(340a) All Surface Areas Are Not Comparable.: BET Versus Rlrs

The expanding development of microporous solids such as zeolites and MOFs has driven researchers in these areas to employ conventional Brunauer-Emmett-Teller (BET) analyses to estimate surface areas and even to claim record-high surface areas. The assumptions of the BET model, however, assume the surface covers before pores fill, an assumption which is violated in microporous materials.  As such, conventional BET analyses of adsorption data must be modified to take into account the different mechanisms (pore-filling vs. surface-covering) that exist when micropores are present.. The physics of  sorption processes require that conventional “BET “ analyses of adsorption must be modified to reflect the transition between initial physisorption to monolayer sorption to filling of the pores  with condensing sorbate.

How should we interpret the resulting estimate of a "monolayer volume" (based on the standard volume adsorbed for nitrogen or argon) in terms of an "equivalent surface area" of a highly curved surface and/or of a three-dimensional pore network?  Conventional BET analyses [1,2] of surface areas employ a calculation of the surface area covered by each molecule on a flat (two-dimensional) surface.  For nitrogen, the area per molecule is estimated to be 0.162 nm^2/molecule, and for argon it is 0.138-0.182 nm^2/molecule, depending on the source of the estimate and the assumed reference state. Basic estimates of these areal densities come from liquid or solid densities and associated atomic/molecular volumes.  When applied to truly three-dimensional zeolite and metal-organic framework (MOF) systems, the surface covered by each molecule is probably less:  six molecules will surround a single molecule of similar size in a plane, but this does not make the surface of that molecule six times the flat covered surface of a single molecule! When applied to the truly three-dimensional metal-organic framework (MOF) systems, the surface covered by each molecule is probably far less:  six molecules will surround a single molecule of similar size in a plane, but this does not make the surface of that molecule six times the flat covered surface of a single molecule!

We emphasize that the methods discussed in this section are different from the standard BET analysis, and emphasize that using the “standard” BET range of 0.05 < P/P° < 0.3 for microporous materials should not be done. Note that the C_BET values determined from the naïve application of the “standard” method are negative, and give ridiculous isotherms with asymptotes in them.

We review the work of Rouquerol and coworkers and its implementation and testing by Snurr and coworkers [4], a procedure we call the Rouquerol-Llewellyn-Rouquerol-Snurr modification of the Brunauer-Emmett-Teller method, or RLRS-BET method (pronounced "rollers"); the term "rollers-BET" is an allusion to the Snurr group's method of "rolling" a probe molecule along the surface to estimate the equivalent surface area.  We emphasize that this method is different from the standard BET analysis, and that using the "standard" BET range of 0.05 < P/P0 < 0.3 for microporous materials should not be done---in many cases, the resulting C values are negative, yielding ridiculous isotherms with asymptotes in them.  The RLRS-BET method, though in some cases yielding reasonable surface area estimates [4,5], is entirely empirical, and is not based on physically meaningful assumptions (as the original BET theory is for flat surfaces).

[1] P.H. Emmett, S. Brunauer, The Use of Low Temperature van der Waals Adsorption Isotherms in Determining the Surface Area of Iron Synthetic Ammonia Catalysts, J. Am. Chem. Soc., 59 (1937) 1553–1564.

[2] S. Brunauer, P.H. Emmett, E. Teller, Adsorption of Gases in Multimolecular Layers, J. Am. Chem. Soc., 60 (1938) 309–319.

[3] K. Hammond,  and W.C. Conner, Analysis of Catalyst Surface Structure by Physical Sorption, Advances in Catalysis 56, 1-101 (2013)

 [4] K.S. Walton, R.Q. Snurr, Applicability of the BET Method for Determining Surface

  Areas of Microporous Metal–Organic Frameworks, J. Am. Chem. Soc., 129 (2007) 8552–8556.

[5] Y.-S. Bae, A.Ö. Yazaydín, R.Q. Snurr, Evaluation of the BET Method for Determining Surface Areas of MOFs and Zeolites that Contain Ultra-Micropores, Langmuir, 26 (2010) 5475–5483.

[6] J. Rouquerol, P. Llewellyn, F. Rouquerol, Is the BET Equation Applicable to Microporous Adsorbents, in:  Stud. Surf. Sci. Catal., 2007, pp. 49–56.