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We present unique nonlinear rheological data of well-defined symmetric Cayley-tree poly(methyl methacrylates) in shear and uniaxial extension. Earlier work has shown that their linear viscoelasticity is governed by the hierarchical relaxation of different generations, whereas the segments between branch points are responsible for their substantial strain hardening as compared to linear homopolymers of the same total molar mass at the same value of imposed stretch rate. Here, we extend that work in order to obtain further experimental evidence that will help understanding the molecular origin of the remarkable properties of these highly branched macromolecules. In particular, we address three questions pertinent to the specific molecular structure: (i) Is steady state attainable during uniaxial extension? (ii) What is the respective transient response in simple shear? and (iii) How does stress relax upon cessation of extension or shear? To accomplish our goal, we utilize state-of-the-art instrumentation, i.e., filament stretching rheometry and cone-partitioned plate shear rheometry for polymers with 3 and 4 generations, and complement it with state-of-the-art modeling predictions using the branch-on-branch (BoB) algorithm. The data indicate that the extensional viscosity reaches a steady state value, whose dependence on extensional rate is identical to that of entangled linear and other branched polymer melts. Nonlinear shear is characterized by transient stress overshoots and the validity of the Cox-Merz rule. Remarkably, nonlinear stress relaxation is much broader and slower in extension compared to shear. It is also slower at higher generation, and rateindependent for rates below the Rouse rate of the outer segment. For extension, the relaxation time is longer than that of the linear stress relaxation, suggesting a strong "elastic memory" of the material. These results are described by BoB semiquantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than three entanglements long, this is a very promising outcome that gives confidence in using BoB for understanding the key features. Moreover, the response of the segments between generations controls the rheology of the Cayley trees. Their substantial stretching in uniaxial extension appears responsible for strain hardening, whereas coupling of stretches of different parts of the polymer appears to be the origin of the slower subsequent relaxation of extensional stress. Concerning the latter effect, for which predictions are not available, it is hoped that the present experimental findings and proposed framework of analysis will motivate further developments in the direction of molecular constitutive models for branched and hyperbranched polymers. [ABSTRACT FROM AUTHOR]

Non-linear correlations are found between the melt strength and fundamental shear flow properties such as low frequency loss tangent, crossover frequency, and zero-shear-rate viscosity for a series of polypropylene (PP) melts. The very good non-linear correlations suggest rheotens as a reliable rheological test to characterize extensional rheology relevant to fabrication, despite its non-homogeneous and non-isothermal flow kinematics. The rheotens model of Doufas [J. Rheol. 50, 749-769 (2006)] with a modified Giesekus (MG) viscoelastic constitutive equation is expanded to the case of PP melts. A single set of molecular parameters per material predicts the rheotens force curves very well over a wide range of processing conditions. The rheotens model is proposed as a tool for determination of rheological parameters of constitutive equations applicable to the simulation of complex polymer processes. Molecular considerations and predictions of the rheotens model are extensively discussed. A multi-mode MG model predicts the non-linear steady shear data (shear and first normal stresses) very favorably satisfying linear viscoelasticity. The oscillatory shear data and model predictions satisfy both the Cox-Merz [J. Polym. Sci. 28, 619-621 (1958)] and Laun [J. Rheol. 30, 459-501 (1986)] rules. The model exhibits stable numerical behavior without singularities or turning points in the prediction of steady shear viscosity even at quite high shear rates (e.g., on the order of 20 000 s-1), problems that have been reported for other constitutive equations. [ABSTRACT FROM AUTHOR]

We have studied stress overshoot behavior in startup shear of four monodisperse polymer melts with a range of chain entanglement from Z=24 to 160 entanglement points per chain. In the elastic deformation regime defined by γτR>1, where τR is the Rouse relaxation time, (i) the peak shear stress σmax scales with the time tmax at the peak to -1/2 power, in contrast to an exponent of -1/4 in the viscoelastic regime (for γτR<1), (ii) σmax changes linearly with the elapsed strain at the stress peak γmax, which scales with the applied shear rate as γ1/3, (iii) a supermaster curve collapses time-dependent shear stress growth curves up to the stress maximum at all shear rates for all the four styrene-butadiene rubber samples. [ABSTRACT FROM AUTHOR]

A recent, nonlinear viscoelastic theory for predicting the thermomechanical response of glassy polymers has been shown to predict behaviors from enthalpy relaxation to temperature-dependent mechanical yield in various modes of deformation quite well. The foundation of this theory rests on a “material clock” that depends on the potential energy of the system. The molecular basis for the clock and the Rational Mechanics framework for the constitutive equation are briefly reviewed. The theory is then used to predict and explain much more complicated behavior of glassy polymers: the change in compressive yield stress during physical aging at different temperatures, the peculiar enthalpic response of glassy polymers previously compressed to different strains, “volumetric implosion” on samples subjected to tensile strains, and the dependence of the shift factor on aging time and applied stress. [ABSTRACT FROM AUTHOR]