Detection of Elementary Charges on Colloidal Particles

We have succeeded in determining the charge of individual colloidal particles with resolution higher than the elementary charge. The number of elementary charges on a particle is obtained from the analysis of optical tracking data of weakly charged silica spheres in an electric field in a nonpolar medium. The analysis also yields an accurate value of the particle size. Measurement of the charge as a function of time reveals events in which the particle loses or gains an elementary charge due to ionization or recombination processes at the surface.

Figure 1

Electrophoretic measurement of a silica particle in dodecane. (a) The particle position ($x$, relative to the initial position) during the application of a square wave voltage, resulting in a typical triangular shape with changing amplitude as the particle charge changes (indicated by arrows). The Brownian motion in the $y$ direction perpendicular to the field (with chosen initial position $5\mu \mathrm{m}$) is unaffected by the field. (b) The 120 corresponding mobilities are shown, and guidelines indicate multiples of the elementary mobility ${\widehat{\mu }}_e$. (c) Histogram of the electrophoretic mobility showing peaks at multiples of the elementary mobility. The right axis indicates the number of elementary charges.

Figure 2

Analysis of the electrophoretic mobilities from Fig. 1b. $R^2(\mu )$ from Eq. (5) is shown for the experiment in Fig. 1, with $M=120$. The straight line shows the quadratic expectancy $M{\mu }^2/12$ for random mobility data and $M=120$. Values of the experimental curve that are below this quadratic trend indicate a clustering around multiples of the corresponding mobility $\mu$. ${\widehat{\mu }}_e$ is determined as the local minimum indicated by the double arrow. The minimum, maximum, and average of the absolute value of the measured mobilities are also indicated.

Figure 3

High resolution charge histogram. The 1200 measurements on 10 particles of the charge ${\tilde{Z}}_i={\mu }_i/{\widehat{\mu }}_e$ show peaks in the charge histogram at multiples of the elementary charge $e$.