Nonlinear Viscoelasticity of Polymer Melts

Abstract

Large amplitude oscillatory shear has been employed to study the nonlinear viscoelastic properties of three polymer melts. The resins studied included a DuPont high-density polyethylene, a Union Carbide low-density polyethylene, and a Dow polystyrene. The equipment used consisted of a small-gap, concentric cylinder rheometer with a controlled-speed motor unit and a rack-pinion, oscillating drive mechanism. The torque was monitored by means of a torquemeter based on magnetic stress anisotropy in a steel tube and the strain was monitored by means of a displacement transducer. A signal proportional to the rate of strain was generated by integrating the strain with respect to time. Strain amplitudes up to 10 and frequencies between 0.5 and 30 sec−1 were employed. For purposes of material characterization, plots of stress versus rate-of-strain are employed. This is a closed stationary curve. Its “openness” is an indication of elasticity and its deviation from an elliptical shape is an indication of nonlinearity. Three material functions, obtainable from these curves, are defined and used for characterization. The first function is the amplitude ratio; the second function is related to the extent of the elastic component of the response, and the third one is a measure of nonlinearity. It was found that the extent of nonlinearity in the response is primarily a function of the strain amplitude rather than the frequency. The amplitude below which the response is practically linear depends strongly on the molecular structure. The response of the high-density polyethylene was practically linear up to a strain amplitude of 10.

Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials

“…For example, they can also be observed with the xanthan gum solution (Fig. 8c, 0 10 g = , -1 0.15 3.75 rad.s w = -) and have been observed for other material systems including a micelle solution (Ewoldt et al (2008)), a polystyrene solution (Jeyaseelan and Giacomin (2008)), molten polystyrene (Tee and Dealy (1975)), and a polymer melt in the absence of long-chain branching (Stadler et al (2008)). Some nonlinear viscoelastic constitutive models also show secondary loops, including a non-affine network model (Jeyaseelan and Giacomin (2008)) and a single mode Giesekus model (Ewoldt and McKinley (submitted in concert with this manuscript)).…”

“…frequency and amplitude { , 0 }. These two parameters define an experimental test space in which results can be compactly represented, which is now known as the Pipkin diagram (Pipkin (1972) Methods for analyzing LAOS include Lissajous curves (Philippoff (1966); Tee and Dealy (1975)), Fourier transform rheology (e.g. Wilhelm (2002)), Stress decomposition (Cho et al (2005); Ewoldt et al (2008); Yu et al (2009)), computation of viscoelastic moduli (Hyun et al (2002); Ewoldt et al (2008)), decomposition into characteristic waveforms (Klein et al (2007)), and analysis of parameters related to Fourier transform rheology (Debbaut and Burhin (2002); Hyun and Wilhelm (2009)).…”

On secondary loops in LAOS via self-intersection of Lissajous–Bowditch curves

“…The interpretation of secondary loops has, to date, been limited to the study of specific material examples, being related to physical microstructural features such as non-affine deformation (Jeyaseelan and Giacomin (2008)) and 3/13 the absence of long-chain branching in polymer melts (Stadler et al (2008)). However, such secondary loops have been observed for many different material systems including micellar solutions (Ewoldt et al (2008)), a polystyrene solution (Jeyaseelan and Giacomin (2008)), several molten polymers (Tee and Dealy (1975), Stadler et al (2008)), star-polymer networks (Rogers and Vlassopoulos (2009)), as well as Xanthan gum solutions and an invert-emulsion drilling fluid (see Ewoldt et al, Rheol Acta, accompanying manuscript). Nonlinear constitutive models can also show secondary loops, examples include a non-affine network model (Jeyaseelan and Giacomin (2008)), a tube-based model of entangled linear polymers (Leygue et al (2006); Stadler et al (2008)), and a single mode Giesekus model (demonstrated here).…”

Nonlinear Viscoelastic Behavior of Concentrated Xanthan Gum Systems in Large Amplitude Oscillatory Shear (LAOS) Flow Fields : Stress Waveform and Lissajous Pattern Analysis

“…Tee and Dealy [62] found that for molten thermoplastics at moderate frequencies, stress versus strain rate loops are more distinctive than stress versus strain loops. They have also elucidated that, for a purely Newtonian viscous fluid, the stress versus strain rate loop shows a straight line through the origin with the linear viscoelasticity having the effect of opening out the line into an inclined elliptical Lissajous pattern.…”

“…In this study, in order to characterize the nonlinear viscoelastic behavior of concentrated xanthan gum systems, we would like to rely on an old-fashioned intuitive way suggested in the earlier days when some pioneering works on LAOS rheology had begun to appear. In the middle of 1970's, Tee and Dealy [62] proposed a useful graphical method composed with three material functions, as demonstrated in Figure 8, to interpret the linear and nonlinear viscoelastic properties for several commercial resins. Even though these functions do not provide a complete characterization of the nonlinear properties of complex fluids, they supply the basis for a simple characterization method and have a merit to be computed directly from the data without the use of assumptions as to the nature of a material.…”