Jens Kromann Nielsen

Elongational Viscosity of Monodisperse and Bidisperse Polystyrene Melts

The start-up and steady uniaxial elongational viscosity have been measured for two monodisperse polystyrene melts with molecular weights of 52 and 103kg∕mole, and for three bidisperse polystyrene melts. The monodisperse melts show a maximum in the steady elongational viscosity vs. the elongational rate, ϵ, of about two times the limiting value of 3η0 expected for a Newtonian fluid, whereas the bidisperse melts have a maximum of up to a factor of seven times the Trouton limit of 3η0. The Wiest model which incorporates anisotropic drag and finite extensibility may be used to interpret the results in molecular terms.

Viscosity overshoot in the start-up of uniaxial elongation of low density polyethylene melts

The transient uniaxial elongational viscosity of BASF Lupolen 1840D and 3020D melts has been measured on a filament stretch rheometer up to Hencky strains of 6–7. The elongational viscosity of both melts was measured at 130°C within a broad range of elongational rates. At high elongation rates, an overshoot or maximum in the transient elongational viscosity followed by a steady viscosity was observed. The steady elongation viscosity was about 40%–50% less than the maximum at high strain rates. The steady elongational viscosity as a function of the elongation rate, ϵ, decreases approximately as ϵ−0.6 in both melts at high strain rates. The transient elongational viscosity, measured at a specific elongation rate at 170°C on the BASF Lupolen 3020D melt, did not follow the time temperature superposition principle based on linear viscoelasticity during the decrease in the transient elongational viscosity towards the steady state.

Stress relaxation of narrow molar mass distribution polystyrene following uniaxial extension

The stress in the startup of uniaxial elongational flow until steady state, followed by stress relaxation, has been measured for a narrow molar mass distribution polystyrene melt with a molecular weight of 145kg∕mol. The experiments are conducted on a filament stretching rheometer, where a closed loop control of the midfilament diameter ensures controlled uniaxial extension. The closed loop control algorithm is extended to apply to the stress relaxation part of the experiment. It ensures a constant midfilament diameter, by controlling the motion of the end plates. By dividing the measured stress with the theoretically predicted stress from the Doi and Edwards model during relaxation, the stretch factors corresponding to each imposed stretch rate are obtained. These stretch factors converge to a unique envelope and eventually converge to unity for long times for all measured elongational rates.

A constitutive analysis of transient and steady-state elongational viscosities of bidisperse polystyrene blends

The transient and steady-state elongational viscosity data of three bidisperse polystyrene blends were investigated recently by Nielsen et al. [J. Rheol. 50, 453–476 (2006)]. The blends contain a monodisperse high molar mass component (ML=390kg∕mol) in a matrix of a monodisperse small molar mass component (either MS=103kg∕mol or MS=52kg∕mol at two different weight fractions). The experimental data are analyzed in the framework of the molecular stress function model of Wagner et al. [J. Rheol. 49, 1317–1327 (2005)], which is based on the assumption of a strain-dependent tube diameter and the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37, 3934–3942 (2004)]. The dilution of the long chains in the matrix of the short chains is identified as the origin of a drastic increase in the tube-diameter relaxation time of the long chains, leading to a large stretching potential of the long-chain component and an increasing steady-state elongational viscosity with increasing strain rate. In ad...

Observing the chain stretch transition in a highly entangled polyisoprene melt using transient extensional rheometry

We measure the viscoelastic properties of a highly entangled narrow molecular weight polyisoprene melt with approximately 280 entanglements per chain in steady and transient shear and in elongational flows. The storage and loss moduli of the melt are found to be well described by the Milner and McLeish model. The relaxation modulus G(t,γ) is measured using stress relaxation after a sudden shearing displacement and we experimentally determine the Rouse time τR by observing strain-time separability G(t,γ)=G(t)h(γ) for t>τR. The transient elongational properties are measured using three distinct instruments: the Sentmanat extensional rheometer (SER) universal testing platform from Xpansion Instruments, its counterpart, the extensional viscosity fixture (EVF) from TA Instruments, and a filament stretching rheometer (FSR). The kinematics obtained in each device is sensitive to the aspect ratio of the sample and care must be taken to achieve homogeneous deformation conditions. Especially for the SER and EVF instruments, a second aspect ratio associated with the rectangular cross-section of the sample is also important. We find that the initial growth in the tensile stress follows the prediction given by the Doi–Edwards reptation model for Deborah numbers based on the Rouse time less than about DeR=0.04. For DeR=0.04, the stress difference follows more or less the Doi–Edwards prediction in the limit of infinite stretch rates and, for DeR>0.04, the measured stresses are well above those that can be predicted by the basic Doi–Edwards model. When DeR>1, the stress difference also exceeds the linear viscoelastic prediction. In conjunction with this strain-hardening response, a stabilization is obtained whereby the limiting Hencky strain before sample rupture is markedly increased. We compare our observations in the regime 0.04 1 is interpreted as a signature of chain stretching for elongational deformation rates faster than the inverse Rouse time.We measure the viscoelastic properties of a highly entangled narrow molecular weight polyisoprene melt with approximately 280 entanglements per chain in steady and transient shear and in elongational flows. The storage and loss moduli of the melt are found to be well described by the Milner and McLeish model. The relaxation modulus G(t,γ) is measured using stress relaxation after a sudden shearing displacement and we experimentally determine the Rouse time τR by observing strain-time separability G(t,γ)=G(t)h(γ) for t>τR. The transient elongational properties are measured using three distinct instruments: the Sentmanat extensional rheometer (SER) universal testing platform from Xpansion Instruments, its counterpart, the extensional viscosity fixture (EVF) from TA Instruments, and a filament stretching rheometer (FSR). The kinematics obtained in each device is sensitive to the aspect ratio of the sample and care must be taken to achieve homogeneous deformation conditions. Especially for the SER and EVF ins...

Elongational dynamics of multiarm polystyrene

The startup of uni-axial elongational flow followed by stress relaxation and reversed bi-axial flow has been measured for a branched polystyrene melt with narrow molar mass distribution using the filament stretching rheometer. The branched polystyrene melt was a multiarm Aq−C−C−Aq pom-pom polystyrene with an estimated average number of arms of q=2.5. The molar mass of each arm is about 28kg∕mole with an overall molar mass of Mw=280kg∕mole. An integral molecular stress function constitutive formulation within the “interchain pressure” concept agrees reasonably well with the experiments.

Elongational Dynamics of Narrow Molar Mass Distribution Linear and Branched Polystyrene Melts

The startup of uni‐axial elongational flow followed by stress relaxation as well as reversed bi‐axial flow has been measured for narrow molar mass distribution (NMMD) linear (Mw = 145 kg/mole) and branched multi‐arm polystyrene melts, using the filament stretching rheometer. The branched polystyrene melt was a multiarm An‐C‐C‐An pom‐pom polystyrene with an estimated average number of arms of n = 2.5. The molar mass of each arm is about 28 kg/mole with an overall molar mass of Mw = 280 kg/mole. The principle of time‐strain separability fails completely to describe the dynamic elongation data. Similarly the Doi‐Edwards model with any ‘stretch evolution’ equation is not capable of capturing the reversed dynamic of NMMD melts. An integral molecular stress function constitutive formulation within the ‘interchain pressure’ concept, seem to agree with all experiments for linear melts.

Measurement of Reversed Extension Flow Using the Filament Stretch Rheometer

The measurement of material functions with reversed extension flow is demonstrated using the Filament Stretching Rheometer (FSR). This includes startup of uniaxial elongational flow (potentially until steady state) followed by biaxial squeezing, and large amplitude oscillatory elongation (LAOE). The latter is applicable on highly extensible elastomers, whereas in LAOE measurements on liquids (including polymer melts) the LAOE flow needs to be imposed upon a constant strain rate uniaxial elongation. The used Filament Stretching Rheometer allows measurements on polymeric fluids (including polymeric melts) from room temperature until 200 °C.