Molecular Stress Function (MSF) Theory: Development a New Strain Energy Function

Molecular stress function (MSF) theory is a successful development of Doi-Edwards (DE) model for prediction of strain hardening phenomena in extensional flows. This model includes a molecular stress function, f, into DE strain measure, SDE, using variable tube diameter assumption. In this regards, we investigated the original MSF model for long chain branched polymers of Wagner et al. [J. Rheol. 47(3):779-793, 2003]. This model supposed that the strain energy function of a deformed branched molecule is related to its backbone stretching and side chain compression. Indeed, when the strain rate goes up the inverse of Rouse time of the side chains, tR, the side chains maybe stretched during the deformation. On the other hand, in the case of hyper-branched molecules such as Cayley tree structure of LDPEs, considerable parts of side chains are pined at the both ends, and these segments can be stretched. In this study, a new strain energy function is proposed based on MSF framework with both backbone and side chain stretching. However these stretchings are different. Stretching of side chains is modeled by the interchain pressure concept of Marucci and Ianniruberto [Macromolecules 37: 3934–3942, 2004]. Finally, we compare the strain measure of these two hypothesizes (Side chain compression and side chain stretching) in wide range of extensional rates.