I assume that you have the exact mass of the nanoparticles. And I also assume that you insert it to a solution. Then you should use two electrodes and a current-time measuring device according to the intensity of the ions that you expect to have inside the solution (usually I measure it with simple multi-meter, but in your case I think more precise device is needed). Finally you will get a current-time data and you can easily convert it to Volt-time data.
Note: I used this method to measure the current obtained form Mg+2 ion movement between two Cu electrodes in a vacuum chamber at P=10 Pa.