Different methods for determining the specific surface often give different results. Therefore, it is much more reliable to look at the dependence of the specific surface area on any parameter first by one method, then by another, etc. Most often, the dependencies are the same.
The remark of Borisov is correct. Gas adsorption of a small molecule like N2 has a relatively fast kinetics and may 'see' the total surface area and for N2 gas adsorption the standard cross sectional area (16.2A^2) is recommended/ accepted. The BET (N2) method is generally accepted, but the resulting BET(N2)-area is still a relative value and not n absolute value.
Adsorption from solution of a large MB ion (!) has an adsorption that is dependent on the solution conditions, MB in aqueous solution can dimerise or adsorb in a dimerised state, MB diffusion in aqueous solution is relatively slow (time scale of the adsorption rather different from N2 Gas ads.), MB may not 'see' the total area (in the case of micropores), has a molecular cross section that depends on the orientation in the adsorbed state.
With adsorption from solution there is no generally accepted method (as with the BET(N2)). So more work is needed to make sure what the value of the obtained area means.
That depends on how your probe interacts with your surface. Different molecules will behave different at the solid surface. Imagine for example that your surface has negative sites distributed homogeneously, the mechanism of adsorption is something near to Langmuir, but if the surface is not homogeneous, they can behave like a Freundlich like..
That said, nitrogen molecules are also susceptible to have different behave on different surfaces, the molecule has a quadropole moment that changes the monolayer formation depending on the surface of the adsorbent. So, the BET method makes use of the multilayer formation to avoid this problem of assembly of monolayer to estimate a more exact value for the surface area.
What I recommend is to be sure if your adsorption isotherm fullfill the requirements of the fitting theory you are using. I see a lot of papers published using BET to isotherms where the theory doesn't apply (as microporous materials, or even with negative C constants), and getting extraordinary high surface areas that doesn't make any sense (as 3000 m²/g) .
MB . With MB the Freundlich eq. should not be used, because this equation applies to adsorption values far below the adsorption capacity and gives no answer with respect to the adsorption capacity.
N2. The BET(N2/16.2 nm2) is a well accepted method for the surface area determination and the limitations are well known, therefore quoting a BET area has a well known meaning. When one considers with N2 adsorption a different molecular area for N2 (a different orientation) this should be specified and the results cannot directly be compared with results ob stained with the standard BET(N2) method (inter laboratory comparison is difficult).
Negative C values are due to using a wrong relative pressure range. When the 'machine' (manufacturers calculation code) gives a negative C, the linearisation has to be recalculated by hand till the C is no longer negative. In general this leads to a high C value. With a high C value the linearised BET line goes through the origin.
With microporous surfaces adsorption is pore filling rather than surface coverage; therefore the BET theory does not apply. Yet, the obtained specific surface area gives an impression of the pore filling capacity for molecules of similar size as N2. Therefore for comparison of a given material and samples with different micropore volumes the obtained values can be used for sake of comparison. The absolute magnitudes of the areas have however no physical meaning.
Methylene blue method indicates liquid phase adsorption of MB molecules, whereas BET surface area measured by gas phase adsorption of N2 Molecules. In general, MB method can be used to get approximate measurements of Surface area without much spending. While BET method can give exact surface area of a material however it's little costly.
the BET method surface area value is less than the value given by methylene blue method because BET method measures only the external surface area since N2 gas does not penetrate into the pores of the material m while MB method measures both external and internal surface areas
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