Abstract
The data set of steady and transient shear data reported by Santangelo and Roland Journal of Rheology 45: 583–594, (2001) in the nonlinear range of shear rates of an unentangled polystyrene melt PS13K with a molar mass of 13.7 kDa is analysed by using the single integral constitutive equation approach developed by Narimissa and Wagner Journal of Rheology 64:129–140, (2020) for elongational and shear flow of Rouse melts. We compare model predictions with the steady-state, stress growth, and stress relaxation data after start-up shear flows. In characterising the linear-viscoelastic relaxation behaviour, we consider that in the vicinity of the glass transition temperature, Rouse modes and glassy modes are inseparable, and we model the terminal regime of PS13K by effective Rouse modes. Excellent agreement is achieved between model predictions and shear viscosity data, and good agreement with first normal stress coefficient data. In particular, the shear viscosity data of PS13K as well as of two polystyrene melts with M = 10.5 kDa and M = 9.8 kDa investigated by Stratton Macromolecules 5 (3): 304–310, (1972) agree quantitatively with the universal mastercurve predicted by Narimissa and Wagner for unentangled melts, and approach a scaling of Wi−1/2at sufficiently high Weissenberg numbers Wi. Some deviations between model predictions and data are seen for stress growth and stress relaxation of shear stress and first normal stress difference, which may be attributed to limitations of the experimental data, and may also indicate limitations of the model due to the complex interactions of Rouse modes and glassy modes in the vicinity of the glass transition temperature.Graphical abstract
Highlights
The scarcity of reliable shear flow data of unentangled polymers in the nonlinear-viscoelastic regime has made the understanding and modelling of shear flow behaviour of unentangled polymers challenging
According to the coupling model (CM) of Ngai et al (1997), the glassy and Rouse modes cannot be separated in the vicinity of glass transition temperature as they are combined; the molecular units are densely packed together and the understanding of their interactions would require the solution of a “many-body” problem at different length scales and in several viscoelastic relaxation zones
The nonlinear shear rheology of unentangled polymer melts in the vicinity of the glass transition temperature is determined by an inseparable combination of Rouse and glassy modes (Ngai et al (Ngai et al 1987, Ngai et al 1997))
Summary
The scarcity of reliable shear flow data of unentangled polymers in the nonlinear-viscoelastic regime has made the understanding and modelling of shear flow behaviour of unentangled polymers challenging. Plazek et al (1993) showed the breakdown of the conventional Rouse model for low molecular weight polymers near the glass transition temperature when there is a stronger temperature dependence of the segmental relaxation time compared to the terminal relaxation time. Demonstrated that the shear viscosity data of two unentangled polystyrene melts investigated by Stratton (1972) are in nearly quantitative agreement with model prediction assuming only orientation of strands in shear flow with no stretch. The objective of this paper is to analyse the set of steady and transient data reported by Santangelo and Roland (2001) in the nonlinear range of shear rates of an unentangled PS melt (PS13K) by using the single integral constitutive equation approach developed by Narimissa and Wagner (2020) for Rouse melts.
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