In this report, silica-platinum metallodielectric particles were submitted to alternating electric field produced by ITO electrodes. Under

influence of uniform electric field, intrinsic asymmetry of Janus particles induced symmetry breaking that led to a phoretic motion. Frequency

dependent dynamics was studied experimentally, and a reversal of phoretic motion is observed. A model involving the charging of double layer

similar to that of ACEO is proposed to explain the phenomenon.

Electric Charging and Dynamic

Behavior of Janus Particles

Tzyy-Shyang Lin, Hong-Ren JiangSoft Matter and Active Material Lab, Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan

Abstract

Introduction

Reference1. T. M. Squires and M. Z. Bazant, J. Fluid Mech. 560, 65 (2006).2. T. M. Squires and M. Z. Bazant, J. Fluid Mech. 509, 217 (2004).3. S. Gangwal, O. Cayre, M. Bazant, and O. Velev, Phys. Rev. Lett. 100, 058302 (2008).4. M. Z. Bazant and T. M. Squires, Curr. Opin. Colloid Interface Sci. 15, 203 (2010).5. J. L. Anderson, Annual Review of Fluid Mechanics 21, 61 (1989).6. K. T. Chu and M. Z. Bazant, Phys. Rev. E 74, 011501 (2006).7. D. Lastochkin, R. Zhou,P. Wang,Y. Ben and H. Chang, J. Appl. Phys. 96, 1730 (2004)

Results & Discussion

Method

Preparation of Janus Particles:Hexagonal close packed 2mm silica particle

monolayer was put into sputter, and platinum was

coated. The hemisphere under shadow was shaded

and only the other hemisphere was coated. Thus

metallodielectric Janus particles were made.

Preparation of Janus Particles:Janus particles were put into chamber formed by

two ITO (indium-tin oxide) slides and parafilm spacer.

The ITO glass slides served as electrodes, which were

connected to function generator. The chamber height

can be controlled to vary from 10mm to 500 mm.

Mean Square DisplacementFig. 3. Schematic of

experimental apparatus.

Function

Generator

Fig. 1. Schematic

illustration of ICEP.ref.3

Fig. 2. Preparation of JP.

Mean square displacement (MSD) was used to

calculate the velocity of particles.

MSD = 4𝐷𝑡 +2𝑉2𝐷𝑟𝑡

𝐷𝑟2+𝜔2 +

2𝑉2 𝜔2−𝐷𝑟2

𝐷𝑟2+𝜔2 2 +

2𝑉2𝑒−𝐷𝑟𝑡

𝐷𝑟2+𝜔2 2 [ 𝐷𝑟

2 − 𝜔2 cos𝜔𝑡 − 2𝜔𝐷𝑟 sin𝜔𝑡].

Where 𝜔 is average angular velocity, 𝐷𝑟 is the rotational diffusion constant, 𝐷 the

diffusivity, 𝑉 the self-propelling velocity. In short timescale, rotational and angular

velocity terms can be neglected, so the equation can be simplified to

MSD = 4𝐷𝑡 + 𝑉2𝑡2.

We track particles’ positions and calculate MSD, then perform quadratic fit to

determine particles’ velocity.

Fig. 7. Reversal frequency

against NaCl concentration.

Fig. 6. Phoretic velocity of Janus

particle at 1kHz.

Reversal of MotionThe behavior of 2mm silica/Pt Janus particle

under uniform electric field goes through several

stages. Defining a structural dipole 𝑃𝑠 as shown in

figure 4, at low frequencies, the particles swims with

velocity 𝑣 ⊥ 𝐸, with orientation 𝑃𝑠 ∥ 𝑣; when frequency

is increased, the velocity decreases, until the particle

halts, then phoresis occurs again with reversed

orientation, 𝑃𝑠 ∥ − 𝑣, as in figure 5.

ICEP at Low FrequencyPhoretic velocity of the first “forward swim” stage

is proportional to the square of applied electric field

strength, as shown in figure 6; this corresponds to the

ICEP prediction. As ICEP predicts, the forward

phoresis decays at “RC time” 𝜏𝑐 = 𝜆𝑎/𝐷 ; this

timescale proportional to EDL thickness 𝜆, as in figure

7, 𝑓𝑟𝑒𝑣 ∝ 𝑐 ∝ 𝜆−1 ∝ 𝜏𝑐−1.

Timescales and Electrode DimensionWhile reversal timescale matches the EDL

thickness, it is found that the timescale also depends

on the physical separation between the electrodes.

Shown in figure 8, with fixed electrode voltage, the

reversal frequency is inversely related to chamber

height 𝑑 ; whereas in figure 9, when chamber

thickness 𝑑 is fixed, the field strength 𝐸0 = 𝑉/𝑑 has

essentially no effect on reversal frequency.

Mechanism of Reversal MotionWhile “forward” motion can be attributed to ICEP,

the capacitive charging theory with blocking electrode

fails to explain the reversed motion. For capacitive

charging, three timescales have been identified: 𝜏𝑎 =𝑎2/𝐷 , 𝜏𝑐 = 𝜖𝜏𝑎 , 𝜏𝑑 = 𝜖𝜏𝑎 , 𝜖 = 𝜆/𝑎 . Yet even the

fastest 𝜏𝑐 is of order 10kHz, so it can not account for

the phenomena we observed at high frequency.

Besides capacitive charging, faradaic charging

may be present at electrode-particle system. During

faradaic charging, double layer is charged with co-

ions generated from chemical reaction at the surface

of electrode, as illustrated in figure 10b, in contrast to

counter-ions attracted in capacitive case, illustrated in

figure 10a, so the flow direction is opposite to ICEO,

leading to a reversed phoresis.

The phoretic velocity can be obtained using

Smoluchowski equation

𝑈𝑓 ∝𝜀𝜁′

𝜂𝐸0

where 𝜁′ is the effective zeta potential. For reaction

limited condition, the potential is proportional to the

rate of formation of ions, 𝜁′ ∝ 𝑘𝑓; rate constant can be

estimated by Arrhenius relation, so we have

𝜁′ = 𝐴0exp(E0𝑎/𝑉0)Combining the two, we obtain an expression for

phoretic velocity driven by faradaic charging

𝑈𝑓~𝜀𝐴0𝑉

𝜂𝑑exp

𝐸0𝑎

𝑉0

While ICEP velocity can be written as

𝑈𝑐~𝜀𝐸0

2𝑎

𝜂

1

1 + 𝜔2𝜏𝑐2

The two velocities cancel at 𝜔~𝑓𝑟𝑒𝑣 , 𝑓𝑟𝑒𝑣𝜏𝑐 ≫ 1

𝑈𝑐~𝑈𝑓 → 𝑓𝑟𝑒𝑣 =𝛼

𝜆

𝑉

𝑎𝑑exp −

𝑉𝑎

2𝑉0𝑑

where 𝛼 is a proportionality factor, 𝑎 is particle radius.

This relation is plotted in figure 7-9 in red alongside

experimental results.

When a metallodielectric particle consisting of one conducting hemisphere and

one non-conducting hemisphere is put under electric field, polarization of the particle

induces electro-migration of charged species and the formation of a screening

electric double layer. In contrast to intrinsic double layer of colloid particles, this

induced double layer possesses nonuniform zeta potential. With the external electric

field, they bring about a variety of induced electrokinetic phenomena. At low

frequencies, and relatively small applied field, the well-studied induced charge

electro-osmosis (ICEO) and induced-charge electro-phoresis (ICEP) ref.1.2 take place,

resulting in a slip velocity of magnitude 𝑈0 ∝ 𝐸02𝑎 around the metal side. Where 𝐸0

the strength of applied electric field, 𝑎 the radius of the particle.

While the standard Poisson-Nernst-Planck (PNP)

model and linearized Guoy-Champan-Stern (GCS) yields

satisfactory results at low frequencies and small field

regime, most models fail at timescales smaller than the

“RC time” and field stronger than thermal voltage, that is:

𝑓 > 𝐷/𝜆𝑎 , 𝐸0𝑎 > 𝑘𝐵𝑇/𝑒 . At this regime, the linear

approximation of the standard model breaks down and

highly nonlinear terms become significant.

Though theories have been proposed to account for large applied field and steric

effects, many anomalies still lay unanswered, such as flow reversal observed at high

frequency planar ACEO. Furthermore, the existing literature focus on planar

electrodes, whereas the investigation on curved electrodes at high frequencies is

lacking both experimentally and theoretically.

In sight of this, we investigate the dynamic behavior of curved electrode through

exploring dynamic behavior of metallodielectric Janus particles.

𝑃𝑠

Ptsilica

Fig. 4. Illustration of a JP.

Fig. 5. Stacked image of JP’s

trajectory. external electric

field of (a) 5kHz (b) 800kHz.

(a)

(b)

←v

←v

𝑬𝟎

Fig. 8. Reversal frequency

against chamber thickness.

Fig. 9. Reversal frequency

against applied field strength.

Fig. 10. Comparison between

(a) capacitive charging and

(b) faradaic charging.

(a)

(b)