One of the most precise measurements in polymer science is also the simplest and cheapest. Intrinsic viscosity, which is measured from the flow time of a solution through a simple glass capillary, has considerable historical importance for establishing the very existence of polymer molecules. It also provides considerable physical insight. In this lab, each group will study the intrinsic viscosity of hydroxypropylcellulose, a common polymer derived from cellulose--hopefully at a different temperature.
Viscosity in general
For a discussion of viscosity, refer to the "HowTo" document on using the Wells-Brookfield cone and plate viscometer. The viscosity measured in a capillary viscometer is not obtained at a defined shear rate. Of several fixes to this problem, the simplest is simply to ignore it. This amounts to assuming that the fluid is Newtonian over the entire range of shear rates encountered by the fluid as it passes down the capillary.
The Ubbelohde capillary viscometer
The most useful kind of viscometer for determining intrinsic viscosity is the "suspended level" or Ubbelohde viscometer, sketched below:
The viscometer is called "suspended level" because the liquid initially drawn into the small upper bulb is not connected to the reservoir as it flows down the capillary during measurement. The capillary is suspended above the reservoir. In conjunction with the pressure-equalization tube, this ensures that the only pressure difference between the top of the bulb and the bottom of the capillary is that due to the hydrostatic pressure--i.e., the weight of the liquid. Other designs, e.g., the Cannon-Fenske viscometer, do not provide for this, and will give erroneous results in an intrinsic viscosity determination. Such viscometers are useful in other experiments--e.g., checking the stability of some polymer solution, where one is only interested in measuring a change in the flow time.
Use of the Ubbelohde viscometer
The theory of the viscometer is relegated to Appendix I. For now it is sufficient to accept that a capillary viscometer measures a viscosity as defined in the Wells-Brookfield handout, although no parallel plates or force determinations are involved. Capillary viscometry is conceptually simple: the time it takes a volume of polymer solution to flow through a thin capillary is compared to the time for a solvent flow. It turns out that the flow time for either is proportional to the viscosity, and inversely proportional to the density.
We define the relative viscosity to be the ratio [pic]. For most polymer solutions at the concentrations of interest, [pic]. Thus, to a very good approximation, the relative viscosity is a simple time ratio:
We also define a "specific viscosity" to be the fractional change in viscosity upon addition of polymer:
Both ηrel and ηsp depend on the polymer concentration, so to extract the "intrinsic" properties of the polymer chain itself, one must extrapolate to zero concentration. Measuring at zero concentration (c=0) would be useless, but this concept of extrapolating to c=0 is very important in polymer characterization and in thermodynamics generally. The two quantities that are commonly plotted vs. concentration and extrapolated to c=0 are ηsp and c-1ln(ηrel). A typical plot is shown below--real data taken in our lab.
Note that both plots have the same intercept, which is called [η], the intrinsic viscosity.
Exercise: prove the second relation in the above equation--i.e., that [η] obtained from [pic] vs. c plots is identical to [η] obtained from [pic] vs. c plots.
The units of [η] are inverse concentration. Intrinsic viscosity has "grown up" around some fairly unconventional units regarding concentration. The most commonly used concentration is g/dL (grams per 100 mL) so [η] is usually expressed as...
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