Realization of energy-saving glass using photonic crystals

Abstract

This work successfully developed an energy-saving glass with wavelength selectivity. The glass is composed of a SiO₂ substrate and two layers of three-dimensional photonic crystals. Each crystal is composed of identical and transparent polystyrene spheres after their self-assembling. The glass then possesses dual photonic band gaps in the near-infrared region to suppress penetration of thermal radiation. Experimental results show that the energy-saving glass decreases temperature increment in a mini-house. Moreover, the temperature after thermal equilibrium is lower than that inside a counterpart using ordinary glass.

Keywords

energy-saving glass / photonic crystals / polystyrene spheres / self-assembly

Introduction

Maintaining indoor comfort is expensive and energy consuming to people in urban heat island or tropical zone because of thermal radiation. For example, solar radiation brings a large amount of heat into a building through windows during a hot summer day. The radiation spectrum mainly covers visible and near-infrared (near-IR) regions [¹,²] such that normal glass windows are transparent . At the same time, the room gets hot and emits thermal radiation in mid-IR range. Because the mid-IR cannot penetrate through windows, heat accumulates and temperature rises in the room. Extracting the heat costs usually more than 43% of total power usage . While a curtain can reduce heat accumulation and diminish the cost for air-conditioning, the cost for illumination becomes its trade-off. Fortunately, energy-saving glass has provided a promising solution [³,⁴]. It possesses wavelength-selective transmittance and consumes zero energy [⁵,⁶]. Visible light can get into the room for illumination, and thermal radiation in near-IR region is simultaneously blocked. Such wavelength-selectivity has been realized using various sub-wavelength structures [⁷–⁹].

Wavelength-selective transmittance is an intrinsic property of photonic crystals (PCs) which are composed of one-, two-, or three-dimensional periodic structures [¹⁰–¹⁴]. These structures can be generated in many cost-effective ways, self-assembling [¹⁵–¹⁷] for example, to facilitate applications of PC’s. Applications of PCs include optical filters [¹⁸], sensors [¹⁹], and emitters [²⁰,²¹]. Each of them has a bandgap prohibiting the propagation of electromagnetic waves. The bandgap varies with materials and dimensions of components. Moreover, it also depends on incidence direction and polarization. However, PCs have rarely been used for energy-saving glass because each PC has single bandgap and its bandwidth is really narrow.

The objectives of this work are, therefore, to generate multiple bandgaps and realize a prototype of energy-saving glass using PCs. Fabricated PCs should be able to stay on a SiO₂ (normal glass) substrate. The bandgap caused by PCs should fall in the near-IR region to prohibit penetration of the major part of thermal radiation. Self-assembled three-dimensional (3D) PCs will be utilized because of both its fabrication easiness and cost-effectiveness. Both transmittance through a sample and its capabilities of blocking heat will be demonstrated experimentally at the end of this work.

Design and numerical methodology

Bandgap calculation

Figure 1 shows a schematic view of a general 3D PC, having periodically arranged cubes along the x-, y-, and z-direction. a is the period along each direction, and e is the relative permittivity to that of vacuum e₀ (8.854 × 10^-12 F/m). A 3D PC can be in other forms, for example, sphere packing in face centered cubes. They can be fabricated using the self-assembly method, which is much easier than others. Thus, the self-assembly method is employed here for polystyrene spheres to compose 3D PCs. Their photonic bandgaps are predicted via the well-known plane-wave expansion method [²²,²³]. The method is applicable to any 3D PC because it solves Maxwell’s equations for 3D periodic structures analytically.

The plan-wave expansion method is briefly described below. It starts from Faraday’s law and Ampere’s law, which are Eq. (1) and Eq. (2), respectively.

(1)\nabla \times \mathit{E}(r,t)=-{\displaystyle \frac{\mathrm{\partial }\mathit{B}}{\mathrm{\partial }t}},

(2)\nabla \times \mathit{H}(r,t)={\displaystyle \frac{\mathrm{\partial }\mathit{D}}{\mathrm{\partial }t}}+\mathit{J},

where E and H are electric and magnetic field, respectively; B and D are magnetic and electric flux density; J is electric current density, while r and t are position vector and time, respectively.

Solving equations for proposed PCs are facilitated using five assumptions. First, no electromagnetic wave source is inside the PC. Second, all involved materials are linear, isotropic, and homogeneous. Third, magnetic field is homogeneous. Fourth, both electric and magnetic fields oscillate in the form of a sinusoid wave. Finally, the materials involved are non-magnetic. These five assumptions lead to the equations below.

(3)J=\mathrm{0},

(4)\mathit{D}={ϵ}_{\mathrm{0}}{ϵ}_{\mathrm{r}}\mathit{E}\left(\mathit{r},t\right)\mathrm{and}\mathit{B}={\mu }_{\mathrm{0}}{\mu }_{\mathrm{r}}\mathit{H}\left(\mathit{r},t\right),

(5){\mu }_{\mathrm{0}}{\mu }_r=\mathrm{constant},

(6)\mathit{E}\left(\mathit{r},t\right)=\mathit{E}\left(\mathit{r}\right){\mathrm{e}}^{\mathrm{j}\omega t},\mathit{H}\left(\mathit{r},t\right)=\mathit{H}\left(\mathit{r}\right){\mathrm{e}}^{\mathrm{j}\omega t},

(7){\mu }_r=1,

wherem₀ = 4p× 10^-7(N/A²) is the magnetic permeability in vacuum; the subscript r symbolizes “relative,” and j is the square root of (–1); and w is angular frequency. When these five assumptions are substituted into Eqs. (1) and (2), Eq. (8) can be obtained.

(8)\nabla \times \left({\displaystyle \frac{\mathrm{1}}{{ϵ}_{\mathrm{r}}}}\nabla \times \mathit{H}\left(\mathit{r}\right)\right)={\displaystyle \frac{{\omega }^{\mathrm{2}}}{c_{\mathrm{0}}^{\mathrm{2}}}}\mathit{H}\left(\mathit{r}\right),

where c₀ = 3 × 10⁸ m/s is the light speed in vacuum. After a little tedious derivation, Eq. (8) will become Eq. (9). A typical problem needs solving an eigen-matrix.

(9){\displaystyle \sum _{G^{\text{'}}}{\displaystyle \sum _{{\lambda }^{\text{'}}\mathrm{=1}}^{\mathrm{2}}{H}_{G,G^{\text{'}}}^{\lambda ,{\lambda }^{\text{'}}}{h}_{G^{\text{'}}}^{{\lambda }^{\text{'}}}={\displaystyle \frac{{\omega }^{\mathrm{2}}}{c_{\mathrm{0}}^{\mathrm{2}}}}{h}_G^{\lambda }}}

where H is an element of 2 × 2 matrix; h is expansion coefficients; and G and G’ are the reciprocal lattice vectors.

Programs based on MATLAB have been employed to solve Eq. (9) and validated with examples in Ref. [²⁴]. It is then used for the photonic crystals, which are composed of polystyrene and free space, in this work. The inputs are relative permittivity of polystyrene e_r = 2.5 [²⁵] and air e_r = 1, respectively. Each permittivity is assumed constant within the spectral range of interest for simplicity.

Figure 2 displays the band diagram obtained from the codes developed. One inset shows the coordinate defining wave propagation directions. The other inset shows a unit cell and the correlation between period a and sphere diameter d. From Fig. 2, it can be observed that a bandgap exists between 0.59 and 0.63 normalized frequency along the normal direction, L-G [²²]. Because the normalized frequency is also a/l, the bandgap can thus be linked to the diameter of sphere clearly, where l is the incidence wavelength.

Diameter determination for PCs

Major parts of solar radiation are in visible and near-IR regions, while an energy-saving allows transmission of the former but reduces penetration of the latter. For functioning in the visible range, all involved materials shall be transparent. Our PCs are thus composed of polystyrene spheres, which are commercially available in various diameters. A PDMS film is going to hold these PCs on a SiO₂ substrate, and they are also transparent. On the other hand, the diameters of our PCs shall be carefully selected to prohibit near-IR light transmission. Considering the availability of spheres and their bandgaps from Fig. 2, two types of spheres are selected.

Table 1 lists the diameter (d = 508 nm and d = 707 nm) of the selected spheres and their theoretically predicted bandgaps. One bandgap covers 1130 nm≤l≤1210 nm, while the other covers 1572 nm≤l≤1683 nm. Both are in the near-IR region, but they are isolated because spheres are not available in all sizes. Thermal radiation in these two ranges are expected to be blocked if spheres can form PCs successfully.

Fabrication of photonic crystals

Constant-temperature ultrasonic oscillation method for self-assembling PCs

Figure 3 depicts a constant-temperature ultrasonic oscillation fabrication system developed in this work. The system is custom-designed to provide a well-controlled environment for prompt and cost-effective PC fabrication. The system is composed of an ultrasonic oscillator, a thermostatic water bath, a sample holder, and two pumps with pipes. The oscillator generates acoustic waves shaking the sample and its holder. The energy from waves assists self-assembling spheres into a PC. The bath stores water and maintains its temperature at 55°C, higher than room temperature. The warm water not only offers energy assisting PC formation but eliminates uncertainty from surroundings. An example of uncertainty is the raising temperature of oscillator resulting from absorbed acoustic waves. The sample holder prevents the direct contact between the sample and water in the container, while it allows propagation of acoustic waves. Two pumps and pipes construct a circulation sub-system, assuring sufficient amount and constant temperature of water in the oscillator.

Samples of fabricated PC

The fabrication of a PC starts from preparation of the polystyrene water solution. It is filled into a micropipette and dropped on a film of PDMS and a SiO₂ substrate. The PDMS is hydrophobic to benefit self-assembly. The sample is then put into the oscillator for ultrasonic oscillation. In no more than 15 min, all water in the solution evaporates, and a PC sample is generated.

Figure 4 presents the SEM images of fabricated PCs using our system. The diameters of the commercially available polystyrene spheres are 508 nm and 707 nm in Fig. 4(a) and (b), respectively. The diameter of the spheres is identical for each PC sample, and the spheres are periodically aligned within a large area. The compactness and uniformity of the spheres have confirmed the fabrication success of two PCs. The current sample size is 10 mm in diameter, but the system is expandable for larger samples. The current sample size satisfies the measurement requirements in this work.

Results and discussion

Realization of dual bandgaps

Figure 5 exhibits a schematic view of the proposed energy-saving glass prototype. It is composed of two PC samples to utilize their dual bandgaps in the near-IR region. To separate the two PCs, the prototype includes a Teflon ring with a thickness higher than the height of the PC inside. Moreover, the ring is acid-resistant and good for sealing. The PC is thus well protected even after a long-term use as a window in reality.

Figure 6 shows the transmittance (t) spectra through two PC samples and the energy-saving glass prototype at normal incidence. The first major finding is the transmittance suppression due to the bandgap. For each PC sample, a valley is in spectrum, and its spectral range agrees well with the numerical prediction as mentioned earlier. The numerical programs and design strategy are both successful. Second, the t of the prototype is lower than both PC samples within the near-IR region, making it promising to block thermal radiation. Third, the bandgaps of the individual PC also function well for the prototype to further diminish the t in two spectral ranges. The PC sample using 707-nm-diameter spheres can block more radiation than the other sample using 508-nm-diameter spheres because the thickness of the former is larger. Finally, the t through the prototype is lower than 0.3 and the average is less than about 0.1 at 1.0 mm≤l≤2.0 mm. Although the t through the prototype increases monotonically with l, the solar radiation at longer wavelengths are relatively trivial. As a result, the prototype is able to take advantages of the two PCs and fulfill the criteria of energy-saving glass, reducing near-IR penetration.

Radiative heating experiments

Figure 7 displays a testing set-up built for further demonstration of the capabilities of the PC samples and the prototype in maintaining comfort. The set-up is mainly composed of a halogen lamp, a chamber, and a thermometer. A schematic view and relative positions of all elements in the set-up are given in Fig. 7(a). The lamp emits thermal radiation containing both visible and near-IR light. Part of thermal radiation transmits through a window of the chamber. Normal glass, the two PC samples, and the energy-saving glass are mounted as the window one by one. The other sides of the chamber are sealed to mimic a room under solar light. The thermometer measures the air temperature inside the chamber and records the data together with the heating time every minute. Each heating process starts from the room temperature of 28°C and lasts 15 min. The period is considered long enough for the chamber to reach a steady-state. Figure 7(b) is the photo of the set-up for clarity.

Figure 8 shows four experimental results, temperature (T) variation with time (t) within the 15 min after heating. The temperature curve of glass results from a window using a SiO₂ substrate without any PC. Its temperature raises fast and is higher than others. The temperature inside the chamber is 47°C after 15 min heating, which is 19°C higher than room temperature. The temperature profile of PCs are between those of the glass and the prototype because each of them has one bandgap, reducing the penetration of thermal radiation. Accordingly, T after 15 min is lower than 47°C, and the rising speed of temperature is relatively slow. The PC sample using 707-nm-diameter spheres can block more radiation than the other PC sample such that its steady-state temperature is lower. For the spectrum of the energy-saving glass prototype, it is not only the lowest among four but reaches the lowest steady-state temperature of 35°C after 15 min. Moreover, the speed of increment is relatively slow in contrast to that of normal glass. Therefore, it is clear that each of the PC developed can block the thermal radiation partly. The prototype combining two PCs can be a promising candidate as energy-saving glass by maintaining comfortable temperature in a room.

Conclusions

A prototype of energy-saving glass has been successfully realized using dual bandgaps in the near-IR region generated from two PCs. Each PC is composed of polystyrene spheres of identical diameter (d = 508 nm or d = 707 nm) built on a transparent PDMS film above a SiO₂ substrate. A constant-temperature ultrasonic vibration system has been custom-designed for PC fabrication. Measuring normal transmittance through PCs and the prototype has confirmed the bandgap. A radiative heating experiment further confirms capabilities of passive energy-saving and comfort maintaining. The success of this work has largely expanded the application areas of PCs for tailoring radiative properties in multi-bands or a broadband.

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