Consider just the pores in a porous sample. Let r = pore radius and l = pore depth. From this, we obtain the surface area = 2*Pi*r*l and volume = Pi*r2*l per pore. Multiple this by the number of pores on the particle. The surface area of pores can be far larger than the surface area of the macroscopic particle itself.

Is this the relationship the you are missing?

Professor Weimer, thank you for answering

I understood but I mean that sample D has greatest surface area, obviously it must have smallest pores and smallest pore diameter, but you can see that sample C has smallest pore diameter in this case. I don't realize why sample C could have smaller pore diameter than sample D.

> I mean that sample D has greatest surface area, obviously it must have smallest pores and smallest pore diameter

Unfortunately, I cannot see the "obvious" in your statement. In fact, I see exactly the opposite, as I have explained with my statements. Perhaps you should explain with equations to prove your statement. I fear otherwise that you have obviously taken a wrong turn in your thinking.

Excuse me Professor

Whether can it be concluded that a porous particle has large surface area may refer to have fine pore in particle?

This is my opinion.

Unfortunately, I cannot understand your new question. It is only more confusing. My guess now is, you need to read basic background information on how to measure and calculate the surface area of porous materials. You have an idea that is wrong and has no basis in anything realistic about such materials, and I cannot write an answer here that will be long enough and any better than what you will find in such resources to fix what you are not seeing.

You're right. I'm probably confused. I'd better study more.

Thank you so much professor

As you think, it is usual that the particles having smaller pores also have a larger specific surface area but the surface area of one gram of particles depends also on the number of pores is in that particle, ie of its porosity. There may be a particle having very small pores but only a small number of pores and hence a small specific surface area

I understood Mr. Cuellar

My main problem is analyzing of Specific Surface Area (SSA) and pore diameter.

According to attachment table SSA of sample B is smaller than sample A but in pore diameter sample A is larger than sample B. Your answer means sample B may be have less porosity and then have less SSA.

As well as this condition is in between sample C and D.

We analyzed that SSA are decreased in sample A to B due to increasing in agglomeration in particles. Then SSA of sample C and D were increased due to decreasing of agglomeration.

But the pore diameter variation were decreasing from sample A till C and then was increasing for sample D. How do I analyze these conditions?

Sample A, B, C and D are 10, 20, 30 and 40% wt. starch content in fuel mixing respectively for sol-gel auto combustion synthesis.

Dear Arash as you have noticed that sample D  have highest surface area of around 48.21 m2 /gm but having an average pore diameter of 9.32 nm. Whereas the sample C have surface area around 28.931 m2/g but it have an average pore diameter of 7,6 nm. Even though the average pore diameter is more in sample D than the sample C, the number of pores present in sample D or the porosity of it is more than the sample C and hence sample D is having more surface area.

As you have mentioned that since the surface area of sample D is more and obviously should have smallest pore is not always true. Because it is not only the pore size alone which determines the surface area but also the number of pores present also matters a lot.

Dear Bikash , yes you're right. I don't know how I can analyze this situation (?) that in sample  A till C pore diameter was decreased and then to sample D was increased. Also variable in specific surface area for all samples weren't linear.

Thank you so much  

First off, surface area measurements can have an error of between 1 to 3% so your surface areas should not have decimal places. Likewise your pore diameters should have at most 1 decimal place. Now the relationship between pore volumen and surface area to give you the pore diameter is just trigonometry. However, your samples could easily be non-porous with these low surface areas. The aerosil silicas produced by Degusa can have up to 200 m2/g surface area and they are non-porous, giving a Type II isotherm. If you believe your samples to be mesoporous then run a full adsorption/desorption isotherm and you should see a well defined hysteresis loop.

Best regards,

Malcolm

4V/S only really applies to cylindrical pores, as it is derived from that geometrical model, so this might give you erroneous numbers anyway. If you know the average NP diameter and density of the bulk solid, then you can readily calculate the external surface area per gram. Have a look and see how much that accounts for (I'd assume a slightly higher error in surface are measurement than Malcolm, maybe 5%). Given the 10nm pore diameter calculated by BET, there cant be that many pores per nanoparticle anyway (unless the NPs are pretty big!) I'd guess the majority of the surface area is external

what about the porosity of these samples. Are they micro, meso or maco porous material because this does matter in this case 

If you use the method of Rouquerol, which I described above, and you find that the máximum value for which you can use the p/p° values is at about 0.1 then the samples are microporous. You can determine the micropore volumen by using the t-plot analysis, which in the case of microporous materials you are looking for the linear portion of the plot in values of about 0.8 to 1.5. If your samples are mesoporous, macroporous or nonporous a linear portion of the t-plot from 0.354 up to about 0.8 should pass through the origin i.e. no positive intercept. Mesoporous samples will give you a hysteresis loop if you run the full nitrogen adsorption/desorption  isotherm. The amount adsorbed at a relative pressure of 0.96 on the desorption branch will give you the pore volumen of all pores below 50 nm i.e. micro and mesoporosity. For macroporous materials you should use mercury intrusión porosimetry which covers a pore range from about 150 µm down to 7.5 or 3.75 nm (the lower limit depends on the máximum pressure reached in the device 2000 or 4000 atmospheres.

The specific surface area of a particle is a function of porosity.