If we have carbon mesoporous material for caluculating the total specific surface area(external&internal) but how?what method we should follow?and If any possibility is there to maintain external surface area is>2nm and internal surface area is
External surface area IS NOT the area of pores larger than 2 nm.
To evaluate external surface area and total surface area you need to use the Subtracting Pore Method based on gas adsorption developed by Kaneko's group based on alpha-S plot. You only need the adsorption isotherm! (N2 at 77K or Ar at 87 K work very well).
Kaneko, K.; Ishii, C.; Ruike, M.; Kuwabara, H. (1992). "Origin of superhigh surface area and microcrystalline graphitic structures of activated carbons". Carbon. 30 (7): 1075–1088.
Mercury porosimetry is great technique, much better than other methods (e.g. gas porosimetry for BET surface area) for meso- and nanopores. It's extremely consistent from 100 nm down to roughly 5 nm, or potentially 3-4 nm with more robust models (the one I use is 30,000 psi, while others go to 60,000 or potentially higher). The ancient Micromeritics machine I use works very well.
http://www.micromeritics.com/Repository/Files/Mercury_Porosemitry_Theory_poster_.pdf
From what I gather, differential intrusion or cumulative pore area vs. pore size are the two most relevant plots, although they really do present the same data.
While it may well beat BET, trying to turn XRD/SAXS data into surface areas certainly carries its own set of problems (e.g. you need to know your particle shapes, and they need to be rather consistent). In my field, internal vs. external pore area is really a pre-determined cutoff that varies depending on your carbon structures, and it's generally extremely easy to see in the data, since you get a huge spike that peters out and then rapidly increases again as you hit the internal area. For my fuel cell catalyst powders, the cutoff is around 10-20 nm for an average 25 nm mean particle size.
There are new machines for smaller regimes - I've been very interested in trying a nanoperm-porometer, which gets you down to 0.5 nm pores (i.e. membrane pores too). This site also has a good overview of your other options:
https://www.seika.com/en/product/measure/porous/nanoperm/
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