Particles stick to the surface by means of molecular forces which depend on surface energy. When particle is removed it would distort the footprint and then surface tension would restore the surface and erase the footprint. On the other hand, too low surface tension would cause the footprint flow and distortion.

William P. de Haan Interesting question.

You almost have a Stokes'Law experiment here. Drop the particle (of known density) into a glycerol/water mix. Measure the terminal velocity and then calculate the size based on Stokes' diameter. Won;t work for your 'mix' case though...

If your materials are in the say > 10 um size point then light scattering would be insensitive to optical properties and a laser diffraction experiment would work. LD is not sensitive to density and irregular particles can only be specified with a single number by equivalent properties. So you'd get an equivalent size by scattering but then again you'd not be getting the weight of a particle as you have a mix and not a single density system.

How many particles do you have? A tedious experiment would be to weigh them one-by-one if they can be separated.

If you know the average size, you can calculate the volume of each particle. You can find the density of a measured volume of particles from the mass of the sample. Once you know the density, you can calculate theass of each particle.

The BET method may give the mean particles size while there is always a size distribution. But the point is that metal particles may be agglomerates of smaller ones and its density is not equal to that of compact metal

What about nano/micro-mechanical resonators? If you need to determine the weight of individual or small numbers of nanoparticles, this might be the right approach. Upon adsorption of a particle, the resonance frequency of a resonator drops due to the added mass. As the relative mass change is larger for smaller resonators, nanoresonators allow for high mass sensitivities.

For a review article see Tamayo et al. 2013 Chem. Soc. Rev. 42, 1287--1311 (DOI: 10.1039/c2cs35293a). Reportedly, yoctogram resolution has been achieved; see Chaste et al. 2012 Nature Nanotechnology 7, 301–304 (DOI: 10.1038/NNANO.2012.42).

Hope this approach suits your measurement requirements at all. Good luck.

Alternative way of weighing the isolated particle adsorbed on a surface may be by means of measuring the adhesion force between the particle and an AFM probe. Such a procedure needs gathering statistics on measuring different size and mass particles and establishing a mass/force correlation.

As you had indicated in your initial reply, surface forces are very important on the nano-scale. They tend to outweigh volume forces, such as the gravitational pull. While the force needed to break a weak bond is in the order of pN, the weight of a gold nanoparticle of radius 100nm should be ~1 fN approximately (assuming spherical shape and the common value of ~19.3 kg/(dm)^3 for the gold mass density). Indeed, measurement of AFM pull-off forces seems a popular approach to study force interactions between surfaces. Usually it is necessary to run a large number of force-distance curves to work out the distribution of forces, I do agree. That's where the fun starts!