Viscosity of polymers is key to their behavior in the molten state and thus to their processing. The well known equations of rheology giving the temperature, strain rate, frequency and molecular weight dependence of viscosity are the basic equations that theories must explain. This is what de Gennes and other theorists before him had tried to explain (among other properties of course).
In a paper that will be published very soon (J. Macro. Sci. Phys, issue 6, 2009) I show that the admitted view that molecular weight and temperature separate in the expression of viscosity is only an approximation that theoretical models should not therefore succeed to explain. Furthermore, the classical 3.4 exponent for the variation of Newtonian viscosity with molecular weight is shown to represent another curve fitting approximation of the effect of entanglements on the viscosity.
“Shear-Thinning”, the lowering of viscosity with an increase of shear rate, demarking the Newtonian regime, is a fundamental property of polymer melt. I review the use of scaling variable on log-log axes to describe shear-thinning, such as Vinogradov’s plots, and show the limitations of such an approach, which often leads to very wrong extrapolations and predictions when “unwinded”, and the results compared to reality. I also review, using statistical tools from regression analysis, the validity of the time temperature superposition principle, another fundamental concept of rheology, and demonstrate that the principle is not valid, even when a graphical fit “ looks good”.
The WLF equation (due to Williams Landel and Ferry in the sixties) describes well the temperature dependence of the horizontal shift factor, log aT. This well admitted equation is also critically reviewed and compared to other simple curvefitting equations which provide as good results, although offering a very different insight into the physics responsible for melt or rubber deformation. In particular, it can be shown that the interpretation of the shift factor in terms of the ratio of Newtonian viscosity is an approximation limited to a narrow temperature range. Same such approximation also applies to the ratio of the terminal times, calculated from plots of G’/w vs w in dynamic experiments. The vertical shift factor, log bT, is not equal to (T1 p1/Tp), as predicted by the temperature dependence of modulus, according to rubber elasticity. This is clearly coming out of accurate shifting done analytically, instead of graphically.
The concept of relaxation time and spectrum of relaxation times, another mammoth concept in rheology, is critically examined to show that it is fundamentally wrong to apply it directly to polymer melt deformation (unless it is accepted as a curvefitting tool, on the same basis that polynomials or Fourier series descnbe well any type of curves). In that context, it is shown that models such as the Rouse model, de Genne’s, Doi & Edwards’, and all their improved versions (for instance by Klein, Montfort, Graessley, Larson, Wagner, Marrucci, or MacLeich), that describe (well?) the molecular weight and temperature dependence of relaxation times, are necessarily limited in their description of melt deformation to the linear regime where the curvefitting power of such mathematical tools gives the impression of their success.
I suggest that these Pantheonic models are not capable (without an extreme demonstration of mathematical modeling skills, that looks more and more like an exercise of cover-up) to describe the non-linear regime, which is the only regime important to real life, i.e. to processors of plastic melts. In particular, the present understanding of shear-thinning, normal stresses and strain-hardening of polymer melts in terms of chain reptation / renewal deserves critical attention.
Forty years ago, the polymer field was dominated by chemists and physical chemists who understood linear visco-elasticity in terms of networks of dashpots and springs, but were puzzled by large amplitude strain rates and strain behavior, especially by the effect of strain. Their interest and success in describing rubber elasticity and swelling” molecularly” (under equilibrium conditions) in terms of Gaussian chains whose length could affinely be related to macroscopic strain, can be viewed as the birth mark of modem physics, "a la" de Gennes, but also, perhaps, the source of the mis-understanding of what entanglements are, and how their existence affect the melt deformation, in particular what entropic deformation means. I critically review the present classical understanding of the influence of entanglements on melt deformation, and expose its limitations.
Another model of melt deformation and of the influence of entanglements will be presented in a series of articles and blogs. This model elaborates a profound different understanding of the source of viscoelastic behavior and of rubber elasticity.
If you want to be emailed the following paper (1.44MB): “The Great Myths of Polymer Melt Rheology Fart I.pdf” insert your email address in the comments box for this blog. You can also find it in issue #6 (2009) of the I. of Macromolecular Physics.
Part II of the Great Myths deals with transient and steady state, and the stability of the entanglement network, the subject of my next blog.
