Hertz–Knudsen equation
In surface chemistry, the Hertz–Knudsen equation, also known as Knudsen–Langmuir equation describes evaporation rates, named after Heinrich Hertz and Martin Knudsen.
Definition
[edit]Non-dissociative adsorption (Langmuirian adsorption)
[edit]The Hertz–Knudsen equation describes the non-dissociative adsorption of a gas molecule on a surface by expressing the variation of the number of molecules impacting on the surfaces per unit of time as a function of the pressure of the gas and other parameters which characterise both the gas phase molecule and the surface:[1][2]
where:
| Quantity | Description |
|---|---|
| A | Surface area (in m2) |
| N | Number of gas molecules |
| t | Time (in s) |
| φ | Flux of the gas molecules (in m−2 s−1) |
| α | Anomalous evaporation coefficient, 0 ≤ α ≤ 1, to match experimental results to theoretical predictions (Knudsen noted that experimental fluxes are lower than theoretical fluxes)[3] |
| p | The gas pressure (in Pa) |
| M | Molar mass (in kg mol−1) |
| m | Mass of a particle (in kg) |
| kB | Boltzmann constant |
| T | Temperature (in K) |
| R | Gas constant (J mol−1 K−1) |
| NA | Avogadro constant (mol−1) |
Since the equation result has the units of s-1 it can be assimilated to a rate constant for the adsorption process.
See also
[edit]References
[edit]- ^ Kolasinski, Kurt W. (2012). Surface Science: Foundations of Catalysis and Nanoscience, Third Edition. p. 203. doi:10.1002/9781119941798.
- ^ R. B. Darling, EE-527: Micro Fabrication, Virginia University (retrieved Feb. 9 2015).
- ^ Holyst, Robert; Litniewski, Marek; Jakubczyk, Daniel (2015). "A molecular dynamics test of the Hertz–Knudsen equation for evaporating liquids". Soft Matter. 11 (36): 7201–7206. doi:10.1039/c5sm01508a.