I have collected N2 adsorption isotherms using standard conditions at 77 K and up to 1 atm pressure for porous covalent organic frameworks. I want to calculate the micropore surface area of these samples using collected isotherms. I have calculated the total surface area using BET and Langmuir equations using software provided by Quantachrome Instruments. Can anybody give me idea about these calculations of in micropore surface area, pressure range for these calculations, etc.?
Thanks a lot.
If you have a "knee" in your isotherms graph (at low p/po values) you have presence of micropores (< 2 nm), you can use the t-plot method (available in Quantachrome software) to estimate the contribution of surface area for micropores.
Strictly speaking, you can not measure the surface area of micropores because the BET model does not apply to micropores. For micropores it is therefore more relevant to report a volume than a surface. This volume can be obtained using the t-plot model. Using this model, your software will also probably calculate a contribution of the micropores to the surface but this is only an "apparent" surface, that can be substracted from the overall surface area measured by BET to evaluate the mesoporous or external surface area.
The best way to calculate the microporosity (i.e. on Activated Carbons) is the Dubinin-Radushkevich equation. The microporous volume obtained represents
the most important parameter of the D−R model because it describes the precise form of the solid. For use the D-R method you must have several data between 10-4 and 10-6 (p/p0). (see Stoeckli, F.; López-Ramón, M. V.; Hugi-Cleary, D.; Guillot, A.
Micropore sizes in activated carbons determined from the Dubinin−
Radushkevich equation. Carbon 2001, 39, 1115)
To expand on what Juliette posted:
The recent IUPAC report "Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution" Pure Appl. Chem. 2015; 87(9-10): 1051–1069 does point to applying BET method to microporous materials, by referencing the method of Rouquerol (J. Rouquerol, P. Llewellyn, F. Rouquerol. Stud. Surf. Sci. Catal. 160, 49 (2007).).
In recent Quantachrome software this "point selection method" is available under "edit data and tags" as the "micropore BET assistant". It is described in the attached technote.
An equivalent technique for choosing P/Po points for calculating BET of microporous materials is to select a wide range of data points for single-point BET calculation. The single point values will go through some maximum value. Use that point and the previous four (5 in total) for the multi-point BET calculation.
Then use the t-plot method to find the non-micropore area (so-called "external area") micropore area being the difference between it and the BET area. Make sure the data points used for t-plot are in the appropriate P/Po range. Micropore volume is taken from the intercept of the t-plot.
Of course, the most reliable method available today is to use NLDFT. Even when using the Rouquerol or single-point approach to BET, it can nevertheless still over or underestimate (depending on pore size and shape) the true surface area because of the micropore filling limit being mis-interpreted as the monolayer coverage. Furthermore, simple pore volume estimations (like t-plot) do not take into account the differences in the density of the fluid filling the micropores and its variance with pore size! NLDFT overcomes both of these limitations of the legacy methods.
Starting from the smaller pore size, due to the higher overlapping potential that can overcome the translation energy of the N2 easier, pores are filled and then progress into larger pores, until the monolayer N2 is formed for the sample. Actually you calculate the BET surface by monolayer adsorption per sample weight of N2 in your sample : S=V*Na*A/Va(Na=6.02*10^23, Va=22.4 g/mol, V is volume for monolayer adsorption per sample weight ). That is basic principle under the assumption that the upper layer for condensation is in equilibrium with the first layer for adsorption on the homogeneous surface. However, the realtionship of monolayer volume and relative pressure is linear within certain pressure range which allow us to get the monolayer volume from that diagram.
Dear Pradip S Pachfule please take a look at the following attached PDF.