In 1938, Brunauer, Emmet, and Taller, based on Langmuir's theory, developed a theory of multi-molecular adsorption. The basic assumption of their theory (in short BET theory) is the possibility of applying the Langmuir equation to each adsorbent layer. BET equation describing the amount of substance adsorbed by the unit mass of the adsorbent, as a function of the gas pressure, which describes the physical adsorption where the formation of multi-molecular layers occurs. This equation is known as BET. Using the BET isotherm, the most important parameter of the porous structure, i.e. the specific surface, is determined. The specific surface means the specific for each material the sum of the external "geometrical" surfaces of individual grains per unit of mass or volume. The surface area of the SBET material is determined by adsorption isotherms analysis (most often nitrogen at 77-78 K) using a specific linear form of this equation.

The BET method is used to determine the specific surface area of powders and other porous materials and is considered the most adequate for the size of the surface, as the physicochemical boundary between the solid and the surrounding phase of the molecule at the molecular level.

From the range of pressures 0.03-0.35 we can calculate the BET specified surface area from the linear form of the isotherm.

From this same range, we can calculate the Adsorption average pore width (4V/S). This means hydraulic pore width and of course the average value. 10 nm means mesopores but does not exclude other types. So, for obtaining more accurate pore width values the using BJH theory for adsorption or desorption branch of isotherms should be used (all range of p/p0). For micropores, the t-plot method should be used. Then the range of pressures is from 0.03-0.6 p/p0. for the calculation of Smic, the calculate the statistical thickness t=13.99/(0.034-log(p/p0))^0.5 for all points from the range 0.03-0.6 and draw the linear curve.Smic=SBET-Sext where Sext=SBET*b (from the linear equation). For obtaining the micropores width the HK (Horvath-Kawazoe) or DFT should be applied.

You can always apply the SAXS technique for obtaining pore size distributions if you have a two-phase system with quite a nice electron density differences.

In 1938, Brunauer, Emmet, and Taller, based on Langmuir's theory, developed a theory of multi-molecular adsorption. The basic assumption of their theory (in short BET theory) is the possibility of applying the Langmuir equation to each adsorbent layer. BET equation describing the amount of substance adsorbed by the unit mass of the adsorbent, as a function of the gas pressure, which describes the physical adsorption where the formation of multi-molecular layers occurs. This equation is known as BET. Using the BET isotherm, the most important parameter of the porous structure, i.e. the specific surface, is determined. The specific surface means the specific for each material the sum of the external "geometrical" surfaces of individual grains per unit of mass or volume. The surface area of the SBET material is determined by adsorption isotherms analysis (most often nitrogen at 77-78 K) using a specific linear form of this equation.

The BET method is used to determine the specific surface area of powders and other porous materials and is considered the most adequate for the size of the surface, as the physicochemical boundary between the solid and the surrounding phase of the molecule at the molecular level.

From the range of pressures 0.03-0.35 we can calculate the BET specified surface area from the linear form of the isotherm.

From this same range, we can calculate the Adsorption average pore width (4V/S). This means hydraulic pore width and of course the average value. 10 nm means mesopores but does not exclude other types. So, for obtaining more accurate pore width values the using BJH theory for adsorption or desorption branch of isotherms should be used (all range of p/p0). For micropores, the t-plot method should be used. Then the range of pressures is from 0.03-0.6 p/p0. for the calculation of Smic, the calculate the statistical thickness t=13.99/(0.034-log(p/p0))^0.5 for all points from the range 0.03-0.6 and draw the linear curve.Smic=SBET-Sext where Sext=SBET*b (from the linear equation). For obtaining the micropores width the HK (Horvath-Kawazoe) or DFT should be applied.

You can always apply the SAXS technique for obtaining pore size distributions if you have a two-phase system with quite a nice electron density differences.

A relative pressure up to 0.6 is too hight for the BET, the standard BET uses 0.05-0.32. But this is the "standard" value, sometimes much lower values have to be used. For activated carbons with a high percentage of micro-pores values up to 0.2 or even lower must be used. For a proper measurement the C-value is positive, y-intercept for the transformation plot is >0 and the correlation value for teh transformation plot is 0.999 or higher.

But no pore volumes are calculated.

The average pore diameter is not enough to determine the porous nature of your material. I recommend that you do a pore size distribution, normally this is done using the BJH method, however if you have microporosity it is better to use a DFT method. Another thing that I can recommend is that the analysis is carried out with Ar and not with N2. When you make the measurement of microporous materials with N2 you can have erroneous readings, due to the N2's quadrupole moment, which leads to specific interactions with functional groups or exposed ions on material surfaces.

Do you have measured full isotherm? For calculating surface area using BET model relative presure 0-0.25 is sufficient. But you can't properly calculate pore size from it. For calculation of pore size distribution you have to measure full adsorbtion-desorbtion isotherm. So, then from desorbtion curve using BJH or DFT model you can calculate pore size distribution.

You can use the nitrogen absorption desorption to know the type of your material and the BJH technique can help you to calculate the distribution porosity and the pores size

Thanks to everyone! I really appreciate your help and recomendations; I will try the BJH method. Now I am curious, do you know how did I get a size of 10 nm (mesopores) if the BET presure is not sufficient to calculate pores with this dimension?

Thanks

Depending on the instrument used pore sizes from 0.1 to 300 nm on diameter can be measured.

Joan Concha What is ment by BET pressure? The BET is just an algoritm to analyze the data obtained at different relative pressures. The isotherm is a plot of moles of gas (or cm3 of gas) adsorbed as a function of relative pressure (p/p0).

You should first obtain the full adsorption isotherm, then, according to its shape, you can more or less guess which type of pores your solid has (the type of the isotherm, according to iupac: type I if micropores, type II if non-porous or large pores, type IV if mesopores, etc...).

Only AFTER you identify the type of porous solid you should use a model.

It cannot be done in reverse, since you don't know which type of porous solid you have.

Fernando Vallejos-Burgos :

Suppose after determination of porosity type we deal with a type IV isotherm with a type H3 hysteresis which means the substance has slit-like pores.

Is BJH method an appropriate method for determining pore size distribution?

The basic assumption in both BET and BJH methods is having cylindrical pore sizes.

Maryam Khandan

No: the BET method does not assume pore shapes. The BET method is only strictly valid for non-porous samples (check its derivation).

BJH is for cylindrical pores, so wouldn't work either.

I would recommend using the more advanced DFT method (in any NLDFT or QSDFT flavors) for this task.

Another option is a modification of the BJH method for slit-shaped pores, such as

Article Improved calculations of pore size distribution for relative...

Fernando Vallejos-Burgos: Many Thanks! Very helpful.

Would you please help me with another question too?

Considering the erroneous specific surface areas reported by BET and BJH in case of materials having slit-like pores, why BJH method always determines higher surface areas than BET method?

Slit formed pores are mostly found in carbons and activated carbons. Cylindrical pores appears on oxides. But what model you use must be explained when the results are published.

Maryam Khandan

I wouldn't worry too much about it, since both models are basically incorrect for slit shaped pores, then whatever explanation exists is anyway not applicable.

It is irrelevant which one is less wrong or more wrong.

In any case, if you [really] have to choose one, I would go for BET surface area only because it allows easier comparison with other literature.

You get different results when You use different algorithms in the calculations. BET is not an absolute method, the same concerns BJH and DFT but You can compare different materials. Always mention how the results are calculated.

Fernando Vallejos-Burgos Thanks so much.

Hi Maryam,

For being able to assess micropores by physical adsorption your instrument must be able to work at relative pressures around 1e-5. Micropore size distributions can be calculated by DFT but you must have a library of these routines. These are normally provided by manufacturers. Finally, be aware that BET calcultations for the surface area of microporous materials must be interpreted as apparent surface areas. You may want to read the following paper which explains why and gives criteria for improving these calculations: Article Is the BET Equation Applicable to Microporous Adsorbents?

Víctor Baldovino Hi Victor,

Thanks so much for your answer and the referred article.