1. Polymer Properties
Exercise 4

2. Viscoelasticity and rheology
Effect of molecular weight on viscosity
Effect of temperature on viscosity
Above the critical molecular weight the zero viscosity of polymer can be calculated using equation:
Below the critical molecular weight the constant  is 1.0, above the critical molecular weight  = 3.4.
Zero viscosity is determined by rheology measurement: dynamic viscosity at zero frequency.
For amorphous polymers above the glass transition, WLF equation can be applied:
Reference temperature Ts
C1 = 8.86 and C2 = 101.6
Reference temperature Ts = Tg
C1 = and C2 = 51.6

3. 1. Viscosity
Viscosity of an amorphous PVC was measured to be 3.9105 Pas at temperature 122 oC. For processing, the viscosity should be below 2104 Pas, but at least 5000 Pas.
At what temperature should the processing be done?

4. 1)
Amorphous PVC follows WLF equation in the temperature range T = Ts  50 °C.
Solve for the temperature at which the viscosity is at most 2104 Pas :

5. 1)
When the lowest acceptable viscosity is 5000 Pas, the temperature is:
Processing should be done within the temperature range oC.

6. 2. Viscosity and Mw
Zero viscosity of a linear polyethylene was determined to be Pas at 190°C. For polyethylene the constants for comparison of Mw and zero viscosity are k = 3.410-15 Pas and  = 3.5. The temperature dependence of the viscosity of PE in melt can be estimated with Arrhenius-type equation.
What is the molecular weight Mw of PE?
How much should the temperature be altered in order to reduce the viscosity by half?

7. 2a)
The weight average molecular weight for the polymer can be calculated from equation:

8. 2b) Temperature dependence for the viscosity by Arrhenius:
When viscosity is reduced by half by altering temperature:

9. 2b)
Activation energy for HDPE is 27 kJ/mol, the temperature can be solved:
=1/
T2=513.8K = 241°C
The temperature should be increased by 51 °C in order to reduce the viscosity by half.

10. 3. Stress-strain (Creep)
Tensile stress shear stress  
Strain
Shear rate
Viscosity
Creep compliance

11. 3. Creep
Polypropylene PP rod attached to the ceiling (length 200 mm, width 25.0 mm, thickness 3.0 mm) is loaded with 30 kg´s. How much will the polymer creep in two minutes when the creep compliance J(t) follows the equation (t is time in minutes)?
J(t) = exp(-t/6min) GPa-1

12. 3) Stress imposed on the cross section of the polymer rod is:
Creep  at the moment t is obtained from the Strain:
Where

13. 3)
Creep at two minutes:
PP rod has strained during the two minutes time:

14. 4. Viscosity and chain length
When the polymer chain are long enough to form stable entanglements, longer than the critical chain length Zw > Zc,w, the polymer viscosity  and chain length Zw can be connected by:
where K is a constant

15. 4)
The usual processing temperature of polystyrene cups is 160 oC and the melt viscosity is then 1.5102 Pa  s, provided that the mainchain length of PS is Zw = 800. The quality of the polymer however varies and one day the Zw = 950. Processing is tuned for a particular viscosity range.
How should the processing temperature be altered so that the melt viscosity would still be 1.5102 Pa  s?
Glass transition temperature of PS is 100oC.

16. 4)
Viscosity is increased when the molecular weight increases. By increasing the temperature the viscosity can be kept lower.
Solving the constant K first:
Viscosity of the novel polymer grade at 160oC:

17. 4)
The viscosity of this polymer at the glass transition temperature can be obtained using WLF equation:
The new processing temperature T2 can be solved from WLF equation:

18. 4)
The processing temperature should be about 4oC higher so that the viscosity would remain the same.