Motion-based threat detection using microrods: experiments and numerical simulations

Nanoscale

PAPER

Cite this:

Nanoscale

, 2015,

, 7833

Received 21st October 2014,

Accepted 23rd March 2015

DOI: 10.1039/c4nr06208f

www.rsc.org/nanoscale

Motion-based threat detection using microrods:

experiments and numerical simulations

†

Barath Ezhilan,

Wei Gao,

Allen Pei,

Isaac Rozen,

Renfeng Dong,

Beatriz Jurado-Sanchez,

Joseph Wang*

and David Saintillan*

Motion-based chemical sensing using microscale particles has attracted considerable recent attention. In

this paper, we report on new experiments and Brownian dynamics simulations that cast light on the

dynamics of both passive and active microrods (gold wires and gold

–

platinum micromotors) in a silver

ion gradient. We demonstrate that such microrods can be used for threat detection in the form of a silver

ion source, allowing for the determination of both the location of the source and concentration of silver.

This threat detection strategy relies on the di

ff

usiophoretic motion of both passive and active microrods

in the ionic gradient and on the speed acceleration of the Au

–

Pt micromotors in the presence of silver

ions. A Langevin model describing the microrod dynamics and accounting for all of these e

ff

ects is pre-

sented, and key model parameters are extracted from the experimental data, thereby providing a reliable

estimate for the full spatiotemporal distribution of the silver ions in the vicinity of the source.

1 Introduction

Controlled migration and self-propulsion of microscale par-

ticles is a challenging task with a broad range of technological

and biomedical applications. A classical way to manipulate col-

loidal suspensions relies on phoretic transport, by which exter-

nally imposed gradients of various fields (such as temperature,

electric field, solute concentration

etc

.) can lead to the

migration of colloidal particles. Recent advances in micro-

fluidic technologies have spurred a renewed interest in the

theoretical understanding and practical application of such

transport mechanisms.

1,2

In recent years, phoretic e

ects have also been used for the

autonomous self-propulsion of microparticles. Catalytically

active microparticles such as bimetallic microrods can indeed

self-generate and sustain surface asymmetries leading to their

propulsion through a variety of self-phoretic mechanisms.

These artificial micromotors o

er a broad range of potential

applications ranging from drug delivery, microscale assembly

and transport, robotics, to motion-based chemical/biochemi-

cal sensing.

–

Potential environmental applications of micro-

motors have grown rapidly in recent years, indicating a myriad

of innovative remediation and monitoring applications based

on new motion-based phenomena.

–

Specifically, micro-

motors that exhibit a concentration dependence of their self-

propulsion velocities could mimic chemotactic search strat-

egies employed by microorganisms in biological settings and

hence be used to trace plumes of hazardous chemicals to their

source. Recently, Gao

et al.

reported that Ir/silica Janus

micromotors, powered by extremely low levels of hydrazine

fuel, display a well-defined concentration/speed dependence,

thus holding considerable promise for tracing concentration

gradients of this pollutant. Experiments have shown that

–

Pt micromotors exhibit directed movement toward high

hydrogen peroxide concentrations through

‘

active di

usion.

’

In addition, an unusual speed acceleration of Au

–

Pt micro-

motors in the presence of silver ions has also been reported.

This specific unexpected e

ect of silver upon the speed of cata-

lytic micromotors has been exploited for designing a new

motion-based trace silver sensing protocol. The specific accel-

eration has been attributed to the underpotential deposition

of silver onto a platinum segment, which increases the electro-

catalytic activity. The highly selective motion-based response is

characterized by a defined concentration dependence, with the

speed of the micromotors providing quantitative information

down to the nanomolar level. This silver-based acceleration

has also formed the basis for a motion-based detection of DNA

hybridization in connection to silver nanoparticle tags.

While previous studies have separately focused on phoretic

migration in an external gradient and on self-phoretic propul-

sion in the absence of external gradients, the combined use of

both transport strategies has been widely unexplored and

could lead to novel avenues for the control of colloidal

†

Electronic supplementary information (ESI) available. See DOI: 10.1039/

c4nr06208f

Department of Mechanical and Aerospace Engineering, University of California

San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA. E-mail: dstn@ucsd.edu

Department of Nanoengineering, University of California San Diego, 9500

Gilman Drive, La Jolla, CA 92093, USA. E-mail: josephwang@ucsd.edu

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motions or the sensing of external fields. Because of the ubi-

quity of Brownian motion at the length scales relevant to these

suspensions, the non-trivial interplay of phoretic migration,

self-phoretic propulsion and Brownian fluctuations is of sig-

nificant theoretical and practical interest. In the context of bio-

logical transport, this is analogous to the coupling between

swimming, chemotactic migration and Brownian motion,

which is known to lead to a rich variety of non-trivial

phenomena.

In this paper, we perform experiments using both passive

tracers (Au microwires) and active swimmers (Au

–

Pt micro-

wires) near a silver ion source using methods described in

section 2. Passive tracers in an electrolyte gradient move

towards lower concentration of electrolyte as explained by clas-

sical theories of di

usiophoresis.

29,30

This e

ect causes a

marked depletion of gold microwires near the silver ion

source, thus enabling spatial detection of the source. Active

swimmers (Au

–

Pt microwires) also exhibit a di

usiophoretic

response to the externally imposed silver ion gradient (similar

to passive tracers) while additionally accelerating in regions of

higher silver ion concentration.

This silver-based accelera-

tion characteristic of Au

–

Pt micromotors is utilized to develop

a strategy for accurate spatiotemporal sensing of the silver ion

concentration in the domain by fitting experimental data to a

numerical model. In section 3, we introduce a Langevin model

and Brownian Dynamics (BD) simulation methodology to

analyze the non-trivial coupling of di

usiophoresis, silver-ion

induced speed acceleration and Brownian motion. Key model

parameters are extracted from the experimental velocity data of

both passive tracers and active swimmers, from which the

spatiotemporal evolution of the silver ion concentration in the

domain is deduced. Results from the experiments and BD

simulations are reported in section 4 where the spatiotemporal

dynamics, density and velocity profiles of both passive tracers

and active swimmers are analyzed in detail. We conclude in

section 5.

2 Experimental methods

2.1 Micromotor preparation

The Au

–

Pt microwires were prepared by sequential electro-

deposition of gold and platinum into 200 nm diameter cylindri-

cal pores of an alumina membrane template (catalog no. 6809-

6022; Whatman, Maidstone, U.K.). A thin gold film was first

sputtered on the branched side of the membrane to serve as a

working electrode. The membrane was assembled in a Teflon

plating cell with aluminum foil serving as an electrical contact

for the subsequent electrodeposition. A sacrificial copper layer

was first electrodeposited into the branched area of the mem-

brane using a 1 M cupric sulfate pentahydrate solution

(CuSO

·5H

O; Sigma-Aldrich, St. Louis, MO), at total charge of

10 °C and a potential of

−

1.0 V (

vs.

Ag/AgCl reference elec-

trode) along with platinum wire as a counter electrode. Sub-

sequently, a Au segment was plated from a gold plating

solution (Orotemp 24 RTU RACK; Technic Inc., Anaheim, CA)

and electrodeposited at a total charge of 1.5 °C and a potential

−

0.9 V. Platinum was then deposited galvanostatically using

a current of

−

2 mA for 50 min from a platinum plating solu-

tion (Platinum RTP; Technic Inc.). The resulting Au

–

Pt micro-

wires had a length of around 2

m. The sputtered gold layer

and the copper sacrificial layer were simultaneously removed

by mechanical polishing with 3

–

m alumina slurry. The

bisegment Au/Pt microwires were then released by immersing

the membrane in 3 M NaOH for 30 min. The synthesized

micromotors were separated from solution by centrifugation at

10 000 rpm for 5 min and washed repeatedly with ultrapure

water (18.2 M

cm) until a neutral pH was achieved. Between

the washing steps, the micromotor solution was mixed with

ultrapure water and briefly sonicated (25 s) to ensure the com-

plete dispersion of micromotors. All micromotors were stored

in ultrapure water at room temperature and their speed was

tested before each experiment.

2.2 Silver ion source preparation

Planar sources of elemental silver were fabricated through a

photolithographic process. After patterning 50

m cylindrical

wells in a photoresist film on a glass coverslip, 10 nm of Ti

and 100 nm of Ag were deposited onto the glass by electron

beam evaporation (Temescal BJD 1800 E-beam Evaporator).

The remaining metal film and underlying photoresist were

stripped o

in acetone, resulting in well-defined Ag films to

serve as sources of Ag

ions. For the duration of the experi-

ments, these Ag films can be considered as infinite sources,

since they continuously release Ag

ions in the presence of

hydrogen peroxide.

2.3 Setup

A schematic of the experimental setup is shown in Fig. 1.

A known volume of a solution containing the Au

–

Pt microwires

Fig. 1

(color online) Schematic of the experimental setup. Silver source

(black dot in the center) releases Ag

into a fuel enhanced (0.1% hydro-

gen peroxide) solution containing Au

–

Pt active microwires or Au passive

microwires. The movement of the micromotors was followed using an

inverted microscope.

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was dropped onto the planar silver source. The wires were

allowed to settle in the plane of focus before the same volume

of hydrogen peroxide fuel (0.1%), essential for microwire pro-

pulsion and silver dissolution, was added using a pipette.

Control experiments performed with an inert source made of

glass (instead of the active silver ion source) showed no convec-

tive perturbations or phoretic drift due to the transient

inhomogeneities in the mixing process. This suggests that the

peroxide and microrod solutions mix rapidly on timescales sig-

nificantly higher than the phoretic timescales relevant to our

problem. Based on their self-electrophoretic mechanism, the

micromotors self-propel at a speed of 10

−

in a 0.1%

hydrogen peroxide solution. This micromotor speed increases

dramatically in the presence of Ag

ions. Micromotor speeds

were determined with movies taken at 45 frames per second

using NIS-Elements AR software (Nikon, USA). Individual

micromotor trajectories were tracked and Origin software was

used to analyze the data.

2.4 Data extraction

2.4.1 Velocity tracking.

The time of fuel addition to the

microwire sample was taken to be the start of the experiment

(

= 0). microwire velocities were tracked at 0 s, 2.5 s, 5 s, 10 s,

15 s, and 20 s after adding hydrogen peroxide and were

averaged over 10 frames for each time interval. The distance of

each micromotor from the center of the Ag source was

recorded at the beginning of the 10-frame interval. Over

150 micromotors were tracked per time interval per video for

3 movies.

2.4.2 Density measurements.

Density measurements were

made at 0 s, 2.5 s, 5 s, 10 s and 20 s after fuel addition.

A known volume of solution containing the Au

–

Pt microwires

(for experiments with active tracers) or Au microwires (for

experiments with passive tracers) was dropped onto the silver

source. The swimmers/tracers were allowed to fully settle to

the plane of focus before addition of the hydrogen peroxide

fuel (0.1%). Rings with radii ranging from 25

m to 125

and with spacing

m between them were defined on the

captured images at the specified times. The number of micro-

wires within each consecutive pair of rings was counted,

divided by the area, normalized by the initial number of micro-

wires (at

= 0) and ensemble-averaged over 3 movies to obtain

the wire density at discrete radial positions

= [25 + (

−

0.5)

]

m for

...

20 using the following expression:

;

Þ¼

ðÞ

;

where

is the radial position of each particle,

(

= 0) is the

total number of particles at the time of fuel addition (

=0)

and the symbol

〈

〉

denotes an ensemble average over 3 distinct

realizations of the experiment.

3 Langevin model and Brownian

dynamics simulation

3.1 Particle fluxes

We describe the two-dimensional dynamics of

= 1000 par-

ticles (either passive tracers or active swimmers) using a Lange-

vin model. A particle with index

‘

’

≤

) has center-of-

mass position

and orientation

parametrized in the plane

of motion as

= [cos

, sin

]. During a short time interval

the center-of-mass displacement is calculated using the follow-

ing Langevin equation as the sum of self-propulsive, di

usio-

phoretic and Brownian contributions:

;

ðÞ

;

½Þ

ˆ

ffiffiffiffiffiffiffiffiffiffiffiffi

;

where

ˆ

is a unit vector pointing radially outward

from the position of the source at the center of particle

.Brow-

nian fluctuations also lead to changes in the particle orien-

tations, which are also captured by a Langevin equation:

ffiffiffiffiffiffiffiffiffiffiffi

ðÞ

In eqn (2) and (3),

and

denote two-dimensional

random vectors whose components follow a random Gaussian

distribution with zero mean and unit variance. The trans-

lational and rotational di

usivities

and

can be estimated

for rod-like particles

as:

ðÞ

where

log

‘

log

‘

where

ℓ

and

denote the length and inverse aspect ratio of a

particle, respectively, and

is the viscosity of the suspending

fluid. The micromotors have a length of 2

m and aspect ratio

≈

10. Based on these values, we estimate the Brownian trans-

lational di

usivity coe

ffi

cient to be

≈

4×10

−

, and

the rotational di

usivity to be

≈

−

and

are the self-propulsive and di

usiophoretic vel-

ocities of the catalytic micromotors, which both depend on the

evolving silver ion concentration

[

] in the domain. The

functional dependence of the self-propulsion velocity on the

silver concentration is obtained by fitting a logarithmic curve

to the micromotor speed

vs.

silver ion concentration data of

Kagan

et al.

ðÞ¼

;

,

1169 log

ðÞþ

116

;

otherwise

where

should be expressed in Molar units. To simulate the

dynamics of passive tracers (Au microwires), we simply set

=0.

The di

usiophoretic slip velocity of a spherical object in an

ionic gradient was previously derived

29,30

and is expressed as:

Þ¼

log

;

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where the coe

ffi

cient

is the sum of

‘

chemiphoretic

’

and

‘

electrophoretic

’

contributions:

Þþ

̃

βζν

here,

and

are positive coe

ffi

cients,

is the adsorption

length,

̃

is the di

erence between anion and cation mobilities

normalized by their sum, and

is the surface zeta potential.

This peculiar

‘

log-sensing

’

property was also verified by recent

experiments on di

usiophoresis in controlled electrolyte gradi-

ents.

1,2

We assume in our simulations that

is a constant

independent of the silver concentration, and the weak depen-

dence of

on salt concentration was indeed shown by

Palacci

et al.

to play only a minimal role. The simpler scaling

for

∼

has also been suggested,

where

is the

Bjerrum length (

= 0.7 nm in water). This estimate gives

≈

−

and

∼

≈

−

. As we shall

see in section 3, a more reliable estimate for

can in fact

be extracted from the experimental data.

3.2 Silver ion evolution

In order to integrate eqn (2) and (3) in time, we require knowl-

edge of the silver concentration field

(

), which varies both

in space and time. Specifically, silver ions di

use radially into

the domain from the boundary of the infinite silver source

located at

=25

m. We consider a finite-size compu-

tational domain of exterior radius

domain

= 150

m. Silver ions

are injected into the domain by the following surface reaction:

Þþ

2Ag

Þþ

2OH

At the surface of the source, we expect the rate

of silver

ion produced by the surface reaction to balance the di

usive

flux away from the source:

;

where

is the silver ion di

usivity and is set to 1.6 × 10

−

(di

usivity of silver ions in water). The silver ion flux

the source surface is expected to depend on the rate constant

of the reaction and on the concentration of hydrogen peroxide

near the surface: its value is not known

a priori

but will be

extracted from the experimental data as explained in more

detail in section 3.

A second boundary condition for the silver concentration is

provided far away from the source:

0at

1

;

and in practice we enforce this condition at

domain

Assuming an axisymmetric distribution, the evolution of

the concentration of silver ions

(

) inside this domain is

governed by the di

usion equation, in spherical coordinates:

;

subject to boundary conditions (10) and (11). Solving this

equation analytically using Laplace transforms, we derive the

solution for the normalized silver ion concentration as a func-

tion of radial position and time:

;

ðÞ

erfc

ffiffiffiffiffiffiffi

exp

erfc

ffiffiffiffiffiffiffi

At long times

≫

, the normalized silver ion concen-

tration profile reaches a steady state given by:

lim

1

;

Fig. 2(a) shows the normalized silver ion concentration pro-

files according to eqn (13) at di

erent times

. It can be seen

that, as time increases, the normalized silver ion concentration

on the source surface (

) increases, asymptotically reach-

ing a value of 1 at infinite time:

(

∞

. The concen-

tration of silver ion in the domain also gradually increases

everywhere as a result of di

usion.

Using the solution of eqn (13) for the silver ion concen-

tration, we calculate the di

usiophoretic velocity

(

)as

follows:

exp

erfc

ffiffiffiffiffiffiffi

erfc

ffiffiffiffiffiffiffi

At long times

≫

, the di

usiophoretic velocity also

reaches a steady state given by:

Þ¼

lim

1

;

Þ¼

The spatial dependence of the di

usiophoretic velocity at

erent times is illustrated in Fig. 2(b), showing the logar-

ithm of the silver ion concentration profile. At short times,

Fig. 2

(color online) (a) Normalized silver ion concentration pro

fi

le and

(b) its logarithm as a function of radial position and time.

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when the silver ions have not yet di

used significantly into the

domain (

→

0), the model of eqn (15) predicts a nonphysical

increase in the logarithmic silver ion profile. To remedy this,

we set

to zero when the silver concentration

fall below

the critical value of

min

= 0.2

, which suppresses the non-

physical increase of

∂

log

∂

with

in limit of

→

0. A similar

method was previously used by Hong

et al.

3.3. Model parameter extraction

The model described above has two unknown parameters: the

usiophoretic coe

ffi

cient

, and the surface silver ion flux

on the surface of the source. As we explain here, both of

these parameters can be extracted from the experimental data,

using two sets of experiments involving passive particles and

active micromotors. First, it can be noticed that while the self-

propulsion velocity

in eqn (6) depends on the surface ion

flux

, the di

usiophoretic velocity

in eqn (15) does not

and only involves

. This implies that

can first be

extracted from data for passive particles (Au microwires). Such

data for the velocity

vs.

distance from the source is shown in

Fig. 3(a), and can be fit to the model of eqn (15) to obtain the

estimate

=10

−

. Once

is known, the active

micromotor (Au

–

Pt microwire) data, shown in Fig. 3(b), can

then be used to obtain the best fit value of

= 2.52 × 10

−

for the silver ion flux. This estimate for

, coupled with the

analytical solution of eqn (13), enables prediction of the full

spatiotemporal silver ion concentration profile throughout the

domain with good resolution.

3.4 Simulation method

= 0, the particle positions and orientations are initialized

with a uniform isotropic distribution. The governing equations

are non-dimensionalized using the following scales for

lengths, time, and silver concentration:

;

The self-propulsion and di

usiophoretic contributions to

the translational flux can be calculated analytically using

eqn (6) and (15). Time integration of the Langevin equations

for the particle motions are performed using a second-order

Adams

–

Bashforth time-marching scheme. The swimmer/tracer

density profiles were calculated in the same fashion as the

experimental profile measurement described in section 2, but

ensemble-averaged over 12 simulation runs.

3.5 Model assumptions and limitations

The model described above is the simplest model that

accounts for all relevant e

ects including self-propulsion,

usiophoresis, and di

usion of silver ions. However, it is

also based on a number of simplifications and approximations

that may have a quantitative impact on the results. First, we

note that the classical expression for the di

usiophoretic vel-

ocity used here was originally derived for spherical par-

ticles.

29,30

While we do not expect the dependence on

change significantly for rod-like particles such as the micro-

motors considered here, di

usiophoresis may also lead to a

rotational flux contribution, though this flux is negligible

unless strong gradients exist on the scale of the particles,

which is not the case here. Second, we have neglected the

ect of the microrods on the distribution of silver ions. This

ect can be twofold: on the one hand, the reaction of the

silver ions with the microrods is expected to deplete the silver

concentration in their vicinity; on the other hand, motion of

the particles may also lead to convection and stirring of the

silver ions beyond the simple e

ect of molecular di

usion.

Finally we note that we have ignored both steric and hydro-

dynamic interactions between micromotors on the basis that

the suspensions used in the experiments were dilute; these

interactions may play a minor role in the fronts that form near

the silver source, where the density is higher, yet we do not

expect them to significantly modify the results.

4 Results and discussion

As the fuel is added at

= 0, the silver ions are produced on

the surface of the source at

and rapidly di

use into the

domain (as shown in Fig. 2). This drives the formation of silver

ion gradients in the domain, to which both passive tracers and

active micromotors respond in unique ways as explained

below.

4.1 Passive tracer dynamics

The spatiotemporal dynamics of passive tracers are illustrated

in Fig. 4(a) and (b) (and accompanying video). Over time, the

tracers progressively move away from the source due to di

usio-

phoresis. This results in the complete depletion of tracers

near the source. As shown in the passive tracer density profiles

in Fig. 5, a sharply defined depletion front progresses radially

outward over time. The interface between the depletion region

Fig. 3

(color online) Experimental data showing velocity as a function

of radial position and time for (a) active swimmers (Au

–

Pt micromotors)

and (b) passive tracers (Au microwires).

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near the source and the rest of the domain also grows sharper

with time. Fig. 3(a) shows the velocity profile of passive tracers

for di

erent times. It can be seen that the wires reach a vel-

ocity of up to 14

−

. The peak in the velocity is reached

very close to the depletion front. The scatter in the passive

tracer velocity at any given radial location is a consequence of

Brownian fluctuations. Further from the source (

≥

100

m), a

velocity of 2

–

m is reported, which corresponds to contri-

butions solely from Brownian motion.

4.2 Active swimmer dynamics

The spatiotemporal dynamics of active swimmers are illus-

trated in Fig. 4(c) and (d) (and accompanying video). A

depletion front advancing radially outward as a result of di

siophoresis can be clearly seen. However, the depletion e

ect

is reduced by the motility of the swimmers and in particular,

the speed acceleration of the micromotors near the source

Fig. 4

(color online) Spatiotemporal dynamics of passive tracers (Au microwires): (a) experiment and (b) simulation. Spatiotemporal dynamics of

active swimmers (Au

–

Pt micromotors): (c) experiment and (d) simulation. Also see the accompanying video.

Fig. 5

Passive tracer (Au microwires) density as a function of radial

position and time: (a) experiment and (b) simulation.

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where the silver concentration is high. This near-source accel-

eration enables the micromotors to overcome the di

usio-

phoretic flux away from the source and still swim near the

source, resulting in a more di

use interface between the

depletion region and rest of the domain. It can be seen from

Fig. 3(b) that the micromotors reach velocities up to 30

because of the combined e

ect of silver induced speed accel-

eration and di

usiophoresis. The peak velocities are always

attained closer to the source where the acceleration due to the

presence of silver ions is the strongest. The scatter in the vel-

ocity data of active swimmers [Fig. 3(b)] at any given radial

location is much higher compared to the passive tracers [Fig.

3(a)]. This is because, even while the self-propulsion and di

siophoretic velocities are only functions of the radial position,

the net translational flux is given by their vector sum (as

expressed in eqn (2)) and is dependent on the swimmer orien-

tation: swimmers pointing towards the source (

ˆ

,

0) have

a reduced velocity compared to swimmers pointing away from

the source (

ˆ

0). Because of this e

ect, the depletion

front is found to become more di

use with time, and the

speed at which it advances away from the source is also

reduced compared to the case of passive tracer rods as can be

seen from Fig. 6.

4.3 Simulation

vs.

experiment

Fig. 4 (and accompanying video) illustrate that the experiments

(Fig. 4(a) and (c)) and the Brownian dynamics simulation

(Fig. 4(b) and (d)) compare well and the simulations capture

all the key qualitative features reported in experiments. The

location of the depletion front for both passive tracers and

active swimmers [see Fig. 5 and 6(a)

versus

(b)] matches well

between experiments and simulations. The only mismatch

observed is the presence of the stronger peak in the simulation

density profiles, while such clear peaks are absent in the

corresponding experimental profiles. This mismatch may be a

consequence of several e

ects, including: the particular way in

which the di

usiophoretic velocity is calculated (see section 2);

inaccuracies in the di

usion coe

ffi

cients, which were obtained

using slender-body formulas for high-aspect-ratio rods in an

unbounded fluid whereas the particles in the experiments

reside near a substrate; and the neglect of steric repulsion

ects (excluded volume), which likely become important

inside the high-density front at the edge of the depletion

region. The overall agreement between experiments and simu-

lations, however, validates our modeling approach, assump-

tions, and silver ion concentration sensing method.

5 Summary

We have applied a combination of experiments and Brownian

dynamics simulations to demonstrate the use of both passive

and active microrods for the spatial detection of a silver ion

source and the accurate spatiotemporal sensing of the result-

ing silver ion concentration.

First, experiments were performed, where microrods were

dropped onto a planar silver ion source. Our experiments

revealed that the dynamics can be very di

erent based on

whether the microrods are passive or active. Gold microwires,

which are passive, progressively move away from the source

due to di

usiophoresis in the developing gradient of silver

ions. On the other hand, Au

–

Pt microrods, which are active,

also undergo speed acceleration proportional to the silver ion

concentration (as has been shown in recent experiments by

Kagan

et al.

), which weakens the di

usiophoresis-induced

depletion and enables them to swim closer to the source. We

note that this is the first experimental study to look at the com-

bined migration and self-propulsion of microparticles when

subjected to both externally-imposed and self-generated

chemical gradients.

A theoretical model was also proposed based on a simple

Langevin equation, accounting for self-propulsion, di

usio-

phoresis, translational and rotational Brownian motion,

coupled with a di

usion equation for silver ion concentration.

Our model was shown to have two unknown parameters,

viz

the di

usiophoretic coe

ffi

cient and the surface silver ion flux.

Both of these parameters were extracted from two distinct sets

of experimental data involving passive and active microrods,

respectively. Once these parameters were known, the di

usion

equation was analytically solved to obtain the full spatio-

temporal evolution of the silver ion concentration in the entire

domain, and numerical simulations were performed to inte-

grate the Langevin equation for comparison with the experi-

mental data. Good overall agreement between experiments

and simulations was reported. This study, which combined

experiments and theory together with passive and active micro-

rods, suggests novel uses for such particles in technological

applications requiring biochemical sensing, from chemical

threat detection to environmental remediation.

Acknowledgements

This project received support from the Defense Threat

Reduction Agency-Joint Science and Technology O

ffi

for Chemical and Biological Defense (Grant no. HDTRA1-

13-1-0002). D. S. acknowledges support from NSF grant

Fig. 6

Active swimmer (Au

–

Pt micromotor) density as a function of

radial position and time: (a) experiment and (b) simulation.

Nanoscale

Paper

Nanoscale

,2015,

,7833

–

7840 |

7839

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