Plasmon-Enhanced Properties of Metallic

Proceedings of the ASME 2012 Summer Heat Transfer Conference HT2012 July 8-12, 2012, Rio Grande, Puerto Rico

HT2012-58183 PLASMON-ENHANCED PROPERTIES OF METALLIC NANOSTRUCTURES AND THEIR APPLICATION TO DIRECT SOLAR ABSORPTION RECEIVERS Wei Lv Arizona State University Tempe, AZ, USA

Todd P. Otanicar Loyola Marymount University Los Angeles, CA, USA

Robert A. Taylor University of New South Wales Sydney, NSW, Australia

Rajasekaran Swaminathan Arizona State University Tempe, AZ, USA

ABSTRACT Plasmon resonance in nanoscale metallic structures has shown its ability to concentrate electromagnetic energy into subwavelength volumes [1-3]. Metal nanostructures exhibit a high extinction coefficient in VIS and NIR spectrum due to their large absorption and scattering cross sections corresponding to their surface plasmon resonance [4]. Hence, they can serve as an attractive candidate for solar energy harvesting material. Nanofluids have been proven to increase the efficiency of the photothermal energy conversion process in direct solar absorption collectors (DAC) [5, 6]. Early work has evaluated the extinction coefficient impacts on DAC [7]. The present work extends this with a quantitative comparison between core-shell nanoparticle suspensions and solid-metal nanosphere suspensions in a DAC. Ultimately, this study seeks a better understanding of how to best utilize the plasmon resonance effect to maximize the efficiency of nanofluid-based DACs or other volumetric heating systems. NOMENCLATURE

Am

Solar-weighted absorption coefficient

AR

Area [m2]

c0

Speed of light in vacuum

cp

Specific heat

C

E

Cross section [m2] Mean particle diameter [nm] Spectral solar irradiance [W m-2um-1]

Ei

Electric field (i=0, 1, 2, 3)

D

fv

G h h H

Volume fraction [%] Incident solar flux on the collector plan [W m-2] Planck constant [J s] Hear transfer coefficient [W m-2K-1] Thickness of the solar collector

I k k kB l

L m 

m

n qr Q

S T U

r

Vf

Patrick E. Phelan Arizona State University Tempe, AZ, USA

Ravi S. Prasher Arizona State University Tempe, AZ, USA

Intensity [W m-2 str-1  m ] Thermal conductivity [W m-1K-1] Imaginary component of refractive index Boltzmann Constant [J K-1] Mean free path [m] Length of the solar collector Normalized complex refractive index 1

Mass flow rate [kg s-1] Real component of refractive index Radiative flux [W m-2] Scattering or absorption efficiency Incoming solar radiation [W m-2  m1 ] Temperature [K] Velocity [m s-1] Particle radius [nm] Fermi velocity [m/s]

Subscripts Abs Absorption bo Bound electron bulk Bulk material property eff Effective ext Extinction exp Experimental i Directional in Collector inlet out Collector outlet w Wal g Glass sca Scattering p Plasmon Bulk material property  Greek Symbols Polarizability 

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Real component of dielectric constant, [F/m or kg mm / ' (mV2 s2)] Imaginary component of dielectric constant, [F/m or kg  '' mm / (mV2 s2)] Wavelength, [µm]   Extinction coefficient, [1/m]  Relaxation frequency  Size parameter 0 Free electron scattering time INTRODUCTION Surface plasmon resonance is caused by the confining force of free conduction electrons. The large optical polarization associated with the surface plasmon resonance (SPR) brings on a vast local electric field boost at the nanoparticle surface as well as strongly enhanced light absorption and scattering by the nanoparticle at the SPR frequency [8]. Noble metallic nanostructures have proved to have strong SPR effect as reflected in their intense colors. Moreover, the plasmon resonance frequency can be tuned by the shape, size, particle concentration and the surrounding media [9, 10]. As a result, many different shaped and complex metallic nanostructures have been studied, ranging from nanospheres, core-shell nanoparticles to nanorods. These hybrid nanostructures are excellent photothermal energy converters and can generate localized heat without heating the bulk volume. Hence, the applications of metallic nanoparticles by utilizing the outstanding light concentrating and converting capacity are active in various areas such as cancer diagnosis and photothermal therapy by implementing plasmonic gold nanostructures [11,12], plasmonic enhancement of photocatalytic water splitting [13], localized surface plasmon resonance enhanced microalgal growth [14], light trapping in thin-film solar cells [15-17], infrared thermal emitters [18], photodetectors [19], and metamaterials [20]. This work will emphasize the surface plasmon effect in application to direct solar absorption collectors (DAC). Solar thermal collectors using dispersions of small particles acting as direct solar collectors have been studied in recent years [21, 22]. Unlike conventional surface absorbing solar thermal collectors, direct absorption is a volumetric approach which has several advantages. The absorption efficiency of incoming sunlight in a highly absorbing particles-embedded media goes beyond that of surface absorption of a similar material. Secondly, the overall thermal resistance can be reduced by reducing the need for convection and conduction heat transfer between the absorbing surface and the working fluid [23]. The optical properties of nanoparticle suspensions (nanofluids) could have dramatic impacts on the absorption and emission of DAC energy systems. The spectral properties of a system are of great importance for a well-designed system whose main thermal transport process is radiation. In this work, the authors research potential nanostructures and compare the optical properties of graphite, metallic nanospheres and core-shell nanoparticles-based water

Inclusions: Core-shell NP

Fig. 1.

Solid NP

Direct absorption solar collector using core shell multifunctional nanoparticles and solid nanoparticles.

suspensions. Next, a solar weighted efficiency table will be presented. Lastly, a one-dimensional volumetric absorption model is used to calculate the overall system efficiency of different nanostructures laden nanofluids-based DAC. NANOFLUIDS OPTICAL PROPERTIES MODEL Figure 1 shows the basic scheme of the direct absorption system. The top part is a glass with glazing which reduces the infrared thermal emission. The major part of solar energy is absorbed in liquid film which contains different kinds of heat transfer fluid (water, therminol VP-1, ionic liquid) laden by nanoscale structures. Only water is considered as basefluid here for simplicity. There are three groups of nanoscale particles to be discussed here: solid metallic nanospheres, graphite nanospheres, and core-shell nanoparticles made of metal shell with Si core. Figure 1 contains the basic geometric scheme of a volumetric DAC containing either core-shell nanoparticles or solid metallic nanospheres. In this work, the core of the coreshell nanoparticles is made of dielectric material (silicon), and the shell and solid nanospheres can be made of metallic materials (Ag, Au, Al, Cu and Ni). Due to the SRP effect, different materials will have different peak absorption frequencies. The core-shell nanoparticles’ SPR frequency depends also on particle size, shape, shell thickness and dielectric properties of the core and surrounding media [21]. In our application, we plan to investigate materials which have the best solar energy harvesting capability. For economic considerations, relatively low-cost graphite nanoparticles are also considered. Various calculations and models have been made on the impact of an electromagnetic field on the spectral and optical

2



properties of solid and core-shell nanoparticles [3, 4, 25]. Commonly available nanoparticles in solar nanofluids [26] are in the range of 5-50 nm average particle diameters, for which most of the incident light from the sun has a wavelength that is at least 10 times larger. There are two major reasons for choosing this small size of nanoparticles. First of all, in a nanofluid-based absorption system, the absorption cross section is more important than the scattering cross section. Although the absorption cross section will increase with the particle size, the scattering will increase more rapidly which is not favorable in an independent scattering system. Mathematically, we choose the scattering cross section to be a magnitude smaller than the absorption cross section Csca / Cabs  0.1 . By doing that, although different material

 particle 

II.

Csca

128 5 2 6  2 a   3 b   3 r2 3 4  2 a  2 3 b

Cabs  where

8 2  3



r23 Im(

2

 2 a   3 b )  2 a  2 3 b

(5)

(6)

 a ,  b are effective dielectric functions,  i (1, 2,3) are

dielectric functions for the core, shell, and embedding regions, and r1 , r2 the core and shell radii. Then we are able to

The absorption, scattering, and extinction efficiencies for solid metallic and graphite nanoparticles can be calculated by the following equations, which can be found in several standard texts such as Bohren and Huffman [27]:

calculate the extinction efficiency of a nanoparticle by (7) Qext  (Cabs  Csca ) /  r22 Note: in the dipole limit, or more specifically, where the particle radius is smaller than 25 nm, we assume the scattering is negligible for later discussion, then Qext  Qabs .

2

 m2  1   2 m2  1 m4  27m2  38   Qabs  4  2 ) 1  ( 2  2m 2  3    m  2  15 m  2 Qext  Qabs  Qsca

Metallic shell dielectric core nanoshells

With the quasi-static approximation, the electric field of the core, shell, and outside region can be calculated from the Laplace equations and specified boundary conditions [29]. The numerical result of the electric field in the core, shell and outside the particle can be found in several articles [30]. We apply the bulk optical properties from literature [31] for the dielectric core and surrounding media. Since the spectrum ranges from the visible to the infrared region, we use a wavelength-dependent dielectric function for the dielectric materials in the core and embedding media. Then one can easily obtain analytical expressions for the absorption and scattering cross sections [30]:

Metallic and Graphite nanospheres

m2  1 8 Qsca   4 2 m 2 3

(4)

where particle is the effective nanoparticles’ extinction coefficient in the nanofluid.

has different results, the characteristic radius is smaller than 50 nm for most materials. This limit also applies for core-shell nanoparticles [39]. Another important reason is considering the stability of the dispersion of nanoparticles. The large size nanoparticles will fall out of the base fluid by the gravity. When the nanoparticle diameter is much smaller than the wavelength of the incident field, we can omit higher order terms in the Mie scattering solution and the approximation of Rayleigh scattering (  D /   1) is applicable. For larger particles, which are of higher order multipoles, especially quadrupole plasmon resonance should be considered [26]. In this work, the size of nanoparticles is limited to those smaller than 50 nm. And for the core-shell nanoparticles, we can use the quasi-static approximation [29, 30].

I.

3 f vQext 3 f vQabs  2D 2D

(1) (2)

However this may not be an accurate approximation for larger particle sizes or for nanoparticle aggregates, which is beyond the scope of our study.

(3)

where m is the relative complex refractive index of the nanofluid (divided by the real part of the refractive index of the fluid),  the size parameter, which is defined as [27]  D /  , D the nanoparticle diameter, and  the incident wavelength. Note that for materials which are optically anisotropic (e.g. graphite), the absorption, scattering, and extinction efficiencies are the average of the parallel and perpendicular graphite planes. For nanoscale metallic and graphite nanoparticles with very small size parameters, the scattering efficiency is much smaller than the absorption efficiency owing to Qsca being proportional to  4 . If it is negligible, the scattering efficiency simply drops out of the nanoparticles’ extinction coefficient equation [28]:

III. Resultant radiative properties Based on single-particle extinction efficiencies and particle concentration, we can work towards the properties of the total fluid mixture. When the solar collector has sizable absorption path lengths (>1 mm), the effective direct solar absorption collection can be achieved for nanofluids of < 0.6% volume fraction [32]. If the volume fraction is high, the incident solar energy will be absorbed at the surface where the heat is easily lost to the environment. Since the volume fraction is lower than 0.6%, from Kumar et al.’s earlier work [33], only independent scattering needs to be considered

3



which makes it easier to analyze the optical properties. For comparison, we set the volume fraction fv, to be 0.004% for each nanostructure suspension. When multiple scattering is negligible, the extinction coefficient is calculated from the absorption and scattering efficiencies by equation 4. After computing the nanoparticles' extinction coefficient, it is necessary to incorporate the absorption of the surrounding medium. In our model, water as the base fluid is actually a good absorber in the near infrared and infrared spectrum. From a first-order method reported and experimentally verified [26], the total extinction coefficient of the nanofluid is found from a simple addition of the base fluid extinction coefficient,  fluid and that of the particles,

 particle

 (leff )  1/  eff  1/  0  AV f / leff

where  0 is the bulk metal free electron scattering time, A a geometric parameter ranging from 2 to 1 (in our model we assume it to be 1) [34], and Vf the Fermi velocity. For the effective mean free path, we use a model proposed by Granqvist and Hunderi [33]:

leff 

(8)

where the basefluid extinction coefficient is found using handbook optical property data [3l] through the following:

 fluid 

4 k fluid

(9)



IV. Drude-Lorentz model & size effect In order to calculate the absorption and scattering cross sections of nanoparticles, we need to compute the dielectric function of metallic nanostructures. For graphite nanoparticles, the calculation is straightforward. Taking the parallel and perpendicular grains refractive index into equations 1-4, one can get the effective extinction efficiency from the average of the two planes. As for metal and core-shell nanoparticles, modifications will be needed to calculate the effective dielectric function of metallic components since the electron mean free path is close to or even bigger than the particle size. From Palik [31] we can get the optical properties of the bulk metallic material. When the dimension of the nanostructures decreases below the mean free path of the bulk material the interaction of the oscillation with the boundary increases, hence the optical properties needs to be adjusted. This effect has been demonstrated both numerically [23, 34], and experimentally for metallic nanoparticles [30]. The Drude-Lorentz model is adapted to model the size effect of metallic nano-components using [29]:

 ( )   ( )exp   p2 where

p

1 1   p2 2   i bulk   i (leff ) 2

is the bulk plasmon frequency,

the electromagnetic wave, bulk metal and leff

1/3 1 (r2  r1 )(r22  r12 )  2

(12)

For the dielectric core and surrounding dielectric media, we can use the optical properties from literature [31] without any modifications. Figure 2 shows the computational results of the optical properties of several nanofluids. These metal materials are chosen for comparison since they have been considered for direct solar absorption collector application. The inclusions in the fluid are different sizes of graphite, solid metal nanoparticles and corresponding core-shell nanoparticles. For graphite nanoparticles, which are the green chain dotted line in figure 2, different size graphite nanoparticles laden nanofluids have identical spectral extinction coefficient as they overlapped on one line. As for solid metal NPs, some exhibit surface plasmon effect which can be observed by the absorption peak at plasmon resonance frequency, like Au, Ag, and Cu. We can see the ‘small’ variance between different sizes of solid metallic nanoparticles. As for core-shell nanoparticles, the ratio effect (ratio between core and total radius r1/r2) is obvious. The extinction peaks arise for most metallic shell Si core nanoparticle except Ni. What’s more, the surface plasmon resonance frequency can be tuned to longer wavelengths by adjusting the core-shell ratio and material intrinsic optical properties. The full width at half maximum (FWHM) extinction coefficients of core-shell nanoparticles laden nanofluids is larger than the corresponding solid metallic nanoparticles suspensions. All

:

 nanofluid   particle   fluid

(11)

(10)

 the frequency of

 bulk the relaxation frequency of the

the effective mean free path. The

modification to the electron decay time   1/  is particle-sizedependent for small particles [35]:

(a)

4



(b)

(d) Fig. 2. Extinction coefficients of graphite, solid metal nanoparticles, and core-shell nanoparticles at different size (the shell thickness of core-shell NPs is 3nm, volume faction 0.004%) these calculated optical responses indicate that the metallic shell dielectric core nanoparticles-laden fluids can serve as promising candidates for direct absorption solar collectors, which require great light concentrating and absorption ability in the solar spectrum. Note the shell thickness of core-shell nanoparticles are 3 nm. The two peaks around 1.5 m and 2 m are caused by the water that is a much stronger absorber in the infrared spectrum than the nano-composites used in the study. SOLAR WEIGHTED EFFICIENCY (c)

The solar-weighted absorption coefficient ( Am ), which represents the percentage of solar energy absorbed across a fluid layer of selected thickness [36], can be calculated to quantitatively appreciate the absorption ability:

Am 

 E (1  e



4 kx



 E d 

)d 

(13)

where E is the solar irradiance per unit wavelength at a certain wavelength, and x is the thickness of the fluid layer, which we set as x = 1 cm. Each nanofluid’s solar-weighted coefficient at a volume faction of 0.004% is listed in Table 1 for all nanofluids considered here. And the metallic shell thickness is still kept at 3nm for core-shell nanoparticles. From figure 2, we observed a noticeable surface plasmon effect on solid Au, Ag and Cu nanoparticles and Au,

(d)

5



Ag, Cu, Al core Si shell nanoparticles. The SPR effect on metallic nanostructures will largely enhance the absorption and scattering ability of the nanocomposites at the plasmon resonance frequency, which is reflected as an extinction coefficient peak in the extinction spectrum. Consistent with figure 2, the plasmatic metallic materials in core-shell form exhibit greater solar-weighted efficiency than in solid nanophere form since the FWHM of the peak extinction coefficients become broader. Some core-shell nanoparticles’ plasmon resonance frequency matches the solar spectrum quite well. For Ni and Graphite, the corresponding solid nanoparticles demonstrate good solar absorption ability. Although they do not show strong surface plasmon effect, they still can serve as decent and cost-effective materials for direct solar absorption nanofluids. However ， as for plasmatic nanostructures suspension, there is a possibility that the simple adding method underpredicts the extinction coefficient of the mixtures. One of the coauthors has studied the effective extinction coefficient of nanoparticle suspensions via different methods

10nm

0.5523

0.7346

0.8336

18nm

0.6033

0.8592

0.9088

25nm

0.6760

0.8958

0.9273

Ni NPs 6nm

0.9114

Ni-Si core shell NPs(3nm shell) 0.9332

10nm

0.9142

0.9129

18nm

0.9216

0.8982

25nm

0.9302

0.8586

Graphite NPs 6nm

0.9493

10nm

0.9494

18nm

0.9498

25nm

0.9506

6nm

0.6818

Ag-Si core shell NPs(3nm shell) 0.8754

10nm

0.6417

0.8807

0.9212

18nm

0.6278

0.8099

0.9017

25nm

0.6489

0.7428

0.8651

including Maxwell-Garnet theory and the simple adding method that we used here. When compared to the experimental results, both of them underpredict the plasmonic nanoparticles suspension, although the latter one works better. Future work will be needed to precisely predict the effective extinction coefficient of the mixture. It is beyond the scope of our discussion here. We refer the reader to Refs. [32, 37] for details regarding the Maxwell-Garnet theory and onedimensional adding method for nanofluids extinction coefficient modeling. The last column in table 1 is listed for higher loading, core-shell nanoparticles-based nanofluids. The core-shell structure makes it possible to dynamically control the size of nanoparticles by changing the environment properties like temperature, ph or magnetic field. One possible way, as demonstrated by one of the co-authors [38], is by adding temperature-sensitive gel in the core so that the size of the core-shell nanoparticles can be controlled. Assuming we use 0.004% volume percentage 20-nm radii core-shell nanoparticles initially, by expanding 25% of the initial radius, the volume percentage increases to 0.0078% which has a strong effect on the mixture’s optical properties as presented in column 3 of table 1.

Cu NPs

Cu-Si core shell NPs(3nm shell) 0.9438

VOLUMETRIC ABSORPTION SOLAR COLLECTOR MODEL After the radiative properties are calculated, a numerical model is needed for prediction of direct solar absorption collector efficiency. The structure of the solar collector is illustrated in figure 1. The incoming solar energy enters the top thin glass, and is volumetrically absorbed in the liquid film. Most of the solar energy is captured by the nanoparticles due to their large surface area and light concentrating ability. They convert the photon energy into phonons and then the

Table 1 Solar weighted absorption coefficient (AM1.5, 

 280  2500(nm)

x=1.0cm).

0.7610

Volume fraction(0.004%) Au-Si core shell NPs(3nm shell) 0.8821

Volume fraction(0.008%) Au-Si core shell NPs(3nm shell) 0.9397

10nm

0.7361

0.8862

0.9199

18nm

0.7236

0.8476

0.9170

25nm

0.7309

0.7844

0.8856

Ag NPs

Ag-Si core shell NPs(3nm shell) 0.9386

Particle Size 6nm

Volume fraction(0.004%) Au NPs

6nm

0.7983

Cu-Si core shell NPs(3nm shell) 0.8855

10nm

0.7659

0.8916

0.9221

18nm

0.7458

0.8820

0.9312

25nm

0.7502

0.8274

0.9119

Al NPs

Al-Si core shell NPs(3nm shell) 0.6584

Al-Si core shell NPs(3nm shell) 0.7908

6nm

0.5540

6



thermal energy diffuses to the liquid medium. There are also reflection, convection and radiation loss though the boundaries. The simplified radiative transport equation for a onedimensional medium, which neglects the scattering term, is expressed as: dI i , (14)    , I b, (T ( y ))   e, I i , dy where   , and  e, are the spectral absorption and extinction

radiative energy loss coefficient h on the top surface are assumed to be 24 W m2 K 1 which is derived from experimental data [7] and the bottom is set to be perfect insulation and no heat loss. At last but not least, we define the receiver efficiency [27]:

coefficients, I the intensity, and I b , the spectral blackbody intensity. The in-scattering term is neglected here since when the size of the particle is in the Rayleigh regime (r  25 nm), the scattering efficiency is trivial compared to the absorption efficiency. This approximation is made for solid nanoparticles [23] and core-shell nanoparticles in the Rayleigh regime [39]. The subscript i is used to characterize the direction of the light propagation, (+1) for incoming and (-1) for outgoing light. The boundary conditions are specified by Kumar and Tien [22] as

where m , c p , Tout , Tin , G , AR are the mass flow rate, specific heat of fluid, the outlet temperature, the inlet temperature, the solar flux incident, and the collector area respectively. The reader is recommended to find more details from the coauthors’ work [5, 6, 7, 23]. In order to get the best efficiency, the back surface is set to be perfect reflector.

I 1, ( L)   w, Ib, (T ( L))  w, I ,

(15)

I 1, (0)  S (1   g ,   g , )   g , I 1, (0)   g , Ib, T (0) 

(16)

where L represents the bottom of the solar collector,

 w,





m c p (Tout  Tin )

(19)

GAR



the

 w,  g , the spectral reflectances of the wall and glass,  g , the spectral glass absorptance, and the spectral wall emittance,

S  the spectral radiation incident on the receiver. Blackbody radiation is assumed for the spectral properties of the incoming light and emitted radiation: I  (T ) 

where n

2n 2 hc02   hc  5 exp( 0 )  1  k BT  

(a)

(17)

is the effective real part of the refractive index of the

medium, h Planck’s constant, k B the Boltzmann constant, and

c0 the speed of light in vacuum. The above equations are coupled with the 2D energy equation with specified boundary conditions, k

 2T qr T    c pU y 2 y x

(18)

x=0, 0