(550a) Adsorptive Characterization of Porous Solids: Error Analysis Guides the Way

Adsorptive characterization using nitrogen at 77 K is one of the most widely used techniques to assess textural properties of porous adsorbents. Especially the pore volume, specific surface area and pore size distribution are frequently reported. Despite the fact that most popular methods to deduce these quantities, the method posed by Brunauer, Emmet and Teller (BET) [1] for the specific surface area and the method developed by Barrett, Joyner and Halenda (BJH) for pore the pore size distribution, [2] have been used for many decades, there are still inconsistencies in the exact calculation procedure of these methods and still wrong and/or statistically insignificant conclusions therefrom, as will be elucidated in detail in this contribution. Based on a thorough error analysis on the accuracy of volumetric nitrogen adsorption measurements, the influence of experimental uncertainties is analysed. This yields not only insights in the uncertainty in derived properties (pore volume, BET surface area and BJH pore size-distribution) but also generates practical recommendations to optimize accuracy of N₂ adsorption measurements. Consequently, guidelines are developed to obtain representable accurate textural properties.  Especially the derivation of specific surface areas requires attention, as erroneous results are easily obtained. A variety of sorbents (MOFs, zeolite, activated carbon and alumina) has been used in this work to ensure that obtained conclusions and posed guidelines hold for a wide range of commonly used porous materials. For (BJH) pore size distributions, statistically irrelevant or highly inaccurate results are frequently obtained. MIL-101, arguably the metal-organic framework (MOF) most reported on, has been characterized by a multitude of researchers and serves thus well to exemplify the current state of characterization using N₂ sorption in literature. In many cases the determination of pore volume and specific surface areas has been executed wrongly and underlines a clear potential for standardized determination conditions for textural properties. In summary, to improve the meaningfulness of derived properties and to minimize statistical uncertainties, practical recommendations and guidelines are proposed for experimental operation variables and data analysis. Some of these are:

• The relative uncertainty in pore volume is lowest when the V_manifold/V_cell ratio is between 2 and 3.
• A simple two-point BET method is proposed to determine a priori the upper relative pressure boundary of the BET window (close to saturation), as alternative to the method reported by Rouquerol et al.
• For the lower relative pressure limit determination it is suggested to analyse Studentized residuals. Provided the model isotherm is correct, data points become eligible for possible exclusion when | res_i^s| > 2-3.
• The magnitude of the 95% confidence interval found for BJH-pore size distributions severely impedes drawing quantitative conclusions.

REFERENCES

[1] S. Brunauer, P.H. Emmett, E. Teller, Adsorption of gases in multimolecular layers, Journal of the American Chemical Society, 60 (1938) 309-319.

[2] E.P. Barrett, L.G. Joyner, P.P. Halenda, The Determination of Pore Volume and Area Distributions in Porous Substances. I. Computations from Nitrogen Isotherms, Journal of the American Chemical Society, 73 (1951) 373-380.