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

The authors develop an ultrasensitive method for the measurement of the charge carried by a colloidal particle in a nonpolar suspension. The technique uses the phenomenon of the resonance of a particle held in an optical tweezer 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 (gamma<1) the particle is confined to the optical axis, while at high fields (gamma>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.