Introduction

This lab will begin with simple explanations of viscosity (internal friction) and the basics of its application in polymers. As a simple example, we provided an animation with two funnels, each containing a different fluid, for example, orange juice and maple syrup.

You can press the "GO" button to start the fluids in motion. This simple demonstration should serve as a solid display of the fundamental properties of two different types of fluids. After watching the animation, it is obvious that maple syrup flows at a much slower rate than orange juice. Polymer solutions can be compared in a similar way. Flow properties in polymer solutions depend almost entirely upon their molecular weight.

To demonstrate flow properties in general, the user will use what could be called the ‘dropping-ball method.’ In this method, a vessel is filled with a solvent, like water, in which a metal ball of known volume and mass is dropped into—the distance the ball travels over a time period t is measured. How long the ball takes to travel the distance for different solvents is a simple way to compare the levels of flow between materials. This little experiment will help to further illustrate flow properties, and is a little bit less scientific in its appearance. In this animation, simply pull the lever to drop the metal balls into the two beakers and watch the difference in time between the two solvents.

Now that you have some basic background information on the flow properties of polymers and liquids in general—you can perform a polymer solution virtual experiment. We have provided a capillary-type, drop-time viscometer lab. You are probably wondering just what is a capillary-type, drop-time viscometer. First of all, viscosity determines the rate at which a liquid flows - in our case the liquid is a diluted, polymer solution. The funnel animation above showed that maple syrup is more viscous than orange juice. A viscometer is simply a device used to measure viscosity. In this virtual lab, you will run time trials for polymer solutions, use this information to find the viscosity, and finally, use the viscosity to determine the molecular weight. You are probably wondering why the end result of a viscosity experiment is a molecular weight? Molecular weight and viscosity have more in common than you might think. Think of the polymer molecules as if they were tiny balls.

If you fill a funnel with large balls, it takes a long time for them to leave through the funnel’s opening. On the other hand, tiny balls in a funnel ‘flow’ out much faster. You can see how this may prove useful in the study of polymers - the viscosity can be a dead giveaway of the molecular weight.

Flow Properties, Viscosity, and Molecular Weight

In the previous paragraphs, we used animations and some general information to get you up to speed with flow, viscosity, and molecular weight - now its time to learn the formulas that make it all work. Flow is the irreversible, viscous property of a material as opposed to the reversible, elastic behavior of some materials. Viscous fluids support shear stress and exhibit shear strain and the viscosity is defined by this ratio:

Stress(s ) = [Viscosity(h )] * [Strain Rate]

If this equation is true for a material, the stress versus shear rate flow curve is linear and the material is known as a Newtonian fluid. Only a small number of specific examples exist, as only a few simple fluids have the molecular make-up to behave in this manner.

We can illustrate the terms in this definition for the case of laminar flow in which the fluid layers move smoothly over one another.

Here, the portion of the fluid abcd is steadily deformed as the upper plate is pulled along by force F. The instantaneous deformation illustrated here is described by a strain bb'/h. The strain rate, then, is the rate of change of bb'/h = v/h. The applied shear stress is just s = F/A where A is the area of each plate.

Previously, we used the example of funnels filled with orange juice and maple syrup. When released, the orange juice will obviously pour out of the funnel at a much faster rate. It is said that maple syrup is a more viscous fluid than orange juice. This of course is elementary when compared to polymer viscosity, but it is a good example to demonstrate flow properties and how it could be tied in to the study of polymers. In the field of polymers, a solution of high molecular weight carries a viscosity that is noticeably higher than that of a solution of lower molecular weight. We can understand this using a simplified model of a ball-like configuration for the polymer molecules in a dilute solution. Because of the velocity gradient in a direction perpendicular to the flow, a larger ball will experience a wider range of shear rates and, as it deforms, provide greater drag than does a smaller (lower molecular weight) ball.

This leads us to the task of measuring viscosity of dilute solutions. In the past, a drop-time capillary viscometer was the instrument of choice for the measurement of characteristics of polymer solutions. In this sort of viscometer, the solution is released from the capillary in which the time t is recorded for the meniscus of the solution to travel some distance d. This time is called an efflux time, and it is measured for several concentrations of the polymer solution, as well as for the solvent with no polymer in it. In recent times, there is more of a push towards dual-capillary viscometers that are arguably more efficient. At any rate, the goal when using a viscometer is to, of course, obtain a viscosity for the solution, and ultimately characterize the solute molecules. The efflux time measured when using the viscometer is used to find the relative viscosity (RV or h rel), which is the ratio of solution viscosity divided by solvent viscosity; so that, in terms of efflux times:

h rel = t / to

where t is the efflux time of the solution and to is the efflux time of the solvent. From the relative viscosity all other solution viscosity quantities can be obtained. However, before we use the relative viscosity, there is another quantity, the specific viscosity (h sp), that can be calculated using the efflux times of solution and solvent. The specific viscosity can be defined as the fractional increase in viscosity caused by the presence of the dissolved polymer in the solvent.

h sp = [t - to] / to

From the specific viscosity and the concentration ( c ) of the solution, the reduced viscosity (h red) can be obtained.

h sp / c = h red

The reduced viscosity changes as a function of concentration. A plot of reduced viscosity versus concentration would look something like this:

h red = k’[h ]2c + [h ]

The y-intercept, [h ], is the intrinsic viscosity which is related to the slope which is k’[h ]2. The intrinsic viscosity is the quantity that relates viscosity to the molecular weight and the intrinsic structural differences of the solute molecules—it is obviously important in determining the molecular weight. There is, however, a second way to calculate the intrinsic viscosity. This method involves calculating the inherent viscosity (h inh) from the relative viscosity, and finally, using it to calculate the intrinsic viscosity.

ln h rel / c = h inh

Once again, the inherent viscosity changes as a function of concentration. So, the graph of inherent viscosity plotted versus concentration looks like this:

And again, the intrinsic viscosity, [h ], is the y-intercept, but in this case the slope is different—it is k"[h ]2. In the following equation, we can relate the intrinsic viscosity to the inherent viscosity:

h inh = k"[h ]2c + [n]

Now, we have obtained the intrinsic viscosity using two different methods. It is normal procedure to calculate it using both methods; if the results from each calculation match, then the measurements taken were most likely correct. Displaying both plots of intrinsic viscosity on the same graph should also back up your results—with the two lines meeting at the same y-intercept.

Now, you have the information necessary to calculate the molecular weight. The equation:

[h ] = K’ Ma

is all you need to complete the calculations. This is called the Mark-Houwink equation. M represents the viscosity average molecular weight, and K’ and a are Mark-Houwink constants. These constants depend upon the polymer-solvent combination you are dealing with. One last thing to remember—these equations and this experiment in general deals with diluted solutions. If you try to use this data for a polymer solution that is too concentrated, the calculations will not be as accurate. For example, if the solution is too concentrated, the molecules may be close enough to each other to start to interact. This could cause the viscosity to increase in ways that these equations do not support.

Viscosity can be used to determine flow properties other than molecular weight. For example, the melt flow index (MFI) is another useful piece of information when studying polymers that also ties in to molecular weight. The melt flow index is a measure of how much polymer flows through an orifice over a given time period under a constant pressure. This index also gives you an indication of what the molecular weight is.

For a more complete discussion of solution viscosity, see Ferry, J. D. (1980) Viscoelastic Properties of Polymers, 3rd ed. (JohnWiley & Sons, New York) or Sperling, L. H. (1986) Physical Polymer Science. (John Wiley & Sons, New York)