Linear and nonlinear viscoelastic properties of bidisperse linear polymers: Mixing law and tube pressure effect

In this manuscript, we extend the tube-based model that we developed for predicting the linear viscoelasticity of entangled polymers [van Ruymbeke et al., J. Non-Newtonian Fluid Mech. 128, 7-22 (2005)] to the prediction of the extensional rheology of monodisperse and bidisperse linear polymers and confront the results to experimental data. This model is based on the concepts of stretch-orientation separability [McLeish and Larson, J. Rheol. 42, 81-110 (1998)] and inter-chain pressure [Marrucci and Ianniruberto, Macromolecules 37, 3934-3942 (2004)]. In order to deal with polydisperse samples, a new mixing law is proposed. As it does not require knowledge of the full linear relaxation spectrum, the proposed model is a powerful predictive tool. Very good agreement is found between theoretical and experimental results. For bidisperse samples, the individual contribution of each component is determined, and it is shown that only few percent of long chains are enough to generate the strong strain hardening observed in the experimental data. Last, we discuss the value of the tube diameter relaxation time. For monodisperse samples, this parameter is found to scale with M-2. However, for bidisperse samples, as it was already observed by Wagner et al. [J. Rheol. 52, 67-86 (2008)], the tube diameter relaxation time of the long component must be rescaled, which is contrary to the inter-chain pressure model and opens several new questions. (c) 2010 The Society of Rheology. [DOI:10.1122/1.3478316]