Exploring the theoretical foundation for nonlinear entangled polymeric liquids Shi-Qing Wang, University of Akron, DMR 1105135.
Exploring the theoretical foundation
for nonlinear entangled polymeric liquids Shi-Qing Wang, University of Akron, DMR 1105135
The research aims to establish the conceptual and phenomenological foundation for the science of polymer dynamics under large deformation. Progress has been made in different directions. We achieved new understanding about melt extension behavior, i.e., identified mechanisms for different types of failure during and after melt stretching. We clarified the confusion in the literature about strain hardening of low-density polyethylene. We demonstrated that polymer entanglements respond differently to shear and extension.
In this highlight we focus on a in-depth examination of the foundation of the current paradigm. We carried out five different kinds of experiment to compare with the predictions of the tube model. We find that none of these new experiments is consistent with the physics contained in the tube model. Below we discuss the results from three such experiments.
Our current theoretical understanding based on the tube model is predicated on the ansatz that chain retraction would occur freely after Rouse time tR, which has the consequence as shown in Fig. 1: When the shear rate is much lower than the reciprocal Rouse time, 1/tR, i.e., WiR <<1, chains cannot get extended beyond its equilibrium size. The corresponding network could only deform non-affinely. However, Fig. 2 reveals full elastic recoil as long as the imposed strain has not resulted in yielding that occurs at gmax or t max>> tR, in contradiction to the picture of Fig. 1. The tube model visualizes barrier-free chain retraction that would accelerate stress relaxation relative to that in the linear response regime. But the completely overlapped data in Fig. 3 show identical stress relaxation up to a step strain of 0.7, in contrast to the tube model prediction that chain retraction would produce a 13 % difference between the stress relaxation curves. Finally, we performed a step shear using a low rate corresponding to WiR = 0.1 and explored how the state of chain entanglement would evolve after shear cessation by applying, after different waiting time tw, a sudden startup shear with a high rate and determining the resulting shear stress maximum smax. The non-monotonic blue squares in Fig. 4 indicate that the sheared sample becomes less entangled after step shear, which is unexpected by the tube model because it perceived no chain stretching, and thus no driving force to weaken the entanglement network during relaxation.
Fig. 2 Recoverable strain gr as a function of imposed g produced at different dimension-less rates WiR ranging from 0.1 to 3.5. Full elastic recovery corresponds to gr/g ~ 1.
Fig. 1 Depiction of the "shapes" of and relationship among three initially mutually entangled chains at different stages of shear.
Fig. 4 Probing the change in the state of entanglement during relaxation from a step strain imposed sufficiently slowly.
Fig. 3 Stress relaxation curves after two respective step strains of 0.1 and 0.7 for styrene-butadiene rubber with Mw=160 kg/mol.
Photo of the current group: after graduation of two Ph.D., two new Ph.D. bound graduate students (second and third from left) have joined the group, along with a visiting scientist (first left).