Behavior of concentrated polystyrene solutions in large‐amplitude oscillating shear fields

Abstract

SynopsisThe limits of linear viscoelastic behavior of polystyrene solutions have been investigated by subjecting them to large-amplitude oscillatory strains, yo. At strains less than one we find that the dynamic storage modulus G'(o,yo) and the dynamic loss modulus G"(o,yo) decrease quadratically with increasing strain. As a measure of the size of the linear viscoelastic region, we have determined the strain a t which the moduli have fallen 5% below their zero-strain values. This strain, ~N L , is found to be independent of frequency o at high frequencies but to increase with decreasing frequency at low frequencies. Behavior of this type is in qualitative agreement with the recent constitutive equation developed by Doi and Edwards. More specifically, we find that the rate of decrease of the storage modulus with increasing strain is quite similar to that predicted by their theory, but that the rate of decrease of the loss modulus is much slower. Some possible approaches for improving the agreement with experimental results are suggested. In the course of our work an interesting hydrodynamic instability was observed. The nature of this instability and methods to avoid it are discussed. RHEOLOGY OF HIGH-MOLECULAR-WEIGHT CONCENTRATED POLYMER SOLUTIONSThe viscoelastic behavior of high-molecular-weight polymers is markedly different from that of low-molecular-weight materials. The distinguishing features are: (i) the appearance of a rubbery plateau in the dynamic modulus with a value Gg independent of molecular weight M, (ii) a change in the molecular weight dependence of the steady-state compliance J: from proportional to M to independent of M, (iii) a low-frequency viscosity 70 proportional to M3.4 instead of M , and (iv) the appearance of a large number of nonlinear phenomena phenomena not found in low-molecular-weight materials.3It is generally agreed that these observations are due to entanglement effects.

A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)

“…Because of the quasi linear nature of the UCM model, the oscillatory first normal stress difference can be uniquely divided into three terms, given by Eq. (20). On the contrary, the simulation results of Giesekus model (Fig.…”

“…Experiments were limited by the dynamic range of the torque transducer in the rheometers commonly used at this time, nonetheless, various analysis methods were already suggested at this early stage, especially stress shape analysis and Fourier transform analysis. Pearson and Rocherfort [20] and Helfand and Pearson [21] calculated nonlinear parameters under LAOS utilizing the Doi-Edwards model for polymer dynamics. They investigated the limits of linear viscoelastic behavior of concentrated polystyrene solutions.…”

“…Rochefort [20] (see Appendix D). As the molecular weight increases, the transition to terminal behavior shifts to lower frequencies (analogous to the familiar frequency shift observed in conventional linear viscoelastic properties) and the peak becomes increasingly broad.…”

Tube theory of entangled polymer dynamics

“…This full set of self-consistent equations is clearly very di cult to solve even numerically, and few serious studies have attempted this level of treatment, but they have been shown to perform better in large amplitude oscillatory¯ows than the IAA [321,322]. A di culty is that, even at this level, chain stretch (de®ned as a¯ow-induced increase in the primitive path length) is not taken into account.…”

Flow field visualization of entangled polybutadiene solutions under nonlinear viscoelastic flow conditions

“…As an explanation for these phenomena, attributed both shear banding and non-quiescent relaxation to "elastic yielding", which is a microscopic failure occurring in the bulk of the material under a large and abrupt strain. If such findings are universally valid, not only would the reptation models become unsupported by rheometric measurements, but also a significant amount of nonlinear rheology in polymer melts and solutions [Zapas and Craft (1965); Osaki et al (1981Osaki et al ( , 1993Osaki et al ( , 2000; Pearson and Rochefort (1982); Venerus and Kahvand (1994); Reimers and Dealy (1996); Hyun et al (1999); Sui and McKenna (2007)] would need to be reevaluated. Hence, the purpose of the present collaborative research has been to assess the validity of the results reported by Wang and co-workers.…”