This is not quite so simple, because all nanoparticulate samples have a size distribution. So obviously the easiest samples are perfect spheres or cubes, because here the calculation of the volume of one single nanoparticle is quite straightforward. What you will need to do is to get a good measure of your particle diameter / length / width / thickness. The more homogeneous the samples are, the better. If the samples are too heterogeneous, it will become difficult to impossible to get reliable data.
So suppose you have "spheres", then you can calculate the volume of an individual nanoparticle from the average diameter of the particle. Then you can use the density (I usually assume the bulk density, although this is not in all cases correct) to calculate the weight of one particle and from this you can then simply calculate particle numbers per sample weight. Obviously this will have to be accompanied by a proper error propagation treatment.
There are many ways of getting sizes, light scattering or SAXS would be some, TEM or SEM data would be other options. It must clearly be stated that microscopy data have to be treated with caution (!!!). The reason is that in microscopy (unless you have a reliable software, which is not easy) one tends to perform measurements that are biased by the operator and the sample quality. For example it is impossible to measure particles in the SEM images that do not lie flat on the substrate because you cannot extract a length from such an image due to the fact that it is a projection. Or, more correctly: it is of course possible to measure all kinds of crystals, but because the images are projections you will not get the right particle dimension unless the crystals lie flat on the substrate.
The final thing one has to consider when doing analysis by hand (which often is the only choice) is statistics. Most of the particle size statistics that I see in the literature are not reliable because the authors did not measure enough particles from a sufficient number of microscopy images (that is, you should have a large number of images at a fairly high magnification to measure enough particles with a good accuracy. At low magnification, one pixel error makes a huge mistake in your final numbers). To give you an impression: I once estimated that during my PhD thesis I measured way over 20'000 particles to get reasonable statistics. Yes, it takes a while, but you can learn a lot from such a large dataset.
FYI, see
Inorg. Chem., 2008, 47 (22), 10758.
Cryst. Growth & Design, 2008, 8 (12), 4526.
Langmuir, 2002, 18 (11), 4488.
This is not quite so simple, because all nanoparticulate samples have a size distribution. So obviously the easiest samples are perfect spheres or cubes, because here the calculation of the volume of one single nanoparticle is quite straightforward. What you will need to do is to get a good measure of your particle diameter / length / width / thickness. The more homogeneous the samples are, the better. If the samples are too heterogeneous, it will become difficult to impossible to get reliable data.
So suppose you have "spheres", then you can calculate the volume of an individual nanoparticle from the average diameter of the particle. Then you can use the density (I usually assume the bulk density, although this is not in all cases correct) to calculate the weight of one particle and from this you can then simply calculate particle numbers per sample weight. Obviously this will have to be accompanied by a proper error propagation treatment.
There are many ways of getting sizes, light scattering or SAXS would be some, TEM or SEM data would be other options. It must clearly be stated that microscopy data have to be treated with caution (!!!). The reason is that in microscopy (unless you have a reliable software, which is not easy) one tends to perform measurements that are biased by the operator and the sample quality. For example it is impossible to measure particles in the SEM images that do not lie flat on the substrate because you cannot extract a length from such an image due to the fact that it is a projection. Or, more correctly: it is of course possible to measure all kinds of crystals, but because the images are projections you will not get the right particle dimension unless the crystals lie flat on the substrate.
The final thing one has to consider when doing analysis by hand (which often is the only choice) is statistics. Most of the particle size statistics that I see in the literature are not reliable because the authors did not measure enough particles from a sufficient number of microscopy images (that is, you should have a large number of images at a fairly high magnification to measure enough particles with a good accuracy. At low magnification, one pixel error makes a huge mistake in your final numbers). To give you an impression: I once estimated that during my PhD thesis I measured way over 20'000 particles to get reasonable statistics. Yes, it takes a while, but you can learn a lot from such a large dataset.
FYI, see
Inorg. Chem., 2008, 47 (22), 10758.
Cryst. Growth & Design, 2008, 8 (12), 4526.
Langmuir, 2002, 18 (11), 4488.
Here is more discussion on the same topic:
https://www.researchgate.net/post/How_to_get_the_weight_of_nanoparticles_in_Moles
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