While it has been a little later than I expected, I recently published an article on this issue in the RSC Analyst, which will be free for the next few weeks. The Supplementary Information (always free I believe) contains a comprehensive table of extinction coefficients of citrate-coated silver nanoparticles, from 8nm to 100nm in size (2nm steps). I hope this will be useful.

http://pubs.rsc.org/en/content/articlelanding/2014/an/c4an00978a/

I decided to add an extra part to this original post. It should be noted (previously, maybe incorrectly, I assumed this is known) that for the small silver nanoparticles with Lmax between 390 - 410 nm or so, addition of a monolayer (e.g. a SAM) will change this Lmax value, most likely with up to a 15-20 nm red-shift. Hence the paper concerns citrate-coated silver nanoparticles. We wanted to add this info into the above Analyst paper, but the reviewers suggested to not do so. Plan to publish something else on this in the near future (fingers crossed :-)  )

it would not be a really quantitative measure, right? as I see it would be likely to estimate it, but calculate... if you can plz take a look at one of my question about it...

You can certainly calculate the Ag NP concentration from the absorption spectrum. Of course, the molar absorptivity of your nanoparticles will depend heavily on their size and shape distributions. If there aren't any reported absorptivities for particles in your size/shape regime, you'll have to use a different method to determine their concentration (e.g. atomic emission spectroscopy).

Thank you Alexandre Rodrigues and Zach Erno. Is there an equation to convert the value of the absorbance to concentration? The attached file is an example. Can we translate the peak at about 410 nm with absorbance of about 80 (this is the real value after multiplying by the number of dilutions).

You can determine the concentration using the Beer-Lambert Law (http://en.wikipedia.org/wiki/Beer-Lambert_law) and the molar absorptivity of the particles (ideally, one you've obtained from the literature). However, you'll need to continue diluting your sample until the maximum absorbance value is under 1.0 (otherwise, you're outside the region where the Beer-Lambert Law applies).

Thank you Zach Erno. I got the equation from the link you mentioned and working on it. It si very useful not only for UV-Vis spectrophotometer but also for the IR in different chemical modifications.

Could you tell the details for calculating the concentration

Molar absorptivity also changes with a change in surface ligands on the silver nanoparticles as they are very sensitive to changes in the refractive index around the surface. Do you use the a citrate-mediated formation of nanoparticles? If so, I can provide you with extinction coefficient for your nanoparticles (what ever size).

Yes you can, but that will be estimate. To do that accurately, Atomic absorption spectrometry (AA) or Inductively coupled plasma (ICP-OES OR MS) will be perfect solution.

In UV-Vis, for calculating concentrations from Beer's law, A= Єbc

Є is the molar extinction coefficient,

b is the distance the light, c is concentration and you already know A (peak absorbance from measurements)

Anybody succeeded in determining the concentration of AgNP? Its not that easy and straight forward (using beer-lambart) like any other UV active compound. As Paul Free mentioned, the density of surface ligand plays a crucial role. And excitation maxima changes a bit, with shape, size and surface ligand density. However, if you can obtain a standard curve from a known concentration with series dilution, it is still possible to obtain conc by UV. However, with different batches of NP prepared, they will display little difference in absorbance wavelength and pattern (unless size, shape and surface labeling/charge remains same).

Yeah, you can definitely calculate the concentration of Ag NPs by UV-vis spectrophotometer in absorbance mode.

I agree with Oommen. Or else, you can go for AAS technique.

Navarro, J. R.; Werts, M. H. The Analyst 2013, 138, (2), 583-92.

Extinction = A*d^gamma, where A is 4.2x10^8, gamma is 0.77, and d is diameter of silver nanoparticle in nm.

You can use DLS which its a very simple as UV-visible

the only problems its that its not very accurate

Another technique for calculating the concentration of nano particles in general is Nanoparticle Tracking Analysis, NTA from NanoSight/Malvern. More accurate but DLS and additional gives you a nice size distribution. Much easier but electron microscopy, and you don´t need to prepare your particles. Take a look at www.nanosight.com. Affiliations: I am a Technical Sales Specialist of Nanosight/Malvern

Dear Joerg, is there any literature you can cite to show that NanoSight can accurately determine gold or silver nanoparticle concentration. I believe this technique is difficult to observe smaller nanoparticles?

Dear Paul, please take a look at this as two examples:

In vivo particle tracking and photothermal ablation using plasmon-resonant gold nanostars

Hsiangkuo Yuan, et al. (2012)

Gold cluster formation with phosphine ligands: etching as a size-selective synthetic pathway for small clusters?

Pettibone JM, Hudgens JW. (2011)

Lower size limitation of NTA is about 10 nm (which is true for gold as a good light scatterer) and 30-40 nm for biologics.(protein aggregates, exosomes, etc,).

Manal estimated his particles being around 400 nm ...

It is very likely you need to dilute the sample first. The dilution row needs to be done very carefully! And you need to sample 3-5 measurements to have reliable statistics. Then you can get results by plus minus 10 percent.

I proposed to read the below article:

10.1080/05704928.2011.637186

Yes, if You have callibration A/conc line (based on ASA determination)

The supporting information for: Navarro, J. R.; Werts, M. H. The Analyst 2013, 138, (2), 583-92.

Extinction = A*d^gamma, where A is 4.2x10^8, gamma is 0.77, and d is diameter of silver nanoparticle in nm.

Excerpt:

4.1 Size-dependence of the extinction coefficient for gold and silver nanoparticles

Here, we compare the results of Mie calculations with available experimental data concerning the molar extinction coefficients for gold and silver nanoparticles. One particular aim is to obtain simple power-law expressions for the dependence of the maximum extinction coefficient on particle diameter, i.e.

Extinction = A*d^gamma

4.1.1 Gold nanoparticles

Fitting this power law to experimental data for gold nanoparticles, Liu et al.5 found A = 4.93x10^4 M-1 cm-1 and γ = 3.32 with d the diameter in nanometers. The coefficients were later slightly refined S6 to be A = 4.60x10^4 M-1 cm-1 and γ = 3.34, by inclusion of further data from the literature. The combined experimental data for this fit spans only particles diameters between 5 and 35 nm. Here, we add additional experimental points using commercially supplied gold nanoparticles and the accurate particle concentration supplied by the manufacturer. We plotted the experimental data points (Figure S9), together with the results of Mie calculations (see below).

ICP -MS is the best technique for calculation of concentration of metallic NPs

While it has been a little later than I expected, I recently published an article on this issue in the RSC Analyst, which will be free for the next few weeks. The Supplementary Information (always free I believe) contains a comprehensive table of extinction coefficients of citrate-coated silver nanoparticles, from 8nm to 100nm in size (2nm steps). I hope this will be useful.

http://pubs.rsc.org/en/content/articlelanding/2014/an/c4an00978a/

I decided to add an extra part to this original post. It should be noted (previously, maybe incorrectly, I assumed this is known) that for the small silver nanoparticles with Lmax between 390 - 410 nm or so, addition of a monolayer (e.g. a SAM) will change this Lmax value, most likely with up to a 15-20 nm red-shift. Hence the paper concerns citrate-coated silver nanoparticles. We wanted to add this info into the above Analyst paper, but the reviewers suggested to not do so. Plan to publish something else on this in the near future (fingers crossed :-)  )

Plz, Can u provide me any research paper for further reference of protocol and calculations?  Since i am trying to calculate the concentration of Ag NPs (silver nanoparticles) using the absorbance of UV-Vis spectrum of the Ag NPs colloidal solution.

Jay Narayan Yadav

Some of my published articles uploaded at ResearchGate consider  AgNPs preparation, they all contain the UV-Vis spectra of AgNPs. You can download any of them.

can anyone tel how to prepare a gold nanoparticles sample for ICP MS.

Now that all the discussion is over..... can anybody tell me in simple language how on earth can i determine the concentration of nano silver synthesized by using sodium borohydride as reducing agent.

Hi Raheel Bashir, The paper we published concerns citrate-coated nanoparticles. If you can add citrate solution to your nanoparticles, or at least a small sample, they should still stay stable. As they will now likely be citrate-coated nanoparticles, you can use our Analyst published paper to calculate the size. However note, this assumes that at least the nanoparticle sizes are 8nm or greater. From the paper the beer-lambert law can be used to calculate concentration (just need to look at the supplementary information for the paper).

If you need that paper or more discussion, please feel free to message me directly and I can try and help.

Hi Raheel Bashir, The paper we published concerns citrate-coated nanoparticles. If you can add citrate solution to your nanoparticles, or at least a small sample, they should still stay stable. As they will now likely be citrate-coated nanoparticles, you can use our Analyst published paper to calculate the size. However note, this assumes that at least the nanoparticle sizes are 8nm or greater. From the paper the beer-lambert law can be used to calculate concentration (just need to look at the supplementary information for the paper).

If you need that paper or more discussion, please feel free to message me directly and I can try and help.

Hi Raheel Bashir, The paper we published concerns citrate-coated nanoparticles. If you can add citrate solution to your nanoparticles, or at least a small sample, they should still stay stable. As they will now likely be citrate-coated nanoparticles, you can use our Analyst published paper to calculate the size. However note, this assumes that at least the nanoparticle sizes are 8nm or greater. From the paper the beer-lambert law can be used to calculate concentration (just need to look at the supplementary information for the paper).

If you need that paper or more discussion, please feel free to message me directly and I can try and help.

Paul Free 

thanks a lot.

can you please suggest me how to prepare a silver nanoparticle solution with a minimum concentration of 100 micrograms per ml and with a stability of at least more than two months.

waiting for your reply??

I think this link is very useful, 

http://www.instanano.com/characterization/theoretical/concentration-calculation-from-uv-vis-absorbance/

To use the mentioned link, we need to know the molar absorptivity. What if we have to start from scratch and we do not know it. Then, how can we find the concentration ?  any suggestions ? 

Regards, 

Neha Karekar 

To measure the concentration of silver nanoparticles, we have to do ICP-OES or ICP-MS analysis and also we have to use density and volume of the particles. Pl reference some publication of Prof. T.Pradeep.

Hello,how to start with synthesis of silver nanopaticles using plant extracts? can anybody guide me?

Calculations the concentration of silver nanoparticles are based on the Beer's Lambert law given by: c = A/ε l

Where A = Absorbance of solution at a particular wavelength; ε = Molar Absorptivity; l = Length of Solution Cell; and c = Concentration of Solution (mol/dm3)