I want to find the mobility of platinum nanoparticles first theoretical then experimentally, is there any publication where a charge number is consider for a platinum nanoparticle of a 4 nm diameter.
I am afraid that it will be extremely challenging to determine the charge and the mobility by theoretical means for any particle. The magnitude of the charge and its sign on the surface is highly dependent on the dispersing medium as well as the pH. Experimentally, it is just a 10 minute experiment if done properly. All you need an instrument to determine the zeta potential (e.g. ZetaSizer etc) to determine the surface charge in a given solution and pH. You can also find the mobility from the same data.
Thats correct. Use the Henry's equation with Smoluchowski approximation in the software. All you need is a dilute suspension, known dispersing medium and pH.