There is the relationship between the optical absorption spectrum of gold or silver nanoparticles caused by surface plasmon absorption (in particular, the plasmon resonance and its brodening ) and their sizes. The surface plasmon resonance is the coherent excitation of all the `free ’ electrons within the conduction band. The resonance does not give rise to the most intense absorption for very small clusters. For the larger particles (several tens of nanometres) the excitation of the surface resonance absorption can occurs in visible light region ( 400 -600 nm for Ag and Au nanoparticles). Such absorption spectra can be analysed using Mie theory. In particular, according this theory for nanoparticles smaller than the mean free path of the conduction electrons there is the relationship between the resonance broadening (γ) and the sizes of nanoparticles γ (r ) = γo + AυF/r , where r is the size of nanoparticle, A=3/4 for silver, γo is the velocity of bulk scattering (5•10 to 12 degrees s(-1)), υF is the Fermi velocity (for silver 1.39 • 10 to 6 degrees m/s). Using the experimental absorption spectra and this relation you can determine the size of nanoparticle. I recommend read the following paper, where was presented similar studies for silver.

Realistically TEM is one of the only reliable methods to carry out NP sizing of core shell nanoparticle. I use another piece of equipment in the lab to size called the Nanosight Tracking Analysis device which will also size and give a full size distribution, a lot more detailed then DLS measurement can provide. If you can send your sample to a lab to do this measurement you would have your result in ten minutes. Perhaps Nanosight Ltd in the UK have supplied such a device in your country?

If each particle is an individual single crystal, then it takes 1 difraction pattern and a few minutes for the analysis. The information you can obtain is usually statistically more relevant than the one you obtain by TEM (several million particles minimum versus a few hundred) and the TEM validation is required only when you see that something is going wrong (usually meaning you have a distribution of shapes and not just of sizes).

For further details have a look at my publications. Of interest can be:

https://www.researchgate.net/publication/11527348_Whole_powder_pattern_modelling

https://www.researchgate.net/publication/230824258_X-ray_Diffraction_Methodology_for_the_Microstructural_Analysis_of_Nanocrystalline_Powders_Application_to_Cerium_Oxide

SIlver is straightforward to be done

Article Whole Powder Pattern Modelling

Article X-ray Diffraction Methodology for the Microstructural Analys...

See these articles:

T. R. Jensen; L. Kelly; A. Lazarides; G. C. Schatz: J Clust Sci 10, 295-316, (1999).

S. Schneider; P. Halbig; H. Grau; U. Nickel: Photochem Photobiol 60, 605-610, (1994).

I am familiar with emperical ways to do this for gold nanospheres, using Mie Theory as a theoretical guide.

If you have non-spherical particles, your only hope is to compare your spectra from those of either published ones or simulated ones, and this is a pain because you have to track down such papers or some software tools for analyzing such a system.

If these are spheres, the larger they are, the more likely you can characterize them just by their peak wavelength. This is predictable from Mie Theory; however, it's even better to have an emperical fit that another group did by experimentally verifying the peak wavelength for actual silver nanospheres of varying size.

Here is an article that does this for gold spheres:

http://pubs.acs.org/doi/abs/10.1021/ac0702084

If you have no luck, perhaps you can try measuring the hydronamic diameter via dynamic light scattering apparati?

I know your pain on this by the way, so good luck.

PS,

If you do eventually get to use a TEM/SEM, we've found the most accurate way of sizing is to measure the centroid-centroid spacing between touching spheres. This is less prone to optic errors in the microscope (eg the stigmation is not 100% perfect) and, in the case of SEM, sometimes edges are not clearly defined.

The roughness value in AFM denoted the size of nanoparticles so you can used it

Mukhlis Ismail, is your comment true for all shapes of particles? I don't think so.

Thanks, Martin, for giving useful info. about a free program and the limitations about Mie theory.

There is the relationship between the optical absorption spectrum of gold or silver nanoparticles caused by surface plasmon absorption (in particular, the plasmon resonance and its brodening ) and their sizes. The surface plasmon resonance is the coherent excitation of all the `free ’ electrons within the conduction band. The resonance does not give rise to the most intense absorption for very small clusters. For the larger particles (several tens of nanometres) the excitation of the surface resonance absorption can occurs in visible light region ( 400 -600 nm for Ag and Au nanoparticles). Such absorption spectra can be analysed using Mie theory. In particular, according this theory for nanoparticles smaller than the mean free path of the conduction electrons there is the relationship between the resonance broadening (γ) and the sizes of nanoparticles γ (r ) = γo + AυF/r , where r is the size of nanoparticle, A=3/4 for silver, γo is the velocity of bulk scattering (5•10 to 12 degrees s(-1)), υF is the Fermi velocity (for silver 1.39 • 10 to 6 degrees m/s). Using the experimental absorption spectra and this relation you can determine the size of nanoparticle. I recommend read the following paper, where was presented similar studies for silver.

As noted above, the problem is complex. Unless you only want a rough estimate, you should consider using multiple methods that naturally produce different moments of the distribution. Osmotic pressure produces a number moment, which when compared to a light scattering method can indicate whether your particles are mono- or polydisperse. If you are going to make nanoparticles often, you should find a colleague who can provide access to a dynamic light scattering instrument.

A quick and easy way to get approximate particle size and/or to follow particle formation, is to follow scattering of light by particles, at a non-absorbing wavelength. Method can be called Turbidity titration. Typically, 600 nm has been used for cell suspensions, protein-polyelectrolyte complexes, protein-DNA complexes etc. I have used it for inter-polyelectrolyte complex formation. (Langmuir 22(14), 6093-6101, 2006). Hope it will be useful.

Can I apply the same method to calculate the particle size of other nano metal sulphides?

I think, you should try it out, as you can recover the sample, if it is precious. This method should give approx. relative sizes of particles/agglomerates, irrespective of the shapes of the particles. You may compare sizes at different conditions and get an idea of the variation, and infer from that. Hope you get some interesting info.

Please how to calcul  the γ (r )  from the UV-vis 

Thank you 

You can calculate the size from XRD. very good explanation is here on this link,

http://www.instanano.com/characterization/theoretical/xrd-size-calculation/

Please look to link. Can calculate the the particle size using UV-Vis

http://link.springer.com/article/10.1007/s10854-015-4105-x

Hi Vadiraj

There is something I do not understand in equation 4 of your paper. Is this an equation you derived or did it come from some other reference?  From the sentence leading to the equation, lambda_sub_p appears to be peak wavelength, but when I plug in 340 nm, I get a very different radius than you report. Looking at the UV spectrum, can you explain why you chose 340 nm as the peak wavelength?

Thanks

Dave Boldridge

As discussed above you can calculate the particle size from PXRD using Scherer equation. In simple to predict indirectly from UV, if your lambda max of active drug  shifted to lower wavelength  ( bathochromic shift) then your particle size reducing. If it reverse it indicate larger particle size.

Using Scherrer method like you suggested @ Nandakumar, how can one estimate the FWHM from the UV-Vis analysis? if that works, this method seems to me the simplest and straightforward. i believe the peak wavelenth corresponds with the peak absorbance on the UV-Vis scattering graph.

any can tell me, that how much shift in wavelength is consider in uv visible spectra

Dear Sir Yuriy P. Gnatenko , kindly tell me one thing. from absorption spectrum we can find peak broadness which is in units of "nm" how to convert that width in in units of "s^(-1)" .. i tried c = f x lemba , but didn't work

You might also find these two publications interesting:

Effect of the Solvent on the Size of Clay Nanoparticles in Solution as Determined Using an Ultraviolet-Visible (UV-Vis) Spectroscopy Methodology

March 2015

Applied Spectroscopy 69(6):671

DOI: 10.1366/14-07704

In situ characterization of organo-modified and unmodified montmorillonite aqueous suspensions by UV-visible spectroscopy

June 2015

Journal of Colloid and Interface Science 456

DOI: 10.1016/j.jcis.2015.06.011

Dear Parul T.

you must observe your Maximum wavelength if there is a shift with + or _ 20 nm this is considered as shifting

regards

@yuri something with a factor 200 is wrong in our calculations compared to the article of SOMAYE BASET..I am not sure if we can use that formula, because we recalculated values from the paper and don't get the same numbers. Can you help us?

We checked everything, units etc and still have factor 200 of difference.