Non-linear step strain of branched polymer melts

Pom-pom model by McLeish and Larson (Journal of Rheology 42(81-110), 1998) is a highly successful molecular theory for describing the rheology of long chain branched melts. However, there is a long-standing puzzle in step strain: how can a model that is intrinsically non-separable recover empirical strain-time separation? We investigate the Pom-pom model in step-strain, comparing the qualitatively different behaviour of the single mode integral and differential orientation. Despite this difference when both models are used in a multi-mode form, their behaviour is shown to be comparable. Although neither integral nor differential model can predict exact time-strain separability, both can create a region in which the approximation is a very good one before the longest stretch time has been reached. By transforming to a continuous spectrum we find under certain assumptions, a parameter sub-space where an analytic damping function can be derived. We survey a range of materials produced by two different synthesis routes; high pressure polymerised LDPEs and metallocene catalysed HDPEs. Extracting non-linear Pom-pom parameters from extensional data, we look for spectra that display time-strain separability. Despite the assumptions made in deriving the damping function, the parameter space can be successfully expanded to encompass a general long chain branched melt.