Calculator Inputs
Formula Used
The Arrhenius shift factor relates time scales at temperature T to a reference temperature Tref:
ln(aT) = (Ea / R) · (1/T − 1/Tref)
Then aT = exp(ln(aT)) and log10(aT) = ln(aT) / ln(10). Temperatures must be in Kelvin.
How to Use This Calculator
- Pick single or batch mode for temperatures.
- Enter Ea and choose kJ/mol or J/mol.
- Set Tref and choose its temperature unit.
- Enter T (or a list) using the selected unit.
- Click Calculate to view
aT,ln(aT), andlog10(aT). - Use Download CSV or Download PDF to save results.
Example Data Table
| T (K) | Approx aT | Notes |
|---|---|---|
| 293.15 | ~1.7 | Lower temperature often slows relaxation. |
| 303.15 | ~0.62 | Higher temperature often speeds relaxation. |
| 323.15 | ~0.18 | Shift factors can span many decades. |
Arrhenius Shift Factor Guide
1) Overview of Arrhenius Shift Factors
An Arrhenius shift factor, aT, scales time or frequency data between temperatures. It is widely used for thermally activated processes in polymers, adhesives, glasses, and soft solids. The factor connects relaxation rates to temperature through an activation energy, enabling clean comparisons across tests.
2) Why Temperature-Time Superposition Matters
In many viscoelastic experiments, a 10–30 K temperature change can shift response times by orders of magnitude. By shifting curves horizontally with aT, you can build master curves spanning minutes to years. This reduces experimental time while preserving mechanistic trends across a wider time window.
3) Core Equation and Variable Meaning
This calculator uses ln(aT) = (Ea/R)·(1/T − 1/Tref).
Here, Ea is activation energy (J/mol), R is the gas constant (J/mol·K),
T is the target temperature (K), and Tref is the reference temperature (K).
Small changes in 1/T can strongly affect aT when Ea is large.
4) Choosing Activation Energy Values
Reported activation energies depend on material, mode, and temperature range.
Many polymer segmental relaxations fall around 30–200 kJ/mol, while diffusion-like processes can be lower.
If you fit Ea from data, use multiple temperatures and confirm linearity of ln(rate) versus 1/T.
5) Temperature Inputs and Unit Discipline
Arrhenius shifting requires absolute temperature. If you enter temperatures in °C, the calculator converts to Kelvin. Mixing units is the most common source of error: if Ea is in kJ/mol, it is converted to J/mol internally, and R should remain near 8.314 J/mol·K for consistency.
6) Interpreting aT, ln(aT), and log10(aT)
The shift factor is multiplicative: time at T equals aT × time at Tref for equivalent response.
Values above 1 indicate slower kinetics at T, while values below 1 indicate faster kinetics.
The logarithmic outputs help compare decades of shift and support linear plotting for calibration.
7) Example Dataset and Expected Magnitudes
With Ea = 75 kJ/mol and Tref = 298.15 K, modest offsets can be significant. For instance, around 293.15 K you may see aT near 1–2, while at 323.15 K it can drop below 0.2. Higher Ea values amplify these differences, often spanning several decades.
8) Practical Tips for Reliable Master Curves
Keep Tref within the tested temperature range to minimize extrapolation error. Use batch mode to scan multiple temperatures quickly and identify sensitivity. If your material shows glass-transition effects, verify Arrhenius validity; some systems require alternative shifting models. Always document Ea, R, and temperature units in your report.
FAQs
1) What does the shift factor aT represent?
aT scales time or frequency from Tref to T for equivalent material response. It is a horizontal shift used to build master curves across temperatures for thermally activated behavior.
2) When should I prefer Arrhenius shifting?
Use Arrhenius shifting when the temperature dependence is approximately exponential in 1/T, common for activated relaxations and diffusion-like processes. Near glass transition, behavior may deviate and require different models.
3) Why must temperatures be in Kelvin?
The equation uses absolute temperature in the reciprocal term 1/T. Using °C directly would distort 1/T and produce incorrect aT. This calculator converts °C to Kelvin automatically for computation.
4) What does aT > 1 mean physically?
If aT is greater than 1, the process at T is slower than at Tref, so equivalent response takes longer. If aT is less than 1, the process is faster.
5) Can I change the gas constant value?
Yes. Keep R consistent with your activation energy units. If Ea is in J/mol, R should be in J/mol·K. Using an inconsistent R will scale ln(aT) and cause systematic shifts.
6) How do I choose a good reference temperature?
Select Tref where you have high-quality data and stable measurements. It is best to choose a value near the center of your temperature range to reduce extrapolation and keep shift factors moderate.
7) Why are my results extremely large or tiny?
Large magnitudes occur when Ea is high or when T is far from Tref, because ln(aT) scales with (1/T − 1/Tref). Recheck units, Kelvin conversion, and whether Ea is realistic.