Blog Post:

Measuring a Polymer’s Molecular Weight with a Viscometer

A viscometer measures the viscosity of a given fluid or solution. Viscosity is a measurement of how easily a fluid flows or deforms and depends on makeup of the liquid. For example, a very viscous fluid is honey while a low viscous fluid is water or ethyl alcohol (like distilled spirits). In many cases, viscosity relates to the size of molecules, usually polymers, and how they are dispersed in a fluid, like water. Polymers are chains of molecules connected together to achieve certain physical properties. Examples include plastics for holding food or water treatments to remove the haze in a fish tank. In many cases the length of the polymer, or its molecular weight, is a quality check of if the polymer was made correctly or works correctly for the intended application. Viscosity changes with temperature and thus is a thermophysical property, and it is important to reference the temperature at each viscosity measurement. Knowing the viscosity of a solution or fluid is useful to size various pipes, tanks, and pumps for a chemical process. Figure 1 represents the shear stress a liquid can experience and how easily the liquid reacts to the shear stress is what determines a liquid’s viscosity.

Dynamic vs. Kinematic Viscosity

There are two types of viscosity commonly discussed, dynamic and kinematic viscosity. Dynamic viscosity, or µ, provides insight into the sheering force needed to deform a liquid in a specific direction. (Figure 1). Kinematic viscosity ( $\nu$ ) is sometimes considered and is simply a ratio of the dynamic viscosity to the density ( $\rho$ ) of the fluid:

$\nu=\frac{\mu}{\rho}$

Image represents a graphical depiction of how a liquid reacts to a sheer stress, where x-axis is the velocity of the liquid particles, and the y-axis is the height of the liquid film. — *Figure 1 – A graphical depiction of how a liquid reacts to a sheer stress, where x-axis is the velocity of the liquid particles, and the y-axis is the height of the liquid film.*

Ubbelohde Viscometer

A simple way to measure the viscosity of a liquid is to use a glass viscometer. One type of viscometer is the Ubbelohde Viscometer (Figure 2). The viscometer has three tubes. One tube is for filling and emptying the liquid in the tube and is marked with two fill lines. The liquid to be studied needs to be filled somewhere in between those lines and varies by the size of the viscometer. The middle tube is an air tube that allows the pressure head to only be dependent on height and not total volume of the liquid. The third tube contains the capillary column and start/stop marks used during the experiment.

To measure viscosity, the liquid is loaded above the second line on the measurement tube. Then a timer is started once the liquid hits the second line and the timer is stopped after the liquid reaches the lower line on the tube. Viscosity can then be calculated by multiplying the time by the viscosity constant (different for each viscometer) making this a relatively simple measurement to run.

While this method can be used to measure a liquid’s viscosity it can also be used as an economical method to determine the molecular weight of a polymer. The Mark-Houwink equation relates viscosity ( $\eta$ ) to the molecular weight (M) with two constants called the Mark-Houwink constants (K and $\alpha$ ). These constants are specific to a polymer-solvent system.

$[\eta] = KM^\alpha$

Like determining viscosity, the measurements require known concentrations for polymer in solvent (typically in g/mL) and the measured time it takes to reach the bottom line in the viscometer. Using relationships below involving time and concentration, the molecular weight can be determined.

The relative viscosity $[\eta_{rel}]$ , is related to the time (t) of the solution and the time (t₀) required for the pure solvent to flow.

$[\eta_{rel}] = \frac{t}{t_0}$

The reduced viscosity is given below, with c being the concentration of the polymer in the polymer-solvent solution:

$\frac{(t-t_0)}{tc} = \frac{\eta_{sp}}{c}$

The inherent viscosity is also given below.

$\eta_{inh} = \ln(\frac{\frac{t}{t_0}}{c}) = \frac{\ln \eta_{rel} }{c}$

Then the intrinsic viscosity ( $[\eta]$ ) is determined at the y intercept of plots of $[\eta_{red}]$ and $[\eta_{inh}]$ as described in the equation and Figure 3 below.

$[\eta] = (\frac{\eta_{sp}}{c})_{c \to 0} = (\frac{\ln(\eta_r)}{c})_{c \to 0}$

Figure 3 - Graph of viscosity vs concentration. — *Figure 3 – Graph of viscosity vs concentration.*

Once the intrinsic viscosity has been extrapolated, the following rearranged equation can be used to determine molecular weight.

$\log M = \frac{1}{\alpha} \log (\frac{[\eta]}{K})$

Thus, with the use of a relatively inexpensive method, the molecular weight of a synthesized or complex polymer can be determined easily. This is done by utilizing a viscosity measurement to determine the molecular weight using principles of polymers. Using underlying principles to characterize polymers or other materials is common practice at Sparx. This allows for quick and straight forward measurements that would otherwise require expensive instrumentation that is not always easy to have on hand in a small laboratory.

Blog Post:

Measuring a Polymer’s Molecular Weight with a Viscometer

Dynamic vs. Kinematic Viscosity

Ubbelohde Viscometer

Leave a Reply Cancel reply

Categories

Get in Touch