Objective:
The objective of this lab is to become familiar with the use of a viscometer (Brookfield Couette Viscometer) in the determination of the molecular weight, shear rate, dilution and temperature dependence of viscosity for a series of polydimethylsiloxane (PDMS) polymers.
Instruments to be used:
Brookfield Viscometer (Departmental)
Viscometer is Located in Polymer Characterization Lab (Rhodes 5'th Floor, 505 lab. Second lab on the right coming from the stairwell.)
Materials:
Hydroxy- terminated PDMS of variable molecular weight.
(Silicone oil/viscosity standards)
Toluene
Procedure:
1) Pour the PDMS sample into the viscometer cell. For the first series of measurements leave the viscometer at room temperature. (You will need to determine the temperature in the room).
2) Measure the torque as a function of angular velocity, using 0.3 to 12 Hz.
3) Repeat 1 and 2 for several temperatures, 30°C, 45°C, 60°C, 75°C, 85°C, 95°C.
4) Repeat 1 to 3 for several other molecular weight PDMS samples.
*5) Repeat 1 to 3 for a high molecular weight sample looking at several dilutions of the polymer with toluene. Concentrations of 1, 3, 5, 10, 50, 100, 300, 500, 1000 mg/ml (mg PDMS to total ml with toluene) are needed at a single temperature for several angular velocities. Measure the viscosity of toluene.
Analysis:
1) Plot shear stress versus shear strain for the different shear rates and for the different temperatures. These should be linear plots for a given temperature/molecular weight if the sample is Newtonian (below Me).
2) Use the equations for the Couetteor cone and plate viscometer to calculate the viscosity assuming a Newtonian fluid from the torque and angular velocity.
(Couetter viscometer: For spindle number 31 at 12 rpm the torque reading times 25 is the viscosity in centi-Poise. Other angular velocities can be converted by the ratio of (rpm/12), e.g. for 0.3 rpm the conversion factor from torque to centi-Poise for spindle 31 is 0.625. (You will need to verify this using the equations for the Couetter viscometer.))
3) Use the data available on the web of molecular weight versus viscosity to determine the molecular weight of each polymer sample you have run.
4) Make a log/log plot of the tabulated (from the web) viscosity data versus molecular weight to determine the entanglement molecular weight. Does the web data follow the 3.4 and 1 power-laws discussed in class?
5) Determine if your PDMS is above or below the entanglement molecular weight.
6) Use the Arrhenius function to describe the temperature dependence of the viscosity,
η = η° exp(-Ta/T). What are the values for Ta and η°.
7) Find the WLF parameters for PDMS in the Polymer Handbook and calculate the viscosity at all of the elevated temperatures measured based on the room temperature viscosity.
*8) Construct a plot similar to the plot from Fried in the web notes (Chapter 1 p. 15) of viscosity versus concentration for the shear rates studied.
*9) Make a plot similar to (8) of specific viscosity = (solution/solvent)-1. For the polymer studied can you determine the overlap concentration, c*?
Questions:
1) Is the shear rate used in this experiment below the Newtonian plateau limit? Justify your answer with your data.
*2)a How is the melt viscosity determined in a Couette viscometer such as this Brookfield viscometer starting with the torque and angular velocity? Give the equations and the assumptions involved.
2)b How is the melt viscosity determined in a cone and plate viscometer such as this Brookfield viscometer starting with the torque and angular velocity? Give the equations and the assumptions involved.
3) Are the assumptions applicable to your measurements and samples?
4) How does the melt viscosity of a polymer vary with shear rate? (Make a sketch of log viscosity versus log shear rate and explain the parts of the curve.)
5) From the log/log plot of the tabulated (from the web) viscosity data versus molecular weight (4 above), do the web data follow the 3.4 and 1 power-laws discussed in class? If not, then why?
*6) Middleman Problem 16, p. 118 Couette Viscometer
*7) Middleman Problem 17, p. 118 Couette Viscometer
*8) Middleman Problem 18, p. 118 (Also See Tadmor/Gogos Text) Couette Viscometer
9) Middleman Problem 39, p. 121 Melt Index Question
10) Compare the molecular weight and concentration dependencies of viscosity. What similarities do you see?
11) Explain the association between entanglement molecular weight and the overlap concentration.
* = optional