Everything about The Time-temperature Superposition totally explained
The
Time-temperature superposition principle is a concept in
polymer physics.
Glasses,
metals, as well as
polymers often go through a change of phase which is known as the
glass transition. Polymers have a certain temperature known as the
glass transition temperature in which it transforms from a non-crystalline material that has a soft, rubbery consistency to a material that's hard, elastic and glassy. The glass transition temperature is dependent on the chemical structure and molecular mobility of the polymer. There weren’t really any efficient means to determine the glass transition temperature of polymers; however the time-temperature superposition method allows for an accurate portrayal of the glass transition temperature. The theory behind this method is that a measurement of Tg at a certain temperature and time will be equal and behave the same as a polymer measured at a lower temperature and a longer time. And a key assumption is that all relaxation times have identical temperature dependence.
Time-Temperature Superposition
It has been shown experimentally that the
elastic modulus (E) of a polymer is influenced by the load and the response time. Time-temperature superposition implies that the response time function of the elastic modulus at a certain temperature resembles the shape of the same functions of adjacent temperatures. Curves of E vs. log(response time) at one temperature can be shifts to overlap with adjacent curves.
Shift Factor Calculation
The distance of the shift is referred to as the
time-temperature superposition shift factor aT which is calculated by the following equations:
aT= tT/t0
Where tT is the time that's required to give a specified response at a certain temperature, and to is the time required to give an identical response at the reference temperature.
aT=f0/fT
Where fT is the rate at which the material achieves a particular response at a given temperature and f0 is the rate at which the material achieves the same response time as the reference temperature.
Where the curves overlap each other their elastic moduli will be equal. Therefore,
E(T, aTf) = E(T0,f)
The time-temperature superposition shift factor follows the
Williams-Landel-Ferry equation where C1 and C2 are constants:
Log10(aT) = (-C1*(T-To))/(C2+(T-To)
The shift factors are then utilized to draw the master curve and plotted against temperature.
Conclusion
Time- temperature superposition is a procedure that has become important in the field of polymers to observe the dependence upon temperature on the change of
viscosity of a polymeric fluid. Rheology or viscosity can often be a strong indicator of the molecular structure and molecular mobility. Time-temperature superposition avoids the inefficiency of measuring a polymers behavior over long periods of time at a specified temperature by utilizing the fact that at lower temperatures and shorter time the polymer will behave the same.
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