fdtd simulations inspired by the d aytime passive radiative cooling of … · 2018. 1. 4. · fdtd...

4th International Conference On Building Energy, Environment

FDTD Simulations inspired by the Daytime Passive Radiative Cooling of the Sahara Silver Ant

S.Y. Jeong1, C.Y. Tso1, 2, Y.M. Wong1 and Christopher Y.H. Chao1

1Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology (HKUST), Hong Kong, China

2HKUST Jockey Club Institute for Advanced Study, The Hong Kong University of Science and Technology (HKUST), Hong Kong, China

SUMMARY In the refrigeration cycle, a huge amount of energy is consumed by pumping heat from the cold reservoir to the hot reservoir. However, passive radiative cooling dissipates heat from sky-exposed surfaces to the cold universe by strong thermal radiation within the 8-13 μm electromagnetic spectrum and reflecting radiations elsewhere. This results in the surface temperature being perpetually lower than ambient. It is a potential scheme for dramatically conserving energy for refrigeration and space cooling in buildings. After the discovery of daytime radiative cooling, a wide range of materials have been found promising for an 8-13 μm wavelength range emissive solar reflective cooling device. Here, we consider the thermal selective emitter inspired by the thermoregulatory effect of triangular hairs on Sahara silver ants. FDTD simulations were utilized to optimize the biomimetic surface made of 8-13 μm wavelength range emissive materials such as SiO2 and polydimethylsiloxane (PDMS), and a bottom solar mirror. The result revealed improved emissivity in the transparency window by patterning triangular arrays on the surface.

INTRODUCTION High energy demand for space cooling is a global issue. Nearly 60% of energy consumed in the summer of Hong Kong is due to the air conditioning of buildings (HKSAR 2015). Passive cooling, an indoor temperature cooling strategy without electrical power supply, can bring a tremendous impact as an eco-friendly, energy saving cooling technology offering a novel thermoregulatory scheme for smart environmentally friendly buildings. This energy free cooling technology can further influence aerospace, textile, electronic and photovoltaic systems. The working principle of a passive radiative cooler can be elaborated in two distinct strategies: first, high reflection in the visible and near-infrared spectrum minimizes heat gain from solar radiation; second, strong emission in the mid-infrared spectrum (8~13 μm), enables heat radiation direct to outer space where the temperature is about 3K. Passive radiative cooling below ambient air temperature at night has been demonstrated, however, peak cooling demand occurs during the daytime. Recent studies have shown temperature reduction during the daytime. Raman et al. (2014) recently demonstrated radiative cooling in the daytime with a photonic radiative cooler consisting of seven layers of HfO2 and SiO2. Under direct exposure to sunlight, the cooler was able to reflect 97% of incident sunlight resulting in a net cooling power of 40 W/m2 and a surface temperature of 5 oC below the ambient atmosphere. Chen et al. (2016) simplified the radiative cooler by using three layers of Si3N4, Si and Al, eliminating parasitic heat gain, showing a 60 oC reduction from ambient, theoretically. Furthermore, an

experiment was conducted resulting in a huge temperature reduction of 33 oC below ambient under 24 hours continuous operation. On the other hand, Zhai et al. (2017) developed a selective thermal emitter in infrared wavelengths by incorporating SiO2 micro-particles in a polymethylpentene matrix deposited on Ag film, producing a net cooling power of 93 W/m2. This glass polymer cooler has great cost saving advantage due to its rapid film fabrication rate of 5 m/min. Kou et al. (2017) demonstrated a polydimethylsiloxane (PDMS) coated fused silica mirror which exceeds the performance of a previous multilayer thin film stacked cooler. The cooler provides 127 W/m2 net cooling power during daytime, despite influence of parasitic heat gain from conduction and convection. However, Tso et al. (2017) conducted a field investigation using the photonic radiative cooler of Raman et al. (2014) under Hong Kong’s hot and humid climate. Although the cooler’s temperature was maintained below ambient at night, daytime radiative cooling could not be realized in Hong Kong where the transparency of the atmospheric window is limited due to high humidity. To overcome the excessive heat load due to water molecule emission, extremely strong emission within the 8-13 μm wavelength range is essential for daytime radiative cooling.

Many materials have been found to be strongly emissive in the 8-13 μm wavelength range. However, it has seldom beenconsidered to enhance emission/absorption by geometrymodification. Research has been inspired by the thermalregulatory effects discovered in the Saharan silver ant thatallows the ants to forage during the thermally devastatingdaytime. The triangular prism shaped hairs of the Saharansilver ant, Cataglyphis bombycina, operate as a passiveradiative cooler allowing the ants to discharge excess heatgained from the thermally harsh dessert (Shi et al. 2015). Theunique shaped hair of the ant (Figure 1) allows them to survivein a thermally devastating environment by two heat regulatingeffects. High reflection in the visible and near-infraredspectrum occurs due to enhanced total internal reflectionwithin the triangular hair. The improvement is realised by Mie-scattering that occurs when the wavelength of incidentsunlight and the size of the scattering object are comparable(Bohren et al. 2008). The latter effect, in the mid-infrared rangeof the spectrum where the ant’s blackbody radiationculminates, radiation of heat to the transparent window in theatmosphere is amplified due to the high emissivity of the hair.

In this study, we aim to make use of the thermal regulatory effect of the triangular hairs on Sahara silver ants for application in passive radiative cooling technology. First, we will investigate emission enhancement in the transparency window resulting from the application of the triangular prism structure in a passive radiative cooler. Further comparative study with a conventional flat multi film layered structure

page 45ISBN: 978-0-646-98213-7 COBEE2018-Paper026


cooler will be conducted. This study will be carried out to optimize the triangular structure providing the highest achievable thermal radiation by modifying the geometry, size and number of layers of the triangular prism array. The study represents geometrical manipulation as an alternative method to improve absorption besides various material selections. The structural modification has significance in improving the performance of the passive radiative cooler by downsizing the overall scale of the cooler resulting in less material required but enhancing cooling power. This indicates that the biomimetic radiative cooler could be an attractive energy free solution to reduce air conditioning cost for buildings in the near future.

Figure 1. Triangular prism shaped hair of the Saharan Silver Ant (Shi et al. 2015)

Design of biomimetic passive daytime radiative cooler

In this work, we designed the biomimetic passive daytime radiative cooler with a top window capable of emitting within the 8-13 μm wavelength range together with a bottom Al solar reflector. The thermal emitter is made of SiO2 and PDMS. Both materials are recognised to be strongly emissive/absorptive in the mid-infrared spectrum (Srinivasan et al. 2016). The imaginary part of permittivity of a dielectric medium has a strong correlation with dissipation of energy within the medium, related to absorption (Yu et al. 2010). Both PDMS and SiO2 have a high value of imaginary permittivity within the 8-13 µm wavelength range, resulting in high absorption of the transparency window. Furthermore, the SiO2 substrate wafer (400-500 µm) can be easily sourced and PDMS is a suitable material for fabricating complex structures, such as a triangular shape, which can only be achieved by the nano-printing method. PDMS is deposited on an SiO2 substrate in different geometries so as to study absorption/emission enhancement. Although Shi et al. (2015) reported enhanced reflectivity of triangular hair, the reflection achieved was around ~60%, far below the threshold for preserving the temperature of an object below ambient. Therefore, Al thin film is coated on the back of the SiO2 substrate to improve solar reflection. With Finite Difference Time Domain (FDTD) simulations, we optimized the structure of the biomimetic cooler by considering different geometries, geometry size, substrate layer thickness, number of non-uniform absorber layers. In addition, a comparative study of the emission spectrum of our optimized biomimetic cooler with that of a flat surface was conducted. We used FDTD simulation prior to actual field investigation to optimize geometrical properties of the triangle and the design of cooler that can provide the highest cooling power.

METHODOLOGY FDTD simulations solve Maxwell equations in the time domain with finite difference scheme. In this study, commercial software, Lumerical, is employed for FDTD simulations. Figure 2 illustrates the computational domain, which is a rectangular box of size (width of triangle, 3 µm, 25 um). A periodic unit of the material is situated at the centre of the

computational domain. Dielectric functions of Al, SiO2 and PDMS covering the wavelengths of interest are referred to Kitamura (2007), Rakić (1995) and Srinivasan et al. (2016) respectively. Periodic boundary condition is defined on all lateral planes, whereas a perfectly matched layer condition is defined on both top and bottom planes. Planar incident pulse composed of multiple wavelengths, where the amplitudes are Gaussian distributed, is specified at the incident plane, which is normal to the z-direction. The computational domain is discretised, where the mesh size ∆ is much smaller than the shortest wavelength 𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚 of interest (∆ ≫ 𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚). Time step of simulations is tuned by specifying the stability factor. In this study, we use ∆ = (50 nm. 50 nm, 100 nm) which is slightly larger than ∆ = 𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚

10= 40nm ( 𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚 = 400 nm ) due to the

computational limit and stability factor of 0.99. In the validation section, we show that the mesh size and the stability factor are suitable for reliable simulations.

Figure 2. A cross section of a single periodic unit of the FTDT Simulation model in z-direction. The structure is in order of PDMS triangular prism array, 10 µm silicon dioxide, and 100 nm Aluminum

In FDTD simulations, the emission spectrum of the material cannot be determined directly. But, from Kirchhoff’s law of thermal radiation, emissivity and absorptivity must be equal for each wavelength 𝜆𝜆. Therefore, absorption spectrum 𝛼𝛼(𝜆𝜆) is evaluated. It is defined by the ratio of absorbed power 𝑃𝑃𝛼𝛼(𝜆𝜆) to incident power 𝑃𝑃𝑚𝑚(𝜆𝜆) , i.e., α(𝜆𝜆) = 𝑃𝑃𝛼𝛼(𝜆𝜆) 𝑃𝑃𝑚𝑚(𝜆𝜆)⁄ . By conservation of energy, incident, absorbed, transmitted 𝑃𝑃𝑡𝑡(𝜆𝜆) and reflected power 𝑃𝑃𝑟𝑟(𝜆𝜆) are related by 𝑃𝑃𝑚𝑚(𝜆𝜆) = 𝑃𝑃𝛼𝛼(𝜆𝜆) +𝑃𝑃𝑡𝑡(𝜆𝜆) + 𝑃𝑃𝑟𝑟(𝜆𝜆). In order to determine 𝑃𝑃𝑟𝑟(𝜆𝜆) and 𝑃𝑃𝑡𝑡(𝜆𝜆), planes of reflection and transmission should be defined in the simulation model. On these planes, time dependent solutions of electric field 𝐄𝐄(𝐱𝐱,𝑛𝑛∆𝑡𝑡) and magnetic field 𝐇𝐇(𝐱𝐱,𝑛𝑛∆𝑡𝑡) , where 𝐱𝐱 is the position vector of a point on the measurement plane, ∆𝑡𝑡 is the time step and 𝑛𝑛 is the number of time steps, are recorded. Time domain solutions are transformed into frequency domain via Discrete Time Fourier Transform, which are given by

𝐄𝐄(𝐱𝐱,𝜔𝜔) = ∑ 𝑒𝑒𝑚𝑚𝑖𝑖𝑚𝑚∆𝑡𝑡𝐄𝐄(𝐱𝐱,𝑛𝑛∆𝑡𝑡)∆𝑡𝑡𝑚𝑚 (1)

and

𝐇𝐇(𝐱𝐱,𝜔𝜔) = ∑ 𝑒𝑒𝑚𝑚𝑖𝑖𝑚𝑚∆𝑡𝑡𝐇𝐇(𝐱𝐱,𝑛𝑛∆𝑡𝑡)∆𝑡𝑡𝑚𝑚 (2)

where 𝜔𝜔 = 2𝜋𝜋𝜋𝜋 𝜆𝜆⁄ is the angular frequency and 𝜋𝜋 is the speed of light. Then, Poynting vector 𝐒𝐒(𝜔𝜔) is computed by

𝐒𝐒(𝜔𝜔) = 12

Re∫𝐄𝐄∗(𝐱𝐱,𝜔𝜔) × 𝐇𝐇(𝐱𝐱,𝜔𝜔)𝑑𝑑𝑑𝑑, (3)

where the superscript * denotes complex conjugate. 𝐒𝐒(𝜔𝜔) represents the time-averaged electromagnetic energy flux. In



this study, energy flows in the z-direction only. Hence, x and y-components of 𝐒𝐒(𝜔𝜔) are zero. And, the z-component of𝐒𝐒(𝜔𝜔) through the planes of reflection and transmission gives𝑃𝑃𝑟𝑟(𝜆𝜆) and 𝑃𝑃𝑡𝑡(𝜆𝜆) respectively. The reflection plane ispositioned just upside of the incident plane. Transmittedpower is neglected as Al film is not transparent in theinterested wavelengths. Hence, absorbed power is given bythe difference between incident power and reflected power, i.e.𝑃𝑃𝑎𝑎(𝜆𝜆) = 𝑃𝑃𝑚𝑚(𝜆𝜆) − 𝑃𝑃𝑟𝑟(𝜆𝜆).

VALIDATION Before the biomimetic thermal selective surfaces were studied, a simulation model was built for validation purposes. Chan et al. (2006) studied the thermal selective behaviour displayed by the photonic crystals that made up the top dielectric slab consisting of a pattern of holes and the bottom tungsten slab. The materials are 2D periodic and the size of a periodic unit is 𝐋𝐋 × 𝐋𝐋. The thicknesses of the dielectric slab and tungsten slab are 𝟎𝟎.𝟐𝟐𝐋𝐋 and 𝐋𝐋 respectively. The radius of the holes on the dielectric slab is 𝟎𝟎.𝟒𝟒𝐋𝐋. Dielectric constant of the dielectric slab is set as 5. Dielectric function of the tungsten slab is described by the Drude-Lorentz oscillator model and the model parameters for tungsten are referred to Ordal et al. (1985). The simulated wavelengths range from 0.5 μm to 6 μm. The rectangular mesh is (50 nm, 50 nm, 100 nm) in size, which is approximately 10 times smaller than the minimum wavelength. Time step of the simulations is tuned by the stability factor, which is set to 0.99, ensuring stable convergence. The thermal emission spectrum for 𝐋𝐋 = 2 µm and 𝐋𝐋 = 3.23 µm is shown in Figure 3(a).

We performed 2 simulations for different 𝐋𝐋, i.e. 𝐋𝐋 = 2 µm and 𝐋𝐋 = 3.23 µm. Figure 3(b) shows the simulation results, which are in good agreement with Chan et al. (2006). Despite slightly over-predicted emissivity, emission peaks at nearly the same wavelengths. For 𝐋𝐋 = 2 µm, two emission peaks occur at λ =2 µm and λ = 3 µm . For 𝐋𝐋 = 3.23 µm , two emission peaks occur at λ = 3 µm and λ = 4.2 µm. In conclusion, mesh size of λmin 10⁄ and stability factor of 0.5 are fine enough for reliable simulation results.

Figure 3(a). The thermal emission spectrum for a hybrid 2D-periodic structure consisting of a tungsten slab and a dielectric slab with holes (Chan et al. 2006).

Figure 3(b). The FDTD simulation result for validation of simulation mesh size and time step based on emission spectrum for a hybrid 2D-peridoic structure combined of a tungsten and dielectric slab

RESULTS AND DISCUSSION Optimization parameters for the biomimetic cooler

We have studied four different characteristics to optimize the thermal radiation of the biomimetic cooler. Thickness of the SiO2 thin layer that supports the PDMS triangular array was studied first to investigate the influence of SiO2 thickness on the emissivity of the cooler and to optimize the thickness of the SiO2 bottom substrate. The following study focuses on the structural studies of the PDMS triangle. Three different configurations, geometry of periodic array, size of triangle, and number of layers of triangular array, were studied to optimize the triangular prism. Different geometries of periodic array were considered to compare the emissivity of the triangular structure with other shapes. Emission of different size of triangles was investigated to optimize suitable scale of triangle for the passive cooling effect. Ant hairs are stacked in multi-layers enhancing reflection and emission (Shi 2015), therefore, different number of layers of PDMS triangular arrays were examined.

SiO2 layer thicknesses

Now we turn our focus to the biomimetic thermal selective surface. First, SiO2 is strongly emissive within the 8-10 μm wavelength range. Its significance to radiative absorption/emission must be accounted for quantitatively. Hence, we considered the emission spectra for different SiO2 layer thickness. The top PDMS layer is in triangular form. Two different sides of 8 μm and 11 μm are considered. Figure 4 plots the averaged emissivity in the 8-13 μm wavelength range against SiO2 thickness. The emission becomes stronger with thicker layers of silicon dioxide. This is in accordance with Beer-Lambert’s law that states attenuation of light becomes stronger as the distance of light travelled through a material is increased (Beer 1852). Based on simulations of different thicknesses of SiO2, emissivity of the structure converged constant value at the thickness of 7~8 um. More importantly, the existence of the silicon dioxide layer is more crucial for emissivity due to its strong absorption property in the 8~13 um wavelength range. Typical thickness of the SiO2 substrate is about 500 μm. However, such a layer is too thick for computational FDTD simulations. Thus, in the subsequent simulations, we keep the thickness of SiO2, the PDMS



triangular prism array supporting substrate, at 10 μm, to study the emission enhancement caused by the PDMS triangle.

Figure 4. Averaged emissivity within 8-13 µm of FDTD simulation of PDMS triangular structure at characteristic length of 8 µm and 11 µm with different thickness of silicon dioxide layer from 0-10 µm at every 1 um unit step

Geometries and sizes

Then, we compare the emission spectra for the PDMS absorptive/emissive layer in three different geometries, i.e. uniformly flat surfaces, 1D periodic circular array and 1D periodic triangular array, combined with different characteristic lengths. The geometrical comparison is the main process to confirm the biomimetic surface. A triangular prism array can enhance emissivity compared to a conventional flat layered passive cooler in the transparency window. Furthermore, the reason behind comparing a circle and triangle is to recognize the advantage of the unique triangular ant hair structure over the more widely known hair structure that is a very thin circular rod. Referring to Figure 5, characteristic lengths of flat surfaces, circular array and triangular array are defined by the thickness, diameter and side respectively. For each of the geometries, we varied the characteristic length from 2 μm to 15 μm. Due to Mie scattering, we considered sizes from 2-15 μm to study the scattering effect caused by different sized structures within the 8-13 μm wavelength range. Figure 6(a) and (b) compares the emission spectra in the 8-13 μm range for different geometries with the same characteristic length of 8 μm and 11 μm. With the same characteristic length, the one with triangular PDMS absorbers exhibits the highest emissivity in these wavelengths, followed by circular and flat absorbers. Figure 6(c) plots the averaged emissivity in the 8-13 μm wavelength range against characteristic length for different geometries. It further confirms that triangular arrays show higher emissivity than flat surface and circular arrays, regardless of size. Also, averaged emissivity increases with characteristic length. For the triangular array, averaged emissivity reaches the maximum at about 10 μm. Increasing the length further cannot improve the emissivity significantly.

Figure 5. From left to right: Three different PDMS structures with characteristic length, α. Triangular prism array, circular rod array, and thin plane film.

Figure 6(a). The emission spectrum of circular array, prism array, and flat plane at characteristic length of 8 µm in the wavelength range from 8-13 µm.

Figure 6(b). Emission spectrum of circular array, prism array, and flat plane at characteristic length of 11 µm in the wavelength range from 8-13 µm.

Figure 6(c). Averaged emissivity within 8-13 µm wavelength range of FDTD simulation of three different models (triangular



prism array, circular rod array, and thin uniform film) with different size parameter of 2-15 µm at every 1 µm unit step.

Number of layers of triangular array

The Saharan silver ant has multiple layers of triangularly shaped hair on its upper body to reflect sunlight and emit heat. Multiple layers enhance these processes enabling ants to survive the severe thermal environment. Motivated by multi-layer triangular hairs covering the Sahara silver ants, we studied the emission spectra for different layers of triangular arrays of characteristic length of 2-15 um from 1 to 5. Number of layers was limited to 5 due to computational limits. As illustrated in Figure 7, two different characteristic lengths of 8 μm and 11 μm are compared. Although both show increased emissivity in the 8-13 μm wavelength range with increasing number of layers, enhancement of 1.5% or less can be observed by increasing the number of layers from 1 to 5.

Figure 7. Averaged emissivity within the 8-13 µm wavelength range of FTDT simulation on triangular prism array at characteristic length of 8 µm and 11 µm of different number of layers from 1 to 5

Complex configuration

A single layer PDMS triangular array is a reasonable choice for radiative cooling because of easier fabrication than the multi-layer system. However, a single layer structure shows emissivity minima at a particular wavelength range. For instance, 8 μm array shows the minimum between 11-12 μm, while 11 μm array shows the minimum between 8-9 μm. Combining the arrays of different characteristic lengths together can be synergistic, thereby potentially improving overall emission. We considered three configurations as illustrated in Figure 8. The first two are double layer configurations with the bottom array of 11 μm and top array of 8 μm. In the first design, triangular units in both top and bottom layers are densely packed without any gaps between two adjacent units. In the second design, triangular units in the bottom are densely packed, but separated by 3 μm between each unit. The third is a single layer configuration, in which the triangular units of different sizes are in an alternating arrangement. Figure 9 shows the emission spectra within 8-13 μm wavelength range for the first model from the three configurations that follow. The first configuration showed the highest averaged emissivity in the 8-13 μm wavelength range, which is 0.972. Especially, emissivity in the 8-9 μm and 11-12 μm wavelength range increases significantly. However, the

second and the third configurations do not show unambiguous improvement.

Figure 8. Three different complex structures combined by two different triangular prisms with characteristic length of 8 µm and 11 µm. From the left, a fully packed structure with an upper layer of characteristic length of 8 µm triangle and a bottom layer of characteristic length of 11 µm triangle; middle, a similar structure to the first design but an upper and a bottom triangle share the same centerline resulting in gaps between triangles in the upper array; right, a single layer of two different characteristic length of triangles (8 µm and 11 µm)

Figure 8. Emission spectrum in the wavelength range of 8-13 µm of the first complex model, a single layer of 8 µm characteristic length triangular prism array, and a single layer of 11 µm characteristic length triangular prism array

Al solar mirror

High reflectivity in visible light and near-infrared regimes is essential for the reduction of solar heat gain, which can be achieved by the bottom Al mirror. For all simulation models, we keep the Al mirror layer unchanged, with a uniform thickness of 100 nm. We found that solar reflectivity is independent of the design of the top mid-infrared emitter. Figure 9 shows the full emission spectrum from 0.4-20 μm of the triangular prism array at the characteristic length of 10 μm. The spectral reflectivity is almost the same for all cases, where the average value in 0.4-0.7 μm is about 0.95 and the average in 0.4-2 μm is approximately 0.9. Such high reflectivity is promising for application in radiative cooling.

CONCLUSIONS In this study, biomimetic thermal selective surfaces, inspired by the thermoregulatory effect of triangular hairs on Sahara silver ants, which can be applied in passive daytime radiative cooling, have been investigated. Validated FDTD modelling was conducted to simulate the emission spectra. The top surface made of SiO2 and a PDMS 8-13 μm wavelength emitter and bottom Al solar reflector are optimized by considering the PDMS layer geometry and size, number of layers and combined complex configuration. Table 1 tabulates



the averaged emissivity for some representative cases. Triangular arrays were found to be the best among the three geometries being considered. Averaged emissivity for 8 μm and 11 μm thick uniformly flat PDMS surfaces are 0.8975 and 0.9110 respectively. For single layer triangular counterparts of the same characteristic lengths, emissivity increases to 0.9559 and 0.9600 respectively. In bilayer configuration, emissivity can be further enhanced to 0.9720. By modifying the geometry, averaged emissivity in the 8-13 μm wavelength range can be enhanced by 8.3%, which is significant for the development of an ultra-powerful radiative cooler.

Table 1. Averaged emissivity of the 8-13 µm wavelength range of different geometry and number of layers at characteristic length of 8 µm and 11 µm and three different complex models

Model Configuration Averaged Emissivity (8~13um)

Flat plane characteristic length 8µm

0.8975

Flat plane characteristic length 11µm

0.9110

Single layer circular rod characteristic

length 8µm 0.9114

Single layer circular rod characteristic

length 11µm 0.9256

Single layer triangular prism characteristic length 8µm

0.9559

Single layer triangular prism characteristic length 11µm

0.9600

Double layer triangular prism characteristic length 8µm

0.9667

Double layer triangular prism characteristic length 11µm

0.9674

Complex model 1 0.9720



ACKNOWLEDGEMENTS Funding source for this research is provided by the Innovation and Technology Support Programme via account ITS/013/16 (Innovation and Technology Fund), and also by the Hong Kong Research Grant Council (RGC) via Collaborative Research Fund (CRF) account C6022-16G.

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