Direct measurement of the effective charge in nonpolar suspensions by optical tracking of single particles

We demonstrate a novel technique for the measurement of the charge carried by a colloidal particle. The technique uses the phenomenon of the resonance of a particle held in an optical tweezers trap and driven by a sinusoidal electric field. The trapped particle forms a strongly damped harmonic oscillator whose fluctuations are a function of $\gamma$, the ratio of the root-mean square average of the electric and thermal forces on the particle. At low applied fields, where $\gamma \ll 1$, the particle is confined to the optical axis while at high fields ($\gamma \gg 1$) the probability distribution of the particle is double-peaked. The periodically-modulated thermal fluctuations are measured with nanometer sensitivity using an interferometric position detector. Charges, as low as a few elementary charges, can be measured with an uncertainty of about 0.25 $e$. This is significantly better than previous techniques and opens up new possibilities for the study of nonpolar suspensions.