Porous SiO2 Hollow Spheres as a Solar Reflective Pigment for

Apr 12, 2017 - The SiO2 shell structure undergoes a change with an increase in its thickness: from a continuous network to an amalgamation of nanopart...
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Porous SiO2 Hollow Spheres as a Solar Reflective Pigment for Coatings Zheng Xing,† Siok-Wei Tay,‡ Yeap Hung Ng,† and Liang Hong*,† †

Department of Chemical & Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, 119260 Singapore Institute of Materials Research and Engineering, Agency for Science, Technology and Research, A*STAR, 3 Research Link, 117602 Singapore

‡

S Supporting Information *

ABSTRACT: This study starts with the synthesis of silica hollow spheres (HSs) by utilizing in situ synthesized polystyrene (PS) microspheres as the template for the deposition of a silica (SiO2) shell, followed by a slow gasification step in air to remove the PS core. The size of HS and the thickness of the porous SiO2 shell are tuned by varying the synthesis conditions of the PS latex and those of the sol−gel deposition, respectively. Various HS powder samples are characterized by ultraviolet−visible−near infrared (UV−vis−NIR) spectroscopy to determine their diffuse reflectance. Furthermore, they are used as the filler in an acrylic polymer matrix for the measurement of solar reflectivity on a solar spectrum reflectometer. It turns out that both cavity size and the structure of the SiO2 shell are influential in the reflection of NIR and UV−vis light, respectively. In addition, this study examines the effect on solar reflectivity of a selected metal oxide with a SiO2 HS. In conclusion, the cavity size of the HS has a strong impact on the reflectivity to NIR light whereas the shell itself affects the reflection of UV-blue light. KEYWORDS: silica hollow spheres, nanoshell, solar light reflectivity, cavity effect, coating

1. INTRODUCTION A solar reflective coating decreases or prevents heat radiation from entering buildings or automobiles through reflecting most of the electromagnetic (EM) radiation back to the atmosphere, known as albedo. This solar heat shield contributes to lowering the energy consumption for operating air-conditioners. According to the American Society for Testing and Materials (ASTM) standard, visible light (0.4−0.7 μm) carries 43% of energy and NIR radiation (0.7−2.5 μm) carries 52% of energy.1 The solar reflective coatings currently available in the market employ fine powders of single or mixed-metal oxides, like their traditional application as pigments for enhanced paints and coatings,2 as the NIR reflective component in various polymer matrices.3−6 Among these inorganic oxides, rutile TiO2 is the most widely used white pigment in paint and sunscreens because of its high reflectance in the visible−near infrared (vis− NIR) region (400−2500 nm) and strong absorbance in the near UV.4 Besides the high refractive index (RI) value (2.73) of rutile TiO2, Dupont’s study on Ti-Pure shows that the sum of light scattered at all wavelengths (λ) is maximized to achieve the largest white opacity when rutile TiO2 has a mean size of about 0.2 μm because it is close to the middle of the visible spectrum ∼550 nm. This reflects the fact that particles should have sizes one-half of the λ desired to be scattered. In addition to a high RI and an appropriate particle size distribution that could tune into the light waves, the shapes and structures also affect the back scattering of light. 7 Designing particle morphology, tuning the surface composition of particles, and © 2017 American Chemical Society

implementation of intra-particle voids are useful measures to enhance light reflective efficacy.4,8−10 With the exception of solid particles, hollow sphere (HS) particles, with sizes comparable to the wavelength range of visible light and nanoshells, display noticeable visible-light reflection.11,12 These submicron HS particles are synthesized by using polystyrene (PS) microspheres as the sacrificial core template. Additionally, HSs with the shell constructed by silica sol particles have been found to possess high reflectivity in the UV and visible-light ranges.13 Regarding the application of hollow silica spheres in near infrared (NIR) reflective coatings, 3M glass bubbles with average diameters in the range from 30 to 150 μm are used as a typical demonstration. The layer packed by these glass bubbles shows intense reflectance in the NIR range (0.3−2 μm). Although a flat glass thin film has a relatively low effective RI and a high transmittance to vis−NIR radiations,14 the fact that hollow glass bubbles exhibit high vis−NIR reflectivity could be attributed to light scattering on the bubbles that results in a strong cross-polarized component near the backward direction.15 However, 3M glass bubbles (30−150 μm) obviously do not match the λ of vis−NIR light (0.3−2.0 μm) as the efficacy of Mie scattering requires particle sizes to be approximately comparable with the λ of incident light.16 This type of hollow bead may rely on its inner concave surface and a large Received: December 29, 2016 Accepted: April 12, 2017 Published: April 12, 2017 15103

DOI: 10.1021/acsami.6b16760 ACS Appl. Mater. Interfaces 2017, 9, 15103−15113

Research Article

ACS Applied Materials & Interfaces

The first part of the work focuses on the study of the shell matrix of HS300-t, where t represents the relative shell thickness determined by the TEOS dose used. The SiO2 shell structure undergoes a change with an increase in its thickness: from a continuous network to an amalgamation of nanoparticles, as shown in Scheme 1, with increasing ratio of TEOS

difference in RI between the wall and void to reflect light, which results in spreading of light and hence subsequently facilitates light scattering on the external surface of the beads. Moreover, the understanding of light scattering by a nanoshell of a HS has been correlated with the polarization of the electric dipole.17 A recent study has shown that the radius-to-shell thickness ratio of hollow TiO2 spheres (0.2 μm) is critical to achieving the maximum scattering coefficient with respect to a particular λ of NIR light.18 Besides the radius-to-shell ratio, the porous properties and chemical composition of the nanoshell are also important to light scattering. This work investigates how the size of the porous silica HSs and their nanoshell structures influence solar reflectivity. The HS samples are either packed as a thin powder layer or uniformly distributed in an acrylic polymer matrix in a 1:1 volume ratio in the form of a coating film. The former specimen is for the detection of diffuse reflectance for ultraviolet−visible (UV−vis) spectroscopy, whereas the latter one is for checking reflectivity to different light sources on a solar spectrum reflectometer. In this study, the synthesis of the HSs is the key step. There are a few existing approaches for making HSs: (i) triple W/O/W emulsion, in which a W/O (water-in-oil) silicate emulsion prepared in advance serves as the template and then another continuous aqueous phase provides the precipitant for the silicate that is initially encapsulated by the oil layer;13,19 (ii) alcoholic dispersion polymerization, where a silica sol coexists with styrene in methanol and the sol particles undergo condensation on the PS beads formed in situ;12 (iii) the selective dissolving of a porous silica core from the nanoparticles with a solid silica shell/a porous silica core by incubating the particles in a phosphate buffered saline at 65 °C for one day. This treatment takes advantage of the higher reactivity of the core to the etchant than the shell;20 (iv) the use of PS microspheres prepared by soap-free emulsion polymerization or a copolymer based on PS spheres21,22 as templates, on which a positively charged surface is prepared because this surface suits the sol−gel deposition of tetraethyl orthosilicate (TEOS). The positive surface of the microsphere is normally formed by grafting or coating with a thin hydrophilic layer of weak H+ acceptors, which could be a polymer, such as poly(vinylpyrrolidone) (PVP),23−25 or a fragment of the free radical initiator, such as α,α′azodiisobutyramidine dihydrochloride (AIBA).26 It is important to stress that the detailed preparation conditions of the HSs, including the final incineration step to remove the PS template, will profoundly affect the microstructure of the shell that eventually forms. In this study, we use the approach developed by Nandiyanto26 to prepare HS300 (d = ∼300 nm). However, the synthesis of the PS template and the growth of the SiO2 nanoshell are done in one pot instead of the two-pot protocol as originally reported. Furthermore, to synthesize the smaller HS50 (d = ∼50 nm), an emulsifier is required in the same polymerization system as above to realize the desired size. Nonetheless, for the synthesis of the larger HS2000 (∼2000 nm), the PS beads are synthesized using the dispersion polymerization method in ethanol and the subsequent deposition of SiO2 on the PS beads is conducted separately. In the above preparations, the influence of the three PS templates on the nanoshell formed mainly comes from the relative amount of TEOS versus that of the PS template as both the gelation extent of the silica sol27 and the ease of gas release from the template removal step play key roles.

Scheme 1. Schematic Illustration of the Variation of the Shell Matrix Structure of HS300 with Increasing Thickness

added to the PS template. This variation in shell structure significantly influences both the diffuse UV−vis−NIR reflectance and solar reflectivity profile. The second part of the work reports the incorporation of a small amount of TiO2 or ZnO into the SiO2 shell matrix of HS300, motivated by their greater refractive indices than that of SiO2. The last part investigates the influence of HS size on solar reflectivity, which is in effect related to the reflection and refraction on the concave spherical surface, where the curvature and shell thickness affect the result. In short, submicron to micron HSs with an amorphous silica nanoshell demonstrate diverse capabilities to reflect solar light.

2. EXPERIMENTAL SECTION 2.1. Materials. Styrene was purchased from Sigma-Aldrich and passed through an inhibitor−removal column before use. All other chemicals were used without pre-treatment: ethanol (analytical grade; Merck), PVP (average Mw 40 000; Aldrich), AIBA (97%; Aldrich), ammonium hydroxide (25%; Aldrich), TEOS (≥98.0%; Fluka), Llysine (Sigma-Aldrich), toluene (J.T. Baker, A.C.S), methyl ethyl ketone (MEK) (analytical grade; Merck), methyl methacrylate(main)−ethyl acrylate copolymer (Tg = 36 °C; Paraloid B-82, Rohm&Haas), titanium (IV) butoxide (Aldrich, reagent grade, 97%), zinc acetate (99.9%; Sigma-Aldrich), silver nitrate (>99%; SigmaAldrich), and sodium hydroxide (≥97%; Sigma-Aldrich). 2.2. Preparation of HSx (x = 50, 300, and 2000). 2.2.1. Synthesis of Submicron HS300 Microspheres by Soap-Free Emulsion Polymerization. In a typical preparation, AIBA (23.6 mg) and DI water (50 mL) were fed into a one-neck round-bottom flask. The mixture was stirred for 5 min with Ar bubbling before the introduction of styrene (1 mL) to form an emulsion. The stirring (500 rpm) was continued for another 20 min and then the flask was immersed into an oil bath at 65 °C to initiate the polymerization. After 20 h, the Ar supply was stopped and the oil bath was cooled to 60 °C to prepare for the subsequent sol−gel reaction. To this dispersion system, an 15104

DOI: 10.1021/acsami.6b16760 ACS Appl. Mater. Interfaces 2017, 9, 15103−15113

Research Article

ACS Applied Materials & Interfaces aqueous solution of lysine (2 mL, 3.65 wt %) and a given amount of TEOS (0.8, 1.6, or 3.2 mL) were added. The sol−gel reaction was allowed to take place for another 20 h to carry out the deposition of a silica layer on each PS microsphere denoted by PS@SiO2. The resultant core−shell particles were collected by centrifugation and washed with DI water for a few cycles. It may be noted that a certain portion of silica sol formed stayed in the water phase of the final latex dispersion, and was transferred to the supernatant liquid during the centrifugation. After drying, the powder was heated (at 2.5 °C/min) to 550 °C, at which temperature the sample was maintained for 4 h to gasify the PS cores and to allow for consolidation of the silica shell. The hollow microspheres obtained from this one-pot reaction system have diameters of ca. 300 nm, and are denoted by HS300-t in which the suffix t stands for the amount of TEOS in volume that was added to form the SiO2 shell. Three volumes of 0.8, 1.6, and 3.2 mL were used. Sample HS300-1.6 was selected to enhance the density of its SiO2 shell by raising the calcination temperature by 100 °C, that is, to 650 °C. 2.2.2. Synthesis of Nano HS50-1.6 Using a Proper Emulsifier. CTAB (50 mg) was introduced into the above styrene dispersion system to form micelles for the polymerization of styrene to take place inside. Consequently, PS nano latex particles with an average diameter of ca. 50 nm were produced. After this, TEOS (1.6 mL) and lysine aqueous solution (3.65 wt %) were added to the polymerization system to construct a SiO2 shell on each PS nano particle under the same sol−gel deposition conditions as described above. The final heatremoval step to form HS50-1.6 was also the same as the above preparation. 2.2.3. Synthesis of Micron HS2000-3.2 by the Conventional TwoPot Approach. Styrene (5 mL) was introduced into an alcoholic solution containing PVP (0.6 g) and AIBA (0.04 g) in ethanol (40 mL) in a one-neck round-bottom flask. The solution was magnetically stirred (at 500 rpm) with Ar bubbling for 20 min and subsequently the flask was immersed into an oil bath at 70 °C to undertake polymerization. After 24 h, the polymerization suspension was centrifuged to separate the PS microspheres (ca. 2 μm) from the liquid phase. The solid was purified in ethanol and recovered by centrifugation, and this process was repeated three times. Successively, a given amount of the PS beads (e.g., 1 g) was dispersed in a liquid medium consisting of 1.9 mL of DI water and 93.6 mL of ethanol with the aid of sonication for 5 min. To this suspension, 1.3 mL of ammonia and 3.2 mL of TEOS were added subsequently to start the sol−gel deposition. After 48 h, the PS@SiO2 beads were purified by a few cycles of centrifugation and washing. The final heat-removal step to form HS2000-3.2 was the same as above. The above TEOS dose is the minimum required to sustain the HS structure in the subsequent gasification of the 2 μm PS-core template. 2.3. Doping the Nano SiO2 Shell Matrix of HS300-1.6 with TiO2 and ZnO. 2.3.1. Incorporation of TiO2 into the SiO2 Matrix To Form a Nanocomposite Shell. PS@SiO2, the precursor for HS3001.6, was the starting material for this preparation. PS@SiO2 (0.1 g) was dispersed in 20 mL of ethanol by sonication. To the resulting suspension, 1 mL of H2O and 20 mg of acetic acid were introduced as the catalyst for the sol−gel reaction. Following this, titanium nbutoxide (0.1 g) in 20 mL of ethanol was added into the suspension. The resulting suspension was stirred at 50 °C for 20 h to allow generation of the TiO2 sol particles and their in situ settling into the silica shell of PS@SiO2 where the gelation of TiO2 sol subsequently occurred. After that, the resulting TiO2-PS@SiO2 powder was washed in ethanol and centrifuged. Lastly, the HS300-1.6-TiO2 powder was obtained through calcination in air at 550 °C for 4 h. The energydispersive X-ray (EDX) analysis gives a Si/Ti atomic ratio of 2.8:1. 2.3.2. Incorporation of ZnO into the SiO2 Matrix To Form a Nanocomposite Shell. Zn(Ac)2·2H2O (0.11 g) and 40 mL of 2propanol in a 100 mL one-neck round-bottom flask were stirred at room temperature for 10 min to form a dispersion. The flask was then immersed in an oil bath at 55 °C with stirring for 1 h to form a clear solution. Subsequently, a dispersion of PS@SiO2 (same powder as used above) in 10 mL of DI water was added into this solution. After stirring for 20 min to form a uniform suspension, the mixture was

cooled down to room temperature. A 2 mL NaOH aqueous solution (0.2 M) was injected into the suspension as a hydrolysis catalyst of the zinc salt. The flask was then put back into the 55 °C heating bath to conduct the hydrolysis for 20 min. The resulting suspension was centrifuged and washed using water and ethanol, respectively. Finally, HS300-1.6-ZnO was obtained by the same calcination treatment as above. The EDX analysis gives a Si/Zn atomic ratio of 11.9:1. 2.4. Fabrication of the Composite Coating via Embedding HSx in an Acrylic Matrix. The volume of HSx used approximately equaled that of its precursor, PS@SiO2, because the removal of the PS core does not cause a noticeable change in volume. Furthermore, the volume of the PS core basically dominates the volume of PS@SiO2. In addition, as PS has a similar mass density to B-82 acrylic resin, to achieve 50 vol. % of HSx in the coating composite wherein the acrylic resin constitutes the matrix, the required amount of HSx to mix with the acrylic resin is obtained from PS@SiO2 with exactly the same amount as the acrylic resin used. Experimentally, 1 mL of the formulated B-82 solution (4%) in a binary toluene−MEK solvent (v/v = 1) was mixed with HSx powder left behind from calcining 0.04 g of PS@SiO2 powder by gently stirring the mixture under ambient conditions until an ink-like uniformity was achieved. After that, the resulting coating solution was spread on a glass slide (1 in. × 1 in.) and the liquid film was dried at 80 °C for 24 h. To measure the solar reflectivity of a composite film, three samples were used to assure precision of the data. Additionally, a control sample was checked by using solid silica spheres (SS300) as filler that have the same size as HS300 instead of HS300-1.6. In this control sample, the amount of SS300 used is higher than that of HS300-1.6 so as to keep the same vol. % in both samples. 2.5. Characterization. 2.5.1. Structural Characterization. IR spectroscopy (Bio-Rad Excalibur FTS-3500 FT-IR spectrometer) was employed to verify the nanoshell structure. Transmission electron microscopy (TEM, JEOL 2100 LaB6TEM) was employed to examine the diameter and shell thickness of the HSx samples. The EDX mapping mode of TEM was also used to obtain the distribution of metal elements in the shell of HS300-1.6. The HSx−acrylic composite coating structures were observed by field emission scanning electron microscopy (FE-SEM, JEOL JSM-6700). In addition, the FE-SEM images (at 15 000×) of the PS and PS@SiO2 samples were taken to perform direct measurements of the sizes of the spheres, by which two particle size distribution curves were plotted versus their number %. The Brunauer−Emmett−Teller surface area and pore sizes of HSx were determined on an adsorption instrument (Quantachrome Autosorb 1-C). Thermogravimetric analysis (TGA, Q50) was used by ramping to 900 °C at 10 °C/min under a purge of air (50 mL/min) to determine the wt % of the SiO2 shell in a PS@SiO2 precursor. The ζ potential of the HS300-t spheres was measured on a Malvern Zetasizer Nano ZSP system. To conduct this measurement, a uniform translucent suspension containing 0.4 wt % of a type of HS300-t in water (pH 6.603) is prepared by sonication for 20 min. Subsequently, the suspension (∼1 mL) is injected into a cuvette with electrodes for taking the ζ potential values of the particles. This procedure is repeated three times to assure precision of the readings. The smallangle X-ray scattering (SAXS) analysis was conducted on a Xenocs Nano-inXider instrument under MR mode (medium resolution, beam size = 800 μm, flux = 50 mph/s). The incident light was a Cu Kα beam, whose wavelength is 1.54189 Å and the exposure time for each specimen was 10 min. The background effect of the tape used to load the powder sample onto the SAXS holder was subtracted by using software Foxtrot 3.3.4. 2.5.2. Determination of the Absorbance and Total Diffuse Reflectance of the HSx Samples. This was conducted by UV−vis− NIR spectroscopy (Shimadzu 3600) in the wavelength range from 200 to 2500 nm. The testing specimen was prepared by the following procedure: the reference is made from a given amount of BaSO4 powder, introduced in a cylindrical holder and pressed by a plunger to form a standard white disc. The testing sample is stacked to another BaSO4 disc (substrate) made in the same way. The reflectance measurement is conducted by placing the sample in front of the incident light window and the light reflected from the sample is 15105

DOI: 10.1021/acsami.6b16760 ACS Appl. Mater. Interfaces 2017, 9, 15103−15113

Research Article

ACS Applied Materials & Interfaces concentrated on the detector through a sphere with a barium sulfatecoated inside. The back reflected, diffusely scattered light (some of which is absorbed by the sample) is then collected. The standard white disc is scanned to obtain the reference reflectance, namely, the baseline. Then, the diffuse reflectance obtained from the sample is the relative reflectance with respect to the reference reflectance, which is taken as 100%. Thus, it is possible that the sample shows a reflectance higher than the BaSO4 reference in a certain λ range. 2.5.3. Measurement of Solar Reflectivity Profile of HSx−Acrylic (B-82) Composite Films. This evaluation was conducted on a solar spectrum reflectometer (SSR-6; Devices and Services Company). The reflectometer was calibrated by a blackbody cavity with zero solar reflectance, as well as by a smooth and dense white tile with the designated reflectance reading of 0.859 at the solar irradiance b891 (ASTM E891-87 air mass 1.5 beam normal).28 When conducting the measurement, a sample is subjected to irradiation by a light source and the reflected light is detected by four surrounding detectors to receive IR (with the central λ at ∼850 nm), red (∼650 nm), blue (∼500 nm), and UV (∼350 nm) rays with the color temperature of 3125 K plus two other IR and red detectors to receive rays with the lower color temperature of 2300 K. The reflectivity readings are then plotted versus these light sources, respectively.

hollow concave surface due to a sharp drop in RI from the amorphous silica to the air filling the hollow chamber, which promotes the diffuse reflection on the convex side of the HS. This effect works for the light with λ longer than the size of the vacant chamber.11 The TG analysis (Figure 2) of the PS@SiO2 precursor shows an increase in SiO2 content in the HS300-t series in the order

3. RESULTS AND DISCUSSION 3.1. Effect of the SiO2 Nanoshell Structure on Solar Reflectivity. This study starts by validating the advantage of the hollow spherical structure over its solid counterpart in reflecting solar light and then investigates the effect of shell structure on solar reflectance. The series of 300 nm sized microspheres (HS300-t in Section 2.2.1) was chosen to conduct the examination as this typical particle size is facile to realize through combining the soap-free emulsion polymerization and sol−gel reaction together in one pot. Meanwhile, the most abundant PS cores and the corresponding PS@SiO2 core−shell spheres, which are the precursors for HS300-1.6, show a difference in diameter of ca. 50 nm according to their particle size distribution profiles (Figure S-1 in the Supporting Information). The control sample, SS300, which is the solid SiO2 microsphere, displays an obviously lower and decreasing diffuse reflectance with increases in λ from red to NIR light (λ = 700−2500 nm) (Figure 1), but it maintains a higher

Figure 2. TGA traces of the three PS@SiO2 precursors that show different weight retention rates, which are 51.2, 42.3, and 37.7 wt % of SiO2, respectively.

from HS300-0.8, HS300-1.6 to HS300-3.2. The TEM investigation reveals the impact of SiO2 content on particle size (Figure 3), that is, HS300-t particles show a larger size with increasing t: 294 nm (t = 0.8), 318 nm (t = 1.6), and 357 nm (t = 3.2), respectively. A careful inspection of the TEM images of these three HS300-t samples also shows that their shell layers follow the order of thickness: HS300-0.8 ≈ HS300-1.6 > HS300-3.2 in the range of 10−20 nm. Compared with the silica sol deposition layer in the PS@SiO2 precursor (Figure S-1), a drastic decrease in thickness occurs due to condensation and agglomeration through the PS-core removal process. It is clear that the increase in particle size is not related to the SiO2 shell thickness but rather the expansion of the cavity caused by the gasification of the PS core. The general trend should be that the thicker the initial SiO2 deposition layer (t value) on the PS beads, the larger the expansion, which is related to the pressurizing of gas enclosed during the burning process. Consequently, the changes involve the size of the vacant chamber, the thickness of the shell layer, and even the shape of the HS300-3.2 particles. With the exception of the hollow chamber size, the morphology of the SiO2 shell is crucial to the vis−NIR reflectance. According to the TEM images (Figure 3a2−c2), HS300-0.8 reveals a folding network morphology with numerous curving fringes, which is likely formed through linear coupling of sol particles to form curving fringes and twodimensional extensions of SiO2 tetrahedra at the fringes. HS300-1.6, however, shows a uniform shell consisting of incipient nanoparticles ( HS50-1.6, in the UV range because HS300-0.8 mostly matches the λ of light and therefore prompts the strongest Mie scattering. This figure also shows that the diffuse reflectance profiles of these three HS samples become similar for red light (λ = 700 nm) but HS2000 overtakes HS300 after λ > 1500 nm. As concluded from the previous discussion, Mie scattering from

Figure 9. TEM images of HS300-1.6-TiO2 (a) and HS300-1.6-ZnO (b) and their respective EDX mapping modes showing the distribution of Si with Ti or with Zn (below TEM image).

Figure 10. Diffuse reflectance spectra of HS300-1.6 and the samples derived from incorporating ZnO or TiO2 into the SiO2 shell.

Furthermore, as determined by solar spectrum reflectometry, both acrylic coatings containing the two composite shell 15110

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Figure 12. TEM images of the three HS samples with various diameters of concave chamber as well as shell thickness.

Figure 14. Solar reflectivity profiles of the acrylic coatings containing the three HS samples as pigment: impact of the size of the concave chamber.

Figure 13. Diffuse reflectance spectra of HS samples with different concave chamber volumes and shell structures.

the external surface of the HS is more prominent relative to that of the hollow chamber in the packing layer of spheres, which is required by diffuse spectroscopy. By inspecting the TEM images of these three HS samples and applying the same calculation method used above for obtaining nanoshell density, the shell density values of these three HS samples follow the order of HS50 ≫ HS300 > HS2000. It is because of this that the HS50 powder packing layer, despite comprising even smaller HSs, displays only a marginally weaker diffuse reflectance profile in the red−NIR range than that of the other two. The size effect of the HSs becomes more apparent when they are distributed in the acrylic matrix (v/v = 1) according to the solar reflectivity profiles of the acrylic coatings (Figure 14). As indicated before, this is attributed to the contribution of light reflection and refraction inside the hollow chamber of the individual HS particles. Consequently, the preference for a larger hollow chamber in order to attain a higher solar reflectance is obvious, according to the sequence of the reflectivity profiles of the three coatings. Regarding this conclusion, Lee et al.30 developed an extended Mie’s scattering

model on the basis of hollow TiO2 spheres (