During adsorptive removal of heavy metals or dyes from aqueous solution, nano materials provides much more surface area for adsorption compared to common adsorbent. How one can explain it analytically/mathematically/ experimentally?
Any link/research article/books will be appreciated.
Dear Pradeep
just take simple models for exemplification:
a) cubes of dimension a: area A = 6a²; volume V=a³; ---> A/V = 6a²/a³ =6/a;
thus A/V increases when a decreases.
b) spheres of radius r: area A = 4pi*r²; volume V=4pi/3*r³; ---> A/V=3/r;
thus A/V increases when r decreases.
So also the A/V values of non-symmetric/non-regular shaped particles will behave.
https://en.wikipedia.org/wiki/Surface-area-to-volume_ratio
Dear Pradeep Saw,
Let us consider a hollow cube with edge equal “a”.
Now let completely fill this cube with large amount “N” of spherical particles with radius “R”. Thus, the overall material inside the cube has a volume:
V=a^3
Since the particles’ amount is large, it can be written that along each cube’s edge R*N^1/3 particles are situated, and then, the overall material's volume is given by:
V= (R*N^1/3)^3 = N*R^3
The surface of each spherical particle under consideration is:
Surf = 4*pi*R^2
Then overall surface area in the material inside the considered cube is:
Area = 4*pi*N*R^2
Now one can easily calculate surface-to-volume ratio as a function of a particle radius for the case of equal-sized spherical particles:
Area/Volume = (4*pi)/R
The last equation is actually the answer for your question. Obviously, that area-to-volume ratio is independent on particle’s amount and is reversely proportional to particle’s radius. Of course, real particles have different shape and may have quite different size. In that case, for a proper Area-to-Volume calculation slightly more complicated calculations should be done.
Anyway, the conclusion is simple: a decrease in particles' size results in an increase in specific area and, therefore, in increase of absorbent's “absorption power”. Now it is clear, why nano-sized materials demonstrate the improved absorption properties.
Gerhard Martens sir, Alexander Katz-Demyanetz sir ,thank you for your answers. I really appreciate your effort for such a detailed explanation.
Dear Pradeep,
https://m.youtube.com/watch?v=lKkG27fDfNY
May helpful to you.
Bhaskar Bhatt thank you for your link. It was in fact a well explained Visualization of the mentioned Concept.
Dear Pradeep Saw
http://www.mdpi.com/1996-1944/2/4/2404/pdf
Regards
Dear Pradeep saw,
check the slides 17-20, It answers all of your queries.
Tajkia syeed Tofa The slide was quite useful for the said problem as well as for some other basic understanding. Thank you for sharing.
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