A Simulation on the Optical and Thermal Properties of Multiple

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A Simulation on the Optical and Thermal Properties of Multiple Core-shell Atmospheric Fractal Soot Agglomerates under Visible Solar Radiation Xiaojin Wang, Xiangrui Meng, yongqing wang, and Yan Cao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04909 • Publication Date (Web): 06 Sep 2019 Downloaded from pubs.acs.org on September 6, 2019

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The Journal of Physical Chemistry

A Simulation on the Optical and Thermal Properties of Multiple Core-shell Atmospheric Fractal Soot Agglomerates under Visible Solar Radiation Xiaojin Wang2, Xiangrui Meng 3, Yongqing Wang 3, Yan Cao1,2*

1College

of Chemistry and Chemical Engineering, Anhui University, Hefei 230601,

China 2Institute

for Combustion Science and Environmental Technology, Department of

Chemistry, Western Kentucky University, Bowling Green, KY 42101, USA 3School

of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou

450001, China

ABSTRACT: Soot is an important anthropogenic carbonaceous aerosol that forms atmospheric smog. The atmospheric presence of smog raises great concerns about human health. Soot also absorbs visible light from solar radiation, likely contributing to climate change. This study focused on the optical and thermal effects of soot via a numerical simulation approach and included regular biomass, diesel, acetylene, and propane soot, and three carbon surrogates for soot. To make the simulation more similar to real 1

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soot aerosols, two major sub-models were integrated, which involved their core-shell structures and their fractal agglomerate structures. Four kinds of shell materials, such as non-absorbing (water, sulfuric acid, salt) and weak-absorbing (brown carbon) materials were studied in their different shell thicknesses. The effects of the shell on the absorption enhancement of the bare soot particles and the dependence of absorption on light wavelength were revealed. The brown carbon shell was found to exhibit greater absorption enhancement, and its absorption was doubled at 360 nm compared to the absorption at 800 nm. Among three soot aggregates from the different aging processes, the most stable embedding-type soot aggregate was found to have the maximum absorption of the incident light, resulting in an increase in the surrounding temperature by 0.35 K.

1. INTRODUCTION Aerosols play a significant role in the Earth’s radiation budget and hydrologic cycle by scattering and absorbing or acting as nuclei of condensation,(1)-(3) while simultaneously causing the largest uncertainties in the climate.(4)(6) Aerosols have received increasing attention due to their association with environmental pollution and health effects in humans.(7) The size distribution and chemical constituents of aerosols determine their physicochemical properties, which correspond to their optical depth and toxicity.(8)(9) Naturally, their compositions can be quite different because of their formation processes and specific sources.(10)(11) Among these aerosols, carbonaceous particles in the atmosphere, which contribute a large portion of the overall mass load, 2


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play a major role in driving climate change. The effect of carbonaceous particles seems significant and even exceeds that of another global-warming gas, methane (CH4).(12)(13) Fine black carbon (BC) and organic carbon compounds, which originate from fossil fuel combustions, are usually called soot particles.(14) Recently, brown carbon (BrC) frequently appeared in the literature, referring to organic carbon that can efficiently absorb ultraviolet (UV) - visible (Vis) light, although BrC is weaker in absorption over this wavelength range compared to black carbon.(15) Moreover, the optical properties of carbonaceous particles are closely related to their chemical compositions, depending on emission sources and secondary reaction pathways,(16) and they are also greatly varied in regions around the world.(17)-(21) Soot particles often exist as fractal-like aggregates containing ten to hundreds of spherical soot monomers, and the diameters of these freshly emitted monomers are between 20 and 60 nm.(22) The freshly emitted soot particles are usually hydrophobic and very likely experience an evolution toward hydrophilic during atmospheric aging.(23)(23) The aging process involves water adsorption and condensation and is followed by another rapid aging stage in which the mixture state of soot undergoes further changes of structures.(25)-(28) The soot particles are embedded, partly coated, thinly coated and partially encapsulated.(29) It was observed that the light absorption of these coated soot cores can be significantly enhanced due to the lensing or focusing effect of the shell, sometimes by at least 30% or even higher by coating.(30)-(33) At the same time, the absorption enhancement was related to the wavelength of light when coated with a weak absorbing material (BrC).(34) Furthermore, the interaction between 3



soot particles and light is still unclear because of their complex structures and compositions. Therefore, further research on the optical properties of soot particles is still needed. Soot particles are found to be strong absorbers and scatterers of visible light, which makes up a substantial part of the solar spectrum (see the Supporting Information for spectra of solar irradiance and atmospheric absorption). However, most recent studies on the optical properties of soot were restricted to the infrared wavelength range,(35)(36) and few studies addressed the visible wavelength range.(37)(38) In this paper, studies on the optical properties of soot particles were carried out in the full wavelength spectrum of visible light using the finite element method (FEM) simulation method. First, the model of the scattering and absorption of a single soot particle was established ， and the scattering and absorption properties of different soot particles and graphite particles as the surrogate for soot were calculated in the visible wavelength range. The effectiveness of the adopted methods was verified by openly published experiments and the Mie theory. Second, the effects of different shell materials and their thickness on the optical properties of the graphite core were studied. The studied shell materials included water (H2O), sulfuric acid (H2SO4), salt (NaCl) and BrC. Finally, a more realistic soot aggregation model was established based on the diffusion limited aggregation algorithm (DLA), and furthermore, the optical and photothermal properties of these aggregations were studied by multiphysics coupling based on the FEM simulation method. Thus, this paper provided a new and efficient method for understanding the optical properties and 4


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warming effects of realistic soot particles. 2. METHODS AND MODELING The FEM simulation method was adopted to study the optical properties and warming effects of soot particles by coupling wave optics and heat transfer. The interaction between light and soot particles was investigated by solving for the electromagnetic field according to the fundamental optical parameters of soot. The extinction cross section  ext is typically used to represent the optical radiation properties of particles, which is expressed as the ratio of the total scattering and absorption intensities to the total incident light intensity.(39) Therefore, the extinction cross section can be defined as

 ext   sca   abs 

1 I0

 (n  S

sca

)dS 

1 I0

 QdV

(1)

where  sca is the scattering cross section,  abs is the absorption cross section, I 0 is the total intensity of the incident light, n is the normal vector, S sca is the scattered intensity vector, Q is the power loss density, S and V are the surface area and volume of the particle, respectively. If the freshly emitted soot particles are coated with shell materials, the absorption enhancement Eabs is defined to indicate the enhancement intensity of the coated particle to an equivalent uncoated particle, which is expressed as the ratio of the absorption cross section of the core/shell particle to the absorption cross section of core particle (Equation 2).(34)

Eabs 

 abs core / shell  abs core

(2)

The freshly emitted soot particles tend to form aggregates for stabilization during the aging process in the atmosphere. The aggregation model of the soot particles was 5



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established using the DLA method, and the morphology of the soot particle aggregates is defined by the fractal equation as follows:(40)

R  Ns  k f  g   a  where

Ns

Df

is the number of concerned monomers, a

(3) is the mean radius of

concerned monomers, D f is the fractal dimension, Rg is the radius of gyration of aggregates and k f is the structural coefficient, which is always between 1.23 to 3.5 for soot aggregates.(41) Previous simulation studies by other researchers only focused on the optical properties of soot particles, whether using the T-matrix or discrete dipole approximation (DDA) methods.(42)(43) However, the FEM simulation method used in this paper can be carried out by coupling wave optics and heat transfer, which helps directly studying the photothermal properties of soot particles. In other words, this model (see the Supporting Information for more details of the model and methods) involves the light absorption of soot particles and heat transfer within the surrounding atmosphere. The absorption power density p(r ) in the soot particle can be obtained by

p (r )  where 

 2 Im  (r,  ) E(r ) 2

(4)

is the frequency of light, Im( (r,  )) is the imaginary part of the

permittivity of soot particle, which corresponds to the absorption of the particles, and

r is the position vector. E(r ) represents the electric field which can be solved in this optics model. When the absorption power density can be obtained, it is further used as the heat source in the heat transfer model of the soot particles. The heat 6


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transfer model throughout the particle and its surroundings can be solved by(44)

 c p T t     k (r )T (r )   p(r ) where 

and c p

(5)

are the position-dependent mass density and specific heat

capacity, respectively. T and t are the temperature and time, respectively. k (r ) is the position-dependent thermal conductivity and r is the position vector. In addition, the temperature distribution around the soot particle can be obtained according to the boundary conditions. 3. RESULTS AND DISCUSSION 3.1. Optical Properties of Different Soot Particles. Soot particles vary according to sources and regions. This study typically involved investigations on optical properties of three kinds of soot particles and three kinds of graphite particles. First, the effectiveness of the FEM method was verified by openly published experimental results and the Mie theory. Figure 1a shows the extinction results of polystyrene latex spheres (PSL) with a diameter of 600 nm.(45) The black dashed line represents results from the applied FEM method in this paper. Even though the y-axis is different for theoretical and experimental methods, both of them represent the similar trend of extinction abilities of the particles. It was found that extinction spectra of the PSL agreed well with each other in the same wavelength range, and the maximum extinction appeared at the wavelength of 500 nm. The missing extinction results within the wavelength range of 300 nm and 430 nm in the FEM method was due to the lack of optical constants of PSL in this range. In addition, the effectiveness of the applied FEM method was further verified by comparing the extinction results 7



of the noble metal silver (Ag) with a diameter of 92 nm because of the abundance of experimental data (Figure 1b).(46) The verification supported the accuracy of the prediction of the optical properties of particles using the adopted method in this study.

Figure 1. (a) Extinction spectra of PSL with a diameter of 600 nm via experimental, MiePlot and FEM results. The black dashed line represents the result from FEM, the black solid line represents the result from the MiePlot, and the blue solid line represents the results from experimental measurement appeared in openly published papers. (b) Extinction spectra of Ag nanoparticles with a diameter of 92 nm via experimental, MiePlot and FEM results.

Three kinds of soot particles (diesel soot,(47) acetylene soot, and propane soot(48)) and three carbon surrogates for soot particles (graphite 1,(49) graphite 2 and pyrolytic carbon(50)) were investigated in their optical properties.(51) The diameter of freshly emitted spherical soot monomer was set to 50 nm, and the studied wavelength ranged from 300 nm to 800 nm, covering the entire visible region of sunlight. Figure 2 shows the extinction and absorption cross section of studied particles, which shows that these particles are good light absorbers because of the almost equivalent extinction 8


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and absorption cross sections. Interestingly, the extinction result of graphite 1 was close to those of acetylene soot and propane soot at the relatively longer wavelength (> 500 nm) versus that of pyrolytic carbon, which was close to that of soot particles at a short wavelength (< 400 nm). Diesel soot showed a relatively weaker extinction effect than other particles. It is notable that the aforementioned studies were based on the single particle model. Moreover, Figure 3 shows the scattering properties of those particles that were revealed by their far-field scattering patterns. Generalized scattering patterns of the involved particles were found to exhibit the tendency of forwarding scattering in a shorter wavelength range and dipole antenna scattering in a longer wavelength range. Moreover, graphite particles incurred stronger light scattering in a shorter wavelength range compared to that of soot particles, but scattering was comparable in the longer wavelength range.

Figure 2. (a) The extinction cross section of the studied particles (50 nm in diameter). (b) The absorption cross section of the studied particles (50 nm in diameter).

9



Figure 3. (a) The far-field scattering pattern of the acetylene soot (50 nm in diameter) irradiated by the incident light at 300 nm, 400 nm, 500 nm, 600 nm, 700 nm and 800nm. (b) The far-field scattering pattern of the propane soot (50 nm in diameter). (c) The far-field scattering pattern of the diesel soot (50 nm in diameter). (d) The far-field scattering pattern of the graphite 1 (50 nm in diameter).

3.2. Optical Properties of Soot Particles with Different Shell Materials. Soot particles in the atmosphere tend to be the internal core in a core-shell mixed structure after undergoing an aging process. The treatment of these mixtures as core/shell structures have been applied and confirmed in many previous studies by investigating their microscopic images.(52)(53) However, shell composition varies with sources and 10


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regions and usually has a non-absorbing composition. These structures have been extensively studied but there is a lack of studies about the consistency of their increasing role in absorption enhancement as a shell outside of soot particles to form a core-shell structure, especially those weak-absorbing BrC from similar emission sources.(54) This section only focused on graphite 1 as a core material because of its available physical parameters and comparable properties close to those of soot (as further exhibited in Section 3.1). Four kinds of typical atmospheric shell materials, such as H2O, H2SO4,(55) NaCl(56) and BrC, and their different thicknesses, were investigated for their absorption enhancement contribution to the overall formed core-shell particles; this investigation yielded a further understanding of their enhancement mechanisms. Figure 4 shows the absorption enhancement Eabs of soot particles coated with H2O compared with bare particles. The coating shell thickness is 10 nm, 30 nm, 50 nm and 70 nm, and the ratio of water shell mass M w and soot core mass M g is 0.78, 4.29, 11.56 and 23.95, respectively. It is clearly seen that the water shell can effectively enhance the absorption efficiency of visible light by soot particles. The enhancement increased with the thickness of the water shell but in a decreasing tendency. The scattering electric field was also calculated in this model (Figure 5) to further exhibit the mechanism of the interaction of the water shell with the extinction of soot particles. The shell structure can significantly change the scattering and absorption of core particles, through affecting the polarization of particles in the electromagnetic field. It can be seen that soot particles of approximately 50 nm tended 11



to forward scatter in a shorter wavelength range (300 nm wavelength), which can be enhanced by the water shell (consistent with the conclusion of Mie scattering theory).(57)(58) Moreover, the enhancement of the forward scattering increased with the shell thickness. In addition, for longer wavelengths, the scattering of the particles was like a dipole antenna (consistent with the far-field scattering pattern in the last section). In addition to H2O, there are other non-absorbing shell materials, including H2SO4(59) and NaCl that were also of interest because of their availability in atmospheric conditions. The results shown in Figure 6a of the soot particle coated with H2SO4 showed a similar absorption enhancement effect compared to that of the soot particle coated with H2O. However, a larger increase in Eabs was found when the soot particle was coated with NaCl, as shown in Figure 6b, where Eabs was over 5 when the coating thickness was 50 nm.

Figure 4. The absorption enhancement Eabs of the soot particles coated with H2O. The diameter of the soot core was 50 nm, and the H2O shell thickness was 10 nm, 30 nm, 50 nm and 70 nm, respectively.

12


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Figure 5. The scattering electric field of the soot particles coated with water shell (the incident light is from above with wavelength of 300 nm, 500nm and 800nm). The diameter of the soot core was 50 nm, and the H2O shell thickness was 10 nm, 30 nm and 50 nm, respectively.

Figure 6. The absorption enhancement Eabs of the soot particles coated with (a) H2SO4 and (b) NaCl. The diameter of the soot core was 50 nm, and the shell thickness was 10 nm, 30 nm and 50 nm, respectively.

It is well established that the soot particles coated with the non-absorbing shell can have significant absorption of visible light.(54)(60) Unlike the H2O and H2SO4 13



non-absorbing coatings, BrC was weak-absorbing material and performed differently when coated on soot particles. Some studies indicated that the absorption of BrC can be an important factor in aerosol radiative forcing. The refraction index of BrC can only be found at specific wavelengths in the literature,(61)(62) and this literature provided a model predicting the refraction index of BrC that can be expressed as RI  1.7( 0.2)  k BrC i . This equation helped with predicting a soot particle coated

with weak absorbing BrC using the established simulation model. Figure 7 shows the absorption enhancement of the soot particle coated with BrC, and it can be seen that BrC shells have a larger Eabs compared to that of the soot particle with the H2O and H2SO4 shells. It was expected to find that there was a great difference of Eabs for soot particles with different shells, revealing that Eabs of soot with BrC shells was greater than those of soot with non-absorbing shells. Most significantly, Eabs was very different in shorter and longer wavelength ranges in the soot with greater BrC shell thickness, indicating stronger wavelength dependence of BrC shells.

Figure 7. The absorption enhancement Eabs of the soot particles coated with BrC. The soot core 14


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was 50 nm in its diameter, and the BrC shell thickness was 10 nm, 30 nm and 50 nm, respectively.

3.3. Optical Properties and Warming Effect of Soot Aggregation. The previous sections focused on the model of a single particle. In reality, the freshly emitted soot particles tend to form aggregates due to particle collisions and water interactions, which induce the rapid aging of soot particles in a mixed state. Usually, these aggregated soot particles tend to form a compact spherical shape coated with shell materials after restructuring to reach a new stable state. In this study, DLA was applied to establish typical and relatively simple twelve-particle aggregates (50 nm diameter for each particle) for the different aging processes. The fractal dimension

D f was set to 1.3, 2.0, and 2.8 for the three soot aggregates, such as the freshly emitted soot aggregates, the partly coated soot aggregates and the embedded soot aggregates, respectively (see the Supporting Information for the text-based descriptions of the positions of soot monomers).(63)(64) And the single soot particle overlapping was set to be 0.1, which made it closer to the real soot aggregates and avoided problems of grid generation in numerical simulation. Freshly emitted soot aggregates existed as an elongated structure, while the partly coated soot aggregates were more compact and were partially surrounded by water. Embedded soot aggregates had a relatively stable structure and showed a spherical shape coated with a water shell. Figure 8 shows the calculated absorption, scattering and extinction cross sections that revealed their optical properties. It can be seen that the freshly emitted soot aggregates and the partly coated soot aggregates had similar extinction effects. 15



The freshly emitted aggregates tended to absorb more light, rather than scattering more light, due to their large irradiated area and small interactions between particles, while the embedded soot aggregates possessed a much stronger light extinction and the extinction cross section was close to 10000 nm2 at the 300 nm wavelength. It can also be seen that these three soot aggregates exhibited stronger light extinction at shorter wavelengths, and there is only a small difference in the optical properties at the longer wavelengths. To investigate the warming effect of soot particles, a model combining optics and heat transfer was established in order to understand the photothermal behaviors of the studied particle systems. Considering the stronger extinction characteristic of soot particles at shorter wavelengths, while the solar radiation is mostly found in visible light, a focus on the incident light at 450 nm wavelength was chosen. The ambient temperature was set to be 293.15 K. Figure 9a shows the temperature distribution around the freshly emitted soot aggregates, revealing that there was only a slight increase in temperature of the freshly emitted soot aggregates as they reached the steady state. It was also notable that the temperature varied with the polar angle  and azimuthal angle  of the incident light due to the slender structure of freshly emitted soot aggregate (Figure 9b). Figure 10 shows the temperature distribution of both the partly coated soot aggregates and the embedded soot aggregates. It can be found that the temperature increase of the partly coated soot aggregates was less than that of the freshly emitted soot aggregates even though the partly coated soot aggregates were coated with water shells. This was due to the elongated structures of 16


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freshly emitted soot aggregates, which resulted in larger illumination areas at some incident light angles and more light absorption. Therefore, both water shell and aggregation states could affect the absorption and temperature increase of the soot aggregates, but in different manners. The results also revealed a maximum temperature rise, close to 0.35 K, in the case of the embedded soot aggregates due to their stronger absorption properties. Similarly, the water shell in aggregate cases can also efficiently enhance the absorption of the core structure of the soot aggregates. Overall, the optical properties and warming effects of the soot particles were related to a variety of factors, including size, shape, chemical composition and mixture state. There were still other important factors that affect the behaviors of soot, such as particle concentrations and size distributions, which encourage further research in the field.

Figure 8. Absorption (dotted line), scattering (dashed line) and extinction (solid line) cross section of the soot aggregates with different shapes ( D f =1.3, 2.0 and 2.8).

17



Figure 9. (a) Isosurface map of the temperature distribution of freshly emitted soot aggregates ( D f =1.3). (b) Maximum temperature of the freshly emitted soot aggregates at different polar angles  and azimuthal angles  of the incident light.

Figure 10. (a) Isosurface map of the temperature distribution of the partly coated soot aggregates ( D f =2.0). (b) Isosurface map of the temperature distribution of the embedded soot aggregates ( D f =2.8).

4. CONCLUSIONS A numerical simulation method coupling optics and heat transfer was established to investigate the optical properties and warming effect of soot. Results revealed that, 18


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The extinction result of graphite 1 was close to that of acetylene soot and propane soot at the relatively longer wavelength (> 500 nm), versus that of pyrolytic carbon which was close to that of soot particles at short wavelength (< 400 nm). While diesel soot showed a relatively weaker extinction effect than those of other particles. All of these particles tended to scatter light forward at the short wavelength and showed a dipole antenna scattering at the longer wavelength. To make the simulating more realistic, two major sub-models have been integrated, which involved their core-shell structures and their fractal agglomerate structures. Four kinds of shell materials, including non-absorbing (H2O, H2SO4, NaCl) and weak-absorbing (BrC) in their different shell thickness, were studied for their effects on the absorption enhancement compared to bare soot particles. All of these shell materials can enhance the scattering forward effect at short wavelength. NaCl shell showed the strongest absorption enhancement among those non-absorbing shell materials. The absorption enhancement increased with shell thickness. However, weak-absorbing shell material BrC exhibited even better absorption enhancement ( Eabs was close to 6 at 360 nm). At last, three fractal soot aggregates from different aging process, such as the freshly emitted soot aggregates ( D f  1.3 ), the partly-coated soot aggregate ( D f  2.0 ) and the embedded soot aggregate ( D f  2.8 ) were also investigated, and found that the embedded soot aggregate had the maximum absorption of incident light which resulted in an atmospheric temperature rising by 0.35K.

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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Solar spectral irradiance and atmospheric absorption, the models and methods to calculate the temperature profile of soot aggregates, the text-based descriptions of the positions of these single soot particles for three soot aggregates.

AUTHOR INFORMATION Corresponding Author *Phone: (270)7790202; E-mail: [email protected]

Notes: The authors declare no competing financial interest.

ACKNOWLEDGEMENTS Authors are grateful for financial support from the National Key Research and Development Program of China-Intergovernmental International Scientific and Technological Innovation Cooperation in No. 2016YFE0108400, the National Natural Science Foundation of China (No: 21676001), and the U.S. Department of Agriculture (5040-12630-004-00D).

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A Simulation on the Optical and Thermal Properties of Multiple

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