During the last decade, global warming has led to climate change and has triggered more extreme weather events, hotter heat waves1, drier droughts2, colder winters3, and larger storm surges4, endangering the survival of flora and fauna on Earth, including human beings. To achieve the Paris Agreement aims, it will be necessary to strictly limit the total amount of cumulative carbon emissions5,6,7,8. On the other hand, particulate matter (PM) generated by human activities not only pollute the air, but also affect Earth’s radiation budget9. The radiative effect of PM is the opposite of that of greenhouse gases. The direct scattering of short wavelength solar radiation by anthropogenic PM particles increase planetary albedo, thereby exerting a cooling influence on the planet10,11. The global mean radiative forcing due to aerosol–radiation interactions is ~−0.35 W m−2; aerosol–cloud interactions is ~−0.45 W m−2; greenhouse gases is ~+2.83 W m−2 12.

Anthropogenic PM includes secondary organic aerosols and secondary inorganic aerosols (SIA), the main components of SIA are sulfate and nitrate13,14,15. SIA particles are taken as the portion of Aitken and Accumulation mode particles16,17. In previous studies, it was concluded that sulfate also absorb longwave radiation, but the aerosol radiative effect is generally small because the opacity of aerosols decreases in longer wavelengths of infrared (IR) regime11. The major natural sources of ambient PM, such as marine aerosol, mineral dust, Saharan dust, smoke plumes, and their mixtures have been found to enhance the greenhouse effect18,19,20,21,22,23,24. Recently literature found that the dust in the atmosphere is substantially coarser than represented in current global climate models. They also found the contribution of very coarse dust (diameter ≥5 μm) was underestimated, and the coarse particles could cause warming of the atmosphere24. More recently, they stated that climate models consistently underestimate the amount of coarse dust in the atmosphere, and the climate model must be revised25. The improved description of the dust size distribution and its vertical distribution, as well as the IR optical properties, are important for a reliable estimate of its radiation effects23.

The atmosphere often contains a mixture of different types of PM particles, and the mixing process leads to change in sulfate and mineral dust loads, thus altering their impact on the atmospheric radiation. Transmission electron microscopy (TEM) has been used to observe the size, structure and composition of individual fine particles, which is essential for assessing the radiation properties of PM particles and understanding their climatic effects26,27. It has been observed that mineral dust particles often get coated with sulfates and other soluble materials28. The fine (PM2.5) and coarse (PM10) particles were intended to apply to the two major atmospheric particle distributions which overlap in the intermodal size range between 1 and 3 μm17,29. The interaction of the composite PM particles with atmospheric radiation may be different from that of homogeneous PM particles. Theoretical analysis of the relationship between various types of PM mixtures, particles sizes, absorption coefficients, and wavelength are important for the investigation on radiative properties and climate modeling. The atmospheric window offers a direct and strong driving force to dissipate heat into space in the form of thermal radiation under appropriate atmospheric conditions30,31,32,33,34. The application of radiative cooling as a passive cooling option for buildings has a great potential to compensate the problems raised by global warming35,36. The PM in the atmospheric window would affect the absorption and scattering effects of thermal radiation37.

In this paper, we discuss the thermal radiation properties of sulfate and SiO2/sulfate core/shell mixture particles in atmospheric window, including ED and MD resonance behavior. We also used the three-dimensional finite difference time domain (3D-FDTD) method to simulate the electromagnetic fields inside and around PM particles with various sizes and core/shell structures. In this study, we used the World Health Organization air quality guidelines values to simplify the calculation of thermal radiation power density changes in a clear atmosphere with and without PM particles. These calculations of power density changes preclude any differences in geographical and seasonal distributions. From the conceptual experimental results, it was found that different optical properties related to particle size have a significant effect on the thermal emissivity, potentially affecting the temperature of the surrounding environment.

Results and discussion

The atmosphere has a highly transparent window for IR wavelengths in the range from 8 to 13 μm [the so-called first infrared atmospheric window (IRW1)] and a relatively transparent window for IR wavelengths in the range from 16 to 24 μm [the so-called second infrared atmospheric window (IRW2)]; they are highlighted by the light-cyan and yellow areas, respectively, in Fig. 1a. According to Planck’s law and Wien’s displacement law, when the surface temperature is 250, 300, and 350 K, the corresponding maximum wavelengths λmax of the thermal radiation are 11.51, 9.50, and 8.25 µm, respectively. These thermal radiation peaks from the Earth’s surface coincidentally fall within the IRW1. For these same temperatures, ~31, 38, and 41%, respectively, of the thermal radiation energy distribution is concentrated in IRW1, and ~29, 24, and 20%, respectively, in IRW2. The higher the surface temperature, the greater the effect of IRW1 on thermal radiation; furthermore, the effect of IRW1 will also be greater than that of IRW2. This feature of IRW1 permits heat to dissipate through thermal radiation emission, with the potential to provide a passive cooling mechanism for the Earth.

Fig. 1: Atmospheric IR absorption spectra and infrared absorption spectra of sulfate and nitrate.
figure 1

a Black-body emission curves of the Earth at various temperatures (black curves), with atmospheric IR absorption spectra at an air mass of 1.0 (gray area) as a reference. be IR absorption spectra of ammonium sulfate (NH4)2SO4, sodium sulfate (Na2SO4), ammonium nitrate (NH3NO3), and sodium nitrate (NaNO3) in the wavelength range from 4 to 20 µm (Recalculated from Sigma Library of FT-IR Spectra).

A recent report displays that the main constituents of both PM10 and PM2.5 particles are generally organic matter, sulfate, and nitrate38. Figure 1b–e present the IR absorbance spectra of the major components of SIA—(NH4)2SO4, NH3NO3, Na2SO4, and NaNO3, respectively—in the wavelength range from 4 to 20 µm39. Table S1 of Supplementary Note 1 lists the IR absorption bands of (NH4)2SO4 and Na2SO4 in IRW140,41,42. The \({\upsilon }_{3}\)(SO42−) modes of (NH4)2SO4 and Na2SO4 are strong absorption bands in IRW1 and would block heat transfer of thermal radiation to space. The radiative forcing caused by sulfate from fossil fuel and biofuel emissions has been estimated to be −0.4 W m−2 (range: −0.6 to −0.2 W m−2); for nitrate, it is estimated to be −0.11 W m−2 (range: −0.3 to −0.03 W m−2); the value for ammonium is included within the sulfate and nitrate estimates12. The effect of PM on global climate is uncertain because the effect of PM can be to cool or to warm, depending on its optical properties. In this study, we chose (NH4)2SO4 for analysis because it is one of the major species of SIA, and because it features a strong absorption band and induces scattering in IRW1.

Comparison of absorption efficiency (Q a) for different sizes of sulfate particles

Figure 2a, b presents the absorption cross-section (Ca) and absorption efficiency (Qa) [where Qa is the normalized Ca to the cross-section area of the particles] contours of (NH4)2SO4 spheres, calculated by Mie theory, for wavelengths in the range from 4 to 20 µm, and for particle diameters (Dp) ranging from 0.1 to 10 µm (see Supplementary Note 2 for definitions of Qa and Ca). The value of Ca becomes larger as the particle size increased, and is more obvious than 5 µm. In the normalized Qa contour, all of the particle sizes resulted in three bands, corresponding to the three IR active vibration modes, at wavelengths of ~7, 9, and 16 µm. Two strong absorption bands for the particles having diameters of ~2 and 4 µm appeared at wavelengths of 9 and 16 µm, respectively, corresponding to the ED resonance of the (NH4)2SO4 particles. The two strong absorption bands are included within IRW1 and IRW2, suggesting that these particles would greatly decrease the transparency of these IR windows—and intensify the greenhouse effect.

Fig. 2: Absorption efficiency coefficient Qa for different sizes of sulfate particles.
figure 2

a, b Contour diagrams of the absorption efficiency factor (Ca) and (Qa) of (NH4)2SO4 particles for wavelengths in the range from 4 to 20 µm and for diameters (Dp) from 0.1 to 10 µm; c Qa spectra obtained for values of Dp of 0.5, 2, and 2.5 µm; d Qa spectra obtained for values of Dp of 5, 8, and 10 µm; e maximum and average values of Qa obtained for values of Dp from 0.1 to 10 µm in IRW1 (blue and blue dotted curves) and IRW2 (black and black dotted curves); f trends in the average values of Qa, the particle number effect (Ep), and the values of \({Q}_{a}\times {E}_{p}\) in IRW1 for various values of Dp.

Figure 2c, d present the Qa of (NH4)2SO4 particles having values of Dp of 0.5, 2, and 2.5 µm (PM2.5) and 5, 8, and 10 µm (PM10–2.5), respectively. In Fig. 2c, the particle having a value of Dp of 2 µm gave the largest value of Qa because of ED resonance at a wavelength of ~9 µm. In Fig. 2d, the values of Qa of the particles having diameters of 5, 8, and 10 µm were not significantly different, but the absorption band became broader as the size increased. When the size of a particle increases, higher-order modes of resonance would dominate the Qa spectrum. Further information about the values of Qa for particles having different sizes is provided in the Supporting Information (see Supplementary Note 3 and Fig. S1 for detailed contribution of 2n-poles analysis).

To verify the influence of the PM with different particle sizes in the IRW, we calculated (Fig. 2e) the maximum value of Qa in IRW1, the average value of Qa in IRW1, the maximum value of Qa in IRW2, and the average value of Qa in IRW2. In the range of IRW1, the maximum value of Qa for particle size Dp of 2 µm is 2.46. This Qa peak arose from the ED resonance of the 2-µm particle. The average value of Qa in IRW1 and IRW2 can represent a particle’s influence on thermal radiation for the overall IRW1 and IRW2 absorption, respectively. Because resonance of high-order modes broadens the Qa peak, the average values of Qa in both IRW1 and IRW2 gradually increased upon increasing the value of Dp.

In general, atmospheric particles are normally classified into different modes according to their size, formation processes, and atmospheric age. Particles with a size between 0.01 and 0.1 μm (Aitken mode) account for the majority of the number of atmospheric particles, but they rarely account for more than a few percent of the total mass13,16. Particles with diameters between 0.1 and 1.0 μm (accumulation mode) usually account for a large portion of the total aerosol mass and have the largest surface area. This makes these particles performing significant importance to atmospheric chemistry. Particles <1.0 μm contribute to the optical properties of atmospheric aerosols. Although the particles with larger values of Dp provided higher average value of Qa, the number of particles would decrease upon increasing the value of Dp. Both the number of particles and the value of Qa should be considered when calculating the absorptance of these particles. We consider the number of particles and the value of Ca to calculate the absorptance of these particles with different sizes. At the same mass concentration, the number of particles is proportional to \(\frac{1}{{{D}_{{{{{{\mathrm{p}}}}}}}}^{3}}\), and the surface area is proportional to \({{D}_{{{{{{\mathrm{p}}}}}}}}^{2}\). We define \(\frac{1}{{D}_{{{{{{\mathrm{p}}}}}}}}\) as the particle number effect (Ep), the values of \({Q}_{{{{{{\mathrm{a}}}}}}}\times {E}_{{{{{{\mathrm{p}}}}}}}\) can indicate the absorption capacity of particles with different sizes under the same mass concentration. Figure 2f displays the tendencies of the average value of Qa, the value of Ep, and the value of \({Q}_{{{{{{\mathrm{a}}}}}}}\times {E}_{{{{{{\mathrm{p}}}}}}}\) in IRW1 for various values of Dp. Although particles of larger size provided higher average values of Qa, they would also introduce a decrease in the value of Ep. The value of \({Q}_{{{{{{\mathrm{a}}}}}}}\times {E}_{{{{{{\mathrm{p}}}}}}}\) reached a maximum at a value of Dp of 1.4 µm; it decreased when the value of Dp increased in the range of PM10–2.5. As revealed in the curve of \({Q}_{{{{{{\mathrm{a}}}}}}}\times {E}_{{{{{{\mathrm{p}}}}}}}\), the overlapping part of the size distribution (1–3 μm) of fine particles and coarse particles would perform the greatest influence on thermal radiation absorption, and the influence of PM2.5 on the absorption of thermal radiation would be greater than that of PM10–2.5.

3D-FDTD simulations of the optical properties of SiO2/sulfate core/shell mixtures

In the same way, we also analyzed the most abundant compound in the Earth’s crust, silicon dioxide (SiO2). The maximum value of Qa appears around Dp of 2.5 µm at the wavelength of ca. 9 µm. The coating of atmospheric particles is often resulting from enhanced hygroscopicity due to aging mechanisms such as condensation, condensation, and heterogeneous chemical reactions28,43. To further investigate the optical behavior of PM, we used the 3D-FDTD method to simulate the electromagnetic field inside and around particles of various values of Dp. Aged PM may be fractionally or entirely encapsulated within a nearly spherical shell. We studied the optical properties of homogeneous sulfate and SiO2/sulfate core/shell mixtures of PM (see Supplementary Note 4 and Fig. S2 for detailed homogeneous sulfate PM analysis). According to transmission electron microscope images43, we assumed that silica or SiO2 formed the core, coated by a concentric spherical shell of (NH4)2SO4, Fig. 3a provides a schematic representation. The radius of the particle was 0.02, 0.25, 1, or 4 μm; the core/shell ratio was set at 0.5 and the core radius was 0.01, 0.125, 0.5, or 2 μm. Figure 3b presents the values of Qa of core/shell particles having values of Dp of 0.04, 0.5, 2, and 8 µm for wavelengths ranging from 4 to 20 μm; the Qa spectrum was similar to that of homogeneous (NH4)2SO4, the optical properties of core/shell particles are dominated by the shell. For a value of Dp of 2 µm, the maximum value of Qa of 2.54 occurred at a wavelength of 8.97 µm. Figure 3c–j present 3D-FDTD simulations results of the normalized electric field intensities (|E/E0|2) and normalized absorption rates per unit volume (\({P}_{{{{{{\mathrm{abs}}}}}}}=0.5\omega {\varepsilon }_{{{{{{\mathrm{image}}}}}}}|E/{E}_{0}{|}^{2}\) with the unit of W/m3 (V/m)−2) of the core/shell particle having sizes of 0.04, 0.5, 2, and 8 µm. All of the simulation results are normalized by the electric field intensity [with the unit (V/m)2] of the incident light source. For the electric field distribution of the particle having a value of Dp of 0.04 and 0.5 µm (Fig. 3c, d), the shell thickness (0.01 µm and 0.125 µm) was smaller than the penetration depth of (NH4)2SO4 (\({d}_{{{{{{\mathrm{p}}}}}}}=\frac{\lambda }{4\pi k}=0{{{{{\rm{.43}}}}}}{{{{{\rm{\mu }}}}}}{{{{{\rm{m}}}}}}\)), such that the light field could penetrate partially into the SiO2 core. The extinction coefficient of SiO2 at a wavelength of 9 µm (k = 0.759) is, however, smaller than that of (NH4)2SO4 (k = 1.665). The penetrated light field and the lower extinction coefficient of SiO2 result in a small absorption rate inside the SiO2 core (Fig. 3g, h). The electric field distribution in (Fig. 3c, d) clearly reveal that although the electric field distributed on the outer edge of the particle shell, the area of spatial distribution of the high electric field regime for the particle of 0.5 µm is much larger than that of 0.04 µm. In Fig. 3e, i, the electric field distribution of the particle having a value of Dp of 2 µm reveals a dipole resonant pattern similar to that in the homogeneous case in Fig. S2. Because of the high absorption rate and small penetration depth of (NH4)2SO4 particle having a value of Dp of 2 µm, the light field had difficulty reaching the SiO2 core. Most of the light was absorbed by the outer layer of (NH4)2SO4; therefore, the values of Qa were similar for both the core/shell (Qa = 2.54) and homogeneous (Qa = 2.46) cases at a wavelength of 9 µm and a value of Dp of 2 µm. Figure 3f, j present the electric field distribution and absorption rate pattern for the particle having a value of Dp of 8 µm. Here, the behavior in the core/shell case was very similar to that in the case of the homogeneous particle having a diameter of 8 µm. Because the shell thickness was much larger than the penetration depth of (NH4)2SO4, the light could propagate in and be absorbed by only the (NH4)2SO4 shell; it could not reach the SiO2 core.

Fig. 3: The Qa spectra and simulated E-field intensities and absorption rates of 0.04, 0.5, 2, and 8 µm core/shell structure particles.
figure 3

a Schematic representation of the core/shell structure, with SiO2 as the core surrounded by a concentric spherical shell of (NH4)2SO4. Here, the core/shell ratio is set at 0.5. b Qa spectra of core/shell structures having values of Dp of 0.04, 0.5, 2, and 8 µm. cf Simulated E-field intensities and gj simulated absorption rates of c, g 0.04-, d, h 0.5-, e, i 2-, and f, j 8-µm core/shell structure particles.

Scattering characteristics of sulfate particles

Furthermore, in this paper, we also calculated the scattering effect of the sulfate particles having diameters from 0.1 to 10 µm for wavelengths in the range from 4 µm to 20 µm. The results show that the scattering effect is much smaller than the absorption effect at longwave regimes (see Supplementary Note 5 and 6 for detailed scattering characteristics analysis). We also calculated the forward scattering efficiency (FWQs) and the backward scattering efficiency (BWQs). As the particle size increased, the value of BWQs/ (BWQs + FWQs) decreased. We suggest that backward scattering efficiency (BWQs) of particle diameter <5 µm is more important, because the smaller Dp, the more the number of particles and it would drive the scattering of thermal radiation back from the particles and, thereby, decrease the thermal emission going out to space beyond the atmosphere.

The changes in thermal power density of longwave radiation for different cases

To further explore the effect of PM on the thermal radiation balance of the atmosphere, we tested six cases (see Supplementary Note 7 for detailed case description). We estimated the absorptance of PM in the atmosphere by using the radiative transfer model. To estimate the warming effect Patm of PM, we calculated the thermal radiation from the atmosphere in the absence and presence of PM. (see Supplementary Note 8 and 9 for detailed analysis of PM absorptance and Patm). Table 1 presents the changes in thermal power density of longwave radiation for six different cases. The atmosphere displays positive radiative forcing, due to thermal radiation absorption by PM. Table 1 display three cases for homogeneous sulfate (case 1–3) and the other three cases for sulfate/SiO2 core/shell mixtures (case 4–6) at various mass concentrations, respectively. The World Health Organization air quality model confirmed that 92% of the world’s population lives in places where air quality levels of PM exceed the Air Quality Guidelines. The Air Quality Guidelines included in cases 1, 2 and 4, 5 as references should be reasonably representative in our calculations. In cases of severe air pollution, the warming effects of PM comprising homogeneous sulfate or sulfate/SiO2 core/shell mixtures are 27.01 and 32.46 W m−2, respectively (case 3 and 6). The longwave PM radiative effect may cause (NH4)2SO4 to behave like a “greenhouse PM” or “greenhouse particles.”

Table 1 The changes in the thermal radiation power density by different cases.

Comparison of atmospheric transmittance under clear sky and presence of PM

Figure 4 shows the atmospheric transmittance in the absence (clear sky) and presence of PM, including homogeneous sulfate and sulfate/SiO2 core/shell mixtures at different concentrations. It can be clearly observed from Fig. 4a, b when the concentration of PM increases to 20, 50, and 1,180 μg m−3, the atmospheric transmittance decreased, especially in IRW1 (light-cyan areas). Sulfate has a strong absorption band around the wavelength of 9 μm, and the decrease in transmittance can be clearly observed. As far as we known, the injection of sulfate particle into the stratosphere is the most discussed proposal for solar geoengineering. However, in addition to the risk of ozone loss and heating of the lower tropical stratosphere44, it is also likely to absorb the earth’s radiation and warm the earth’s surface. The atmospheric transmission spectra in the presence of homogeneous sulfate and sulfate/SiO2 core/shell mixtures at same concentrations 1180 μg m−3 are shown in Fig. 4c. For the IR radiation absorbed by both sulfate and sulfate/SiO2 core/shell mixtures, the transmittance of the core/shell mixtures case is lower than that of the homogeneous case, as shown by the dashed box. Because the light field could penetrate partially into the SiO2 core of the set core/shell mixtures, the absorption rate of SiO2 in the dashed box of spectral regime is greater than sulfate.

Fig. 4: The atmospheric transmittance in the absence and presence of PM.
figure 4

a Presence of homogeneous sulfate, and b Presence of sulfate/SiO2 core/shell mixtures at different concentrations from 20, 50 to 1,180 μg m−3. c Presence of homogeneous sulfate and sulfate/SiO2 core/shell mixtures at same concentrations 1,180 μg m−3.

Conceptual experimental results

To confirm the thermal radiation behavior of (NH4)2SO4 experimentally, we set up an apparatus to conduct a conceptual experiment in the laboratory. We prepared several samples containing 0.1 wt% (NH4)2SO4 in KBr, and measured the cooling rate of different samples shielding (see Supplementary Note 10 and 11 for detailed experimental concept analysis). We found that the larger the shielding area, the slower the cooling rate. From this experiment, we suggest that the thermal radiation absorption of PM in the atmosphere would increase the temperature of the surroundings. The thermal emissivity of the samples composed of different (NH4)2SO4 particle sizes was also measured. Different optical properties related to particle size have a significant effect on the thermal emissivity.


According to our findings in this study, sulfate displays strong IR absorption, especially in the atmospheric window. The IR absorption properties of (NH4)2SO4 make it behave like “greenhouse PM” producing positive radiative forcing that may increase the temperature of its surroundings. An increase in the concentration of sulfate would reflect more of the incoming solar radiation back into space, but it would also capture more of the outgoing thermal radiation back to the Earth. (NH4)2SO4 and sulfate/SiO2 core/shell particles having diameter of ~2 µm display the maximum absorption efficiency factor (Qa) of 2.46 and 2.54, respectively, at a wavelength of ca. 9 µm. At the same concentration, considering the factors of particle size and number together, the size of (NH4)2SO4 particles with the strongest absorption capacity appears at 1.4 µm. The particle size also has an important influence on the scattering efficiency factor (Qs), as the particle size decreases, the scattering phenomenon of (NH4)2SO4 gradually becomes dominated by BWQs. The BWQs would drive the thermal radiation scattered back from the particles of the PM, thereby decreasing the thermal emission going out to the space beyond the atmosphere. The absorption of particles at resonant conditions would be increased, even if the sizes of particles are much smaller than the wavelength. The relationship of particles size, absorption coefficients, and wavelength effect is very important for the investigation of resonance phenomena on particles. The simplified k distribution would lose the dependence of calculation results on wavelength. In this study, we used the LBL method to observe the resonance effect of PM particles with different sizes in broadband of spectral regime from 4 to 20 µm.

It is extremely difficult to describe the mixing state of an PM particle. In this study, we use simplified assumptions such as homogeneous (NH4)2SO4 and sulfate/SiO2 core/shell particles to discuss the effect of sulfate on thermal radiation absorption in IRW1 under resonance conditions Once the optical properties of various materials are known individually, the optical properties of mixed PM can be calculated and correctly averaged45. To evaluate how the longwave aerosol radiative effect varies as a function of size distribution and aerosol burden, we also briefly analyze the dependence of the longwave radiative effect as a function of median radius, distribution width, and sulfate/SiO2 weight fraction to discuss the use of statistics data and treatment of uncertainties (see Supplementary Note 12 for a detailed discussion of uncertainties). In this study, we only concern on the effect of IR resonance properties of SIA particles on LWPMRE without comparing it with a climate model. Comparison with climate models is difficult, but important to assess the quantitative impact of climate model on SIA. However, this is beyond the scope of this study, and we will analyze more PM species in future work and also investigate the LWPMRE of the aging process of the PM particles.


Sample fabrication

(NH4)2SO4 and KBr were purchased from Sigma–Aldrich. The (NH4)2SO4 and KBr particles were crushed to sizes of several hundreds of micrometers, using a bead crushing machine (Beads Crusher µT-12), and then ground in an agate mortar to sizes of a few micrometers. The (NH4)2SO4 particles (particle sizes: ca. 2–20 μm) were mixed into KBr at a content of 0.1 wt%; the mixed powder was pressed into several tablets, using a tablet press. The (NH4)2SO4 particles were observed through scanning electron microscopy (SEM, NOVA NANO 450). Fourier transform infrared spectroscopy (FTIR) was performed using a Fourier transform infrared spectrometer (Bruker VERTEX 70). The emissivity spectra of the samples in the mid- and far-infrared wavelengths (2.5–25.0 μm) were measured using the emissivity measurement kit (Emission Adapter, A540) and MCT detector of FTIR (Vertex 70, Bruker), and the blackbody furnace (IR-563/301. Blackbody system) was used as a correction source for the emissivity spectra. Temperature measurement data were recorded using K-type thermal couples and a paperless high-speed recorder (KR2000 Series Graphic Recorder).

Simulation method

High-resolution FTIR transmittance spectral data of (NH4)2SO4, Na2SO4, NH3NO3, and NaNO3 were obtained from the Sigma Library of FT-IR Spectra. The optical constant of (NH4)2SO4 used in the simulations at a wavelength (λ) of 9 µm was 0.99 + 1.7i. Mie theory was used to simulate the thermal radiation properties of the (NH4)2SO4 particles. The absorption cross-section (σa) and the scattering cross-section (σs) were computed numerically using the Matlab code. The electric field distribution of the (NH4)2SO4 particles was simulated using the 3D-FDTD method (RSoft FullWAVE).