Argon and N2 are standard gases for BET surface area measurements for powders. For thin films adhered to the surface of a substrate such as silicon, however, the mass is below the threshold of the sensitivity of the device. Krypton, very expensive, has been shown to work for low sample masses. I would like to understand how the adsorption process is different for each that results in higher sensitivity. The literature mentions sublimation but to me that doesn't get at the core reason.
Dear Michael,
The cross sectional area of Kr and N2 are 0.202 nm2 ans 0.162 nm2 respectively. Kr molecules are larger by about 25% and so, Kr should not be more suitable that N2 for the low specific surface area measurement. But… it is more suitable!
The reason of using Kr is due to its lower vapour pressure (267 Pa) compared to N2 (101325 Pa) at 77 K. The gas adsorption amount in the volumetric method is calculated from the difference between the number of dosed molecules and number of unadsorbed gas molecules at equilibrium pressure. In other words, by assuming both molecular sizes equal and adsorption pressure equal to 50 Pa, it is necessary to measure the pressure change of 0.16% (=50/30450) for N2 and 38% (=50/130) for Kr at the same relative pressure (P/Po=0.3, N2=30400Pa, Kr = 80Pa).
Obviously, it is easier to measure larger pressure change, and therefore, the accuracy of the measurement is better. For this reason, the lower the saturation vapour pressure at the adsorption measurement temperature, the more accurate the measurement of low surface areas and so Xe, with vapour pressure equal to 0.23 Pa at 77K, is still a better gas to measure low surface areas. Unfortunately, Xe is much more expensive than Kr…
Hi Michael,
adsorption isotherms are measured by calculating the difference between a quantity of gas injected and the quantity that remains in the vapor phase after equilibration. The injected quantity is known very accurately (piston with calibrated volume). The main source of error is on the quantity that remains in the device after each injection.
The interest of Krypton is that its saturating pressure at 77K is so low (2 mm Hg) that the latter quantity is negligible. Hence the accuracy of the measurement.
Cedric
In fact the low sublimation level of Kr at 77K is the reason why it is mainly used for low-k materials and thin films. Gas adsorption is based in the equilibrium between the adsorbed gas molecules and the non-adsorbed free gas molecules at the test temperature. The sensitivity of the method that you are using (BET, Langmuir isotherm or whatever) depends on the accuracy of your pressure gauge to distinguish the mass of adsorbed molecules. If your material has enough pore volume or the size of mesopores is large enough, the adsorption is favored and both N2 or Ar are good probe molecules for the surface area and porosity. When pore volume is reduced such as in thin films, the equilibrium is not easily reached and gases with low sublimation capacity are needed.
On the other hand, you are right considering Kr as an expensive gas but you will not need a large amount of it. The isotherms can be recorded in liquid N2 or liguid Ar up to p/p* = 0.5 or even lower just to determine surface area. There are some methods in literature to determine also pore size mainly based in microscopic approaches, such as NLDFT or GCMC, but some previous information on the microstructure of sample and properties of the gas molecules are necessary.
Have you considered Xe (may not be a 'cheaper' alternative to Kr)? Xe is a stronger X ray and electron scatterer (compared to Ar). Also Xe and Kr adlayer orientation, I believe, is more sensitive to surface defects. The Xe and Kr adlayers have been probed using LEED, atomic He scattering, Xrays etc to complement adsorption isotherms.
Because Kr has a way larger an atomic radius compared to Ar or N2-molecule, with respect to its cross-sectional area, it can be used as a molecular probe (an adsorbate) to evaluate Langmuir monolayer capacity, which is directly linked to the surface area, or else- BET multilayer model, etc. But the size of a probe is restricted in the terms of the pores structure and size accessible to the adsorbate, so it all depends on the substrates nature. I am not sure of the nature of micro-mesoporos or even uniform porous structure of thing films you're working on.You'd better check on the previous experience from other related studies, but it's common to employ adsorbates other than the conventional ones, e.g: N2, Ar, CO2, phenol, J2, MB etc, whenever it comes to adsobtion studies to evaluate the superstructure of porous materials
As the saturation vapor pressure is low ~2 torr, at 77K, the dead space correction for unadsorbed gas is small enough to permit the measurement of quite small adsorption with reasonable precision. With Kr, specific surfaces as low as 10 cm2/g can be estimated. Please refer the book: Adsorption, Surface Area and Porosity by S. J. Gregg and K. S. W. Sing for more details.
Dear Michael,
The cross sectional area of Kr and N2 are 0.202 nm2 ans 0.162 nm2 respectively. Kr molecules are larger by about 25% and so, Kr should not be more suitable that N2 for the low specific surface area measurement. But… it is more suitable!
The reason of using Kr is due to its lower vapour pressure (267 Pa) compared to N2 (101325 Pa) at 77 K. The gas adsorption amount in the volumetric method is calculated from the difference between the number of dosed molecules and number of unadsorbed gas molecules at equilibrium pressure. In other words, by assuming both molecular sizes equal and adsorption pressure equal to 50 Pa, it is necessary to measure the pressure change of 0.16% (=50/30450) for N2 and 38% (=50/130) for Kr at the same relative pressure (P/Po=0.3, N2=30400Pa, Kr = 80Pa).
Obviously, it is easier to measure larger pressure change, and therefore, the accuracy of the measurement is better. For this reason, the lower the saturation vapour pressure at the adsorption measurement temperature, the more accurate the measurement of low surface areas and so Xe, with vapour pressure equal to 0.23 Pa at 77K, is still a better gas to measure low surface areas. Unfortunately, Xe is much more expensive than Kr…
Vanessa answered perfectly. We indeed often use Kr instead of N2 adsorption for estimating the surface area of macrocellular solids.
Alain
Measurement of very low surface area samples by BET using nitrogen or argon adsorption at liquid nitogen temperature has a limited detection. The common alternative is krypton adsorption, at liquid nitrogen temperature (i.e. 77.4 K), which improves the detection limit significantly and allows to measure surface areas down to 0.05 m2 or less.
A question related to BET measurements... suposing that I have hundreds of m2/g, what is the minimum material mass that I could measure with N2 or Kr.
@ Erica Antunes
For Nitrogen at 77 K, usually you need to have ~ 10 m2 of sample inside the cell. So if your sample has "hundreds" of m2/g, then you need "hundreds" of milligrams. As a reference, for very high surface area samples (1000 - 2000 m2/g), then even 10 mg will do the job in a well-calibrated apparatus.
For Krypton, you need much less, say, 10 times less... however, you will have the problem that the weighing is not reproducible (too difficult to weigh and load less than a mg; most will stick in the walls of the cell).
Dear Fernando Fernando Vallejos-Burgos
Do you have any experience with carbon nanotube films?
Would be possible to measure surface área of carbono nanotubess films?
Thanks for your time and for share your knowledge!
I have limited experience on those.
You can probably estimate their surface area according to your preparation method. Then, just compare to what other people have reported for measurements of low surface areas with Kr.
I sure that you cannot measure the area with N2 at 77 K.
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