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3.1.2.1.2b) Viscosity/temperature shift factor aT, and Arrhenius plot
ОглавлениеThe following holds for the viscosity/temperature shift factor aT in general:
Equation 3.8
aT = η(T) / η(Tref)
The dimensionless factor aT is the ratio of the two viscosity values at the temperature T and at the reference temperature Tref. For polymers, this relation is only valid for the values of the zero-shear viscosity η0. The following holds for the temperature shift factor according to Arrhenius (with T in [K]):
Equation 3.9
The semi-logarithmic, so-called Arrhenius plot presents the temperature shift factor aT on the y-axis on a logarithmic scale versus the reciprocal temperature 1/T on the x-axis (with the unit: 1/K).
In order to estimate viscosity values at temperatures at which no measuring values are available, proceed as follows:
1 Select Tref (e. g. a temperature, at which an η-value is available).
2 Calculate the shift factor aT for another available η(T)-value (using Equation 3.8).
3 Calculate the flow activation energy value EA (using Equation 3.9).
4 Calculate the shift factor aT for the desired η(T)-value (using Equation 3.9).
5 Result: Calculate the desired η(T)-value (using Equation 3.8).
Table 3.5: Temperature-dependent viscosity values, see the example of Chapter 3.5.4b | ||||
T [°C] | 50 | 60 | 70 | 80 |
T [K] | 323 | 333 | 343 | 353 |
η [Pas] | 2.00 | 1.55 | 1.26 | 1.00 |