Towards more realistic kinetic models for concentrated solutions and melts

Abstract

In this paper we consider modifications of two kinetic models for concentrated polymer solutions and melts: the simplified uniform (SU) version of a thermodynamically admissible single segment reptation model by Öttinger [A thermodynamically admissible reptation model for fast flows of entangled polymers. J. Rheol. 43 (1999) 1461–1493] and Fang et al. [A thermodynamically admissible reptation model for fast flows of entangled polymers. II. Model predictions for shear and extensional flows, J. Rheol. 44 (2000) 1293–1317] and the encapsulated FENE dumbbell (EFD) model [R.B. Bird, J.R. Deaguiar, An encapsulated dumbbell model for concentrated polymer solutions and melts. I. Theoretical developments and constitutive equation, J. Non-Newtonian Fluid Mech. 13 (1983) 149–160]. The two modified models incorporate double reptation, convective constraint release (CCR), and chain stretching. In the modified SU model, orientation and stretching are still modelled in a decoupled way, while in the case of the modified EFD model they are modelled in a coupled way. Quantitative comparisons are made for a number of shear and extensional flows between the predictions of the modified EFD model with those of the SU model, the modified SU model, the original EFD model and a recent simple constitutive model by Marrucci and Ianniruberto [Flow-induced orientation and stretching of entangled polymers, Phil. Trans. R. Soc. Lond. A 361 (2003) 677–687]. The models’ predictions are also tested against experimental data for entangled polystyrene solutions. For steady simple shear flow it is shown that good quantitative agreement with experimental data using physically realistic parameters requires that orientation and stretching be modelled in a coupled way. In particular, predictions with the modified SU model of the steady shear viscometric functions are only accurate with a maximum chain stretch ratio parameter an order of magnitude smaller than is required by the polymer chemistry. The use of the modified EFD model with realistic model parameters leads to better overall fits in all cases with the experimental data than either variant of the SU model or the Marrucci–Ianniruberto model.