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Abstract
Microscopic thin film doped with different species of nanoparticles displays a unique wavelength selectivity in the context of micro/nanoscale radiative heat transfer. We propose a methodology to shift, broaden, and suppress the thermal radiative selectivity in the desired wavelength ranges. Measured transmittance spectra of potassium bromide pellet doped with a single species of nanoparticles are compared with the theoretical prediction using refractive indices that are extracted by refitting transmittance spectra curve according to the Lorentz-Drude model. For a media doped with more than two species of nanoparticles, a successive effective dielectric function using the refitted complex refractive indices and Maxwell Garnett theory is used to evaluate the thermal radiative selectivity of the composites. It has been confirmed theoretically and experimentally that the wavelength selectivity in the transmittance spectra can be influenced by choosing proper species of materials and varying volume fractions of multiple nanoparticles. This work has shed light on the design and fabrication of novel composites doped with multiple particles for applications such as thermophotovoltaics, radiative cooling, and biosensing.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Interests in nanomaterials have rapidly increased recently in the past few decades both theoretically and technologically. Properties of nanostructures incorporated with nanoparticles are significantly dissimilar from those of bulk materials due to their small-scale optical properties and thermal effects. The novel properties, such as spectrally selective emission spectrum, enhanced thermal radiative heat transfer, may find applications in the areas such as photo electronics, catalysis, magnetism, and thermal sensing which are not exhibited in their corresponding bulk materials. In particular, semiconductor and metallic nanoparticles embedded in a dielectric host matrix have received great interest since they offer a wide range of applications spanning from electronics and optics to biosensing.
The effective dielectric function of composites doped with more than one constituent can be modeled using effective-medium approximation (EMA) that treats composites as a macroscopically inhomogeneous medium. Almost all the common composites fall into this broad category. One example is a metal-dielectric composite, consisting of a collection of metallic and dielectric grains arranged in random distributions. A variety of methods estimating effective optical properties of such composites have been developed, including approximate methods, rigorous bounding techniques, and numerical methods. Methods for calculating the effective medium of dielectric heterogeneous have attracted much attention. Lorentz-Lorenz model [1–3], Maxwell Garnett model [4] and Bruggeman EMA model are commonly adopted by effective-medium theories. The basis of EMA theory is to define a dielectric function of an effective medium that, from an electromagnetic point of view, is identical with the assumed ideal microstructure, which typically is modeled as non-interacting spherical or ellipsoidal inclusions.
Nowadays, the development of a spectrally selective surface has attracted more attention due to its wide applications in energy engineering. Radiative cooling is a strategy to dissipate excess heat into outer space which services as a heat sink and stands out because of the ability to operate without external energy consumption [5–7]. The basis for radiative cooling is the infrared transmission window of the atmosphere. Note that the earth’s atmosphere is relatively transparent between the wavelength of 8 $\mu$m $\sim$ 13 $\mu$m, also known as “sky window” [8]. This window allows the radiation emitted by the object on earth to escape to outer space without absorption by the atmosphere. Therefore, an ideal design of an infrared emitter with enhanced radiative cooling capability is that the emitter has wavelength selectivity with an extremely low reflectance in “sky window” but a very high reflectance elsewhere. The sharp spectral tuning supported by selective phonon resonant nanoparticles of interest, when incorporated as inclusions in an infrared (IR) transparent film, enables the desired wavelength selectivity of the composite material. Therefore, it is practical to achieve a strong emission with the sky window by adjusting the species and volume fractions of nanoparticles.
While some previous work was dedicated to design and fabricate wavelength selective emitters and absorbers, multiple nanoparticles embedded composites specifically for the applications of radiative selectivity have not been well studied. Optical properties of composite materials doped with one kind of nanoparticles have been investigated before [9–12]. However, emissive/transmitting properties of different species of nanoparticles embedded thin films have not been studied in detail to the best of our knowledge. To achieve an ideal spectrum of composite material for a specific purpose, a series of experiments need to be conducted, and this is time- and efforts-ineffective to explore and confirm the species and concentrations of materials. This work reveals a way to estimate the spectra of composite materials by providing a range of parameters of multiple nanoparticles, such as species, sizes, and volume fractions of different nanoparticles. This facilitates the process of the experiments to obtain the desired optical spectra.
The complex refractive indices of various species of nanoparticles are usually required for the simulation of optical spectra. In this paper, a simulation approach is provided to evaluate the transmittance spectra of a free-standing thin film containing two or more species of nanoparticles that are suitable for potential applications. Ideally, one wants to build a spectrally selective thermal emitter for a specific wavelength band as per the requirements. In this case, the broadband between 8 $\mu$m $\sim$ 13 $\mu$m in transmittance spectra is desired to match the above mentioned “sky window” with the help of simulation method proposed here. In this paper, a potassium bromide (KBr) disc served as host materials and boron nitride (BN) and silicon nitride (Si$_3$N$_4$) nanoparticles are selected as inclusions. The proposed method of predicting transmittance spectra of multiple nanoparticles doped composites consist of two steps as follows. Firstly, to obtain an effective dielectric function of a KBr thin film mixed with a single species of BN nanoparticle with an unknown dielectric function in the wavelength range of interest (as shown in Fig. 1(a)) by refitting the experimental spectra curve using the Lorentz-Drude model. Secondly, to apply Maxwell Garnett theory for the calculation of transmittance spectra of a KBr thin film when adding another species of Si$_3$N$_4$ nanoparticles into the mixture (Fig. 1(b)) . Simulated spectra of the composites of interest doped with multiple nanoparticles have been validated by comparing with the experimental transmittance data using the Fourier Transform Infrared Spectrometer (FTIR).
Fig. 1. Schematic of potassium bromide (KBr) pellets with multiple nanoparticles. (a) KBr pellet doped with boron nitride (BN) nanoparticles, and (b) KBr pellet doped with BN and silicon nitride (Si$_3$N$_4$) nanoparticles.
2. Design and fabrication
2.1 Materials and Instruments
Three different powders were selected for this study. KBr powder used for making the pellets for transmittance measurement in the wavenumber range of 40000 cm$^{-1}$ to 400 cm$^{-1}$ was purchased from BUCK Scientific, Inc. ( USA ). Si$_3$N$_4$ nanopowder with a purity of 99% (80 nm in diameter) and BN nanopowder with a purity of 99.8% (70 nm in diameter) were supplied by US Research Nanomaterials, Inc. ( USA ) and used without further purification. Hydraulic Rosin Press was purchased from DABPRESS, Inc. (USA). The hydraulic pressure was provided by the Strongway 46278 Hydraulic Pump with Gauge and Hose. KBr quick press kit with a 7 mm die set was purchased from International Crystal Laboratories, Inc. (USA). Traditionally, powdered samples are mixed with KBr and a pellet is made under hydraulic press [13]. Here. KBr is selected as a host material (matrix) because it has a wide spectral transmittance in the mid-infrared (MIR) range of interest, and it produces a smooth, transparent disk when mixed with powdered solids [14]. While taking into account the feature of high transmissivity of KBr, the analysis of wavelength selectivity due to multiple nanoparticle inclusions can be conducted easily.
2.1.1 Pellet sample preparation
Figure 2 shows the schematic of hydraulic press mold for the pellet preparation including two dies – one with a short bolt and the other with a long bolt. The stainless steel collar is used to confine the KBr powder in a circle. The two types of fabricated samples are KBr pellet doped with BN nanoparticles and KBr pellet doped with BN and Si$_3$N$_4$ nanoparticles. To keep the consistency of the results between two sample pellets, we prepared two same raw sample materials: 550 mg KBr nanopowders served as the host material, 4.5 mg BN nanoparticles and 20 mg Si$_3$N$_4$ nanoparticles as inclusions. All of the parts of the equipment contacting with sample powders were cleaned using successive washes of acetone and deionized water and dried with dry nitrogen gas. To fabricate the first sample, KBr and BN nanoparticles are mixed and ground with an agate mortar and a pestle for 5 minutes to obtain an approximate homogeneous mixture, then heated the mixture in the oven overnight at 120$^{\circ }$C to remove the water absorption of the KBr. To avoid the crack of the pressed pellet, 19 mg of mixed powders that can fully cover the top surface of the shorter bolt was pressed into the stainless steel hollow collar with 7 mm diameter. The shorter bolt was first inserted into the collar, then the longer bolt. The assembly was placed under a hydraulic pressure at 5500 psi for 1 minute to form a pellet, which is retained inside of the collar chamber when both bolts are removed. The prepared pellet of doped BN and Si$_3$N$_4$ nanoparticles with a volume fraction of 1% and 3%, respectively, were fabricated and dried once again for 24 h before the FTIR measurement. Similarly, the second sample was made following the same steps to mix BN and Si$_3$N$_4$ nanoparticles with KBr. The free-standing KBr pellet is shown in Fig. 2(c).
Fig. 2. (a) Explode view of schematic of hydraulic press mold for KBr pellet. (b) The working process of hydraulic press mold. (c) The transparent KBr pellet in the collar
2.1.2 FTIR transmittance measurement
Infrared spectroscopy uses infrared radiation to measure what fraction of the incident radiation is absorbed in a particular wavelength. The transmittance spectra of sample disc are measured with the apparatus shown in Fig. 3. The IR spectra of the samples were measured from the wavenumber 400 m$^{-1}$ to 4000 cm$^{-1}$ by the standard KBr pellet method. The transmission spectra were recorded with an aperture set to form a 3.5 $\mu$m diameter circle onto the disc. FTIR spectrometry can quantify the abundance of chemical functional groups. For sample disc characterization, the disc was analyzed on a Jasco 6600 spectrometer equipped with Deuterated Lanthanum $\alpha$ Alanine doped TriGlycine Sulphate (DLaTGS) detector. The spectrometer provides with a ceramic light source from 2.5 $\mu$m to 25 $\mu$m and the optical spectra are obtained at a resolution of 4 cm$^{-1}$ with 32 scanning rate. The sample disc was located at one side of the collar that also serves as a specimen holder. The sample was placed vertically to the optical path inside the sample chamber with a holder. Each transmittance measurement included a background measurement at the beginning, and the characteristic transmission peaks of the samples were identified by comparison with the reference.
3. Results and discussion
3.1 Single species of nanoparticles: transmittance spectra refitting
A KBr sample pellet doped with BN nanoparticles with a thickness of 170 $\mu$m was prepared by the hydraulic press method as discussed in the previous section. Its transmittance spectrum (red curve) was measured as shown in Fig. 4 in comparison with that of a pure KBr pellet (green curve) without any inclusion. It’s shown that a distinguishing feature for the resonant absorption due to the existence of BN nanoparticles into KBr matrix is the appearances of two narrow absorption/emission bands centered at 7.09 $\mu$m and 12.45 $\mu$m in the transmittance spectra, which exactly fall into the sky window of interest. The rest of the transmittance spectra of the sample pellet excluding two narrow bands is slightly lower than the transmittance of the pure KBr pellet owing to the decrease of KBr concentration and the difference of the grinding particle sizes of KBr and BN.
Fig. 4. Transmittance measurement of a pure KBr pellet and a KBr pellet doped with BN nanoparticles in comparison with refitted spectra using the Drude-Lortenz oscillator model. The sky window is highlighted with the blue area.
To determine the effective dielectric function of a KBr sample pellet doped with BN nanoparticles, a practical calculation has been conducted in this work as outlined by Verleur et al. [15] which described how a well-known but laborious method for obtaining optical constants from transmittance data for bulk materials can be made more useful and convenient if an automatic curve-fitting routine is used. Complex refractive indices of sample pellet are extracted by refitting measured transmittance spectra to calculated transmittance data. Its corresponding dielectric function $\varepsilon (\omega )$ of a mixture of dispersing BN nanoparticles into the KBr pellet can be predicted using the Lorentz-Drude oscillator model, given by [15]
In this work, a free-standing film structure (air-sample pellet-air) is considered for the normal transmission calculation and measurement. The generalized transmission coefficient at the interface between air and sample pellet is modified according to Eq. 2.1.26(a) and Eq. 2.1.28 in Chow’s book [16]
Here, $\tau _{m}$ and $\tau _{r}$ are measured and refitted transmittance data, respectively. Index $\textit {i}$ indicates different wavelengths over which transmittance measurements are conducted. MATLAB based genetic algorithm is applied to obtain the final optimized resonant frequencies and achieve a good fit between measured and refitted spectra.
Complex refractive indices of the KBr pellet doped with BN nanoparticles can be extracted by tuning several oscillator parameters to match the measured transmittance spectra to calculated transmittance data. The comparison of experimental transmittance spectra and refitting ones match well and is shown in Fig. 4. It can be empirically found that 17 oscillator parameters are suitable to approach the best fit as tabulated in Table 1.
Table 1. Oscillator Parameters of a BN Nanoparticles embedded KBr Pellet
3.2 Multiple species of nanoparticles: transmittance spectra analysis
After the effective refractive indices of the KBr sample pellet doped with BN nanoparticles were obtained as described in the previous section, Si$_3$N$_4$ nanoparticles were dispersed into the sample pellet to acquire experimental transmittance spectra. According to Kirchhoff’s law, the spectral absorptance $\alpha$($\lambda$) is equal to the emittance $\epsilon$($\lambda$) at the thermal equilibrium [17]. Spectral transmittance $\tau$($\lambda$) and reflectance $\rho$($\lambda$) and angle of incidence can be measured using FTIR spectrometer. Spectral absorptance $\alpha$($\lambda$)=1-$\rho$($\lambda$)-$\tau$($\lambda$). In this method, the matrix materials are assumed transparent without any absorption or scattering and there is no reflection on the sample surface when the light is normal to the pellet surface. The reflection by the pellet is usually neglected for simplification due to the high transparency of KBr [18]. Therefore, the reflectance of the KBr sample pellet is negligible. The spectral absorptance/emittance is $\alpha (\lambda )=\epsilon (\lambda ) \approx 1-\tau (\lambda )$.
To predict the transmittance spectra of the KBr sample pellet mixed with two species of nanoparticles, such as BN and Si$_3$N$_4$, the Eq. (3) can be used with the effective dielectric function of the sample pellet mixed with only one species of nanoparticles (here BN). The Clausius-Mossotti approach for $\varepsilon _{eff}$ of the sample pellet containing the second species of nanoparticles (here Si$_3$N$_4$) in a host material (KBr) is given by [19–21]
where $\varepsilon _{h}$ is the dielectric function of the host, $\alpha _p$ is the electric dipole polarizability, $r$ and $f$ are the radius and volume fraction of nanoparticle inclusions, respectively. The size dependent extension of Maxwell Garnett formula can be obtained by deriving an expression for electric dipole polarizability using Mie theory [22] where $a_{1,r}$ is the first electric Mie coefficient given byThe real ($n$) part and imaginary ($\kappa$) part of the complex refractive indices of the pure KBr sample pellet (green curve), the one doped with only BN nanoparticles (blue curve), and the one doped with BN and Si$_3$N$_4$ nanoparticles (red curves) are shown in Fig. 5. The complex refractive indices of KBr, the solid green curves as shown in Figs. 5(a) and 5(b), are extracted from Li’s work [23]. The solid blue curves represent the real ($n$) part and imaginary ($\kappa$) part of the complex refractive indices of KBr embedded with BN nanoparticles in a volume fraction of 1% are refitted from Eqs. (1)–(3). The dash red curves of the complex refractive indices of KBr doped with BN and Si$_3$N$_4$ nanoparticles with a volume fraction of 1% and 3%, respectively, are calculated using Eqs. (4)–(6), the refitted complex refractive indices of KBr with BN nanoparticles and the refractive indices of Si$_3$N$_4$ that are extracted from Kischkat et al’s work [24].
Fig. 5. Refractive index characteristics of KBr pellet doped with different nanoparticles: (a) Real part $n$, and (b) imaginary par $\kappa$
A comparison of measured and calculated transmittance spectra of the KBr pellet doped with two species of nanoparticles of BN and Si$_3$N$_4$ are shown in Fig. 6. Overall, these two curves match well except the offset from 2.5 $\mu$m to 5 $\mu$m and 8 $\mu$m to 9 $\mu$m. The absorption peak at 2.9 $\mu$m is observed which is caused by the vibration of hydroxyl of residual water [18], Although the mixed powder and pellet were dried before the test, little water still exists in the KBr powder and water vapor in the ambient is absorbed during the FTIR measurement. The mismatch 8 $\mu$m to 9 $\mu$m is because the Si$_3$N$_4$ nanoparticles is not randomly distributed into KBr pellet though we have mixed it for 5 minutes when mixing the BN and Si$_3$N$_4$ nanoparticles with KBr powders, and this causes the absorption band from 8 $\mu$m to 9 $\mu$m is narrower than the simulated curves. Both BN and Si$_3$N$_4$ manifest itself by its unique optical feature: (1) two existing narrow absorption bands of BN nanoparticles centered at 7.09 $\mu$m and 12.45 $\mu$m and (2) appearance of one new absorption band of Si$_3$N$_4$ nanoparticles between $8.5$ $\mu$m to $12.2$ $\mu$m. Both of these phenomena yield a low-transmittance (average between 7.5 $\mu$m to 13 $\mu$m as low as 0.083) broadband that matches the atmospheric transparency window very well. In this work, this method of sample preparation has some complications and requires a certain experience to obtain a good quality spectrum in the fabrication of sample. Special factors should include pellet thickness, particle dispersion, pressure influence, etc. Therefore, there is still some little difference between experimental and simulation results. When we propose to create a “sky window” using KBr, BN and Si$_3$N$_4$ to verify our method provided in this work, we take into consideration the principle of KBr pellet fabrication that the volume fraction of both BN and Si$_3$N$_4$ nanoparticles should lie in 2% ˜10% in weight [25]. We created two narrow absorption bands by adding BN and Si$_3$N$_4$ nanoparticles with the limitation of the procedure of the KBr pellet fabrication method. Though the experimental spectrum shown in Fig. 6 is not the optimized in terms of radiative cooling, it is the relatively the best experimental result we got under the KBr pellet fabrication principle.
Fig. 6. Transmittance spectra of sample pellet mixed with BN and Si$_3$N$_4$ nanoparticle in comparison with simulation result
4. Conclusion
The infrared properties have been experimentally investigated for the pellets doped with different species of nanoparticles using FTIR spectroscopy. Lorentz-Drude oscillator model is used to determine the complex refractive indices of the composites (though the dielectric function of a consisting component is not well known) based on experimental measurement. The oscillator parameters for the effective dielectric function of nanoparticle embedded films are extracted through a fitting optimization technique using the predicted and experimental transmittance spectra. A step-by-step simulation method can be derived for multiple nanoparticle inclusions into a matrix. It has been validated for a case with two species of nanoparticles that can be treated as a thin film embedded with a single species of nanoparticles first as an effective medium, into which the other species with known optical properties is then incorporated.
According to simulated and experimental results of the inclusions of BN and Si$_3$N$_4$ nanoparticles into a KBr pellet, a broader-transmittance-band emitter has been designed and fabricated. As predicted, a high transmittance between 8 $\mu$m $\sim$ 13 $\mu$m has been measured experimentally and it can be utilized for radiative cooling through the atmospheric transparency window.
In summary, thermal radiative wavelength selectivity can be tuned while taking into account the combination of multiple nanoparticles. This work has shed light on the design and fabrication of novel nanoscale composites doped with multiple particles for applications to thermophotovoltaics, radiative cooling, biosensing, and radiative thermal management.
Funding
National Science Foundation (CBET-1836967, OIA-1655221); National Aeronautics and Space Administration (NNX15AK52A).
Disclosures
The authors declare no conflict of interest.
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