1. Origin of strain hardening in melt extension Shi-Qing Wang, University of Akron, DMR 1105135 Polymer melts with long chain branching show “strain hardening” (as shown in Fig. 1) upon startup extension, i.e., monotonic stress increase over time above the transient zero-rate viscosity curve whereas their response to startup shear is opposite, thus known as strain softening. Dendritic polyisoprene (from Prof. Avgeropoulos) is studied to show that the different responses to extension and shear is due to an inherent difference in the geometry: during extension the load bearing surface shrinks continuously whereas simple shear involves a constant surface area. In other words, the physical processes are the similar. Moreover, the mechanical response of a LCB polymer to extension is not uniquely different from the same polymer with linear chain architecture. Whether the "strain hardening" shows up due to the geometric areal shrinkage depends on the process of yielding through chain disentanglement. Because of LCB, yielding through chain disentanglement is postponed to high strains. This amplifies the geometric difference, resulting in the stark contrast between shear and extension. LCB also suppress elastic yielding after step extension as shown in Fig. 2. In other words, unlike the linear polyisoprene melt that breaks up some 100 s after step extension involving a stretching ratio of = 2.7, the dendritic PI does not break apart even for a stretching ratio of = 6.7. In summary, our clarification of the physics associated with "strain hardening" provides a new guideline for molecular design of polymeric materials for optimized processing and better properties. Caption of Figure 1: The transient viscosity  + E of the dendritic polyisoprene (d- PI) at seven different applied Hencky rates as a function of time, all above that obtained in the zero-rate limit  + E0. Caption of Figure 2: The relaxing engineering stress  engr of a linear polyisoprene and the d-PI melt, plotted respectively as a function of time after step extension involving stretching ratios of = 2.7 and 6.7 respectively. Figure 1 Figure 2

2. Our findings are far reaching because they clarify textbook level misunderstanding of the extensional deformation behavior of polymeric materials. In other words, the textbook (cf. Fig. 3) contains a misleading description about the viscoelastic behavior of a leading class of polymeric materials, i.e., low-density polyethylene. Because our results are of broad interest to the whole polymer physics community, the PI gave a talk at the 2012 Gordon Research Conference on Polymer Physics. Moreover, the transformative message of our observations has attracted world-wide attention: To disseminate our understanding, we posted a recorded seminar summarizing the status of the rapidly transforming field of nonlinear polymer dynamics. Since its posting in March 2012 on our homepage, with the video files being available both at the UA server and at Youtube, it has been viewed at http://www.youtube.com/watch?v=ffbhZYlkWcA for over 500 times. Figure 3 The textbook information on steady-state elongational viscosity as a function of the Hencky rate, from Fig. 13-22 on p. 399 of The viscoelasticity properties of polymers (J. D. Ferry, Wiley 1980) Figure 4 Evidence of significant elastic deformation right before the specimen breakup to indicate that there is no establishment of fully developed flow state to afford any measurement of steady elongational viscosity as presented in Fig. 3. Origin of strain hardening in melt extension Shi-Qing Wang, University of Akron, DMR 1105135