1 Introduction Considerable progress has been made in recent years towards understanding the rheological behavior of branched polymer liquids (McLeish and Milner 1999). A particularly important advance in this area is the pom- pom model of McLeish and Larson (Bishko et al. 1997; McLeish and Larson 1998). The development of the pom-pom model has been strongly influenced by the highly successful tube model for entangled linear poly- mers (Doi and Edwards 1986). In the pom-pom model, the complex topology of branched polymers is repre- sented by an idealized molecule composed of a backbone that has attached to each end an equal number of branches or arms. As the tube that confines the back- bone is deformed, the backbone is stretched until it is entropically more favorable for the ends (branch points) to withdrawal into the tube, a point that is reached when the backbone stretch equals the number of arms. The unphysically abrupt transition from a stretchable to a fixed-length backbone is smoothed somewhat by a re- cent modification to the model (Blackwell et al. 2000). The effects of multilevel branching structure and poly- dispersity on relaxation dynamics are taken into account by introducing multimode forms of the pom-pom equations (Inkson et al. 1999). The rheological constitutive equations derived from the pom-pom model, which have both an integral (IPM) and approximate differential (DPM) form, have been tested in a variety of flows. The IPM model is rather complicated; quantitative evaluations of this model have been limited to nearly monodisperse polymers with idealized structures. For example, Archer and Varshney (1998) considered a three-arm poly-butadiene melt in ORIGINAL CONTRIBUTION Rheol Acta (2003) 42: 123–131 DOI 10.1007/s00397-002-0263-x Chirag D. Chodankar Jay D. Schieber David C. Venerus Evaluation of rheological constitutive equations for branched polymers in step shear strain flows Received: 19 November 2001 Accepted: 6 May 2002 Published online: 10 July 2002 Ó Springer-Verlag 2002 C.D. Chodankar Æ J.D. Schieber D.C. Venerus (&) Department of Chemical and Environmen- tal Engineering, Center of Excellence in Polymer Science and Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA E-mail: venerus@iit.edu Abstract The pom-pom rheological constitutive equation for branched polymers proposed by McLeish and Larson is evaluated in step shear strain flows. Semianalytic expres- sions for the shear-stress relaxation modulus are derived for both the integral and approximate differen- tial versions of the pom-pom model. Predictions from the ther- modynamically motivated differen- tial pompon model of O ¨ ttinger are also examined. Single-mode integral and differential pom-pom models are found to give qualitatively different predictions, the former displays time–strain factorability after the backbone stretch is relaxed, while the latter does not. We also find that the differential pompon model gives quantitatively similar predictions to the integral pom-pom model in step strain flows. Predictions from multimode integral and differential pom-pom models are compared with experi- mental data on a widely character- ized, low-density polyethylene known as 1810H. The experiments strongly support time–strain factorability, while the multimode pom-pom model predictions show deviations from this behavior over the entire range of time that is experimentally accessible. Keywords Pom-pom model Æ Step-strain flow Æ Branched polymer