Annual production of polyolefins with multiple long side branches per molecule is close to 4 billion pounds in the United States alone. These polymers are inexpensively synthesized, but the best procedures for shaping them into useful articles are rarely obvious. The complexity comes from a lack of fundamental understanding of how long side branches affect polyolefin flow properties, and how flow properties in-turn affect polymer processibility. Thus, even two polymers that appear similar from standard shear rheology tests, can perform quite differently in a real process. The objective of the proposed research is two-fold. First, to determine the fundamental effect of long chain branching on relaxation dynamics of flexible polymers with multiple entangled side branches. Second, to develop a clearer understanding of why LCB polymer rheological properties are often very different in shear and extensional flows. Specifically, the effect of branching (e.g. number per polymer chain, length, and distribution of branches along the chain contour) on nonlinear shear and extensional flow properties of model multi-arm polymers will be addressed. This research will combine polymer synthesis, purification and characterization procedures, nonlinear shear and extensional flow rheometry, and some novel flow birefringence measurements to provide new insights into the dynamics of polymers. %%% Results from this study will help guide emerging theories for multi-arm polymer dynamics and should also help motivate constitutive equations capable of describing branched polymer behavior in various elongation and mixed flows common in polymer processing.