Creep Measurements Confirm Steady Flow after Stress Maximum in Extension of Branched Polymer Melts

Abstract

We provide conclusive evidence of nonmonotonic mechanical behavior in the extension of long-chain branched polymer melts. While nonmonotonic behavior is known to occur for solids, for the case of polymeric melts, this phenomenon is in direct contrast with current theoretical models. We rule out the possibility of the overshoot being an experimental artifact by confirming the existence of steady flow after a maximum in the ratio of stress to strain rate versus strain under both constant stress and constant strainrate kinematics. This observation indicates the omission of important physics from current models for these industrially important materials, whose processing properties depend on extreme molecular extension. Introduction.-Predicting the viscoelastic properties of branched polymer melts from their molecular architecture remains one of the great challenges in polymer physics [1][2][3]. One outstanding problem is the lack of consensus of the evolution of stress in the start-up of constant strain-rate extensional flow. While one laboratory [4] has reported a maximum in stress followed by a steady value, other laboratories have legitimately questioned the maximum [5][6][7] and even challenged the existence of steady extensional flow [8,9]. The molecular origin of a stress maximum is unclear inasmuch as nonlinear models [10] specifically designed for branched polymers show a monotonic increase of stress in constant strain-rate extension.Here, we report observations of extensional flow not with a constant strain rate but with a constant stress (creep). In addition to probing the transient behavior, the creep protocol also allows the measurement of the ultimate steady extensional viscosity. The uniqueness of the steady extensional viscosity independent of the start-up protocol is apparently not a settled matter as evidenced by the reporting of two viscosities at the same steady strain rate [11,12]. The experiments are compared to the small strain predictions [13,14] to illustrate the departure from linear material behavior.A major challenge in extensional rheometry is that large deformations are needed to approach a steady flow state. Deformations are measured in units of Hencky strain defined as ¼ ln, where ¼ L=L 0 is the stretch ratio, L 0 is the initial length, and L is the final length of a given cylindrical shape. The strain rate _ is the time derivative of the Hencky strain. In the classical controlled deformation extensional experiment, a constant _ is imposed and the stress is monitored as a function of time. Typically, Hencky strains larger than four are required to establish a steady tensile stress. However, in many extensional flow devices, sample inhomogeneity will prevent control of the kinematics

A new look at extensional rheology of low-density polyethylene

“…Figure 6 also shows that at fast strain rate, the extensional steadystate viscosity exhibits a power-law behavior with the viscosity scaling approximately asε −0.6 , which agrees with the observations reported in Ref. [11,13]. It should be noted that the identical nonlinear behavior is only observed at Hencky strain values bigger than 4 as shown in Figure 5(b), which cannot be measured by the EVF.…”

“…A maximum in the transient extensional stress of LDPE was observed by several groups [8,9,10]. Steady stress following the stress overshoot was reported firstly by Rasmussen et al [11] and has been experimentally confirmed by comparing the measurements from the filament stretching rheometer and the cross-slot extensional rheometer [12], as well as by comparing the constant stretch rate and constant stress (creep) experiments [13]. Several models have been developed [12,14,15] for the attempt to understand the physics behind the stress overshoot.…”

Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers

“…A stress maximum has been reported in extensional flow of branched polymers [173], analogous to the stress maximum in entangled linear polymers in transient shear flow. In the case of long chain branched polyethylene, for example, Hoyle et al [183] demonstrated and inferred a stress maximum followed by a steady state condition, by using both the FSR device and the cross-slot rheometer.…”

Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

“…Furthermore, we remark that the extensional data do not show a tendency to overlap the dynamic and shear data at low rates, as is normally expected. However, it is reported that for branched polymers the steady viscosity in uniaxial extension is constant at low stretch rate (overlaps with 3 *), then it exhibits extension thickening and after an overshoot it thins at higher rates [59]. Based on this, we conjecture that the data of Figure 7 are in the thinning regime past but close to the peak, and they are above the level of the zero-rate viscosity (not reached) which is expected to coincide with the zero-shear dynamic and shear viscosities, accounting for the Trouton ratio.…”