You will need to estimate the mass per particle to convert from number of particles to mass. If you know the average size of the particle you can used the atomic radii of Au to estimate the number of gold atoms per particle and from the atomic mass of Au calculate the mass per particle.

Alternatively, you could crash the particles out of a known volume of solution through centrifugation and/or an anti-solvent, thoroughly dry the solid and mass it. then you would just take the measured mass divided by the original volume.

You will need to estimate the mass per particle to convert from number of particles to mass. If you know the average size of the particle you can used the atomic radii of Au to estimate the number of gold atoms per particle and from the atomic mass of Au calculate the mass per particle.

Alternatively, you could crash the particles out of a known volume of solution through centrifugation and/or an anti-solvent, thoroughly dry the solid and mass it. then you would just take the measured mass divided by the original volume.

For a rough estimation you could also just use spectroscopic information (resonance wavelength) and the extinction coefficients provided by Orendorff and Murphy (http://pubs.acs.org/doi/full/10.1021/jp0570972) and go the classical way c=extinction/(ext_coeff * d).

You need to know the size distribution of your particles, easiest found from a histogram of TEM images.  Otherwise, your estimate for the mass of a particle will be very crude.  

From no. of particles calculate no. of moles. Convert no. of moles to weight by multiplying it by atomic mass of Au. You will get desire concentration.

I can think of two ways:

a) you need to know the size of your particles. Knowing the size asd assuming you have spheres, you can calculate the volume. With volume and density, you can calcualte the mass.

b) Analyse your solution with ICP-MS.

Regards.

Otmar

In my opinion, inductively coupled plasma mass spectrometry (ICP-MS) is the best solution for you.

well, if the particles were spherical, then it would have been straightforward with ICP MS in single particle mode. However, as you have nanorods, you need to know which is the aspect ratio and the diameter of the nanorods  (you need an imaging technique as TEM for that). By calculating the volume and then knowing that the gold density is 19.3 g/mL, then you can get the mass of a nanoparticle and from that your concentration.

Using the density of Au, you can calculate the mass and therefore the concentration in mg/ml knowing your solution volume or particles/mL.

• number of particles/mL: N=2.1011
• dAu=19.6 g/cm3
• nanorod volume: Pi*(D/2)^2*L - D=diameter[cm], L=length[cm]. These are readily determined by SEM or even AFM.

Therefore: C [mg/mL]=2.1011*19.6*3.14*(D/2)^2*L/1000

Experimentally, spherical Au nanoparticles absorb between 520 and 580 nm depending on diameter. The same should be true for nanorods. Check the literature for Absorbance maxima and extinction coefficients to allow you to measure the actual concentrations of your samples without even needing the particle number per volume.

From my Point of view it Males only Sence to give the concentration of gold particles. For this just multiple the given no./ml by Avogadros number.

Let's make it simple. 1 mole of anything is 6x10exp23 (number 6 plus 23 zeroes) of atoms (when an element) or particles (when a compound). Knowing that the atomic mass of gold is 197 (approx.200) and ssuming for a while that each of your nanorods consist of one gold atom (a nonsense of course), your number of nanorods (2x10exp11) would mean that you have 2/10exp12 (negative exponent) of one mole of gold, that is 4/10exp10 of gram of gold. All you need to know now is how many atoms of gold are  in one nanorod? Multiply that number by the previous number, and you get the needed concentration in grams - multiply it by 1000 to convert to milligrams.  If you cannot determine the number of gold atoms in one nanorod, you will need the average nanorod volume. Muliply it by the gold's density (19.3 g/ml) then divide by 200 (or by 197). Enter the result into the previous calculations as the number of gold atoms in one nanorod.

The answer mentioned by Dr. Hurth is the most appropriate one. This can be followed to get concentration of nano gold particles.

If we multiply particles/ml concentration with the Avogadro number, we can get the answer in moles.  Can concentration of nanopaticles be represented in this manner?

You need to convert the numer of particles into the total amount of mass. If you know the exact size of the rods you can estimate the volume of each particle by calculating the volume of a cylinder (approximation to rod). This volume multiplied by the number of particles hgives you the total volume of particles in your suspension. Now you calculate the mass by multiplying the density of gold and the volume you obtained in the step before.

Could this work ?

For real nanorods, the concentration you are looking for is best determined by ICP. Alternatively, CV is an ok route if you are certain of your rod composition.

On the other hand, for most applications of nanorods, bear in mind that what you are looking for is among the least relevant parameters. The concentration "mg/mL" is not predictive of much for particle suspensions except ion count when totally dissolved. Suggestions that you find the number of particles per rod and convert require that you have a very monodisperse supply of nanorods. The error involved is very large for very common small changes in dimension.

The two answers given by Dr. Cedric Hurth will give different values (big difference), the accurate one of course will be the second answer but the first one depends on the assumption of the particle shape which can't be the same for even two particles

Is there any published literature which have used method described by Cedric?

It depends on your application. Consider the meaning of concentration. In the use people are taught in high school or undergraduate, concentration delivers a count of centers of interest that scales with volume. For many cases these centers of interest are atoms or discrete ions, and extension of the idea to narrow size distribution macromolecules is not a terribly misleading thing to do from an error propagation point of view.

For a nanoparticle the problem is rather different. If, in the special case of counting centers of mass for the particles, count/ml is the concentration. However, if you are predicting the surface area or number of gold atoms, or reactivity, scaling will dramatically vary with size distribution, requiring you to have a model of the variation in size or shape. Once you have that, integration is trivial. Lack of the distribution leads to the common difficulties in calculating things like catalytic activity, phonon wavelength intensity distribution, risk or exposure levels.

Since mg/mL scales with atomic centers, you will need the particle dimension and size distribution to calculate from particles/mL. In principle that can be acquired with scattering measurements or excessive microscopy. If you actually need just the mg/mL ratio because your application is independent of size and shape, you are better off sidestepping the debate. Run an ICP-OES measurement and call it a day.