Page 1

Plasmonic “pump–probe” method to study

semi-transparent nanofluids

Yasitha L. Hewakuruppu,1,* Leonid A. Dombrovsky,4Chuyang Chen,3

Victoria Timchenko,1Xuchuan Jiang,3Sung Baek,1and Robert A. Taylor1,2

1School of Mechanical and Manufacturing Engineering, University of New South Wales,

Kensington, NSW 2052, Australia

2School of Photovoltaic and Renewable Energy Engineering, University of New South Wales,

Kensington, NSW 2052, Australia

3School of Materials Science and Engineering, University of New South Wales, Kensington, NSW 2052, Australia

4Joint Institute for High Temperatures, Krasnokazarmennaya 17A, Moscow 111116, Russia

*Corresponding author: yasitha.hewakuruppu@gmail.com

Received 2 July 2013; revised 28 July 2013; accepted 29 July 2013;

posted 30 July 2013 (Doc. ID 193246); published 19 August 2013

Nanofluids have been increasingly used in a wide range of thermal applications. Although these appli-

cations can benefit greatly from investigating the behavior of nanoparticles under different heating sce-

narios, there is a lack of experimentsthat can achievethis. To overcome this challenge, an optical “pump–

probe”-type experiment is suggested in this paper. In experiments of this type, a set of “pumping” nano-

particles are specifically selected to absorb laser radiation. These particles represent a flexible tool for

volumetric heating. A second set of “probing” nanoparticles can be tailored to scatter a separate optical

probing signal. This work presents a selection procedure for nanoparticles of both types. The

selection procedure is then demonstrated for a specific example where the pump and probe wavelengths

are of 980 and 532 nm, respectively. Gold nanorods with diameters of 10 and a length of 58 nm are se-

lected as the “most suitable” absorbing particles, while silver nanospheres with a diameter of 110 nm are

selected as the “most suitable” scattering particles. These particles are synthesized and shown to exper-

imentally match the desired optical properties. Overall, this paper proposes and demonstrates an

approach by which it is possible to design and fabricate particles for a wide range of optical studies

in semi-transparent nanofluids. © 2013 Optical Society of America

OCIS codes:

(240.6680) Surface plasmons; (160.4236) Nanomaterials.

http://dx.doi.org/10.1364/AO.52.006041

1.

The unusual thermal properties of nanofluids have

been studied for a wide range of heat transfer and

other applications. Using nanoparticles to enhance

the properties of conventional fluids has become im-

portant to the development of an increasing number

of diverse applications during the last decade [1,2].

Applications of nanofluids range from nanospheres

being used in heat transfer [3] to nanoshells and

Introduction

nanorods being used in medicine for cancer treat-

ment [4,5]. Some of the reported observations of en-

hanced fundamental thermal properties [3,6–8]

(thermal conductivity, convective heat transfer coef-

ficient, boiling heat flux) of nanofluids are still not

well explained, creating a need for further detailed

experimental studies. For instance, one of the

common simplifications used in the analysis of nano-

fluid data is to assume a uniform volume fraction of

nanoparticles in the host liquid. Generally speaking,

this assumption is incorrect, but there is a lack of ex-

perimental and theoretical studies in the literature

concerning migration, preferential concentration,

1559-128X/13/246041-10$15.00/0

© 2013 Optical Society of America

20 August 2013 / Vol. 52, No. 24 / APPLIED OPTICS6041

Page 2

and

particles. In nanofluid heat transfer applications,

where the nanoparticles are participating, such

information is critically important. Experimental ob-

servation using properly designed optical measure-

ments represents an effective way to study these

phenomena. Optical techniques are ideal because

there is no perturbation of the fluid during the ex-

periment. It is also possible to measure the fields

of particle motion, volume fraction, and potentially

temperature which cannot be obtained with physical

probes. Thus, in this work we propose an optical

pump–probe-type technique where one light source

is used to heat up a fluid and another light source

is used to investigate the behavior of nanoparticles

within the fluid. As such, the main objective of this

study is to present a nanoparticle selection method

for designing such optical pump–probe experiments.

Following this, suitable nanoparticles are designed

and fabricated for a specific example. Measurements

of the optical properties of the selected nanofluid are

presented to demonstrate the feasibility of actually

fabricating nanofluid dispersions to meet the desired

specifications.

agglomerationofsuspendednano-

A.

We propose that the class of experiments best suited

for future fundamental investigations on nanopar-

ticle suspensions are optical “pump–probe” tech-

niques. Here, the pump is a high-powered heating

laser and the probe is a low-powered diagnostic laser

of considerably different wavelength. The medium is

seeded with carefully tailored nanoparticles of speci-

fied size, shape, and material, as discussed below.

Figure 1 shows a generic schematic of this type of

configuration, i.e., one which could be used to obtain

any of the field measurements stated above.

In these experiments, nanoparticles characterized

bystrongabsorptionofthepumpradiationsourceare

suspended in a host medium. Coupled with the pump

radiation, these nanoparticles act as a flexible tool

for volumetrically heating transparent host media.

Various types of nanoparticles (including composite

particles with gold or silver coatings) are expected

to be good potential candidates due to strong plas-

monic resonant absorption in the visible and/or

near-infrared spectral ranges [9]. Previous studies

have proposed absorbing nanoparticles (mainly, gold

nanoshells and nanorods) for use in laser-induced

thermal treatment of tumors [4,5,10,11], and for

“Pump–Probe” Approach

the “next generation” volumetric solar thermal

collectors (namely carbon allotropes and noble

metals) [12–15].

In previous nanoparticle studies, physical sensors

such as thermocouples or pressure taps were used as

probes [16]. However, much less disturbance of the

system can be achieved with noninvasive optical

probing. Hence, we propose that a probing beam

(as shown in Fig. 1) should be used in conjunction

with a second set of “probing” nanoparticles. These

particles should be characterized by strong scatter-

ing to be easily observed in the experiment. The

use ofa probe light source which isin the visible spec-

tral range is advantageous because relatively in-

expensive optical cameras can be used to detect

the scattered light. This optical signal can then be

used to study fluid-particle interactions during volu-

metric heating of nanofluids. It is possible to use the

probe signal to detect motion of particles, their clus-

tering or agglomeration, degradation of surfactants

(under prolonged heat), and potentially the temper-

ature of the fluid.

B.

The proposed “two-nanoparticle” approach may seem

complicated, but it actually allows for greater optical

response and much more design freedom. The main

reason for going to this approach is that “pumping”

nanoparticles (which are appropriate for heating) are

very small, highly absorbing, and close to the

Rayleigh region. Therefore, these particles cannot

be observed using measurements based on scatter-

ing. On the other hand, particles which are good scat-

terers can be made of materials which do not absorb

and can be independently studied using light of a

completely separate wavelength. It should also be

noted that these two particles are “locally thermally

dependent” as the fluid temperature will be the same

in the case of continuous pumping radiation. This fol-

lows from the low heat capacity and very fast heat

transfer from nanosized particles to the surrounding

liquid. Additionally, this approach is stable on the

time scales of the experiment as the sedimentation

of small particles is negligible with proper surface

functionalization.

Considering the above, it is clear that utilizing sep-

arate “pumping” and “probing” nanoparticles repre-

sents a pathway toward improved accuracy optical

experiments. The challenge in this approach, how-

ever, is to select “optically independent” particles

which strongly absorb the pump radiation and those

which strongly scatter the probe radiation.

“Two-Particle” Approach

2.

Process)

Computational tools which predict the interaction

and propagation of light within a medium of small

participating particles are well-known and widely

used in various applications [17]. This section of

the paper presents a nanoparticle selection pro-

cedure which employs these techniques to design

Generalized Methodology (Nanoparticle Selection

Fig. 1.Schematic of an optical pump–probe experiment.

6042APPLIED OPTICS / Vol. 52, No. 24 / 20 August 2013

Page 3

appropriate particles for the optical pump–probe ex-

periments described above.Input parameters for this

method are the pump and probe wavelengths and the

dimensions of the test sample. The main optical

properties of various nanoparticles at the pump

and probe wavelengths are calculated first to find

suitable “pump absorbing” and “probe scattering”

nanoparticles. The proposed selection procedure

then gives us the best combination of particles

(one absorbing and one scattering) for the experi-

ment under consideration.

A.

The initial step in selecting absorbing and scattering

nanoparticles isto calculate the far-field optical prop-

erties of different types of nanoparticles. Important

properties include absorption and scattering cross

sections of single nanoparticles at both pump and

probe wavelengths. In this study we consider both

spherical particles such as nanospheres and nano-

shells as well as nonspherical particles such as

nanorods.

For homogeneous and two-layered spherical par-

ticles (nanospheres and nanoshells), Mie theory [9]

codes from [18] were used to calculate the optical

properties. The use of classical Mie theory for single

particles means that our analysis is based on the so-

called independent scattering hypothesis where each

particle is assumed to absorb and scatter the radia-

tion in exactly the same manner as if all other par-

ticles do not exist. In other words, each particle is

assumed to be in the far-field zones of all other

particles, and scattering by individual particles is in-

coherent. Stable colloidal suspensions of gold and

silver nanoparticles have been demonstrated by

many studies in the literature [2]. Thus, it seems rea-

sonable to make this assumption as the aggregation

of particles in a well-dispersed nanofluid is expected

to be negligible at the initial stage of the process to be

studied. For homogeneous and two-layered spherical

particles, the input information includes the dimen-

sions of the particle, the indices of refraction (n) and

absorption (k) of the particle material and the refrac-

tive index of the host medium. Using the mathemati-

cal relations available in [17], this work employs a

computational algorithm which calculates the ex-

tinction (Qt) and scattering (Qs) efficiency factors

along with the asymmetry factor of scattering (¯ μ).

The efficiency factor of absorption (Qa) can then be

calculated by subtracting the scattering efficiency

from the extinction efficiency. Cross sections of ab-

sorption (Ca) and scattering (Cs) can be calculated

by multiplying these efficiencies by the cross-

sectional area (πr2

For nonspherical particles such as finite cylinders,

or particles with arbitrary shapes, the discrete dipole

approximation (DDA) [19] is used to calculate far-

field optical properties. A freely available DDA code

is presented in [20]. When the particle geometry

and substance properties are known, this code can

be used to calculate optical properties of single

Calculating Optical Properties of Single Nanoparticles

2) of the spherical nanoparticle.

particles. Moreover, it is also possible to calculate

orientation-averaged optical properties for gold

nanorods. This includes the effects of different

nanorods having different geometrical orientations

with respect to the direction of the incident radiation.

As an alternative to the DDA method one can also

use the finite-difference time-domain method to

calculate optical properties of nonspherical nanopar-

ticles [21,22].

To accurately calculate the optical properties of

nanoparticles, it is also important to include the ef-

fect of their extremely small size on the oscillation of

electrons in the particles. At nanoscale sizes, the par-

ticle dimensions are generally comparable to or even

smaller than the mean free path of electrons in bulk

metals. When any characteristic dimension of a

metal particle is smaller than the mean free path

of conduction electrons in bulk material, additional

electron collisions occur within the particle [9]. These

additional collisions change the dampening constant

of conduction electrons result in indices of refraction

and absorption (n and k) different from those for the

bulk material. Hence, a modification of these optical

constants of the nanoparticle material is necessary to

incorporate this effect. The model by Kreibig and

Vollmer [23] is used in the present work to perform

this modification. The mathematical relations and

application of the Kreibig and Vollmer model for

different types of nanoparticles can be found in

[13,24,25].

B.

Nanoparticles

The next step is to select two batches of nanoparticles

which can strongly absorb the pump radiation and

strongly scatter the probe radiation while not hinder-

ing one another. To satisfy this requirement for the

absorbing particle, we constrain ourselves to nano-

particles with absorption to scattering efficiency

ratios larger than 10 at the pump wavelength. This

value of 10 was used as a guarantee that the absorp-

tion is at least one order of magnitude greater than

the scattering at the pump radiation wavelength. It

also acts as a safety factor which counteracts the im-

pact of polydispersity and other synthesis limitations

encountered in reality. At the same time it is re-

quired that the absorbing particle does not cause

any unwanted absorption of the probe radiation.

Thus, nanoparticles with absorption efficiency at

least 10 times larger for the pump radiation than

the probe radiation are deemed suitable. Hence, only

nanoparticles which satisfy both of the following con-

ditions are selected as candidates as pump radiation

absorbing particles

Selecting Suitable Absorbing and Scattering

Qapump

Qspump

> 10;

(1)

Qapump

Qaprobe

> 10:

(2)

20 August 2013 / Vol. 52, No. 24 / APPLIED OPTICS6043

Page 4

According to the same logic, strongly scattering

nanoparticles should have a scattering-to-absorption

efficiency ratio larger than 10 at the probe wave-

length. Since these nanoparticles should not scatter

the pumping radiation, they must also have a probe

scattering efficiency that is at least 10 times larger

than the pump scattering efficiency. These conditions

can be written as follows:

Qsprobe

Qaprobe

> 10;

(3)

Qsprobe

Qspump

> 10:

(4)

Nanoparticles which satisfy both of these condi-

tions are selected as candidates for probe radiation

scattering particles. Using these four criteria, nano-

particles of different morphologies can be checked

with Eqs. (1)–(4) to rapidly select good absorbing

and scattering particles.

C.

The final step is to select the “most suitable combi-

nation” of absorbing and scattering nanoparticles

from the ones that cleared the above constraints.

This is defined as the nanoparticle pair which satis-

fies the following three conditions with minimum

volume fraction of nanoparticles (e.g., the lowest cost

nanofluid):

(1) The absorption coefficient should account for

more than 80% of the extinction coefficient at the

pump wavelength while the scattering coefficient

should account for more than 80% of the extinction

coefficient at the probe wavelength.

(2) In order to ensure that energy from the radia-

tion sources is not wasted, the normal-hemispherical

transmittance (Tnh) of both sources through the

medium should be less than 5%.

(3) The normal-hemispherical reflectance (Rnh) of

both sources by the medium should be kept to a mini-

mum (i.e., minimizing energy loss).

The flow chart shown in Fig. 2 summarizes the

main steps of the process of selecting the most suit-

able combination according to these requirements.

This section discusses in detail the mathematical

and physical relations used in this process. For con-

venience, these relations are discussed in subsec-

tions which are numbered using the same notation

(1, 2, and 3) in Fig. 2. The process of selecting the best

combination of nanoparticles begins by choosing

one absorbing nanoparticle and one scattering nano-

particle cleared on the basis of Eqs. (1)–(4). The op-

tical characteristics of the resulting composite

medium (host liquid and nanoparticles) can then

bedetermined,asdescribed

subsection.

Selecting Suitable Combination of Nanoparticles

inthefollowing

1.

Containing Nanoparticles

The transport extinction cross section (Ctr

nanoparticle can be calculated using the following

relation [9]:

Calculating Optical Coefficients of a Medium

t) of a single

Ctr

t? Ca? Cs?1 − ¯ μ?:

(5)

In reality, the nanoparticles in a sample of nano-

fluid will not have the same sizes. Thus, polydisperse

particles are considered by assuming Gaussian dis-

tribution of particle dimensions. That is, a mean size

and standard deviation—based on experimental

data—is used to calculate realistic ensemble proper-

ties. With a known standard deviation, the probabil-

ity density function can be calculated for each size

found in the ensemble. Accounting for this, the trans-

port extinction coefficient (βtr) of a sample of

nanoshells can be calculated using the following

relation [17]:

R∞

βtr?3fv

4π

0

R∞

0Ctr

R∞

tP?r1?P?t?dr1dt

0r3

R∞

0

2P?r1?P?t?dr1dt:

(6)

Here, fv, is the volume fraction of nanoshells in the

medium, P?r1? is the probability density functions of

the core radius and P?t? is the probability density

function of the shell thickness. The same procedure

Fig. 2.Flow chart for selecting the best combination.

6044APPLIED OPTICS / Vol. 52, No. 24 / 20 August 2013

Page 5

is used to account for size variations in other particle

types. For instance, the variation in diameter d and

length L are used for this calculation (instead of r1

and t) for cylindrical particles. Only the variation

in the radius is necessary to account for polydisper-

sity in nanosphere ensembles.

The total extinction of light by the medium is

caused by the absorption and scattering of light by

the particles and the host medium. Assuming the

nanoparticlevolumefractions

(fv< 0.01%), it is possible to simply add the extinc-

tion coefficients of the two types of nanoparticles

(βtr

scattering coefficients of the host medium (αhost

and σtr

transport extinction coefficient βtr

embedded medium [12]

are verysmall

absand βtr

sct) and the absorption and transport

host). This allows for computation of the total

totof the particle

βtr

tot? βtr

abs? βtr

sct? ?αhost? σtr

host?:

(7)

Similarly, the transport scattering coefficient of

the medium (σtr

lated as

tot) containing particles can be calcu-

σtr

tot? σtr

sctare the transport scattering

coefficients of the absorbing and scattering particles,

respectively. They can be calculated using the same

relations in Eq. (6) and using Cs(1 − ¯ μ) instead of Ctr

abs? σtr

sct? σtr

host;

(8)

where σtr

absand σtr

t.

2.

As the composite medium is both absorbing and scat-

tering, the continuum approach and the resulting ra-

diative transfer equation (RTE) is a suitable tool to

describe the propagation of radiation through it

[17,18]. Figure 3 shows a layer of absorbing and scat-

tering medium between two reflecting and refracting

walls. This accurately represents the nanofluid con-

tained by two glass walls irradiated by collimated

external radiation.

When such a medium is irradiated by a beam with

a diameter much larger than the sample thickness,

the one-dimensional RTE can be used for this prob-

lem. With the transport approximation, the scalar

Propagation of Radiation in the Medium

RTE (for randomly polarized radiation) looks as

follows [17,26]:

μ∂I

∂z? βtrI ?σtr

4π

Z1

−1I?z;μ?dμ:

(9)

Here, I is the radiation intensity and μ is the cosine of

the angle between the direction of radiation intensity

and z axis. The boundary conditions for the RTE are

given by

I?0;μ? ? R1I?0;−μ? ? ?1 − R1c?qeδ?μc− μ?;

I?z2;−μ? ? R2I?z2;μ?; μ > 0;(10)

where qeis the incident radiative flux and μcis the

cosine of the angle of incidence. R1and R2are the

effective reflection coefficients for the irradiated

(z ? 0) and shadow (z ? z2) surfaces, respectively.

In the case of a two-flux approach, these reflection

coefficients can be averaged over the angles using

the method of Siegel and Spuckler [27]. R1cis the re-

flection coefficient based on Fresnel reflection for the

incidentcollimatedradiation

multiple reflections by the walls.

The analytical solution to this one-dimensional ra-

diative transfer problem, using the modified two-flux

approximation for the case of normal incidence, was

reported in [28]. The same method can be employed

in the present problem to calculate the profile of

irradiance and both the normal-hemispherical reflec-

tance Rnhand transmittance Tnhof the layer.

After calculating these parameters, the internal

loop including 1, 2, and Q in Fig. 2 increases the vol-

ume fractions ofeach particle until conditions1 and 2

are satisfied.

alsoconsidering

3.

The objective function, F, for each nanoparticle com-

bination is calculated as

Objective Function

F ? fvabsfvsctRnhpumpRnhprobe:

(11)

Here, fvabsand fvsctare the absorbing and scattering

particle volume fractions, respectively, which achieve

both characteristics 1 and 2 as defined at the begin-

ning of this subsection. Rnhpumpand Rnhprobeare the

normal-hemispherical reflectance of pump and probe

radiation by the medium when the above volume

fractions are used. This objective function is calcu-

lated for each combination of absorbing and scatter-

ing nanoparticle. For example, if 5 absorbing

nanoparticles and 10 scattering nanoparticles are se-

lected as candidates, then 50 combinations need to be

considered. According to the earlier definition, the

combination of nanoparticles which gives the mini-

mum value for F results is the “most suitable combi-

nation” for the intended radiation experiment.

Fig. 3.Schematic of the 1D radiative transfer problem.

20 August 2013 / Vol. 52, No. 24 / APPLIED OPTICS6045

Page 6

3.

To demonstrate the use and effectiveness of the pre-

sented nanoparticle selection process, an example

problem is considered in this section. To concentrate

more on the selection process, this example problem

is kept simple. A near-infrared wavelength of 980 nm

was chosen as the pump light source as metallic

nanoparticles are known to strongly absorb radiation

in this region (discussed below). A green light source

with a wavelength of 532 nm was chosen as the probe

wavelength. This is a commonly used wavelength

which can be observed by relatively cheap equipment

as it is in the visible range of the spectrum. For sim-

plicity only normal incidence (μc? 1) of both sources

is considered. The thickness of a liquid layer (z2) is

taken equal to 10 mm and it is also assumed that

the host liquid is pure water. The liquid layer is

contained by two refracting and reflecting, but non-

absorbing, quartz walls.

Silica/gold nanoshells and gold nanorods are

known for their extraordinary optical properties

within the visible and near-infrared spectral ranges.

In addition to strong resonance absorption, their ab-

sorption and scattering capabilities can be tuned by

changing the particle dimensions and structure to

suit particular applications. Changing their relative

core radius δ (ratio between the core radius r1and

external radius r2), allows tuning of nanoshell optical

properties [11,29]. In the case of nanorods, the aspect

ratio (AR ? L∕d) is the main parameter used for

tuning the optical properties [25,30]. These unique

optical properties of gold nanoshells and nanorods

make them suitable for use as absorbers of the

near-infrared pump radiation. Thus, for this exam-

ple, silica/gold nanoshells with external radius

ranging from 10 to 100 nm and the relative core

radius (δ ? r1∕r2) ranging from 0.01 to 0.99 were

considered for the pump radiation absorbing par-

ticle. In addition, gold nanorods with diameter rang-

ing from 10 to 25 nm and varying ARs (from 1 to 10)

were also considered for absorbing the pump

radiation.

On the other hand, relatively large silver nano-

spheres show strong scattering and small absorption

of radiation in the visible range. As such, silver nano-

spheres with radii ranging from 10 to 100 nm were

considered as the probing particles.

Results and Discussion (for a Specific Example)

A.

Nanoshells and nanorods provide a rich variety of ab-

sorption and scattering properties. Figures 4(a) and

4(b) show contour plots for a range of different-sized

gold nanoshells showing the values of the absorbing

nanoparticle selection criteria given in Eqs. (1) and

(2), respectively. These plots are generated for the

pump and probe wavelengths used in this example,

980 and 532 nm, respectively (with the host liquid

being water). Note that the darkest area in each con-

tour plot represents the nanoshells which have a

value larger than 10 for the corresponding selection

criterion given by Eqs. (1) and (2). An order of

Filtered Absorbing and Scattering Particles

magnitude change in these selection criteria are pos-

sible with relatively small changes in particle size

and relative core radius, δ. Gold nanoshells suitable

for absorbing pump radiation belong to the area

which is common to the two darkest regions in

Figs. 4(a) and 4(b). According to Fig. 4(a), suitable ab-

sorbing gold nanoshells have external radii smaller

than 40 nm. Moreover, Fig. 4(b) shows that suitable

absorbing particles also have very thin shells (less

than 3 nm) as their δ value becomes large.

Figures 5(a) and 5(b) show contour plots for a

range of different-sized gold nanorods showing the

values of the absorbing nanoparticle selection crite-

ria given in Eqs. (1) and (2), respectively (also gener-

ated for the wavelengths considered). Similar to the

above, gold nanorods suitable for absorbing pump ra-

diation belong to the area which is common to the

two darkest regions in Figs. 5(a) and 5(b). According

to Fig. 5, gold nanorods with a diameter less than

15 nm and an AR between 5.6 and 6.2 are deemed

to be suitable for absorbing the pump radiation

of 980 nm.

In the case of selecting the scattering particle, it

was found that silver nanospheres with a radius be-

tween 55 and 65 nm are suitable to scatter the probe

radiation as they fulfilled the selection criteria

outlined by Eqs. (3) and (4).

Fig.

(b) Qa?980 nm?∕Qa?532 nm?for gold nanoshells.

4.Contourplotof(a)

Qa?980 nm?∕Qs?980 nm?

and

6046APPLIED OPTICS / Vol. 52, No. 24 / 20 August 2013

Page 7

To further investigate the applicability of the

pump–probe method for scattering particles, copper,

titanium dioxide, and silicon dioxide nanospheres

were also considered. Copper particles with a radius

between 55 and 60 nm, titanium dioxide particles

with a radius between 80 and 90 nm and silicon di-

oxide particles with a radius of 45 nm also satisfy the

selection criteria outlined by Eqs. (3) and (4). For

brevity, only silver particles are considered below

as the scattering particles.

B.

Table 1 summarizes the data for the combination of

absorbing and scattering nanoparticles combination

obtained for this characteristic example. It also gives

the volume fraction of particles required to satisfy

the above discussed conditions.

“Most Suitable Combination” of Nanoparticles

C.

It is also interesting to study changes in the absorp-

tion andscattering propertiesofthemedium contain-

ing nanoparticles and the propagation of pump and

probe radiation when the selected nanoparticles are

added. Table 2 presents the absorption coefficient

(α), the transport scattering coefficient (σtr), and also

the normal-hemispherical transmittance (Tnh) and

reflectance(Rnh)ateachwavelengthforfourdifferent

cases. The first case is pure water. The second case is

when the selected absorbing particles are added to

water. In the third case, only the selected scattering

particlesareaddedtowater.Finally,bothkindsofpar-

ticlesareembeddedinwater.Thesecalculationswere

done for the volume fractions specified in Table 1.

When only the transparent host liquid is present,

almost all the radiation is either transmitted or re-

flected by the medium. In the second case, when only

the absorbing particles are present, the large extinc-

tion coefficient at the pump wavelength is a result of

strong absorption. The addition of the absorbing par-

ticles only has a small effect on the propagation of the

probe radiation. This shows that the selection proc-

ess appears to be effective in choosing the absorbing

particles which have a minimum effect on the probe

radiation.

On the other hand, adding only the scattering par-

ticles to water (case 3) causes a drastic reduction in

transmittance at the probe wavelength. In this case,

the reflectance increases because the transport

scattering albedo of the medium is large. Also,

adding scattering particles only has a small effect

on the propagation of the pump radiation. The nano-

particle selection process appears to be successful at

Optical Contribution of Each Component

Fig.

(b) Qa?980 nm?∕Qa?532 nm?for gold nanorod.

5. Contour plot of (a)

Qa?980 nm?∕Qs?980 nm?

and

Table 1.Suitable Combination of Nanoparticles

Particle TypeMaterialDimensions

fvRequired to Fulfil Conditions

Pump radiation absorbing particle

Probe radiation scattering particle

Nanorod

Nanosphere

Gold

Silver

d ? 10 nmaAR ? 5.8

d ? 110 nm

2.6 × 10−7

6.5 × 10−6

aNote: 10 nm is the manufacturer rated sized [31], but TEM results (Fig. 6) show an average nanorod diameter of ∼15 nm.

Table 2.Optical Properties of the Medium

At Pump WavelengthAt Probe Wavelength

Case

α (m−1)

σtr(m−1)

Tnh(%)

Rnh(%)

α (m−1)

σtr(m−1)

Tnh(%)

Rnh(%)

1: Water

2: Water + absorbing particles

3: Water + scattering particles

4: Water + particles of both types

35.0

277.4

38.1

208.4

0.0

10.8

21.8

32.6

64.4

5.2

52.4

4.2

6.5

5.0

8.3

6.1

0.03

7.7

48.6

56.3

0.0

0.07

91.0

84.2

4.9

3.4

8.9

8.3

44.2

42.8

529.7

529.8

20 August 2013 / Vol. 52, No. 24 / APPLIED OPTICS6047

Page 8

prescribing scattering particles. Finally, the medium

containing both kinds of particles has delivered the

desired result by dominantly absorbing the pump

radiation and independently scattering the probe ra-

diation. Both the α∕βtrratio at the pump wavelength

and the σtr∕βtr

ratio at the probe wavelength

are larger than 80% as required. The normal-

hemispherical transmittance of both sources is also

less than 5%.

D.

The particle selected for scattering the probe radia-

tion for the above example were synthesized by

the authors as accurately as possible to match the

prescribed dimensions. The aim of obtaining these

particles is to measure their optical properties at

the pump and probe wavelengths to see if the desired

properties are achieved. It is also intended to vali-

date several main assumptions made during the

current work. The first is neglecting the near-field

scattering effects in calculating α and σtrof the nano-

particle ensemble. The second is assuming random

orientation of nanorods (neglecting the effect of

different orientation of nanorods on scattering of

radiation). Third, it is also required to validate the

method used for including the effect of polydispersity

on the optical properties particles ensembles.

For the pump radiation absorbing particle bare

nanorods with a 10 nm diameter and a length of

59 nm (Part number A12-10-980) was bought from

Nanopartz Inc. [31]. Although the nanorods with a

diameter of 10 nm were ordered from the vendor,

TEM images showed that the mean diameter and

length of the absorbing nanorods are 15 and

87 nm, respectively. The standard deviation of diam-

eter and length are equal to 0.6 and 9 nm, respec-

tively. Despite the fact that the diameter of the

synthesized nanorods is larger than that given in

Table 1, the required AR condition is satisfied. As

the AR determines the position of the primary reso-

nance in the near-infrared region, the currentsample

can perform as the pump radiation absorbing par-

ticle. The mean diameter and standard deviation

of the synthesized scattering nanosphere are equal

to 109 and 35 nm, respectively. Figure 6 shows

TEM images of these particles.

Experimental determination of the absorption

andscatteringcoefficients

particles was done in two steps. First the normal-

hemispherical transmittance and reflectance of

measurements for these nanofluids samples were

measured using a Perkin Elmer Lambda 1050

spectrophotometer with a 150 mm integrating

sphere. With a self-referencing dual beam configura-

tion, this device can take the above measurements

with a negligible error. The inverse problem wasthen

solved to retrieve the absorption and scattering coef-

ficients according to the method of [28]. The maxi-

mum difference allowed between the measured

and matched reflectance and transmittance values

was 5%.

Experimental Characterization of Selected Particles

ofthe synthesized

Figure 7 shows the experimentally measured and

theoretically calculated absorption and scattering co-

efficients of the selected pump radiation absorption

particle. The approximate volume fraction of the

nanoparticles in the sample is 5 × 10−7. The calcu-

lated results also include the effect of size variations

in the sample. It is clear from Fig. 7 that the selected

absorbing particle exhibits much stronger absorption

than scattering. The ratio between absorption and

scattering at 980 nm (pump wavelength) is clearly

larger than 10. However, the ratio between absorp-

tion at 980 and 532 nm (probe wavelength) is around

6. This can be attributed to the polydispersity of

nanorods in the sample and the presence of gold

nanospheres which did not grown into nanorods

during synthesis.

The experimental and computational results show

reasonable agreement with only a small resonance

wavelength offset. The root mean square error be-

tween the computed and experimental absorption

coefficient is 37%. In addition, considering the

polydispersityofthenanorod

computation, results in a wider spectral absorption,

consistent with experimental results. Moreover,

the match between experimental and computational

resultsalsojustifiesthe

calculation of nanorod optical properties in the

sampleinthe

orientationaveraged

Fig. 6.

nanospheres (bottom panel).

TEM images of the gold nanorods (top panel) and silver

6048APPLIED OPTICS / Vol. 52, No. 24 / 20 August 2013

Page 9

DDA code and the assumption of neglecting near

field scattering.

Figure 8 presents both experimentally determined

and theoretically obtained absorption and scattering

coefficients of a sample of the selected probe radia-

tion scattering particles dispersed in water. The

approximate volume fraction of the nanospheres in

the solutions is 5 × 10−6. As anticipated, experimen-

tal results of the scattering particle shows much

stronger scattering than absorption. The experimen-

tally measured ratio between scattering and absorp-

tion at 532 nm (probe wavelength) is 8.3. The ratio

between scattering at 532 and 980 nm is 6.5. These

values are less than 10, which is the selection criteria

in Eqs. (3) and (4). This deviation can again be

attributed to the size variations in the synthesized

nanosphere ensemble. When compared, calculated

and experimental properties show a reasonable

agreement with a root mean square error of 32%.

Similar to above, this shows the accuracy of

accounting for polydispersity in the calculations

and assumptions such as neglecting near field

scattering.

Finally, this section shows that the particles deter-

mined by the proposed selection process can be easily

synthesized to match the required optical properties.

Alternatively, these particles can also be bought from

a number of vendors (e.g., Nanopartz Inc. [31]).

Hence, the introduced pump–probe method and

the presented selection process leads to a relatively

cheap and convenient experimental technique for

research of semi-transparent nanofluids.

4.

An optical pump–probe technique with a flexible

volumetric heating tool was proposed to study the

behavior of nanoparticles in a semi-transparent

nanofluid under different heating profiles. These

types of experiments rely on proper selection of nano-

particles to ensure the pumping and probing proc-

esses are independent. A generalized nanoparticle

selection procedure was developed which includes

Mie theory, DDA calculations, and an approximate

solution to the 1D radiative transfer problem in

aqueous nanofluids—a medium of increasing re-

search interest for a wide variety of applications.

A specific example problem was solved to validate

and demonstrate the use of the selection procedure.

It was found that gold nanorods with diameter of

10 nm and a length of 58 nm can be used as the ab-

sorbing particles while silver nanospheres with

diameter of 110 nm are selected for a model problem

with pump and probe wavelengths of 980 and

532 nm, respectively. The optical properties of the se-

lected particles complied with the design require-

ments. The experimental characterization of the

selected particles showed good agreement with the

requirements—thus displaying the effectiveness of

the nanoparticle selection procedure and the feasibil-

ity of synthesizing them. Overall, the proposed

pump–probe method is an effective technique to

study the dynamic behavior of nanoparticles in

volumetric heating applications.

YH, LD, and RT would like to acknowledge UNSW,

particularly the School of Mechanical and Manufac-

turing Engineering, for supporting this work. LD is

also grateful to the Russian Foundation for Basic

Research (Grant No. 13-08-00022-a) for partial

financial support of his participation in this study.

Conclusions

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