Measurement of Elementary Charges on Colloidal Particles

Measurement of elementary charges on colloidal particles

Filip Strubbe

Supervisor(s): Kristiaan Neyts

I.INTRODUCTION The elementary charge e is a fundamental physical constant with a measured value of ap- proximately 1.602176487(40) × 10−19C. It is the smallest measurable value of the electric charge in stable matter, despite many recent at- tempts to measure fractional charges such as 1/3e and 2/3e [1]. Almost 100 years ago, Robert Millikan carried out the first measurement of the value of e by observing the mo- Figure 1. The particle position in the x- and y- tion of charged oil drops in air under the influ- direction, during the application of a square ence of an electric field [2]. Here, a demon- wave voltage. stration is given of the first measurement of the elementary charge on solid particles in a liquid ned by random Brownian motion. The elec- (see also [3], [4], [5]). Finding the elementary trophoretic mobility µ is calculated in each half charge in a liquid is much harder than in air be- period of the square wave as ∆x/(∆tE). cause of the higher viscosity. This reduces the motion of weakly charged particles in an elec- a) b) tric field to a value which may be below the sensitivity of most measurement systems.

II.EXPERIMENTAL RESULTS For the charge measurement, optical tracking of isolated particles in a liquid is used [6]. The position of spherical silica particles with radius 1.05±0.05µm in pure dodecane is measured as a function of time, while a square wave voltage Figure 2. a) The electrophoretic mobility and b) histogram of the mobility. is applied (see Fig. 1). The motion in the x-direction, which is the As can be seen in Fig. 2a, the mobility direction of the electric field, shows a roughly does not change in a continuous way, but triangular shape, while in the y-direction, per- rather in discrete steps with amplitude µe, pendicular to the field, the motion is gover- the elementary mobility corresponding to a change in the particle charge with e. With —————————————————– the Stokes-Einstein relation we can estimate F. Strubbe is with the ELIS Department, −12 2 −1 −1 Ghent University, Gent, Belgium. E-mail: µe = e/6πηR ≈ 6 × 10 m V s , with [email protected]. the particle radius R = 1.05µm and viscosity η = 1.38 × 10−3Pas, which agrees well with the distance between the peaks in the histogram of the mobility in Fig. 2b and which confirms that the elementary charge is resolved.

III.STATISTICAL ANALYSIS

An estimated value of µe is obtained by analysis of the function R2(µ):

M 2 X 2 Figure 4. High resolution histogram of Z˜ for 1200 R (µ) = (µi − [µi/µ]) , (1) i measurements on 10 particles. i=1 with M the number of mobility measure- IV. CONCLUSIONS ments (see Fig. 3) and µi the measured values In conclusion, we have demonstrated that the of the mobility. For random values of the mo- 2 2 number of elementary charges, the particle size bility, R (µ) has the expected value Mµ /12. and changes of the charge with multiples of the If the mobility values are clustered around mul- 2 elementary charge can be measured on weakly tiples of µe, R (µe) is expected to be much 2 charged particles in a non-polar liquid. This smaller than Mµe/12. Therefore, an estima- method can be used for the characterization tion µê corresponds to a local minimum in of weakly charged colloids, detection of sin- R2(µ). For this experiment with M = 120, we −12 2 −1 −1 gle biomolecule binding events on the particle find µê = (6.18 ± 0.05) × 10 m V s . surface and for studying fundamental electroki- netic phenomena.

ACKNOWLEDGMENTS The research of Filip Strubbe is sponsored by the Institute for the Promotion of Innova- tion through Science and Technology in Flan- ders (IWT-Vlaanderen) and by the IAP VI-10 of the Belgian Science Policy Ofﬁce.

REFERENCES Figure 3. R2(µ) is shown for the experiment in [1] V. Halyo, P. Kim, E. R. Lee, I. T. Lee, D. Loomba, Fig. 1, with M=120. and M. L. Perl, “Search for free fractional electric charge elementary particles using an automated Once µê is known, accurate estimations can millikan oil drop technique,” Phys. Rev. Lett., vol. ˆ 84, 12, 2000. be made of the particle radius R = e/6πηµê [2] R. A. Millikan, “The isolation of an ion, precision and the diffusion constant Dˆ =µ êkT/e us- measurement of its charge, and the correction of ing the Stokes-Einstein relation. Or, using stokes’ law.,” Phys. Rev., vol. 32, pp. 349, 1911. [3] F. Strubbe, F. Beunis, and K. Neyts, “Detection of R = 1.05µm, an estimation for the elemen- elementary charges on colloidal particles,” Phys. tary charge is found: eˆ = 6πηRµê. The value Rev. Lett., vol. 100, 21, pp. 218301–1 to 218301– eˆ for 10 particles is (1.64 ± 0.05) × 10−19C. 4, 2008. [4] “glas in olie,” Knack, p. 59, 2 juli 2008. Each measured mobility µi corresponds to an [5] “patent application filed,” 2008. estimation of the number of elementary charges [6] F. Strubbe, F. Beunis, and K. Neyts, “Determina- Z˜i = µi/µê. Fig. 4 shows a histogram of Z˜i tion of the effective charge of individual colloidal particles,” J. Colloid. Interf. Sci., vol. 301, pp. with clearly visible peaks at multiples of the el- 302–309, 2006. ementary charge e.