## B.E.T. Theory/Equation

DDTea - 15-10-2009 at 15:53

I was touring the quality control lab at a company that produces catalysts a while back (I was seeking a job, but they went for someone with more experience, but I digress). They were showing me the equipment they used to measure the surface area of a catalyst per gram. The senior chemist gave me the example of an 8.5x11 piece of paper: "What is the surface area? 8.5x11x2." Then tore the paper in half and crumpled it into a ball. "Now how do you calculate the surface area?"

Again, this company was interested in catalysis, but the methods they use may be applicable to energetics, especially propellant design. The center of their work in that lab was around the B.E.T. equation (see http://en.wikipedia.org/wiki/BET_theory ). It was an equation developed by 3 members of the Manhattan project, who used to go bowling together, to calculate the surface area of irregularly shaped particles. They company I visited used two methods: wetting with liquid nitrogen, and wetting with mercury (I had never seen so much Mercury in one place! I'm almost happy I didn't have that position...but again I digress.)

The idea, basically, is that we *know* the size of a nitrogen molecule. Since nitrogen will wet the surface of a particle in a fine layer (e.g., catalytic material, rocket propellant), if we measure the amount of Nitrogen coming off the surface of interest when the temperature is raised, we can quantitatively determine the surface area of the particles. (This is my understanding of the process, correct me if I'm wrong). The company had machines that automatically ran the procedure and did the calculations, but I inquired into how at least the calculations were done: "We simply use the ideal gas law." For a nitrogen molecule, I guess that's pretty applicable. I regret not asking them what the procedure was.

I'm posting this in the Energetic Materials forum because I immediately saw a possible application to this field. There are probably some difficulties expanding this to energetic materials and I imagine this approach would strictly be confined to "low order" explosives since rapid temperature changes with high explosives can be dangerous. But this could, for example, help the amateur rocketeer in assessing the quality of his fuel, gram per gram.

Any thoughts on this approach and how applicable it is to energetics? What about actual experimental implementation and obtaining liquid nitrogen? What sort of apparatus would we set up to take the measurements?

Cheers, I hope this turns into something useful to someone.

EDIT 20:22 15/10/09: Does anyone have access to the following journal article: S. Brunauer, P. H. Emmett and E. Teller, J. Am. Chem. Soc., 1938, 60, 309 ? It's the original article explaining BET theory, but my library doesn't have access.

[Edited on 10-16-09 by DDTea]

Magpie - 16-10-2009 at 12:18

It's been a long time since I've read anything on the BET method for determining surface area. This would seem to be a very challenging problem. Has the BET theory been verified by comparing results with calculations for a geometrically simple surface?
DDTea - 16-10-2009 at 13:10

 Quote: Has the BET theory been verified by comparing results with calculations for a geometrically simple surface?

I truly don't know about this. A simple experiment might constitute finding the surface area of a few marbles using LN2, versus determination by integrating the surface area. However, discrepancies might arise due to the porosity of the material, so there remains the question of how "simple" a "geometrically simple" surface really is.

Another concern with this method is the question of how thick the LN2 layers on the surface would be--is it a safe assumption that a 1 molecule-thick layer forms evenly over the entire surface? The procedure for wetting and measuring the off-gassing seems tricky, especially without decent instrumentation. At the lab I toured, the Pressure and Temperature were computer controlled, so the number of moles were easily counted by the Volume of N2 released.

I really need to read this paper to understand how the procedure is done.

merrlin - 16-10-2009 at 16:41

Micromeritics has been making instruments for some time. Below is a link to some of their technical papers. A lab I once worked in had one of their units for determining the surface area of high surface area electrode materials (e.g., ruthenium oxide). Characterization through BET surface area measurements is pretty well established in certain areas of research.

http://www.micromeritics.com/

Attachment: An_Introduction_to_Chemical_Adsorption_Analytical_Techniques_and_Methods.pdf (40kB)
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sparkgap - 16-10-2009 at 20:00

Attached is the original BET paper.

Here's a nonspecialist's question: why wouldn't I use Langmuir's or Freundlich's instead of BET for this particular scenario?

sparky (~_~)

Attachment: betpaper.pdf (1.1MB)
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JohnWW - 16-10-2009 at 22:00

From memory, I believe those three Manhattan Project (Los Alamos, NM, from the late 1930s to late 1940s) scientists were Brunauer, Emmett, and Teller. Ed Teller ("the father of the bomb") died only a couple of years or so ago.
merrlin - 16-10-2009 at 23:50

 Quote: Originally posted by sparkgap Here's a nonspecialist's question: why wouldn't I use Langmuir's or Freundlich's instead of BET for this particular scenario?

I would guess that the reason for using BET is provided in the discussion on pages 312-14 of the paper you provided. The slope and intercept provide for convenient calculation of the volume of gas responsible for monolayer coverage associated with the linear portion of low temperature adsorption isotherms .

sveegaard - 27-1-2010 at 14:51

 Quote: Originally posted by sparkgap Attached is the original BET paper. Here's a nonspecialist's question: why wouldn't I use Langmuir's or Freundlich's instead of BET for this particular scenario? sparky (~_~)

The BET-isotherm accounts for multilayer-adsorption, where a new layer - of for example nitrogen - can adsorb on top on another. This gives theoretical unlimited adsorption, but in reality the sorbent eventually is considered dissolved (or precipitated) in the adsorbent.
The BET-isotherm is widely used in aqueous systems.