Dear Arash,

Are you sure that BET can give different pore diameters with BJH? BET theory points the multi-layer adsorption. Normally, BET equation is used for specific surface area determination, BJH can give the pore diamrters and pore distribution, both of which is based on the sorption isotherm. Additionally, BET equation is suitable for the relative pressure (P/P0) between 0.05-0.35. BJH is given based on the capillary condensation theory, with an asumption that the pore is cylindrical. I think you had better check the report and find the origin of the pore diameter value. Hope my answer can help you.

Best regards.

Dear Xiaojun

I take a snapshot from the report in attachment file. The report calculated by 4V/A equation. A is equal S(total) minus S(external).

Thanks for your answer

Dear Arash,

Here I would like to give you some personal understandings. As the average pore diameter is given by 4V/A equation, the value refers to V (volume) and A (area). Of course, the 4V/A equation is according to the cylindrical pore. A is given by BET equation, which is the same in calculation of average pore diameter by BET and BJH. The difference is that the V used in these two methods is different: a) by BET, V is a single point volume which generally is the total volume less than the biggest P/P0; b) by BJH, V is a definitive volume which represents a volume at a range of  P/P0 (or at a range of pore diameters). Maybe you can see the difference in you report. To sum up, the average pore diameter by BET and BJH is different based on their limiting conditions. 

For which one is more accurate, I think it depends on your samples or your need. As mentioned above, 4V/A just is an equation with ideal limiting condition. So this value should be careful in using.

Dear Arash,

The average pore diameter you derive, is usually obtained by the Gurwitch rule : D= 4V/S where D id the average pore diameter, V is the total pore volume and S the specific surface area usually obtained using the BET model.

However, this geometrical relationship is based on some assumptions :

Pores must be homogeneous in diameter

Pores must be cylindrical and rigid.

Clearly, you can only obtain a single value for D which means an average value.

The BJH method will give you a pore size distribution, a much more informative result.

It is based on geometric calculations of species being desorbed at given relative pressures.

This model requires the Kelvin law which relates the relative pressure at which condensate gas will evacuate pores satisfying this equation

This model also requires a relationship between the relative pressure and the thickness of the adsorbed multilayer. This can be represented by the Harkins and Jura equation, but others may apply.

For applying this model, you need to carefully decide at which relative pressure you start your calculation : the saturation of the mesoporosity is usually the place to start.

This topic is extensively documented :

For instance, Adsorption by powders and porous solids, Rouquerol, Rouquerol, Sing and Maurin, Elsevier, 2nd edition, 2014, and many other reviews....

To answer your question, I would say that it is difficult to compare a single value and a distribution.

Now, the average pore diameter will be a good approximate, at least if your porosity is homogeneous in diameter. In all other cases, the BJH methodology is far more satisfying, if used in an appropriate fashion.

I hope it helps.

Kind regards

The BET equation has been developed to calculate the surface area of a finely divided solid. The equation does neither provide a pore size nor a pore size distribution. What people do to calculate an average pore diameter is to assume to presence of uniform cylindircal pores. The total amount of nitrogen taken up at a pressure of 1 atm and a temprature of 77K gives the total pore volume. With the model of cylindrical pores the total pore volume is 1/4*pi*d*d*l, where d s the mean pore diameter and l is the total length of the pores. If the BET surface area measures the total surface area of the pores the BET surface area S(BET) = pi*d*l. From the two equations l can be eliminated and the average diameter d can thus be calculated.

The Barrett-Joiner_Halenda procedure assumes capillary condensation of the liquid nitrogen within the pores and calculates from the relative pressures and the amount of nitrogen taken up at a given relative perssure of the sorption isotherm taking into account the adsorbed layer of nitrogen and the capillary condensed nitrogen the pore size distribution. That the procedure is not well founded apperars from the fact that the  adsorption and the desortpion branch lead to different pore size distributions. Therefore the desoption branch is usually employed.

We published recently a paper on the subject of accuracy of BET measurements and the BJH distribution. Conclusion is that the meaning of the latter is doubtful and not much value should be given. See attached, contains extensive information.

could you guys help me to calculate dV/dw equation to draw a pore size distribution curve?

Dear Sabrina

I have a xlsx file which is made for calculating PSDs. If you send me your data n = f(p/p°), I will send you the corresponding BJH plot

dear Philippe Trens, 

I also interested to know and calculate pore size distribution curve. 

Excellent discussion. Thanks to all contributors.

Ångström

which equals to 10 nm

BJH actually measures pore throat sizes and is comparable to pore throat sizes derived from mercury injection data.  Both methods measure the volume of porosity accessed via throats or constrictures of a given size.  BJH method requires that you use the desorptive branch for its calculation.  A colleague likened the adsorptive branch as to going to a movie theater and taking your seat.  It is only when you and everyone else are leaving after the movie that you become keenly aware of the size of the doorways (desorptive branch).  When your adsorptive and desorptive branches are the same (no hysteresis), then you can apply BJH to the adsorptive branch.

J.W. Geus Dear Prof. Thank you so much for the valuable noteinformation.

Thanks to all for sharing some valuable information regarding calculation of pore diameter using pore volume and pore surface area.

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Hi..could any one explain why the values in BET analysis written in the form of division of two value like this( BET Surface Area: 0/6265 m²/g ) please?

J.W. Geus I am studying a catalyst developed over a substrate. Can I still use the BJH desorption average pore diameter?

J.W. Geus Arash Motevalian Can we say BET for microporous and BJH for mesoporous materials in general ?

how can calculate specific area and pore volume by liquid adsorbate on solid adsorbent using B.E.T.

thanks for the various explanation! I love the theatre story it made clear!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

BET measures the specific surface area of materials while BJH is a pore size distribution determination method. BET, V is a single point volume which generally is the total volume less than the biggest P/P0 where as BJH, is V a definitive volume which represents a volume at a range of pore diameters.

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