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

Abstract

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 (FSR) and cone-partitioned plate (CPP) 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 indicates that the extensional viscosity reaches a steady state value, whose dependence on extension 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 rate-independent 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 2 described by BoB semi-quantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than 3 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.

Polymer liquids fracture like solids

“…The steady extensional viscosity is obtained by dividing the stress by the strain rate. In this way, extensional viscosity functions have been obtained for a number of polymeric systems [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] . Specifically for a series of linear monodisperse polymers the steady stress has been shown to scale with the Rouse time based Weissenberg number 19 suggesting that that the major contribution to stress comes from stretching and alignment of the polymer molecules in the flow direction .…”

Hyper-branched structure—an active carrier for copolymer with surface activity, anti-polyelectrolyte effect and hydrophobic association in enhanced oil recovery

“…25 Among these are the hyper-branched polymers that performed several unique application prospects in the elds of controllable macroscopic materials, sustained release drug carriers, information storage materials, high-efficiency catalysts, nonlinear optical materials, nanomaterials, water treatment, separation membranes, rheology modiers, etc. [26][27][28][29] Meanwhile, the application to research in oil elds has also gradually become active. Wever D. A.…”

Development of protocols for investigating linear, branched and supramolecular polymers undergoing shear

“…(b) Normalized peak viscosity and (c) peak strain at the maximum viscosity as functions of the Weissenberg number based on the inverse terminal G -G crossover (see text). In (b) and (c), we show for comparison data with linear polystyrene LinPS185k, whereas the lines are drawn to guide the eye (see text) [180].…”

“…Since the issue of steady state is one of the challenges, we elucidate this further in gure 5.2 Results and discussion Figure 5.5: Net tensile stress for G3 (blue) and G4 (red) versus Hencky strain for dierent values of the imposed Hencky strain rate, at 180°C [180].…”

“…Data are shown for G3 (blue) and G4 (red). The dashed lines through the extensional data have a slope of -0.5 [180].…”