The determination of the extinction coefficient requires that you start from a solid sample of quantum dots, weight it, prepare standard solutions with known concentrations and measure their UV-vis absorption spectra. The slope of the absorption vs. concentration plot at a given wavelength is the extinction coefficient. This is true if quantum dots in solution behave accordingly to Beer-Lambert approximation, that is a dilute solute of non interacting particles, ,,. (see: https://www.researchgate.net/publication/239631373_Optical_absorption_spectroscopy_for_determining_carbon_nanotube_concentration_in_solution)

If you, on the other hand, start from a colloidal suspension, you might not need do determine the exctinction coefficient to quantify the concentration of quantum dots, but a simple thermogravimetric measurement as described in the characterization protocol for carbon nanostructures (CNSs) reported by Menna's group at the University of Padova:

I used Eppendorf micropipettes and a TGA Q5000IR by TA Instruments measuring concentrations as low as few micrograms for milliliter of dispersion.

(see for example: https://www.researchgate.net/publication/260566448_An_Insight_into_the_Functionalisation_of_Carbon_Nanotubes_by_Diazonium_Chemistry_Towards_a_Controlled_Decoration).

For a full list of publication you might check the link in attachment.

http://www.chimica.unipd.it/lab205/pubblica/publications.html

Article Optical absorption spectroscopy for determining carbon nanot...

Article An Insight into the Functionalisation of Carbon Nanotubes by...

You would normally measure absorption in a transmission set-up and consider Lambert's (& Beer's) equation

I = I0 exp(-c*a*t)

where

c is the concentration

a is the absorption cross section of a quantum dot

t is the thickness of the sample (e.g. cuvette)

So, my guess is that unless you *know* the absorption cross section of the quantum dots, you cannot determine their concentration, since their product enters the equation.

I don't know what their size is, but you could try to disperse the dots in well controlled manner on a surface (tiny droplets of known volume) and count them in a microscope or determine their concentration in an alternative manner.

as always, you need to do a calibration with known amount of quantum dots.

Thanks Kai Fauth and Titus Sobisch.

But in this case I do not know the concentration of the carbon dots in my solution. The quantum dots are 5 nm in diameter so I dont think that using a microscope will be relevant. 

What other alternative method can be used to determine the concentration i=of the carbon dot solution?

The determination of the extinction coefficient requires that you start from a solid sample of quantum dots, weight it, prepare standard solutions with known concentrations and measure their UV-vis absorption spectra. The slope of the absorption vs. concentration plot at a given wavelength is the extinction coefficient. This is true if quantum dots in solution behave accordingly to Beer-Lambert approximation, that is a dilute solute of non interacting particles, ,,. (see: https://www.researchgate.net/publication/239631373_Optical_absorption_spectroscopy_for_determining_carbon_nanotube_concentration_in_solution)

If you, on the other hand, start from a colloidal suspension, you might not need do determine the exctinction coefficient to quantify the concentration of quantum dots, but a simple thermogravimetric measurement as described in the characterization protocol for carbon nanostructures (CNSs) reported by Menna's group at the University of Padova:

I used Eppendorf micropipettes and a TGA Q5000IR by TA Instruments measuring concentrations as low as few micrograms for milliliter of dispersion.

(see for example: https://www.researchgate.net/publication/260566448_An_Insight_into_the_Functionalisation_of_Carbon_Nanotubes_by_Diazonium_Chemistry_Towards_a_Controlled_Decoration).

For a full list of publication you might check the link in attachment.

http://www.chimica.unipd.it/lab205/pubblica/publications.html

Article Optical absorption spectroscopy for determining carbon nanot...

Article An Insight into the Functionalisation of Carbon Nanotubes by...

The TGA method seems to be logic. Whereas the graphical method of finding the molar extinction coefficient may not work for carbon quantum dots. The major problem with CQD's is they will tend to aggregate if we concentrate them. Once dried it may not redissolve or redisperse in the solvent. It will disperse partially. So again we dont know how much CQDs are there in the solution. As a consequence the resulting absorptivity will be erroneous.

Dear Patrizio Salice

As you suggested to take the solid form of CQDs to determine the extinction coefficient seems to be logic. But in our case, we are not able to separate it out at 12,000 rpm, to get CQDs in solid form. And the particle size is 4 nm. Is there any other method to find out the concentration of CQDs in the unit of mg/ml.

Shivanand H. Nannuri Hi, How about freeze drying method. You can use freeze dryer to get solid form.