Shear and Extensional Rheology of Polystyrene Melts and Solutions with the Same Number of Entanglements

Abstract

We investigate the nonlinear shear and uniaxial extensional rheology of entangled polystyrene (PS) melts and solutions having the same number Z of entanglements, hence identical linear viscoelasticity. While experiments in extensional flows confirm that PS melts and solutions with the same Z behave differently, respective transient and steady data in simple shear over the largest possible range of rheometric shear rates (corresponding to Rouse−Weissenberg numbers from 0.01 to 40) demonstrate that melts and solutions exhibit identical behavior. Whereas the differences between melts and solutions in elongational flows are due to alignmentinduced friction reduction (more effective in melts than in solutions), in shear flows they disappear since the rotational component reduces monomeric alignment substantially. Recent molecular dynamics simulations of entangled polymers show that rotation induces molecular tumbling at high shear rates, and here a tube-based model involving tumbling effects is proposed in order to describe the response in shear. The main outcome is that tumbling can explain transient stress undershoot (following the overshoot) at high shear rates. Hence, the combination of tumbling in shear and friction reduction in extension successfully describes the whole range of experimental data and provides the basic ingredient for the development of molecular constitutive equations.

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

“…Moreover, both shear/dynamic and extensional data exhibit thinning with increased rates. In the former case, the shear data follow a scaling law with thinning slope of -0.7 for both generations, which is smaller than the usual slope of about -0.82 which has been reported for entangled linear polymers [30,16]. On the other hand, the extensional data exhibit a thinning slope of -0.5, again for both G3 and G4, with the latter having higher values (see also Figures 3 and 4).…”

“…The transient shear viscosity exhibits well-known features of polymers [30]. In particular, it greatly depends on the imposed shear rate.…”

“…Uniaxial extension: The extensional stress measurements were performed with a filament stretching rheometer (FSR) [27,38,39] (CPP) fixture in order to avoid experimental artefacts associated with edge fracture. The particular CPP used is described in detail in Costanzo et al [30]. All tools used were made of stainless steel.…”

“…More specifically, the development of the filament stretching rheometer (FSR) allows the measurement of true stress in well-controlled uniaxial extension at large Hencky strains and that of stress relaxation upon cessation of extension [25,27]. At the same time, the implementation of cone-partitioned plate (CPP) in rotational strain-controlled rheometry offers the ability to measure reliably transient shear stress over the largest possible range of shear rates [28][29][30]. It is therefore essential to combine novel macromolecular structures of relevance in processing and state of the art experimental tools in order to provide useful, reliable experimental information in different flow histories, towards a better understanding of the behaviour of complex polymers and a critical assessment of predictive models and their eventual improvement.…”

Stress Undershoot of Entangled Polymers under Fast Startup Shear Flows in Primitive Chain Network Simulations

“…Frequently, after the overshoot the stress monotonically decreases to the steadystate value. However, some experimental data 7,8) at very high shear rates show a stress undershoot following the overshoot, just before reaching the steady state. In the past, such undershoot was not taken too seriously because it could not be clearly distinguished from possible experimental artifacts.…”