Hello Deborah. Probably there are several ways to know the concentration, but the simplest that come to my mind is just to take a small drop of your sample (volume or weight known) say 1uL and cast it on a clean silicon dice and let it evaporate. Once the solvent has gone, check the sample with a SEM, 50nm particles should be easy to observe and count. Of course, you need coat them with a thin conductive film before SEM observation (Au, Ir, C...). Then you will have the number of particles by the measured volume. Same could be done for a TEM prepartion, placing the drop on a TEM grating holder, being careful because of the smaller size of the holder, to avoid the drop breaks and part of the volume is leaked, which will not allow you to have a confiable value.
If your solution concentration is high, may be the PS particles aggregate, making it difficult to count them. In this case you can dilute an aliquot of your solution and try with the SEM again, having the dilution into account at the time to calculate the original solution concentration.
It would be also possible to use some light scattering technique, in this case you need to do some calibration curve with known concentration solutions of PS particles of the same size as in your problem solution.
If your PS particles are highly monodisperse, gravimetric essays could also give you the mass of PS, and from the volume of the spere and density of PS you could determine the number of spheres in the original volume.
you can also do diffraction analysis, and thanks to near-uniform size of nanoparticles (as you can start with an approximation), a ring will appear in the pattern. then analyze the ring obtained and find particle size distribution. then take a few (micro) droplets of solution and evaporate the solvent to obtain mass of nanoparticles in the droplet. Now, you have both particle size distribution and mass concentration of particles in the solution. now you can find number density of particles by assuming a spherical shape (assuming nano-particle density is known)