Simultaneous stress and birefringence measurements during uniaxial elongation of polystyrene melts with narrow molecular weight distribution

Tensile stress and flow-induced birefringence have been measured during uniaxial elongation at a constant strain rate of two polystyrene melts with narrow molecular weight distribution. For both melts, the stress- optical rule (SOR) is found to be fulfilled upto a critical stress of 2.7 MPa, independent of strain rate and temperature. Estimation of the Rouse times of the melts, from both the zero-shear viscosity and the dynamic-shear moduli at high frequency, shows that the violation of the SOR occurs when the strain rate multiplied by the Rouse time of the melt exceeds by approximately 3. The presented results indicate that in contrast to current predictions of molecular theories, the regime of extensional thinning observed by Bach et al. (2003) extends well beyond the onset of failure of the SOR, and therefore the onset of chain stretch in the non-Gaussian regime.

Simultaneous measurement of transient stress and flow birefringence in one-sided compression (biaxial extension) of a polymer melt

Summary Investigation of time dependent behaviour of a polystyrene melt is carried out with the aid of a new apparatus for biaxial extension. Use is made of the method of two impinging fluid streams guided by lubricated trumpet shaped metal walls. The flow birefringence is measured in the plane of symmetry and, at the same time, the force is measured which tends to separate the trumpets. The linear stress-optical relation turns out to be valid in this new flow geometry. An accurate value for the stress-optical coefficient can be determined from the relaxation experiments. The stress build-up as calculated from the optical measurements, is compared with the pertinent result of the theory of linear viscoelasticity. For the desired interconversion of dynamic moduli use is made of the approximation by Schwarzl and Struik. The steady state measurements are checked by the results of the non-linear model of Acierno et al.With 16 figures and 2 tables     

Fingerprinting the processing behavior of polyethylenes from transient extensional flow and peel experiments in the melt state

The flow curves of linear (linear-low and high density) and branched polyethylenes are known to differ significantly. At increasing shear rates, the linear polymers exhibit a surface melt fracture or sharkskin region that is followed by an unstable oscillating or stick-slip flow regime when a constant piston speed capillary rheometer is used. At even higher shear rates, gross melt fracture appears. Unlike their linear counterparts, branched polyethylenes rarely exhibit sharkskin melt fracture and although gross melt fracture appears at high shear rates there is no discontinuity in their flow curve. The various flow regimes of these two types of polyethylenes are examined by performing experiments in the melt state using a unique extensional rheometer (the SER by Xpansion Instruments) that is capable of performing accurate extensional flow and peel experiments at very high rates not previously realized. The peel strength curves of these linear and branched polyethylenes exhibit all of the distinct flow regimes exhibited in their respective flow curves, thereby providing a fingerprint of their melt flow behavior. Moreover, these extensional flow and peel results in the melt state provide insight into the origins and mechanisms by which these melt flow phenomena may occur with regard to rapid tensile stress growth, melt rupture, and adhesive failure at the polymer wall interface.     

An experimental evaluation of the behaviour of mono and polydisperse polystyrenes in Cross-Slot flow

The behaviour of a number of mono and polydisperse polystyrenes are probed experimentally in complex extensional flow within a Cross-Slot geometry using flow-induced birefringence. Polystyrenes with similar molecular weight (M _w) and increasing polydispersity (PD) illustrated the effect of PD on the principal stress difference (PSD) pattern in extensional flow. Monodisperse materials exhibited only slight asymmetry at moderate flowrates, although increased asymmetry and cusping was observed at high flowrates. The response of monodisperse materials of different M _w at various flowrates is presented and characterised by Weissenberg numbers for both chain stretch and orientation using a theory for linear entangled polymers. The comparison of stress profiles against Weissenberg number for each process is used to determine whether the PSD pattern observed is independent of M _w and elucidate which relaxation mechanism is dominant in the flow regimes probed. For monodisperse materials, at equivalent chain orientation Weissenberg number (We _τd), different molecular weight materials were seen to exhibit similar steady state PSD patterns independent of We _τR (chain stretch We). Whilst no obvious critical Weissenberg number (We) was found for the onset of increased asymmetry and cusping, it was found to occur in the “orientating flow without chain stretch” regime.     

Measuring device for precise evaluation of torsional creep and recovery data

An apparatus has been designed and built up to determine the shear creep compliance and viscosity with high accuracy in a wide range of temperature and time. The characteristic feature of this apparatus is the possibility to measure directly the recoverable compliance and to determine the steady state recoverable complianceJ _e . Disturbing instrumental forces are minimized by use of a magnetic bearing. The torque is applied inductively by a modified three phase asynchronous motor. The torsional angle is measured with a laser beam reflected from a mirror to an electro-optical measuring device. Sample thermostating is performed by radiation in a heating chamber, which allows observation of the specimen during measurement.First results of creep and creep recovery measurements are reported, which were carried out on a technical polystyrene above the glass rubbery transition.Dedicated to Prof. Dr. H. Janeschitz-Kriegl on the occasion of his 60th birthday.     

Determination of the molecular weight distribution of linear polymers by inversion of a blending law on complex viscosities

The method presented in this paper allows to calculate the molecular weight distribution (MWD) of linear homopolymer melts from the complex shear modulus data measured in a wide frequency domain. An empirical blending law on complex viscosities is first developed; as a consequence, the variations of the storage and loss modulus as a function of MWD are presented. This simulation demonstrates also the role of the shape of the MWD itself, and shows that one should not postulate a priori the shape of the MWD. An efficient numerical approach based on a Tikhonov regularization method with constraint is used to solve this ill-posed problem; the MWD is hence derived without any assumption on its shape. This method is first applied on simulated data to prove its numerical efficiency. Then the inversion method is applied on complex moduli data of various commercial polymers (polypropylene, polyethylene and polystyrene) and on an artificial mixture of polystyrene that have been presented in the literature. For amorphous polymers, the coupling of the terminal relaxation domains with the transition region at higher frequency leads to errors in the low molecular weight tail: one way to solve this problem is to cut off the experimental data at the high frequencies. This general method needs only a few physical parameters, namely the scaling law for the Newtonian viscosity η₀=f(M _w ) and the plateau modulus G _N ⁰, and leads to reasonable results with respect to the simplicity of the viscoelastic model used. Received: 27 October 1997 Accepted: 24 February 1998     

Deformation and orientation during shear and elongation of a polycarbonate/carbon nanotubes composite in the melt

In this study, we focused on the elongational rheology and the morphology of an electrically conductive polycarbonate/multiwalled carbon nanotubes (2 wt%) composite in the melt. In shear and melt elongation, the influence of the carbon nanotubes was large when the externally applied stress was small. Consequently, the elastic interactions resulting from the carbon nanotubes dominated in the low frequency range of the shear oscillations. The elongational viscosity of the composite was only moderately influenced by the addition of 2 wt% carbon nanotubes. Transmission electron microscopy investigations of the stretched composite showed that isolated carbon nanotubes were oriented in elongation. In recovery after melt elongation, the recovered stretch of the composite was much smaller than the recovered stretch of pure polycarbonate. This effect is caused by the carbon nanotubes network, which prohibited large extensions of the macromolecules and led to a yield stress of the composite.     

The nonlinear strain measure of polyisobutylene melt in general biaxial flow and its comparison to the Doi-Edwards model

The nonlinear strain measure of a polyisobutylene (PIB) melt as determined by analysis of uniaxial, planar, ellipsoidal, and equibiaxial extensions is compared to the predictions of the molecular model of Doi and Edwards. It is found that the universal strain function of the Doi-Edwards model is unable to predict the nonlinear behavior of this polymer melt in general extensional flow. The qualitative agreement between predictions and experimental data for the strain dependence of shear stress and first normal stress difference in shear flow that was considered as powerful evidence for the correctness of the Doi-Edwards model seems to be accidental. The exaggerated strain dependence of the model suggests a need to reconsider the assumptions concerning the chain retraction process.Presented at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.Dedicated to Professor F.R. Schwarzl on the occasion of his 65th birthday     

The effect of far field flow on a spherical crystal growth in the undercooled melt

The effect of convective flow on a spherical crystal growth in the undercooled melt with a moderate far field flow is studied. The asymptotic solution of the evolution of the interface of the spherical crystal growth is obtained by the matched asymptotic expansion method. The analytic result shows that the convective flow in the undercooled melt has a strong effect on the evolution of spherical crystal growth. The convective flow induced by the far field flow makes the interface of the growing spherical crystal enhance its growth velocity in the upstream direction of the far field flow and inhibit growth in the downstream direction, and the interface of the decaying spherical crystal further decay in the upstream direction and inhibit decay in the downstream direction. The maximum growth velocity of the interface of the spherical crystal influenced by the far field flow is obtained.     

Effect of the melt flow direction on the treeing process in polymeric insulation

This paper presents the results of a study of the effect of the residual mechanical stress formed in solid polymers at the stage of production on the initiation and growth of an electrical tree. It is shown that the time to tree initiation and the time to breakdown of polycarbonate samples can be determined from the results of investigation of treeing parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 85–94, January–February, 2009.     

Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow

An algorithm is derived for calculating flow-induced birefringence using a bead-spring model with and without excluded volume effects. The simulation results for the bead-spring model compare well with experimental results for stress and birefringence in extensional flows of dilute solutions of polystyrene molecular weight 2 million in a filament-stretching device in both “theta” and “good” solvents (Orr and Sridhar 1999; Sridhar et al. 2000). In a “good” solvent, both stress and birefringence rise much more rapidly with strain than in a “theta” solvent, making extensional rheology a very sensitive indicator of solvent quality. Received: 7 December 1999 Accepted: 23 May 2000     

Dynamic melt flow of nanocomposites based on poly-ɛ-caprolactam

 The dynamic flow behavior of polyamide-6 (PA-6) and a nanocomposite (PNC) based on it was studied. The latter resin contained 2 wt% of organoclay. The two materials were blended in proportions of 0, 25, 50, 75, and 100 wt% PNC. The dynamic shear rheological properties of well-dried specimens were measured under N₂ at T=240 °C, frequency ω=0.1–100 rad/s, and strains γ=10 and 40%. At constant T, γ, and ω the time sweeps resulted in significant increases of the shear moduli. The γ and ω scans showed a complex rheological behavior of all clay-containing specimens. At γ=10% the linear viscoelasticity was observed for all compositions only at ω>1 rad/s, while at γ=40% only for 0 and 25 wt% of PNC. However, the effect was moderate, namely decreasing G′ and G′′ (at ω=6.28 rad/s; γ=50%) by 15 and 7.5%, respectively. For compositions containing >25 wt% PNC two types of non-linearity were detected. At ω≤ω_c=1.4 ± 0.2 rad/s yield stress provided evidence of a 3-D structure. At ω > ω_c, G′ and G′′ were sensitive to shear history – the effect was reversible. From the frequency scans at ω > ω_c the zero-shear relative viscosity vs concentration plot was constructed. The initial slope gave the intrinsic viscosity from which the aspect ratio of organoclay particles, p=287 ± 9 was calculated, in agreement with the value calculated from the reduced permeability data, p=286. Received: 24 May 2001 Accepted: 27 August 2001     

The determination of a general time creep compliance relation of linear viscoelastic materials under constant load and its extension to nonlinear viscoelastic behavior for the Burger model

Linear viscoelastic materials yield a creep function which only depends on time if creep experiments are performed under constant stress ₀. In practice, this condition is very difficult to realize, and as a consequence, the experiments are performed under constant force. For small strains the difference between the conditions of constant stress and constant force is negligible. Otherwise, the decrease in cross-section has to be taken into account and leads to increasing stress in the course of time for creep experiments under constant load. The Boltzmann superposition principle is solved under the condition of constant load and for strains . The creep complicance C(t; ₀) defined by the ratio becomes, in principle, dependent on the initial stress ₀. As a consequence, a set of creep compliance curves cannot be approximated with a simple parameter fit. Already the application of the solution on the Burger model yields a creep compliance curve with all three creep ranges. Furthermore, the mathematical structure of the time creep compliance relation of the Burger model allows nonlinear viscoelastic extension via the introduction of the yield strength _max and a nonlinearity parameter n _l . The creep behavior of PBT and PC can be described in the range of long times up to initial stresses ₀, being 75% for PBT and 60% for PC of the yield stress _max with only two or one free fit parameter, respectively.     

Viscosity enhancement in the flow of hydrolysed poly(acrylamide) saline solutions around spheres: implications for enhanced oil recovery

We have studied dilute aqueous solutions of hydrolysed poly(acrylamide), in various ionic environments, in flow around single spheres and around two spheres aligned on the axis of flow. The spheres are held on flexible cantilevers, while the polymer solutions, or solvent, are drawn past at controlled flow rates. We estimate the specific viscosities of the various solutions as a function of the strain rate over strain rates encompassing both the shear thinning and extension thickening regimes. For flow of solutions without added salts around a single sphere, we observe shear thinning followed by a significant increase in the non-Newtonian viscosity with increasing strain rate. The shear thinning reduces the maximal extensional viscosities of the solutions, which has important implications regarding the effectiveness of hydrolysed poly(acrylamide) in oil field applications. For flow of polymer solutions around two axially aligned spheres, we observe a significant reduction in the non-Newtonian forces experienced by the downstream sphere in comparison to the upstream sphere. We consider that this is salient to the understanding of non-Newtonian viscosification in porous media flow.     

The shear viscosity dependence on concentration,molecular weight,and shear rate of polystyrene solutions

The solution viscosity of narrow molecular weight distribution polystyrene samples dissolved in toluene and trans-decalin was investigated. The effect of polymer concentration, molecular weight and shear rate on viscosity was determined. The molecular weights lay between 5 10⁴ and 24 10⁶ and the concentrations covered a range of values below and above the critical valuec ^*, at which the macromolecular coils begin to overlap. Flow curves were generated for the solutions studied by plotting log versus log . Different molecular weights were found to have the same viscosity in the non-Newtonian region of the flow curves and follow a straight line with a slope of – 0.83. A plot of log ₀ versus logM _w for 3 wt-% polystyrene in toluene showed a slope of approximately 3.4 in the high molecular weight regime. Increasing the shear rate resulted in a viscosity that was independent of molecular weight. The sloped (log)/d (logM _w ) was found to be zero for molecular weights at which the corresponding viscosities lay on the straight line in the power-law region.On the basis of a relation between _sp and the dimensionless productc · [], simple three-term equations were developed for polystyrene in toluene andt-decalin to correlate the zero-shear viscosity with the concentration and molecular weight. These are valid over a wide concentration range, but they are restricted to molar masses greater than approximately 20000. In the limit of high molecular weights the exponent ofM _w in the dominant term in the equations for both solvents is close to the value 3.4. That is, the correlation between _sp andc · [] results in a sloped(log _sp)/d(logc · []) of approximately 3.4/a at high values ofc · [] wherea is the Mark-Houwink constant. This slope of 3.4/a is also the power ofc in the plot of ₀ versusc at high concentrations. a Mark-Houwink constant - B ₁,B ₂,B _n constants - c concentration (g · cm^–3) - c ^* critical concentration (g · cm^–3) - K, K constants - K _H Huggins constant - M molecular weight - M _c critical molecular weight - M _n number-average molecular weight - M _w weight-average molecular weight - n sloped(log _sp)/d (logc · []) at highc · [] - PS polystyrene - T temperature (K) - shear rate (s^–1) - critical shear rate (s^–1) - viscosity (Pa · s) - ₀ zero-shear viscosity (Pa · s) - _s solvent viscosity (Pa · s) - _sp specific viscosity - [] intrinsic viscosity (cm³ · g^–1) - dynamic viscosity (Pa · s) - | ^*| complex dynamic viscosity (Pa · s) - angular frequency (rad/s) - density of polymer solution (g · cm^–3) - ₁₂ shear stress (Pa) Dedicated to Prof. Dr. J. Schurz on the occasion of his 60^th birthday.Excerpt from the dissertation of Reinhard Kniewske: Bedeutung der molekularen Parameter von Polymeren auf die viskoelastischen Eigenschaften in wäßrigen und nichtwäßrigen Medien, Technische Universität Braunschweig 1983.     

Viscosity enhancement in non-Newtonian flow of dilute aqueous polymer solutions through crystallographic and random porous media

We report results on the flow of dilute aqueous solutions of hydrolysed poly(acrylamide) (HPAA) through beds of spheres packed in simple cubic and body-centred cubic crystallographic arrays. Pressure drop measurements made across the arrays as a function of the flow rate have been used to estimate the specific viscosities of the HPAA solutions as a function of the superficial strain rate. It is found that greater non-Newtonian increases in the specific viscosity occur in the body-centred cubic array, which is thought to be due to the presence of trailing stagnation points, which are not present in the simple cubic array. Experiments have been performed using HPAA solutions in the presence of mono- and divalent cations at various concentrations and, for validity, have been compared with results obtained from a traditional randomly packed porous medium. In addition, a study of mechanical degradation of the polymer in flow through the crystallographic arrays has been carried out and reveals a greater rate of degradation in the body-centred array and also a significant increase in degradation with salt concentration.     

In situ observations of unusual drop deformation and wobbling in simple shear flow

Deformation and wobbling of a liquid drop immersed in a liquid matrix were studied under mild shear conditions for various viscosity ratios. In situ visualization experiments were conducted on a homemade transparent Couette cell incorporated to the Paar Physica MCR500 shear rheometer. The effect of drop or matrix elasticity was examined and was found to play a major role in both deformation and wobbling processes. Experimental results were compared to Jackson and Tucker (J Rheol 47:659–682, 2003), Maffettone and Minale (J Non-Newton Fluid Mech 78:227–241, 1998) and Yu and Bousmina (J Rheol 47:1011–1039, 2003) ellipsoidal models. It was found that the agreement between the Newtonian models and the experimental results required an increase in the drop viscosity. Such increment in viscosity was found to scale with the first normal stress difference.     

Effect of secondary flow on droplet distribution and deposition in horizontal annular pipe flow

In horizontal annular dispersed pipe flow the liquid film at the bottom is thicker and rougher than at the top of the pipe. A turbulent pipe flow experiencing a variation of roughness along the pipe wall will show a secondary flow. Such secondary flow, consisting of two counter-rotating cells in the cross-section of the tube, can change the distribution of the droplets inside the pipe and their deposition at the wall. Here, we compare the behaviour of the droplets (dispersed phase) with and without secondary flow, using large-eddy simulations. It is shown that the presence of secondary flow increases the droplet concentration in the core of the pipe and the droplet deposition-rate at the top of the pipe.     

The effect of molecular weight distribution on the elongational properties of linear polymers

The elongational properties of a series of six polypropylene and two polystyrene samples have been studied at constant rate of strain. A Wagner-type constitutive equation has been used to fit the experimental data, and the shape of the damping function has been correlated with the polydispersity index of the samples. As the memory function or relaxation function of linear viscoelasticity may be derived from the molecular-weight distribution using either molecular or phenomenological models, it is therefore possible to calculate the stress growth function of a linear polymer in elongation from its molecular-weight distribution.     

Dynamics of each component in miscible blends of polyisoprene and polyvinylethylene

The dynamics of the individual components in 1,4-polyisoprene/polyvinylethylene (PIP/PVE) miscible blends are studied using dynamic stress-optical measurements. While the homopolymers are thermorheologically simple and obey the stress-optic rule, the blends show failure of time-temperature superposition and complex stress-optic behavior. The way in which the stress-optic rule fails reveals the relaxation dynamics of each species. The dynamic modulus and complex birefringence coefficient are analyzed to infer the relaxation of each component. The entanglement molecular weight, M _e , and monomeric friction coefficient, ₀, of each species as a function of blend composition and temperature are determined from the contribution of each species to the dynamic modulus. The effect of blending on M _e of each component is small; however, its effect on ₀ of each species is dramatic. Blending strongly speeds the rate of relaxation of the high T _g component (PVE), while more modestly slowing the relaxation of the low T _g component (PIP). The dynamics of each species have different temperature dependencies in the blend, which leads to the failure of the superposition principle. Furthermore, both the difference between the friction coefficients of the two species and the difference in their temperature dependencies is greater in blends rich in the high T _g material (PVE).