for example Vm= 71 cm3.g-1. That's a very high number
This question continues the previous question, which so far I do not know the answer
https://www.researchgate.net/post/Why_is_sometimes_the_pore_volume_calculated_by_the_BJH_method_higher_than_the_pore_volume_obtained_by_the_BET_method
First, what do you not understand after reading literature resources that define Vm from first principles and in practice? Secondly, how is your value "_very_ high"? Compared to what and/or in what context? Finally, you will do far better to make your statement self-contained rather than referencing to a different post.
Dr. Weimer, Thank you for your guidance.
The definition of Vm in the resources is the volume of N2 adsorbed when the entire adsorbent surface is covered with a complete unimolecular layer.
The word "very high" refers to "monolayer" adsorption which seems to be a high number. Because in the calculation of the TPV (total pore volume), the total nitrogen adsorbed (multilayer) is almost below 1cm3.g-1. Of course it can be said that Vm for the entire surface and TPV are only for pores.
Based on analyzes results Vm does not depend on TPV. And as the surface area increases, Vm also increases and vice versa.
I interpret your question is better stated in this way: "Why do I get a value of Vm = 71 cm3/g for my data"? First, address these questions:
* Have you performed a calibration experiment to prove that your testing methods are proper?
* How many replicant tests have you performed to confirm the value is valid?
* Do you expect anything significantly different and why or why not?
Otherwise, we know from the fundamental assumptions in the BET derivation that we have no dependence of Vm on pore volume and that we expect a linear relationship between Vm and S. Are you puzzled by this?
Requirements for test, including repeatability and calibration experiment, are considered. Also, all analyzes show high value. The high value of Vm can be justified by the value of S. I still do not know how much depth of pore should be as the porosity that is reported to be its value. For example, in my sample FESEM image, you can see a particle full of pore but I think that many of them are not considered porosity, but they are in the calculation of Vm and, consequently, S. This can be a reason for tangible difference of values of TPV and Vm.
The question keeps changing. New information is added each time. Now you seem to be asking whether and how TPV and Vm are related. Start from the perspective of a single pore of radius r and length L.
TPV = Pi r^2 L and S = 2 Pi r L
Therefore TPV = S^2/(4 L). We agree that Vm is proportional to S. Therefore, for a single pore, TPV is proportional to Vm^2/L.
For a system with N pores of the same radius and length, the equations are TPV = N Pi r^2 L and S = 2 N Pi r L. The analysis gives TPV = S^2/(4 N L) and TPV proportional to Vm^2/(N L).
How to calculate the TPV (total pore volume) via a single pore. Is it assumed that the length and radius of the total pores are equal? Or are TPV and S the volume and surface area of a single pore, respectively?
if TPV = S^2/(4 L), length of pores of 1g is Hundreds of kilometers!!!
And the last equation
TPV=C Vm^2/L, that unit of C is cm-2. Also C must be different for each sample! Because the results indicate that Vm is not related to TPV. for example;
Vm; 57, 71, 63 cm3.g-1
TPV; 0.312, 0.350, 0.474 cm3.g-1 respectively
See my amended answer above for more than one pore. The next step is to consider when pore sizes follow a distribution in radius and length. One must integrate over the distribution function.
In review, this question demands an understanding of the fundamentals of porous materials. The information you need is presented elsewhere in far better detail than can likely be provided here. By example, search for textbooks or literature resources that explain the fundamental relationships between pore volume and pore area starting from a single pore and working through systems with pore size distribution functions.
This discussion from 4 years ago might help:
https://www.researchgate.net/post/What_is_the_difference_between_BET_and_BJH_methods_for_surface_analysis
Volume adsorbed for monolayer coverage of adsorbent by adsorbate.
Hope this may help..
It depends of the adsorption model that you are using.
Best Regards
SAM
vm represents the adsorbed volume which corresponds to a monolayer coverage. vm is calculated from the slop and intercept of linear bet equation.
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