Milner-McLeish dynamic dilution theory for relaxation of entangled polymers are tested thoroughly against experimental data for linear, star, and star-linear blends of 1,4-polybutadiene using the same set of values for the parameters: the plateau modulus GN0, the entanglement spacing Me, and the equilibration time te for each a. We find that a = 4/3 gives good agreement with all data sets using the literature value for the plateau modulus and an entanglement spacing that is very close to the value calculated from the plateau modulus. While we can also predict linear and star polymer rheology with adjusted Me and te for a = 1, the required value of Me is 40% higher than the one calculated from the plateau modulus. a) Corresponding author. E-mail: rlarson@umich.edu Microstructural changes of a binary polymer blend in simple shear flow across the phase boundaryD. Vlassopoulosa), T. Terakawab), and G. G. Fullerb) a) FO.R.T.H., Institute of Electronic
Structure & Laser b) Department of Chemical Engineering AbstractWe explore the dynamic response of a marginally entangled poly(dimethyl siloxane) / poly(ethyl methyl siloxane) blend in simple shear flow using rheo-SALS (small angle light scattering). Data are collected in both the flow/gradient and flow/vorticity planes. We find that for this model binary blend, exhibiting upper critical solution temperature behavior, shear suppresses the large pre-transitional concentration fluctuations and eventually yields homogenization. The simple modified Cahn-Hilliard-Cook phenomenological model of Lai and Fuller (J. Polym. Sci. Part B: Polym. Phys. 1994, 32, 2461) describes semi-quantitatively the time evolution of the structure factor and orientation angle well, supporting the experimental observations of enhanced orientation with flow. In the phase separated region, when the late stages of spinodal decomposition are reached, the shear-induced anisotropic distortion of the spinodal ring, orienting in the flow direction, and its relaxation upon flow cessation are probed and found to depend on the distance from the spinodal point. At intermediate times the spinodal ring gives rise to unstable butterfly patterns, as a consequence of the coupling of fluctuations with the flow, yielding elongated droplets at later times. The latter turn into streaks at higher rates, suggesting that the mechanism of shear-induced homogenization from the spinodal region, is analogous to that observed in blend solutions. A kinetic phase diagram indicating different microstructures at different temperatures and shear rates, is constructed. These results underline important similarities between binary polymer blends and polymer blend solutions and mark the important parameter ranges for controlling their rheology. Two-fluid demixing theory predictions of stress-induced turbidity of polystyrene solutions in dioctyl phthalateMario Minalea), Kurt F. Wissbrunb), Debora F. Massoudac) a) Seconda Università
degli Studi Napoli b) Consultant, One Euclid Avenue, 4E c) DuPont CR&D - Experimental Station, Bldg.
323/303B AbstractStress induced demixing of a polymer solution is predicted by a two fluid theory reformulated to be able to impose all the interface boundary conditions required. The theory has now been applied to the data on solutions of polystyrene in dioctylphthalate of Rangel-Nafaile et al. (1984) [Macromolecules 17, 1187-1195 (1984)] at one molecular weight at various temperatures, to additional unpublished data at various molecular weights, and to various published experiments in which there was evidence for phase separation. The dependence of elastic compliance on concentration was approximated by an equation which permitted the analytic differentiations and integrations required for the equations of the theory. The prediction of visual cloud point stresses at various temperatures were excellent within the concentration range over which the compliances had been fitted. The calculated demixing stresses were somewhat higher than those measured by extrapolation of photometric data to onset of turbidity, possibly because the onset correlates more closely to the occurrence of concentration fluctuations preceding demixing. The earlier kinetic theories that predict fluctuations but not demixing assumed a monotonic dependence of elasticity on concentration, contrary to theoretical and experimental results, and do not account for the light scattering observation of phase separation in shear flow. Full-tensor alignment criteria for sheared nematic polymersM. Gregory Forest and Ruhai Zhou Qi Wang AbstractThe shear problem for nematic polymers consists in characterizing all stable stationary orientational distributions, steady and unsteady, versus shear rate and material parameters. Continuum theory [cf. Leslie (1968), Ericksen (1960)] provides formulas for the shear response of liquid crystals in terms of a single viscosity ratio, the Leslie tumbling parameter lL. Kuzuu and Doi (1983, 1984) developed a weak-flow asymptotic analysis of kinetic theory, which gives a molecular basis for all continuum theory parameters. In this paper, we develop a mesoscopic extension of the Kuzuu-Doi method, applicable to any tensor model. Our method yields orientational and rheological features of nematic polymers in weak shear with explicit formulas, parametrized by the parameters of the second-moment tensor model. This provides an explicit mesoscopic theory solution to the problem posed by Marrucci and Greco (1993) of how orientational degeneracy of quiescent nematic equilibria breaks in weak shear, leaving a finite set of steady stationary states, whose number, type (in-plane, out-of-plane), stability, phase transitions, and rheological properties scale with parameters of the model. An intriguing feature to resolve is the multiple transitions associated with distinct steady distributions (logrolling, in-plane flow alignment, out-of-plane alignment), each with its analog of the Leslie criterion |lL| = 1. We illustrate our method and its physical predictions by solving the weak shear problem for the Doi quadratic closure model, whose material parameters are nematic concentration and molecular aspect ratio. The predictions are confirmed with numerical simulations of the model, and compared with experimental data in weak shear from the review article of Burghardt (1998). We further predict scaling properties due to changes in concentration and aspect ratio that are less readily available from experiments. Surface forces arising from adsorbed ionic copolymers with hydrophobic and hydrophilic segments in colloidal dispersionsY. K. Leong B. C. Ong, J. H. Tan A. V. M. Chandramalar, Y. Y. Lim AbstractThe effects of ionic copolymers with hydrophobic segments on the yield stress-pH behaviour of ZrO2 dispersions were evaluated. These polyelectrolytes were two alternating copolymers; diisobutylene-maleic acid (DIBMA) and a-methyl styrene-maleic acid (a-MSMA), and a random styrene-maleic acid (SMA) copolymer. At low concentrations, all three copolymers caused a much greater reduction in the maximum yield stress, ty max, (at the neutral charge condition) compared with hydrophilic lyacrylic acid and acrylic acid-ester polymers. The reduction in ty max was as much as 75%. The much larger reduction in ty max was attributed to a thicker steric layer formed by the ionic copolymers with hydrophobic segments. At higher concentrations, all three copolymers caused the ty max to increase. This was attributed to significant hydrophobic effects and attraction. The degree of hydrophobic segment aggregation at the closest point of interaction between particles is now higher. This also caused an overall increase in the entropy relative to the state when the particles are far apart as the degree of hydrogen bonding among water molecules is less when the hydrophobic segments are aggregated. Prediction of rheometrical and complex flows of entangled linear polymers using the DCR model with chain stretchPeter Wapperoma) Roland Keunings Giovanni Ianniruberto AbstractWe study the rheometrical and complex flow response of the double-convection-reptation (DCR) model with chain stretch proposed recently by Ianniruberto and Marrucci (2002) for entangled linear polymers. The single- and two-mode differential versions of the model are used, with parameter values identified by Ianniruberto and Marrucci (2002) for a nearly monodisperse polybutadiene solution. These authors found that the DCR model with stretch predicts well the rheometrical shear behavior of the fluid in the modest experimental range of deformation rates. Our calculations for the higher shear rates reached in the simulations of complex flow reveal anomalous or questionable behavior, namely shear-thickening over an intermediate range of shear rates and large chain stretch reached in fast shear flows. This behavior is shown to be shared by the original integro-differential DCR theory, of which the differential DCR model is actually a mathematical approximation. We also show that the original DCR theory with stretch predicts excessive shear-thinning at high shear rates, while its differential approximation remains stable for all shear rates. Using the Backward-tracking Lagrangian particle method [Wapperom et al. (2000)], we investigate the response of the differential DCR model in start-up flow through an axisymmetric contraction/expansion geometry. We compare the single- and two-mode model predictions (in terms of steady-state vortex structure, chain stretch, and overall pressure drop), and correlate these with the steady and start-up rheometrical responses in shear and extension. Significant chain stretch is predicted in the vicinity of the axis of symmetry and in thin boundary layers located at the constriction wall. As a result, the DCR predictions significantly depart from the stress-optical rule in these flow regions. Chain stretch also affects the flow kinematics, with the appearance of a large upstream steady-state vortex. Surprisingly, however, the predicted pressure drop is not much affected by these kinematical changes, and is qualitatively described by a simple inelastic, shear-thinning model. a) Author to whom all correspondence should be addressed. E-mail: wapperom@math.vt.edu Studies on the texture of nematic solutions of rodlike polymers. 3. Rheo-optical and rheological behavior in shearZhanjie Tan and Guy C. Berrya) AbstractThe texture in shear flow is discussed for nematic solutions of rodlike poly(1,4-phenylene terephthalamide), PPTA, reported here, and poly(1,4-phenylene-2,6-benzobisthiazole), PBZT, reported elsewhere. These are similar, with a sequence of scattering and visual features that develop with time, terminating at a level characteristic of the shear rate in steady state. With increasing shear rate, steady-state flow reveals sequentially a diffuse scattering with a turbid appearance, diffuse scattering with an opalescent appearance, a broad elliptical scattering along the radial direction with poorly-defined striations, a sharp scattering along the radial direction with well-defined striations along the flow, and a clear, highly birefringent sample, with little scattering. These same features are seen, in the same sequence in time, in transient behavior leading to steady-state. This behavior is attributed to the development of striations with twist distortions alternating in angle relative to the flow, and essentially in the sample plane in the fast steady-state flow, reflecting the lower free energy of that distortion in comparison with bend and splay distortions, especially near the parallel plates of the rheometer. The deterioration of this texture at slower flows is associated with increasing distortions out of the sample plane, leading to an essentially chaotic spatial distribution of the order tensor at a slow flow. Rupture of entangled polymeric liquids in elongational flowYogesh M. Joshi and Morton M. Denna) AbstractPolymer melts and concentrated solutions rupture at high rates of elongation in a manner that is reminiscent of the cohesive failure of solids. We propose a simple molecular picture of rupture of a polymer filament, in which catastrophic failure occurs when the frictional force on an entangled chain can no longer balance the tension in the chain. The model, which is fully predictive and contains no adjustable parameters, captures the rupture characteristics of the available data sets and agrees quantitatively with critical stress - critical strain data and the dependence of critical strain on Weissenberg number. a) Corresponding author. E-mail: denn@ccny.cuny.edu Influence of weak elasticity of dispersed phase on droplet behavior in sheared polybutadiene/poly(dimethyl siloxane) blendsWanchai Lerdwijitjaruda), Ronald G. Larsonb,c), Anuvat Sirivata), and Michael J. Solomonb) a) Petroleum and Petrochemical College b) Department of Chemical Engineering AbstractThe contribution of weak droplet-phase elasticity is investigated for blends of polybutadiene in poly(dimethyl siloxane) in a simple shearing flow with droplet-phase Weissenberg number, Wid, up to around unity. The elasticity of the polybutadiene dispersed phase is varied by adding various amounts of high-molecular-weight polybutadiene into low-molecular-weight polybutadiene Newtonian fluid. To isolate the contribution of elasticity, the experiments are conducted at fixed viscosity ratio by varying the experimental temperature to counteract the small effect of high-molecular weight polymer on droplet viscosity. Droplet deformation and relaxation are measured using an optical flow cell mounted on an optical microscope. As the droplet-phase elasticity increases, the steady-state shape deformation at fixed capillary number, Ca, decreases and the critical capillary number for droplet breakup increases. For a 20%-dispersed phase blend, the steady-state capillary number calculated from the volume-averaged droplet diameter increases with increasing droplet-phase elasticity, but is smaller than for an isolated droplet, suggesting that coalescence has little effect on droplet size in these experiments. However in startup of shear flow, the elasticity of the droplet does not affect the droplet shape, either during the startup of shear flow or during the relaxation process after the startup of shear flow for ratios of Wid/Ca up to 0.033. c) Corresponding author. Tel.: 734 936-0772; Fax: 734 763-0459; E-mail: rlarson@umich.edu Effect of surfaces on the static distribution of orientations in suspensions of rod-like particlesRaffy Mor and Moshe Gottlieba) Lisa A. Mondy Alan L. Graham AbstractThe effect of fiber concentration (nL3), fiber length (L), and cylindrical container walls on the static orientation state of a suspension of rod-like particles is examined with computer simulation. The orientation distributions are determined for both confined and unbounded suspensions of otherwise randomly distributed and randomly oriented, non-Brownian, rigid rods. Experimental determination of the distribution of orientations in a suspension confined to a cylindrical vessel is used to validate the results of our computer simulation. For unbounded systems, the simulations are in agreement with theoretical predictions for the concentration at which a departure from isotropic configuration is expected. For systems confined into finite-sized cylinders, the orientation of the rods is not completely isotropic, even when the concentration of particles is very low and the size of the container relatively large (7 times the size of the suspended-rod length). A linear dependence of the anisotropy on the concentration up to the highest concentration examined (nL3 = 76) is found. Finally, we determine that over a large range of concentrations and rod sizes the effect of solid surfaces and free surfaces is confined to a distance of half rod-length from the bounding surfaces. a) Author to whom correspondence should be addressed. E-mail: moshe@inca.bgu.ac.il Extensional stress growth and stress relaxation in entangled polymer solutionsP. K. Bhattacharjeea), D. A. Nguyena), G. H. McKinleyb), and T. Sridhara) a) Monash University b) Massachusetts Institute of Technology AbstractWe report an evaluation of the double constraint release model with chain stretch (DCR-CS) suggested by Ianniruberto and Marrucci [J. Rheol. 45 (2001)], in predicting the transient stress growth and stress relaxation behaviour of two well-characterised entangled polymer solutions undergoing homogeneous uniaxial extensional flow. The experiments are conducted using a filament stretching rheometer. The DCR-CS model belongs to a family of simplified single-segment models that incorporate constraint release, double reptation and segmental stretching into the basic reptation mechanism proposed in the original Doi-Edwards-theory and seeks to extend the predictive capacity of the theory to more complex flow fields. We show that the single-mode DCR-CS differential model performs well in predicting the transient extensional stress growth and steady-state extensional viscosity over a range of stretch rates. The model also predicts the observed stress relaxation following cessation of stretching satisfactorily. We further show that the model predicts shear-thickening even in steady shear flow. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |