Emanuele, Adam, Muneer, I think you missed the main content of Mohnsen's question: he was asking for an example calculation.

Mohsen, it is relatively easy:

- what is the density of the material?

- you assume 20 nm, then assume it is spherical

- you calculate the volume of a sphere with a diameter of 20 nm (you look yourself for the formula in some geometry textbook)

- with the density, you calculate the weight of 1 particle

- then you divide your "100 g" by the weight of 1 particle and you know how many particles you have

- then you take the geometry textbook again and calculate the surface area of a sphere with 20 nm diameter

- then you multiply with the number of particles you had calculated before ...

... and you know the answer to your question.

Muneer, aggregation does not play a role in specific surface as the contacts "area" for spherical particles contacts are striclty point-like, practically no area.

Well, it depends. If the nanomaterial is composed of single spherical particles (20 nm diameter) the calculation if extremely elemental. If you have single non-spherical particles, the determination is already more complicated: a geometrical calculated surface area must consider the shape factor and/or pores size. If you have aggregates, well the determination is even more difficult and it involves fractal dimension concepts and exposed or non exposed surface area.

Emanuele is right. I think you best approximation is to measure the size distribution of the particles with an AFM, TEM or SEM and use ImageJ or other image processing tools to get the area distribution of the particles. Assuming circular particles, you can approximate volume or diameter or other properties, although area is the best bet. This method is not free of errors of course, due to issues with the image measuring and processing. These errors are further enhanced if you make morphological assumptions (like circularity)

Hi Dear Mohsen

I think not only the size of particle play main role to determination of surface, but many parameters also should be consider such as agglomeration and aggregation of particle which can see by SEM and TEM. on the other hand also the pore size and pore volume are very important. the instrument such as the ASAP 2020

Accelerated Surface Area and Porosimetry System more accurate for that aim and you can calculate as you want of amount after determine certain amount (for example 1 gm) using ASAP 2020.

WITH BEST REGRADS

Emanuele, Adam, Muneer, I think you missed the main content of Mohnsen's question: he was asking for an example calculation.

Mohsen, it is relatively easy:

- what is the density of the material?

- you assume 20 nm, then assume it is spherical

- you calculate the volume of a sphere with a diameter of 20 nm (you look yourself for the formula in some geometry textbook)

- with the density, you calculate the weight of 1 particle

- then you divide your "100 g" by the weight of 1 particle and you know how many particles you have

- then you take the geometry textbook again and calculate the surface area of a sphere with 20 nm diameter

- then you multiply with the number of particles you had calculated before ...

... and you know the answer to your question.

Muneer, aggregation does not play a role in specific surface as the contacts "area" for spherical particles contacts are striclty point-like, practically no area.

Bernhard,

I assumed Mohsen knew how to calculate the specific surface area of spheres by knowing the density and diameter.

In addition, I partially disagree with you. Aggregation and agglomeration can have a huge effect in the specific surface area of particles even if the primary particle is a sphere.

Please consider the fundamental work done by Ku and others in Cincinnati.

Ku, B. K. (2010). Determination of the Ratio of Diffusion Charging-based Surface Area to Geometric Surface Area for Spherical Particles in the Size Range of 100–900 nm. J. Aerosol Sci., 41:835–847.

Ku, B. K., and Kulkarni, P. (2012). Comparison of Diffusion Charging and Mobility-based Methods for Measurement of Aerosol Agglomerate Surface Area. J. Aerosol Sci., 47:100–110.

Use BET surface area analyser.

For mathematical calculation give the shape / morphology of the particle.

Emanuele, do you have any pdf or a website to access the publications you mentioned? I still maintain what I said: the surface area for spherical particles is nbot affected by agglomeration, as the contacts are essentially made by points.

What could be affected is the *measurement*, like by BET, which can heavily be affected by surface active agents (tensides) or colloidal stabilizers which may remain on the surface and may prevent N2 (if BET is done using N2) to access the surface (I had some cases long time ago where the surface had an extremely high surface tension, hence adsorbed lots of stuff from where we collected our nano-particles, and instead of hundreds of m² /g specifica surface area, we only measured like 8 or 12 m²/g which was definitely wrong.

To summarize: Mohsen's question was clearly only about "how to calculate", and not "how to measure". For the clean calculation, aggregation does not change the result, for real measurement: yes, results can heavily be affected by agglomeration / aggregation and by adsorption of stuff on the nanoparticle surface.

(by the way; I assumed Mohsen did not know how to claculate, because he asked "how to calculate", so I tried to answer his question :-))

Bernhard,

Interesting topic.

I have the PDFs of the mentioned publications but I'm not in the office. If you are interested I can send them to you on Monday.

A clean calculation provides a useful information only if it is a good approximation of the actual value. What is the uncertainty of the primary particles diameter (mean and GSD)? What is the uncertainty in the number of particles for each agglomerate? Is the density of the compound or the density of the agglomerate? most of the times these info are not available.

For this reason the clean calculation might be affected by errors beside the agglomeration. In additio,n a measured specific surface area can provide more actual information: in your case for example, the BET analysis showed you the presence of tensides. It all depends from what you want ;)

Emanuele, pls send me the pdfs when in office in MON, no hurry.

[email protected]

I agree: it all depends ... (on what you look for, the side parameters, nano-materials, measurement techniques ,,,,)

Emanuele, pls send me the pdfs.

I had the task about evaluation of the surface area (SA) of carbon nanoparticles and their aggregates in liquid medium, in my research. And I used:

step 1 - investigating of geometrical characteristics of nanoparticles;

step 2 - creation of model (nanoparticles have been described using geometrical figures);

step 3 - evaluation of the SA of nanoparticles using model;

The results of evaluation of the SA of carbon nanotubes from this model are in good agreement with the theoretical surface area of nanotubes from Ref. [Specific surface area of carbon nanotubes and bundles of carbon nanotubes / A. Peigney, Ch. Laurent, E. Flahaut, R.R. Bacsa, A. Rousset // Carbon 39 (2001) 507–514 - I have pdf file of this article]. I think, you can use this scheme to evaluation of the surface area of gold nanoparticles.

The aggregation of nanoparticles have a impact on their surface area.

From SEM one can calculate specific  surface area by  formula

S=σ/d ρ  where  d is diameter of particle , ρ density  of particle.In this method assumption is to consider all particles are spherical in shape.

Ref:L. Gao et al sen act (2000).

The most suitable method is BET .

Please see this scholarly article of mine, and please cite it as indicated.

https://www.researchgate.net/publication/238366588_Determination_of_specific_surface_area_and_mean_grain_size_from_well-log_data_and_their_influence_on_the_physical_behavior_of_offshore_reservoirs

Article Determination of Specific Surface Area and Mean Grain Size f...

density of gold = 9.32 gm/cc

particle size = 20 nm

SSA = 6000/(9.32 * 20) = 33 m2/gm

Dear Arijit:

Per your question, please this paper, which might help you.

https://www.researchgate.net/publication/238366588_Determination_of_Specific_Surface_Area_and_Mean_Grain_Size_from_Well-Log_Data_and_Their_Influence_on_the_Physical_Behavior_of_Offshore_Reservoirs_Built_on_and_Cited_by_35_Researchers_including_5_PhD_S

Regards. --- Hilmi

Article Determination of Specific Surface Area and Mean Grain Size f...

Specific surface area=K/D.P

k=Shape factor depends on the particle shape (6 for spherical particle)

D= Average particle size

p=powder material density

It is not true, some particles have porosity you can't just mathematically assume things. There are test that people use such as nitrogen absorption test for carbon black. Calculations based on density is just too simplistic and crude!

Aref, I 50% disagree:

- first, one can check the surface of nanoparticles and determine whether or not they are porous; if yes (very rarely the case!) - then things are different;

- but on the other side, nitrogen adsorption does not always tell you the truth about surface area, because the question is whether or not N2 will be adsorbed on the particles! I made this experience when checking the surface area of my polyaniline nanoparticles - and N2 delivered totally senseless (much too low) values!