I guess you want to calculate the conc of nanoparticles (nM/pM) in the colloidal solution. If yes and NP are spherical in shape, then you can use the following steps:

a) You know the weight of gold taken for NP synthesis (Au only, not gold salt) = W

b) Density of gold = 19.3 gcm-3

c) Now you calculate the volume of gold taken = W/9.320

d) Calculate the average size of nanoparticles using TEM (make sure nanoparticles are monodispersed) (2R)

e) Calculate the volume of a single nanoparticle (assuming sphere) = 4x(pi x R^3)/3 = V

f) You can calculate the number of particles in colloidal solution (N) = (W/9.32) / V

g) Calculate the conc of NP = N / Final volume of colloidal solution

Please read this paper and article. .http://www.labmanager.com/white-papers-and-application-notes/2012/05/measurement-of-gold-nanoparticle-size-and-concentration-by-spectrophotometry#.UvnG6IG6bqA

.hope they will help u..

You can use the dynamic light scattering (also known as photon correlation spectroscopy or quasi-elastic light scattering) ; this is a technique in physics that can be used to determine the size distribution profile of small particles in suspension.

Once you have the diameter of your particles, you can measure the extinction spectra for quantifying the concentration ( such in Beer's law)

Thankyou everyone for your valuable suggestions.

I guess you want to calculate the conc of nanoparticles (nM/pM) in the colloidal solution. If yes and NP are spherical in shape, then you can use the following steps:

a) You know the weight of gold taken for NP synthesis (Au only, not gold salt) = W

b) Density of gold = 19.3 gcm-3

c) Now you calculate the volume of gold taken = W/9.320

d) Calculate the average size of nanoparticles using TEM (make sure nanoparticles are monodispersed) (2R)

e) Calculate the volume of a single nanoparticle (assuming sphere) = 4x(pi x R^3)/3 = V

f) You can calculate the number of particles in colloidal solution (N) = (W/9.32) / V

g) Calculate the conc of NP = N / Final volume of colloidal solution

You can use UV-visible spectroscopy

Shweta Rajawat - Using UV-Visible spectroscopy, how can we calculate the concentration of Au nanoparticles in the solution??

UV-Vis requres a calibration or you need to know the extinction coefficient for the exact size of gold particles you have. It is not a direct measurement of concentration. The most accurate approach has been mentioned previously....use atomic spectroscopy (AA or ICPMS) to determine total gold. On the other hand, if you used the Turkevich method and you know how much Au salt was added, you already know the total gold concentration. In my experience this value is pretty close to the one determined by ICPMS. Then you need a "mean" size that is relevant...preferrably from TEM or SEM depending on the size of your particles. DLS is not a good choice for obtaining the mean size for the purpose of calculating the particle number concentration, as someone else suggested, since it is prone to artifacts and measures the hydrodynamic size not the core Au size.Once you have Au concentration and a mean size, you can estimate the concenration assuming spherical geometry and the usual parameters (radius of equivalent sphere, Au density). BUT....if you have a polydisperse sample, none of these approaches will work, and your estimate will contain a large error and uncertainty. Establish the uniformity of your product first. IMHO

You can use UV-Visible spectroscopy. By using Beer-Lambert Law, you will be able to determine the concentration. UV vis will give you the peak absorbance and for the values of size dependent molar extinction constant, you can refer literature values. 

A=ecl (A-absorbance, e-size dependent molar extinction constant, c-concentration, l-length of cuvette)

I sugest a very easy way to obtain the concentration of a nanòparticles concentrarion as I did for Al nanoparticles soln. Select some known valume of solution and obtain its weight. Then evaporate the solvent to obtain the dry product (particles). Reweight it. Now you can calculate nanopartiles solution concentration

Mr. Vincent A. Hackley I read your answer about how to calculate the concentration of AuNPs, would you tell me the equation I need in order to calculate that concentration after has the mean size and concentration of Au salt.

thank you in advance

I have tried to determine the concentration of AuNPs by applying either Jitendra Satija's method or Beer's Law at the same time. The results are complementary. But according to Satiga' suggested method, you should be sure the size of AuNP and after calculation of number of AuNPs (F), you need to calculate mol of AuNPs by considering avagadro number ( 1 mol is equal to 6.02 x 10^23), then divide it to volume of the collodial solution. 

I compared the results and the deviation is so less :)

Thanks Mr. Sagita. I added a new AuNP concentration calculation method :)

Melike,

you mean colloidal dispersion. Colloidal solution is something like polymer solution, i.e. macromolecules dissolved.

Inductively coupled plasma mass spctroscopy (ICPMS) can be used to find concentration of various inroganic materials up to micro grams. We have used it to determine amount of gold (ug/ml) in gold nanoparticles dispersion to calculate dose and to compare with gold solution of known concetration.

Titus, 

Yes, you are right, I mean collodial suspension. 

Thanks for attention :)

 Hi Melike,

If I would need to find out the concentration of doped nanoparticles(such as NaGdF4 doped Er, and Yb nanoparticles), I don't know the common density of these nanoparticles but the individuals. In this context how would Mr, Satija's procedure will helpful for me , or any others.

I know the M.W, particle size and so the volume, but at some point, I need to know the density of nanoparticles.

Hello Everyone,

How many grams of gold nanoparticle in 17 nM (1mL) the size around 21-29 nm.

Nematallah,

You can use Turkevich method to synthesize gold nanoparticles. In this procedure, HAuCl4 is reduced by NaCit. According to the volume of NaCit, you can adjust the size of AuNPs. The important point is that there is an inverse ratio between the size of AuNPs and the volume of NaCit added. I attached one of our publications, which we synthesize 13 nm AuNPs. In order to synthesize 21-29 nm AuNPs, you are suppose to decrease the volume of NaCit. Moreover, the concentration of our protocol is 14 nM. by centrifugation method, you obtain 17 nM AuNPs, whose sizes are around 20-30 nm. 

Good luck :)

Article Surface-Enhanced Raman Scattering to Evaluate Nanomaterial C...

 Hi Sandip,

I think it is hard, maybe impossible, to calculate the concentration of your doped nanoparticles by Mr. Sajita's method. you can use Beer's law, which is A=E x I x C. you can prepare diluted samples such as 1:10, 1:100, 1:100. by this way, you can find E, extinction factor of your nanoparticle. then, you can measure the UV absorbance of your undilute NP suspension. you know the E and A, so you can find the concentration of NP suspension. I can suggest that you may go back from Mr. Satija's procedure to find the density of your nanoparticle. you found the concentration, find moles, find the volume of a single NP if it is spherical, 4/3 x pi x r3, bla bla.....

I hope it is favourable for you. Good luck :)

Hi Melike,

If you have unknown gold nanoparticles concentration and you diluted your sample(1:10, 1:100, 1:1000...) after that you use UV and Beer's law, what should be the UNIT of the slope Exl=(Aj-Ai)/(Cj-Ci)

Hi Chaker,

The unit of E, extinction coefficient, is M-1 cm-1. E changes according to the size of AuNPs. You can find some theoritical calculations in the literatures and also in the some websites. In the article named as "Extinction coefficient of gold nanoparticles with different sizes and different capping ligands", you may find the answer of your question. As much as I know, there is a relationship between concentration and extinction coefficient of a substance. Therefore, I am not sure about the unit of E obtained by that slope. I can suggest you to check the literature by depending the size of your AuNPs. You will see some values, which are similar to each other. The most important thing is the 10^what. For example, the E of 13 nm AuNPs is around 2- 5 x 10^8 M-1 cm-1, based on literature. You can find your slope value and then you can add this 10^blato the slope value, so you found the E :)). 

Good luck :)

http://www.sciencedirect.com/science/article/pii/S0927776506002554

Thanks Melike,

Actually I want to explain that you can not apply that equation in case of a mass concentration g/L or number of particles/L. My question how can you convert a mass concentration of NPs to molar concentration?

Hi Chaker,

Mr. Satija explained each step how to calculate molar concentration of NPs from mass. Please apply his calculation steps :)

Thanks Melike.

Hi Abdalrahim,

when preparing diluted samples, you do not have to know the concentartion of NPs in the solution. you would know only dilution factors. For concentration values, you would use dilution factors. for instance, 1:10 diluted NP suspension will be scanned by UV/Vis and  the maximum absorbance will be at 520 nm. the value at 520 nm will be recorded. Then, 1:20 diluted sample will be scanned and the value at 520 nm will be recorded,.... and more dilutions and their absorbance values. then, you will draw absorbance vs dilution factor graph. the slope will be extinction factor. the point is that you are suppose to multiple the slope value with 10^-9 if it it nm size. you can compare the experimental result with the theoritical E values. Moreover, you can do the same thing for AgNPs.

Good luck and have a nice day.

Thank you, everyone, I appreciate a lot. I benefited from your discuss 

Thank you so much Melike.

Have a nice day

Abdalrahim,

You are write. I wrote it as 10^-9 but  it must be positive, 10^+9. Sorry. I confused it with the units, M^-1 cm^-1. As a result, you are write, you are suppose to multiple the slope with  10^+9. 

Have a nice day :)

 Jitendra Satija,

Kindly can you please tell me what is 9.32 in above calculation? I am using PLGA for nanoparticle preparation (25 mg PLGA in total final volume 25 ml with density 1.34 gcm-3) and unable to understand calculation. radius of nanoparticle is 90 nm. 

@ Mohammad yasir 

this is 19.3 not 9.32, mistake during writing 

@ Irfan Ahmed

Thanks for your reply. Regards.

How can we calculate the size of any nanoparticles in a solution ? please give suggestions??

How can we calculate the size of Silica nanoparticles in a solution with average size of 50 nm? please give suggestions??

How do you calculate the concentraiton of AgNP without using TEM or UV vis?

AgNO3 = 48.84 mg in 144 ml of Millilq water

MSA = 18.084 of MSA into 60 ml Miq water

NaBH4 = 11.84 NaBH4 in 6 miq water

those are the reagents used to synthesise the particle in total of 210 ml.

you should do the math your own. You need to determine yield. Get the mass concentration. For calculating particle concentration you need to determine size distribution.

You can use a certain scope to do that such AA or, you can use a carbon adsorbent and then check the TGA

and the left solution take it to ICP-Ms

to check how much left

finally combine the both results will get the actu concentratio.

Dear Jitendra Satija

What are the Unit of V and W in your method ?

I I have synthesized Ag nanoparticles, but i did not use your method

for Ag NPs.

ICPS or AAS may the best

Particle size analyzer for nanoparticles can also be used for determination of the same.

How size analyzer can be used

there are particle counter giving you the number of particles according to size. Unfortunately, there is usually limitation for submicron particles.

I usually use Nanosight from Malvern Instruments to determine the concentration of particles. It will give you the concentration of the particles /mL.

Recommend @Harishkumar answer

https://www.youtube.com/watch?v=dAuNQo-TCrw

We have used Atomic absorption spectrophotometer for measuring concentration of nanoparticles

One method is Dynamic Light Scattering (DLS). You can find the apparatus under the manufacturer Malvern, the Zetasizer range.

Hello

Check in these links. It might help you.

https://nanocomposix.com/pages/nanoparticle-volume-mass-and-concentration

Good Luck.

Just weight a certain quantity w/v and dissolve it but if u mean size particles in suspension this is something else

With reference to the comments about Dynamic Light Scattering, it is correct to say that traditionally this would not have been a suitable approach to quantify particle concentration, however a number of recent developments in both algorithms and analysis has lead to the introduction of robust particle concentration measurements via DLS which yield results comparable to counting based techniques but in a calibration free, batch method.

Here are application notes that discuss this on the new Zetasizer Ultra.

https://www.malvernpanalytical.com/en/learn/knowledge-center/application-notes/AN180608AdenoVirusConcentrationMADLS.html

https://www.malvernpanalytical.com/en/learn/knowledge-center/technical-notes/TN180720ParticleConcZetasizerHowTo.html

https://www.malvernpanalytical.com/en/learn/knowledge-center/technical-notes/TN181211GuideToParticleConc.html

If you wanna find the concentration of gold use inductively coupled mass spectroscopy to measure.

for the concentration of AuNPs

use this online software you can find concentration in 2 min

https://nanocomposix.com/pages/tools

if you want to calculate of concentration of gold nano particle you can use of mass spectroscopy.

Dear Bhardwaj,

If the Au Nanoparticles (NPs) are spherical in shape, then you can use the following steps to calculate the concentration of Au NPs:

a) You know the weight of gold taken for NPs synthesis (Au only, not gold salt) = W

b) Density of gold = 19.3 g cm-3

c) Now you calculate the volume of gold taken = W/9.320

d) Calculate the average size of nanoparticles using TEM (make sure nanoparticles are monodispersed) (Diameter = 2R)

e) Calculate the volume of a single nanoparticle (assuming sphere) = 4x(pi x R^3)/3 = V

f) You can calculate the number of particles in colloidal solution (N) = (W/9.32) / V

g) Calculate the concentration of NPs = N / Final volume of colloidal solution

Regards

Rathindranath

Hello, btw, is there anyone can tell/share/explain the method to count liposome/NPs in solution? Thank you

Please follow the given link

https://nanocomposix.com/pages/nanoparticle-volume-mass-and-concentration#target

Agreed with @ Falah Mohammad Aziz

We calculate the concentration of nanoparticles in a solution using UV-VIS as a tool .