Polymers as liquids

Previously, we treated polymers as solid. Now, we are focusing on polymers as liquids. Viscosity is a characteristic property of fluids; a less viscous fluid has low resistance to shear stress, while a highly viscous fluid has higher resistance to shear stress. We have intuition about this – water we would consider to have low viscosity, while something like toothpaste would be highly viscous. The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress. Imagine a sandwich with two plates on either side and a fluid in between. If you push one plate and keep the other static, what happens to the liquid? The plates do not simply slide past the fluid – but rather the liquid is “stuck” at the walls, and is “sheared” when you slide the plates past each other. There is some frictional force in the fluid. This is viscosity.

Figure12.7: laminar shearing of fluid

Source: Wikipedia: Viscocity

Ideal viscous fluids, i.e. Newtonian fluids, have a viscosity ($\eta$) that is independent of shear rate ($\dot{\gamma }$) such that this relationship between shear stress ($\tau$), viscosity, and shear rate would yield a constant value of viscosity no matter what shear is applied:

$$\tau =\eta \dot{\gamma }$$

Figure12.8: Plot of a Newtonian fluid

Source: Lauren Zarzar

Many liquids that consist of small molecules, like water for example, may not be “perfect” Newtonian fluids, but they come pretty close. When we consider polymeric fluids, which could be a polymer melt or a polymer solution, the fact that there are very large polymer molecules now impart significantly different properties to the fluid; most polymer melts are therefore non-Newtonian fluids.

If a fluid is non-Newtonian, then there clearly must be some dependence of the viscosity on the shear rate. There are two general possibilities for how the fluid might behave: either the material increases in viscosity with increasing shear rate, or the viscosity decreases with an increasing shear rate. These are called shear thickening or shear thinning fluids, respectively. A diagram that considers how the shear stress - shear rate curves for shear thinning and shear thickening polymers might look is shown in Figure 12.9. The slope of these shear stress – shear rate curves is called the apparent viscosity, ${\eta }_a$.

Figure12.9: Shear stress - shear rate curves for shear thinning, shear thickening and Newtonian fluids

Source: Lauren Zarzar

An example of a shear thickening material is Ooobleck (which is cornstarch in water) or wet sand. But actually most polymer melts and solutions are shear thinning. Ketchup is a great example of a shear thinning fluid; it will almost certainly never come out of the bottle in any reasonable time if you just turn it upside down, but if you give the bottle a good shake (=shear) suddenly it starts to flow!

PROBLEM

Which plot below shows a shear thinning fluid?

Click here for the answer.

ANSWER

Plot C.

The viscosity is just the slope of the shear stress – shear rate plot. A fluid that increases viscosity with increasing shear rate is shear thickening, while a fluid that decreases viscosity with increasing shear rate is shear thinning. Shear thinning is common in polymers.

Looking back at the plots of shear stress vs shear rate in Figure 12.9, we notice that while at higher shear rates, the apparent viscosity changes rapidly, at low shear rates, the viscosity can actually be relatively constant.  The constant apparent viscosity in the low-shear region is known as the zero shear viscosity, ${\eta }_0$.

The viscosity of polymer melts depends on a number of factors. An important factor is the molar mass. The plot below shows the $Log\left( {\eta }_0\right)$ vs $Log(degreeofpolymerization)$ for a range of different polymers.

Figure12.10: $\mathrm{Log}{\eta }_0$ vs $Log(degreeofpolymerization)$ for a range of different polymers.

Source: Lauren Zarzar (Redrawn from the data of G. C. Berry and T. G. Fox, Adv. Polym. Sci., 5, 261 (1968))

You’ll notice that viscosity increases with molecular weight (which is directly related to degree of polymerization) – by orders of magnitude. Now at first glance, given that the viscosity of the polymers increases so dramatically with molecular weight, we might think that high molecular weight polymers are orders of magnitude harder to process. Actually, because of shear thinning, it’s not as difficult as you might think. Which brings us to the question of why is a polymer shear thinning in the first place? Again, we come back to entanglements!  As you shear a polymer along a specific direction, the polymers slip past each other and there is some disentanglement and actually the polymer chains align in the direction of shear. This polymer alignment during shear actually is very important to the mechanical properties of the polymer products being manufactured because it can impart different mechanical properties along different axes of a material. For example, if you have ever tried ripping a plastic grocery bag along different directions, you’ll notice that in one direction it tears easily, while along the perpendicular direction it is much more difficult – and it is because of polymer alignment during shear imposed during the manufacturing of the bag itself.

Figure12.11: Ploymer alignment with no shear and under shear

Source: Lauren Zarzar

PROBLEM 2

Sample A and Sample B are the same type of linear polymer but different molar weight. You analyze the samples with SEC and obtained the chromatogram below. Which sample has higher viscosity?

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ANSWER 2

Sample A

Recall learning about SEC and how higher molecular weight polymers will elute faster than lower molecular weight polymers (all else equal). Thus, Sample A is the higher MW polymer and we would expect it to have the higher viscosity.