Calculator inputs
Example data table
| Temperature (K) | Binding energy (kJ/mol) | Attempt frequency (s⁻¹) | Estimated residence time (s) | Readable time |
|---|---|---|---|---|
| 250 | 65 | 1.0 × 1013 | 3.8084 | 3.8084 s |
| 300 | 65 | 1.0 × 1013 | 2.0763 × 10-2 | 20.763 ms |
| 350 | 65 | 1.0 × 1013 | 5.0180 × 10-4 | 501.80 µs |
| 400 | 65 | 1.0 × 1013 | 3.0758 × 10-5 | 30.758 µs |
These rows illustrate how rising temperature sharply shortens adsorption lifetime when the prefactor remains fixed.
Formula used
Residence time form:
τ = (1 / ν) × exp(E / (R × T))
or, for molecular energy in electronvolts,
τ = (1 / ν) × exp(E / (kB × T))
- τ = surface residence time in seconds
- ν = attempt frequency or desorption prefactor in s-1
- E = adsorption or desorption barrier energy
- R = gas constant for molar energies
- kB = Boltzmann constant for per-molecule energies
- T = absolute temperature in kelvin
Inverse modes rearrange the same relationship to solve for temperature or binding energy at a chosen target lifetime.
How to use this calculator
- Select the calculation mode based on the unknown you want to solve.
- Choose energy units in either kJ/mol or eV per molecule.
- Enter the prefactor as attempt frequency or attempt time.
- Provide temperature, binding energy, or target lifetime as required.
- Set a temperature range for the Plotly trend graph.
- Optionally enter an energy uncertainty percentage for sensitivity bounds.
- Press calculate to show results above the form.
- Export the summary and graph data using CSV or PDF buttons.
FAQs
1. What does surface residence time mean?
It is the average time an adsorbed molecule remains on a surface before desorbing. Larger binding energy or lower temperature usually gives a longer residence time.
2. Why is temperature so influential?
The equation contains an exponential temperature term. A modest temperature increase can shorten residence time by orders of magnitude, especially for moderate adsorption energies.
3. When should I use kJ/mol instead of eV?
Use kJ/mol when your data comes from chemistry tables, calorimetry, or thermodynamic reporting. Use eV when working with surface science, atomistic modeling, or per-molecule barriers.
4. What is the attempt frequency?
It is the prefactor describing how often the adsorbate attempts to escape the surface potential well. Values near 1012 to 1013 s-1 are common estimates.
5. Why can two surfaces show different residence times?
Different crystal faces, defect densities, coverages, and adsorbate interactions change the effective desorption barrier and sometimes the prefactor, shifting the lifetime strongly.
6. What does the sensitivity range represent?
It shows how much the predicted lifetime changes when the barrier energy moves up or down by the uncertainty percentage you entered. This helps gauge model robustness.
7. Can I solve for temperature or energy directly?
Yes. The inverse modes let you target a required residence time and solve either the operating temperature or the binding energy needed to achieve it.
8. Is this calculator suitable for rigorous reactor design?
It is best for screening, education, and first-pass estimates. Detailed studies may need coverage effects, multiple adsorption states, lateral interactions, and experimentally fitted prefactors.