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Colloidal plasmonic structures for harvesting solar radiation
Renewable Energy xxx (2017) 1e8
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Colloidal plasmonic structures for harvesting solar radiation mez-Malago n Diego Rativa*, Luis A. Go University of Pernambuco, Polytechnic School of Pernambuco, 50720-001 Recife, PE, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 September 2017 Received in revised form 22 October 2017 Accepted 31 October 2017 Available online xxx
Direct Solar Absorption Collectors explore the thermo-optical properties of fluids to convert solar radiation into thermal energy. Colloids of metallic nanoparticles have shown a great potential to convert solar radiation into thermal energy efficiently, because of the matching between the absorption peak of the localized surface plasmon resonance and the solar radiation spectrum. Recently, multilayered metallic nano structures have been broadly studied for Thermo-optical applications due to the possibility to tune the plasmon resonance next to the near infrared region. In this work, using a full-wave field numerical model, we study the solar absorption of metallic nanofluids composed of Solid structures (Sphere, Cube, Tetrahedral, Octahedral), Silica-based structures (Shell and Multilayered) and its elliptical versions. Although a large part of the metallic material is replaced for SiO2 in the nanofluid composition of NanoShell (NS) and Multilayered (ML) structures, the values of solar radiation absorber coefficients are larger than the obtained with solid particles. Also, the quantity of metal is just 18% (NS) and 53% (ML) of the material necessary to fabricate colloids of solid particles. For the elliptical structures, the values of solar radiation absorber condition are larger than the obtained with spherical structures. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Metallic nanostructures Solar radiation absorption
1. Introduction Solar collectors are renewable energy technologies developed during the last decades, which explore the thermo-optical properties of fluids to convert efficiently solar radiation into thermal energy [1,2]. The most common type of solar thermal collector employs a black absorber surface to transfer heat to a fluid that is circulating in tubes embedded within or fused onto the surface [3]. Inserting nanoparticles (NPs) in the fluid, a change of its thermophysical properties is caused, with an efficiency improvement next to 5% in solar thermal collectors [4]. This kind of Nanofluids has found applicability in systems where a fast and effective heat transfer is necessary, such as industrial applications, cooling of microchips, microscopic fluidic applications, etc [5]. On the other hand, to improve the energy transfer efficiency, the solar radiation must be absorbed directly by the working fluid as proposed by the Direct Solar Absorption Collector (DSAC), which is a thermal device composed of a transparent glass box containing the nanofluid. For a nanofluid of water and aluminum nanoparticles, the efficiency of a DSAC can increase up to 10% in
* Corresponding author. E-mail addresses: [email protected] mez-Malago n). (L.A. Go
(D.
Rativa),
[email protected]
comparison with a typical flat-plate solar collector [6]. Also, for a DSAC containing silver nanofluid, its efficiency can achieve a maximum value of 90% [7]. The efficiency of the solar radiation absorption is given mainly because of the matching between the metallic NPs optical absorption and the solar radiation spectrum [8,9]. In the case of gold and silver NPs, by cause of the localized surface plasmon resonance effect at visible region, the absorption peak can be tuned between 400 nm and 1300 nm [10,11], such that is possible to manage the solar radiation absorption efficiency altering the NPs geometry. We have reported previously that the absorption spectrum of metallic nano-ellipsoids (NE) is red-shifted relative to that of a spherical geometry, therefore, it is possible to achieve a solar weighted absorption coefficient close to the ideal condition, managing the aspect ratio of the NE [12]. Recently another study has explored gold nano-rods and nano-sheets for the same purpose [13]. Other plasmonic structures with similar red-shifted resonance peak are the Nano-Shell (NS) [14] and Multilayered structures (ML) [15]. A NS is composed of a core covered by a thin metallic layer, the material properties of both the core and the shell regions, strongly influence the optical properties of the NS. In the particular case of a Silica-NS, with SiO2 core and a Gold or Silver shell, a strong coupling between charges inside and outside of the shell causes a charge separation and consequently a red-shift of the absorption spectrum
https://doi.org/10.1016/j.renene.2017.10.112 0960-1481/© 2017 Elsevier Ltd. All rights reserved.
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up to near IR spectrum [16]. For example, a Silica-NS with a core of 60 nm and a Gold shell with a thickness of 50 nm and 2 nm has a LPSR peak at 650 nm and 1100 nm, respectively [17]. On the other hand, the ML structures are composed of a metallic core, coated with a thin silica layer, and finally surrounded by a thin metallic shell (ex. Au/SiO2/Au) [15,18e21]. MLs work like optical condensers and the electromagnetic field in the centermost dielectric layer can be enhanced multiplicatively with the number of layers [22]. Furthermore, the resonance peak of elliptical NS and ML is red-shifted for the same reasons as reported for NE [12,18]. In this work, the influence of metallic NPs structures on the solar radiation harvesting of solar collectors is analyzed; The nanostructures studied are solids, shells, multilayered, and its elliptical versions. The numerical model and the 3D simulation space are discussed in the methods section, posteriorly the differences between the solar weighted absorption coefficients obtained for the nanofluids containing the selected structures are discussed. We would like to note that chemical preparations of colloids based on the structures studied in this work have been already reported in the literature, allowing its immediate application.
con-ductivity of the medium, respectively. As represented in Fig. 1, in our model, the incident light is ppolarized at normal incidence with the electric field E along the xaxis, propagating in the þz direction. To model an unpolarized light source (solar radiation), the average of the calculations for E0 linearly polarized along the long axis and the short axis of the particle has been carried out.
2. Methods
where ∞ is the high-frequency limit dielectric permittivity, lp is the plasma wavelength, lj is the interband transition wavelength, gk is the damping in the direction k, gj is the transition broadening, 4j is the phase and Aj is the dimensionless critical point amplitude [24,25]. In the case of metallic materials smaller than the mean free path of free electrons, the dielectric permittivity for metallic NPs that accounts for the size dependence is given by Ref. [16]:
2.1. Numerical model We have explored a full-wave time harmonic field theory for the computational model analysis, using the COMSOL Multiphysics 5.0 software, Electromagnetic Waves, Frequency Domain interface (EMW package, for subwavelength geometries). The 3D simulation space has two main regions, the studied structures and a surrounded medium, as can be seen in Fig. 1. The surrounded medium is composed of two spherical regions: an embedding medium (H2O) and a perfectly matched layer (PML). The radius of the embedding and the PML spheres were chosen depending on the NPs diameter, such that NPs size variation further would not affect the simulation results. In the case of Solar Radiation (low-intensity regime), the timeharmonic Electric field within the domain satisfies Maxwell equations in the frequency domain [23]:
s 2 ε E¼0 V m1 ðV EÞ u ε m j 0 0 r r uε0
(1)
where mr ; εr and s are the relative permeability, permittivity, and
2.1.1. Permittivity particle size considerations The bulk metal dielectric permittivity can be described by an analytical expression based on the broadly accepted model for metallic materials, given by Ref. [24]:
X Aj
2
ei4j 4 . þ 2 l 1 l þ i=ðgk lÞ 1 lj 1=l igj j¼1;2 j 3 ei4j 5 þ 1 lj þ 1=l þ igj
εBulk ¼ ε∞
1
l2p
(2)
εNP u; Leff ¼ εBulk ðuÞ þ
u2p u2p u2 þ iu Ly∞f u2 þ iu Lyf þ AL yf ∞ eff
(3)
where εBulk is the bulk dielectric function of the NP's material, u is the angular frequency of the incident light, up is the plasma frequency, vf is the Fermi velocity, L∞ is the mean free path of the electrons, A is the dimensionless parameter (A ¼ 1) and Leff is the reduced effective mean free path of the electrons [26]. The Silver and Gold parameters have been reported in several articles [27,28]. 2.2. Nano-structure geometries It is well-known that for particles smaller than 10 nm, the
Fig. 1. (a) 3D Computational model regions composed of a Metallic Nanostructure studied, an embedding medium (H2O) and a Perfectly Matched Layer; (b) Electric field maps, represented in colors corresponding to the electric field enhancement, jEj/jE0j. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
mez-Malago n, Colloidal plasmonic structures for harvesting solar radiation, Renewable Please cite this article in press as: D. Rativa, L.A. Go Energy (2017), https://doi.org/10.1016/j.renene.2017.10.112
Fig. 2. Spectral dependence of the absorption cross section for Gold and Silver nanostructures (Sphere (a), Tetrahedral (b), Cube (c) and Octahedron (d)) [Left]; and its corresponding term El (1 eax) for x ¼ 1 cm and p ¼ 1 106, compared with the Spectral irradiance ASTM G173-03 [Right].
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percentage of surface atoms starts taking over bulk atoms, increasing their catalytic properties and resulting in large variations in the particle size [29]. Moreover, We are interested in photothermal applications in which the absorption is the main factor that determines the system efficiency. Therefore, the NPs studied have a volume next to (20 nm)3, attending both conditions: a scattering cross section coefficient (ssca) smaller than the absorption cross section (sabs) for all geometries (ssca/sabs < 0.1) and a colloid which could be chemically stable. 2.3. Solar absorption harvesting analysis The NP absorption properties are given in terms of the optical absorption cross section values, obtained by:
sabs[m2] ¼ Qabs[W]/Irad[W/m2]
(4)
where Qabs is the power absorbed by the particle and Irad is the incident irradiance. Most of the previous works report plasmonic nanofluid properties in terms of the optical coefficient absorption for solar collectors with a height of one or a few centimeters and volume fractions at orders of 106 and 104 [12,13,16,22,27]. Therefore, for comparison purposes, we have defined a nanofluid volume of Vfluid ¼ 1 cm3 (collector height and area of 1 cm), a total volume of metallic nanoparticles as VNPs ¼ Nparticles Vparticle and a volume fraction p ¼ VNPs/Vfluid ¼ 1 106. The volume fraction is kept constant for the analysis (except in the volume fraction analysis), compensating volume variations of the particle altering the number of inclusions (Nparticles). Therefore, the coefficient absorption is given by a[cm1] ¼ (Nparticles/Vfluid)
[cm3] sabs [cm2]. The efficiency of a direct absorption solar collector is estimated calculating the solar weighted absorption coefficient, Am which represents the percentage of the solar energy that is absorbed across the fluid layer of selected thickness, given by Ref. [30]:
Z Am ¼
El 1 eax dl Z El dl
(5)
where El is the spectral distribution of the solar intensity and x is the thickness of the fluid layer. The solar weighted absorption coefficient is obtained integrating from 200 nm to 1.5 mm. Although reflections and absorption of the solar radiation, due to the glass containing the nanofluid, reduce the intensity of the solar radiation, most glasses are transparent (90% transmission) in the visible and the near infrared region (350e2500 nm) and the reflection has not an important chromatic dependence, such that we can consider that the solar radiation spectrum is not altered by the presence of a covering glass. 3. Results and discussion 3.1. Solid structures The absorption cross section of Silver and Gold NPs with different solid geometries (Sphere, Tetrahedral, Cube, and Octahedron) are represented in Fig. 2, and its corresponding solar weighted absorption coefficients (i.e. El (1 eax)) are represented on Fig. 2 for a solar collector with x ¼ 1 cm.
Fig. 3. Spectral dependence of the absorption cross section for Gold (a) and Silver (b) NS [Left]; and its corresponding term El (1 eax) for x ¼ 1 cm and p ¼ 1 106 compared with the Spectral irradiance ASTM G173-03 [Right].
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The spectral absorption dependence of the solid NPs is in agreement with the absorption spectrum reported in the literature exploring methods such as Mie Scattering and Discrete Dipole Approximation (DDA) [11], validating our model. Because the sharpest corners, the Tetrahedral and Octahedron geometries have the most red-shifted resonance peaks and consequently a broader spectral absorption [11], such that the Harvesting coefficient shows a better matching with the solar radiation spectrum for that particles. 3.2. Silica-based structures 3.2.1. Nano-Shells In the case of NS structures, the radius of the silica core (SiO2) is kept constant at 20 nm, and the shell thickness selected are 10 nm, 5 nm, and 2.5 nm. As shown in Fig. 3, the absorption resonance peak can be redshifted reducing the metallic shell thickness, whereas the core radius does not play an important role in this effect. In the case of NS with a thickness of 2.5 nm, the absorption resonance peaks are shifted up to 750 nm and 800 nm for Silver and Gold shells, respectively. The harvesting solar radiation spectrum of the nanofluid composed by metallic NS structures are similar to the obtained for NE with an aspect ratio of 3 and 4 [12]. 3.2.2. Multilayered ML structures are composed of a metallic core (radius of 10 nm), a SiO2 layer (thickness T1 ¼ 10 nm and 5 nm), and a metallic layer (T2 ¼ 5 nm and 2.5 nm). As shown in Fig. 4, the absorption spectrum has two resonance
5
peaks, one related to the core contribution (Au: 532 nm and Ag: 400 nm) and the other one with the external metallic shell (redshifted for thinner shells). Consequently, the absorption spectrum is broader than the obtained for Solid and NS structures. Moreover, it is observed that variations in the outer shell thickness are responsible for the red-shift effect, whereas variations in the SiO2 layer thickness do not play an important role in the same effect. For nanofluids constituted of Shells and Multilayered particles, a large part of the metallic material is replaced for SiO2, such that the quantity of metal is just 18% (NS) and 53% (ML) of the necessary material to fabricate a colloid of solid spheres. The dependence of Am on volume fraction for a nanofluid (thickness of 1 cm) containing the solid structures studied are represented in Fig. 5 (aed). The matching between the solar radiation and the solar absorption for nanofluids composed by ML structures is more efficient because of its broader absorption. As can be seen in Fig. 5 (f), for a nanofluid with a volume fraction of 3 105 and x ¼ 1 cm, the solar weighted absorption coefficient of a nanofluid composed of Silver ML is Am ¼ 0.65, whereas for Solid and NS structures the values are Am ¼ 0.45 and Am ¼ 0.55, respectively. Furthermore, for a nanofluid with the same concentration of Gold ML, the absorption coefficient reaches a value next to Am ¼ 0.8. 3.3. Elliptical silica-based structures Similarly, to metallic ellipsoids, where the Transversal and Longitudinal oscillation modes can be tuned modifying the aspect ratio [12], the NS and ML structures are studied for different aspect ratios tuning the plasmon resonance peak. We have explored a NS geometry with a radius RSiO2 ¼ 20 nm and a layer with thickness of
Fig. 4. Spectral dependence of the absorption cross section for Gold (a) and Silver (b) Multilayered structures [Left]; and its corresponding term El (1 eax) for x ¼ 1 cm and p ¼ 1 106 compared with the Spectral irradiance ASTM G173-03 [Right].
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Fig. 5. Dependence of the solar weighted absorption coefficient Am on volume fraction, for a nanofluid with thickness x ¼ 1 cm, composed of Solid (aed), Shell (e) and Multilayered structures (f).
5 nm, as well as, a ML geometry with RAu ¼ 20 nm, an internal layer of SiO2 with thickness of 5 nm, and an external Au layer of 5 nm. As can be seen in Fig. 6, the dependence of Am on volume fraction for a nanofluid with thickness of 1 cm are represented for Solid (a), NS (b) and ML (c) elliptical Gold structures with different aspect ratios. As summarized in Table 1, in the case of nanofluids containing Silver and Gold NPs with volume fractions of p ¼ 3 105 and x ¼ 1 cm, the highest solar weighted absorption coefficient values are obtained for NE and NS with AR ¼ 4. A solar weighted absorption coefficient close the ideal condition can be obtained for silver and gold ML structures with an aspect ratio of AR ¼ 2. Ideal absorber nanofluids are obtained with a volume fraction of p ¼ 1e3 105, such that the mean interparticle distances (10e30 mm) are large enough to avoid partial agglomerations. On
the other hand, silica coatings (transparent) can be explored to protect the metallic nanoparticles enhancing the thermodynamic stability [31], although a reduction in the thermal conductivity of the structure is expected. 4. Conclusions Shell and Multilayered are nanostructures with a red-shifted resonance peak relative to that of a solid spherical geometry. Although a large part of the metallic material is replaced for SiO2 in the nanofluid fabrication of NS and ML, the values of solar radiation absorber condition are larger than the obtained with solid particles. The quantity of metal is just 18% (NS) and 53% (ML) of the material necessary to fabricate colloids of solid particles. Similar to ellipsoids, the plasmon resonance absorption band of
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Fig. 6. Dependence of the solar weighted absorption coefficient Am on volume fraction, for a nanofluid with thickness x ¼ 1 cm, composed of Solid [(a) Au, (d) Ag], NS [(b) Au, (e) Ag] and ML [(c) Au, (f) Ag] elliptical Gold and Silver structures with different aspect ratios AR.
Table 1 Solar weighted absorption coefficient values for a nanofluid composed by Metallic structures and x ¼ 1 cm. Material
Structure
AR
Vol.Ratio Au/SiO2
Am (p ¼ 1 105)
Am (p ¼ 3 105)
Gold
Solid Shell Multilayered Solid Shell Multilayered
4 4 2 4 4 2
1/0 0.18/0.82 0.53/0.47 1/0 0.18/0.82 0.53/0.47
0.85 0.88 0.9 0.78 0.82 0.85
0.94 0.98 0.99 0.93 0.98 0.99
Silver
NS and ML has a Transversal and a Longitudinal oscillation mode that can be tuned modifying the structure aspect ratio. Therefore, Nanofluids containing gold and silver Shell and Multilayered nanostructures are potential candidates to be used in direct absorption solar collectors.
Acknowledgment This work was supported by the Brazilian Agencies: Coordination for the Improvement of Higher Education Personnel (CAPES), the Science and Research Foundation of State of Pernambuco (FACEPE), the Brazilian National Council for Scientific and Technological Development (CNPQ) and the Polytechnic School of Pernambuco. References [1] B. Parida, S. Iniyan, R. Goic, A review of solar photovoltaic technologies, Renew. Sustain. energy Rev. 15 (3) (2011) 1625e1636. [2] T.T. Chow, A review on photovoltaic/thermal hybrid solar technology, Appl. energy 87 (2) (2010) 365e379. [3] J.E. Minardi, H.N. Chuang, Performance of a black liquid flat-plate solar collector, Sol. Energy 17 (3) (1975) 179e183. [4] T.P. Otanicar, P.E. Phelan, R.S. Prasher, G. Rosengarten, R.A. Taylor, Nanofluidbased direct absorption solar collector, J. Renew. Sustain. energy 2 (3) (2010), 033102. [5] R.A. Taylor, T. Otanicar, G. Rosengarten, Nanofluid-based optical filter
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Colloidal plasmonic structures for harvesting solar radiation mez-Malago n Diego Rativa*, Luis A. Go University of Pernambuco, Polytechnic School of Pernambuco, 50720-001 Recife, PE, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 September 2017 Received in revised form 22 October 2017 Accepted 31 October 2017 Available online xxx
Direct Solar Absorption Collectors explore the thermo-optical properties of fluids to convert solar radiation into thermal energy. Colloids of metallic nanoparticles have shown a great potential to convert solar radiation into thermal energy efficiently, because of the matching between the absorption peak of the localized surface plasmon resonance and the solar radiation spectrum. Recently, multilayered metallic nano structures have been broadly studied for Thermo-optical applications due to the possibility to tune the plasmon resonance next to the near infrared region. In this work, using a full-wave field numerical model, we study the solar absorption of metallic nanofluids composed of Solid structures (Sphere, Cube, Tetrahedral, Octahedral), Silica-based structures (Shell and Multilayered) and its elliptical versions. Although a large part of the metallic material is replaced for SiO2 in the nanofluid composition of NanoShell (NS) and Multilayered (ML) structures, the values of solar radiation absorber coefficients are larger than the obtained with solid particles. Also, the quantity of metal is just 18% (NS) and 53% (ML) of the material necessary to fabricate colloids of solid particles. For the elliptical structures, the values of solar radiation absorber condition are larger than the obtained with spherical structures. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Metallic nanostructures Solar radiation absorption
1. Introduction Solar collectors are renewable energy technologies developed during the last decades, which explore the thermo-optical properties of fluids to convert efficiently solar radiation into thermal energy [1,2]. The most common type of solar thermal collector employs a black absorber surface to transfer heat to a fluid that is circulating in tubes embedded within or fused onto the surface [3]. Inserting nanoparticles (NPs) in the fluid, a change of its thermophysical properties is caused, with an efficiency improvement next to 5% in solar thermal collectors [4]. This kind of Nanofluids has found applicability in systems where a fast and effective heat transfer is necessary, such as industrial applications, cooling of microchips, microscopic fluidic applications, etc [5]. On the other hand, to improve the energy transfer efficiency, the solar radiation must be absorbed directly by the working fluid as proposed by the Direct Solar Absorption Collector (DSAC), which is a thermal device composed of a transparent glass box containing the nanofluid. For a nanofluid of water and aluminum nanoparticles, the efficiency of a DSAC can increase up to 10% in
* Corresponding author. E-mail addresses: [email protected] mez-Malago n). (L.A. Go
(D.
Rativa),
[email protected]
comparison with a typical flat-plate solar collector [6]. Also, for a DSAC containing silver nanofluid, its efficiency can achieve a maximum value of 90% [7]. The efficiency of the solar radiation absorption is given mainly because of the matching between the metallic NPs optical absorption and the solar radiation spectrum [8,9]. In the case of gold and silver NPs, by cause of the localized surface plasmon resonance effect at visible region, the absorption peak can be tuned between 400 nm and 1300 nm [10,11], such that is possible to manage the solar radiation absorption efficiency altering the NPs geometry. We have reported previously that the absorption spectrum of metallic nano-ellipsoids (NE) is red-shifted relative to that of a spherical geometry, therefore, it is possible to achieve a solar weighted absorption coefficient close to the ideal condition, managing the aspect ratio of the NE [12]. Recently another study has explored gold nano-rods and nano-sheets for the same purpose [13]. Other plasmonic structures with similar red-shifted resonance peak are the Nano-Shell (NS) [14] and Multilayered structures (ML) [15]. A NS is composed of a core covered by a thin metallic layer, the material properties of both the core and the shell regions, strongly influence the optical properties of the NS. In the particular case of a Silica-NS, with SiO2 core and a Gold or Silver shell, a strong coupling between charges inside and outside of the shell causes a charge separation and consequently a red-shift of the absorption spectrum
https://doi.org/10.1016/j.renene.2017.10.112 0960-1481/© 2017 Elsevier Ltd. All rights reserved.
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up to near IR spectrum [16]. For example, a Silica-NS with a core of 60 nm and a Gold shell with a thickness of 50 nm and 2 nm has a LPSR peak at 650 nm and 1100 nm, respectively [17]. On the other hand, the ML structures are composed of a metallic core, coated with a thin silica layer, and finally surrounded by a thin metallic shell (ex. Au/SiO2/Au) [15,18e21]. MLs work like optical condensers and the electromagnetic field in the centermost dielectric layer can be enhanced multiplicatively with the number of layers [22]. Furthermore, the resonance peak of elliptical NS and ML is red-shifted for the same reasons as reported for NE [12,18]. In this work, the influence of metallic NPs structures on the solar radiation harvesting of solar collectors is analyzed; The nanostructures studied are solids, shells, multilayered, and its elliptical versions. The numerical model and the 3D simulation space are discussed in the methods section, posteriorly the differences between the solar weighted absorption coefficients obtained for the nanofluids containing the selected structures are discussed. We would like to note that chemical preparations of colloids based on the structures studied in this work have been already reported in the literature, allowing its immediate application.
con-ductivity of the medium, respectively. As represented in Fig. 1, in our model, the incident light is ppolarized at normal incidence with the electric field E along the xaxis, propagating in the þz direction. To model an unpolarized light source (solar radiation), the average of the calculations for E0 linearly polarized along the long axis and the short axis of the particle has been carried out.
2. Methods
where ∞ is the high-frequency limit dielectric permittivity, lp is the plasma wavelength, lj is the interband transition wavelength, gk is the damping in the direction k, gj is the transition broadening, 4j is the phase and Aj is the dimensionless critical point amplitude [24,25]. In the case of metallic materials smaller than the mean free path of free electrons, the dielectric permittivity for metallic NPs that accounts for the size dependence is given by Ref. [16]:
2.1. Numerical model We have explored a full-wave time harmonic field theory for the computational model analysis, using the COMSOL Multiphysics 5.0 software, Electromagnetic Waves, Frequency Domain interface (EMW package, for subwavelength geometries). The 3D simulation space has two main regions, the studied structures and a surrounded medium, as can be seen in Fig. 1. The surrounded medium is composed of two spherical regions: an embedding medium (H2O) and a perfectly matched layer (PML). The radius of the embedding and the PML spheres were chosen depending on the NPs diameter, such that NPs size variation further would not affect the simulation results. In the case of Solar Radiation (low-intensity regime), the timeharmonic Electric field within the domain satisfies Maxwell equations in the frequency domain [23]:
s 2 ε E¼0 V m1 ðV EÞ u ε m j 0 0 r r uε0
(1)
where mr ; εr and s are the relative permeability, permittivity, and
2.1.1. Permittivity particle size considerations The bulk metal dielectric permittivity can be described by an analytical expression based on the broadly accepted model for metallic materials, given by Ref. [24]:
X Aj
2
ei4j 4 . þ 2 l 1 l þ i=ðgk lÞ 1 lj 1=l igj j¼1;2 j 3 ei4j 5 þ 1 lj þ 1=l þ igj
εBulk ¼ ε∞
1
l2p
(2)
εNP u; Leff ¼ εBulk ðuÞ þ
u2p u2p u2 þ iu Ly∞f u2 þ iu Lyf þ AL yf ∞ eff
(3)
where εBulk is the bulk dielectric function of the NP's material, u is the angular frequency of the incident light, up is the plasma frequency, vf is the Fermi velocity, L∞ is the mean free path of the electrons, A is the dimensionless parameter (A ¼ 1) and Leff is the reduced effective mean free path of the electrons [26]. The Silver and Gold parameters have been reported in several articles [27,28]. 2.2. Nano-structure geometries It is well-known that for particles smaller than 10 nm, the
Fig. 1. (a) 3D Computational model regions composed of a Metallic Nanostructure studied, an embedding medium (H2O) and a Perfectly Matched Layer; (b) Electric field maps, represented in colors corresponding to the electric field enhancement, jEj/jE0j. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. Spectral dependence of the absorption cross section for Gold and Silver nanostructures (Sphere (a), Tetrahedral (b), Cube (c) and Octahedron (d)) [Left]; and its corresponding term El (1 eax) for x ¼ 1 cm and p ¼ 1 106, compared with the Spectral irradiance ASTM G173-03 [Right].
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percentage of surface atoms starts taking over bulk atoms, increasing their catalytic properties and resulting in large variations in the particle size [29]. Moreover, We are interested in photothermal applications in which the absorption is the main factor that determines the system efficiency. Therefore, the NPs studied have a volume next to (20 nm)3, attending both conditions: a scattering cross section coefficient (ssca) smaller than the absorption cross section (sabs) for all geometries (ssca/sabs < 0.1) and a colloid which could be chemically stable. 2.3. Solar absorption harvesting analysis The NP absorption properties are given in terms of the optical absorption cross section values, obtained by:
sabs[m2] ¼ Qabs[W]/Irad[W/m2]
(4)
where Qabs is the power absorbed by the particle and Irad is the incident irradiance. Most of the previous works report plasmonic nanofluid properties in terms of the optical coefficient absorption for solar collectors with a height of one or a few centimeters and volume fractions at orders of 106 and 104 [12,13,16,22,27]. Therefore, for comparison purposes, we have defined a nanofluid volume of Vfluid ¼ 1 cm3 (collector height and area of 1 cm), a total volume of metallic nanoparticles as VNPs ¼ Nparticles Vparticle and a volume fraction p ¼ VNPs/Vfluid ¼ 1 106. The volume fraction is kept constant for the analysis (except in the volume fraction analysis), compensating volume variations of the particle altering the number of inclusions (Nparticles). Therefore, the coefficient absorption is given by a[cm1] ¼ (Nparticles/Vfluid)
[cm3] sabs [cm2]. The efficiency of a direct absorption solar collector is estimated calculating the solar weighted absorption coefficient, Am which represents the percentage of the solar energy that is absorbed across the fluid layer of selected thickness, given by Ref. [30]:
Z Am ¼
El 1 eax dl Z El dl
(5)
where El is the spectral distribution of the solar intensity and x is the thickness of the fluid layer. The solar weighted absorption coefficient is obtained integrating from 200 nm to 1.5 mm. Although reflections and absorption of the solar radiation, due to the glass containing the nanofluid, reduce the intensity of the solar radiation, most glasses are transparent (90% transmission) in the visible and the near infrared region (350e2500 nm) and the reflection has not an important chromatic dependence, such that we can consider that the solar radiation spectrum is not altered by the presence of a covering glass. 3. Results and discussion 3.1. Solid structures The absorption cross section of Silver and Gold NPs with different solid geometries (Sphere, Tetrahedral, Cube, and Octahedron) are represented in Fig. 2, and its corresponding solar weighted absorption coefficients (i.e. El (1 eax)) are represented on Fig. 2 for a solar collector with x ¼ 1 cm.
Fig. 3. Spectral dependence of the absorption cross section for Gold (a) and Silver (b) NS [Left]; and its corresponding term El (1 eax) for x ¼ 1 cm and p ¼ 1 106 compared with the Spectral irradiance ASTM G173-03 [Right].
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The spectral absorption dependence of the solid NPs is in agreement with the absorption spectrum reported in the literature exploring methods such as Mie Scattering and Discrete Dipole Approximation (DDA) [11], validating our model. Because the sharpest corners, the Tetrahedral and Octahedron geometries have the most red-shifted resonance peaks and consequently a broader spectral absorption [11], such that the Harvesting coefficient shows a better matching with the solar radiation spectrum for that particles. 3.2. Silica-based structures 3.2.1. Nano-Shells In the case of NS structures, the radius of the silica core (SiO2) is kept constant at 20 nm, and the shell thickness selected are 10 nm, 5 nm, and 2.5 nm. As shown in Fig. 3, the absorption resonance peak can be redshifted reducing the metallic shell thickness, whereas the core radius does not play an important role in this effect. In the case of NS with a thickness of 2.5 nm, the absorption resonance peaks are shifted up to 750 nm and 800 nm for Silver and Gold shells, respectively. The harvesting solar radiation spectrum of the nanofluid composed by metallic NS structures are similar to the obtained for NE with an aspect ratio of 3 and 4 [12]. 3.2.2. Multilayered ML structures are composed of a metallic core (radius of 10 nm), a SiO2 layer (thickness T1 ¼ 10 nm and 5 nm), and a metallic layer (T2 ¼ 5 nm and 2.5 nm). As shown in Fig. 4, the absorption spectrum has two resonance
5
peaks, one related to the core contribution (Au: 532 nm and Ag: 400 nm) and the other one with the external metallic shell (redshifted for thinner shells). Consequently, the absorption spectrum is broader than the obtained for Solid and NS structures. Moreover, it is observed that variations in the outer shell thickness are responsible for the red-shift effect, whereas variations in the SiO2 layer thickness do not play an important role in the same effect. For nanofluids constituted of Shells and Multilayered particles, a large part of the metallic material is replaced for SiO2, such that the quantity of metal is just 18% (NS) and 53% (ML) of the necessary material to fabricate a colloid of solid spheres. The dependence of Am on volume fraction for a nanofluid (thickness of 1 cm) containing the solid structures studied are represented in Fig. 5 (aed). The matching between the solar radiation and the solar absorption for nanofluids composed by ML structures is more efficient because of its broader absorption. As can be seen in Fig. 5 (f), for a nanofluid with a volume fraction of 3 105 and x ¼ 1 cm, the solar weighted absorption coefficient of a nanofluid composed of Silver ML is Am ¼ 0.65, whereas for Solid and NS structures the values are Am ¼ 0.45 and Am ¼ 0.55, respectively. Furthermore, for a nanofluid with the same concentration of Gold ML, the absorption coefficient reaches a value next to Am ¼ 0.8. 3.3. Elliptical silica-based structures Similarly, to metallic ellipsoids, where the Transversal and Longitudinal oscillation modes can be tuned modifying the aspect ratio [12], the NS and ML structures are studied for different aspect ratios tuning the plasmon resonance peak. We have explored a NS geometry with a radius RSiO2 ¼ 20 nm and a layer with thickness of
Fig. 4. Spectral dependence of the absorption cross section for Gold (a) and Silver (b) Multilayered structures [Left]; and its corresponding term El (1 eax) for x ¼ 1 cm and p ¼ 1 106 compared with the Spectral irradiance ASTM G173-03 [Right].
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Fig. 5. Dependence of the solar weighted absorption coefficient Am on volume fraction, for a nanofluid with thickness x ¼ 1 cm, composed of Solid (aed), Shell (e) and Multilayered structures (f).
5 nm, as well as, a ML geometry with RAu ¼ 20 nm, an internal layer of SiO2 with thickness of 5 nm, and an external Au layer of 5 nm. As can be seen in Fig. 6, the dependence of Am on volume fraction for a nanofluid with thickness of 1 cm are represented for Solid (a), NS (b) and ML (c) elliptical Gold structures with different aspect ratios. As summarized in Table 1, in the case of nanofluids containing Silver and Gold NPs with volume fractions of p ¼ 3 105 and x ¼ 1 cm, the highest solar weighted absorption coefficient values are obtained for NE and NS with AR ¼ 4. A solar weighted absorption coefficient close the ideal condition can be obtained for silver and gold ML structures with an aspect ratio of AR ¼ 2. Ideal absorber nanofluids are obtained with a volume fraction of p ¼ 1e3 105, such that the mean interparticle distances (10e30 mm) are large enough to avoid partial agglomerations. On
the other hand, silica coatings (transparent) can be explored to protect the metallic nanoparticles enhancing the thermodynamic stability [31], although a reduction in the thermal conductivity of the structure is expected. 4. Conclusions Shell and Multilayered are nanostructures with a red-shifted resonance peak relative to that of a solid spherical geometry. Although a large part of the metallic material is replaced for SiO2 in the nanofluid fabrication of NS and ML, the values of solar radiation absorber condition are larger than the obtained with solid particles. The quantity of metal is just 18% (NS) and 53% (ML) of the material necessary to fabricate colloids of solid particles. Similar to ellipsoids, the plasmon resonance absorption band of
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Fig. 6. Dependence of the solar weighted absorption coefficient Am on volume fraction, for a nanofluid with thickness x ¼ 1 cm, composed of Solid [(a) Au, (d) Ag], NS [(b) Au, (e) Ag] and ML [(c) Au, (f) Ag] elliptical Gold and Silver structures with different aspect ratios AR.
Table 1 Solar weighted absorption coefficient values for a nanofluid composed by Metallic structures and x ¼ 1 cm. Material
Structure
AR
Vol.Ratio Au/SiO2
Am (p ¼ 1 105)
Am (p ¼ 3 105)
Gold
Solid Shell Multilayered Solid Shell Multilayered
4 4 2 4 4 2
1/0 0.18/0.82 0.53/0.47 1/0 0.18/0.82 0.53/0.47
0.85 0.88 0.9 0.78 0.82 0.85
0.94 0.98 0.99 0.93 0.98 0.99
Silver
NS and ML has a Transversal and a Longitudinal oscillation mode that can be tuned modifying the structure aspect ratio. Therefore, Nanofluids containing gold and silver Shell and Multilayered nanostructures are potential candidates to be used in direct absorption solar collectors.
Acknowledgment This work was supported by the Brazilian Agencies: Coordination for the Improvement of Higher Education Personnel (CAPES), the Science and Research Foundation of State of Pernambuco (FACEPE), the Brazilian National Council for Scientific and Technological Development (CNPQ) and the Polytechnic School of Pernambuco. References [1] B. Parida, S. Iniyan, R. Goic, A review of solar photovoltaic technologies, Renew. Sustain. energy Rev. 15 (3) (2011) 1625e1636. [2] T.T. Chow, A review on photovoltaic/thermal hybrid solar technology, Appl. energy 87 (2) (2010) 365e379. [3] J.E. Minardi, H.N. Chuang, Performance of a black liquid flat-plate solar collector, Sol. Energy 17 (3) (1975) 179e183. [4] T.P. Otanicar, P.E. Phelan, R.S. Prasher, G. Rosengarten, R.A. Taylor, Nanofluidbased direct absorption solar collector, J. Renew. Sustain. energy 2 (3) (2010), 033102. [5] R.A. Taylor, T. Otanicar, G. Rosengarten, Nanofluid-based optical filter
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