Abstract

Absorption cross section (Cabs), scattering cross section (Csca) and asymmetry parameter (ASY) of soot particles in different atmospheric aging status were investigated under fixed equivalent volume radius (RV) using the numerically exact multiple-sphere T-matrix method. The radiative properties of soot particles would be largely diverse in different aging status even RV is fixed. However, there are many insensitive parameters under different aging status. The Cabs and ASY is insensitive to monomers number (Ns) when Ns is larger than a threshold value. For bare and thinly coated soot aggregates, Cabs is insensitive to fractal dimension (Df) when the RV is small, where the relative errors of Cabs for different Df are within 2.5%. However, the effects of Df is obvious for large soot due to the shielding effects of large monomers, and the relative errors for different Df can reach to 18% for bare soot. For thinly coated soot, the changes of ASY with soot volume fraction (fsoot) is small due to the little changes of the fractal structure when the RV is fixed. In addition, for thickly coated soot, ASY is insensitive to Ns due to the unchanged overall spherical structure. Our results give a further understanding of the influences of morphology on radiative properties. It may be helpful for model selection and model simplification.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

As a product of incomplete combustion, soot is the major aerosol that absorbs solar radiation. Detailed knowledge of the radiative properties of soot particles is significant for climate studies [1–3], remote sensing [4, 5] and fire detection [6, 7]. However, there are still large uncertainties in understanding radiative properties of soot particles [8,9].

The radiative properties of soot particles are significantly influenced by the complex morphological factors, such as fractal structure, monomer character and mixing state. Studies have shown that the freshly emitted soot particles are composed of numbers of soot monomers [10]. In addition, the morphology of soot particles varies with different combustion conditions, fuel species and atmospheric aging status. Studies have been conducted to investigate the effects of morphology on radiative properties of fractal-like soot agglomerates [11–13]. However, the soot particles tend to be mixed with other chemical components, which leads to more complex morphology [14,15]. Mie theory [16], a method to calculate the radiative properties of a homogeneous sphere, is commonly applied in climate studies [15, 17, 18]. However, based on situ measurements on urban plumes, the radiative absorption of soot particles has been overestimated in models [14, 19, 20]. The influences of morphology on the radiative properties are still unclear until far.

Although many studies have concerned on the influences of morphology on the radiative properties of soot particles [21–25], to the best of our knowledge, few studies investigate the influences under a fixed particle size. As a matter of fact, this issue is also important. The size distribution of soot particles has great impact on human health [26] and environment [27]. In the climate model, the radiative effects of soot particles are calculated under a given size distribution. The morphology of soot particle is commonly assumed to be spherical, which can be calculated using the Mie theory. However, the radiative properties of soot particles significantly depend on the morphology and mixing status. Therefore, given the size distribution, the calculated radiative effects using Mie theory can introduce large errors.

Nevertheless, it isn’t meant that we should put a morphologically more realistic model to applications due to high computational cost. For example, whether the radiative properties can be calculated using an equivalent volume model with less monomer number than the real morphology is unclear. It is very difficult to reconstruct all the elements of radiative properties with a simplified model. However, it is possible to find a simplified model for a specified problem after knowing the effects of the morphology. To give suggestions to find a relative simple equivalent volume model for the specified problem, there is a need to investigate the effects of morphologies under different fixed equivalent volume radius. In addition, it is also necessary to investigate the sensitivities of morphological parameters on the correlation between radiative properties and particle size.

Although Kahnert [28] has conducted a sensitivity study of the correlation between particle size and radiative properties for bare soot, the monomers radius are among 10–25nm. In physical insights, it is significative because this range is commonly observed in reality. However, in application insights, we are more focused on whether the actual morphology can be simplified as an equivalent volume model with less monomers number, such as a single sphere, which may be not appeared in atmosphere. Therefore, we extended the sensitivity study to morphologies whose monomer radius is not appeared in reality. In addition, the sensitivities of coated soot has not been studied. In this work, we investigated the influences of morphology on the radiative properties of soot particles under fixed particle sizes at first. Then sensitivities of morphologies to radiative properties were analyzed. Recently, the integral optical characteristics has gained increasing attentions [29, 30] due to their essential contributions to calculations of the global radiation forcing. In climate model, bulk Cabs, Csca, and ASY are commonly calculated by cumulative sum of single particles radiative properties based on a given size distribution. To give suggestions for modeling application, Cabs, Csca and ASY were investigated.

The aims of this work is to demonstrate the sensitivity of morphological parameters to radiative properties and provide suggestions for model selection and model simplification. The findings should improve our understanding of the morphological effects and influences of particle size on the radiative properties.

2. Methodology

2.1. Generation of soot particles with different morphologies

Studies have shown that freshly emitted soot particles generally present fractal characteristics [31, 32]. The construction of the structure can be described by the well-known fractal laws [17]:

Ns=k0(Rga)Df
Rg2=1Nsi=1Nsli2
where Ns is the number of the monomers in the cluster, a is the mean radius of the monomers, k0 is the fractal prefactor, Df is the fractal dimension, Rg is the radius of gyration, and li is the distance from the ith monomer to the centre of the cluster.

Diffusion-limited algorithms (DLA), including particle-cluster aggregation (PCA) [33] and cluster-cluster aggregation (CCA) methods [34], are developed to generate fractal-like aggregates. However, the tunable algorithms are more commonly applied due to the adjustable parameters and fast implementation [35, 36]. A tunable DLA code developed by Wozniak et al. [37] was applied to generate soot aggregates in this work. Different from ordinary DLA code, it preserves fractal parameters at each step of the aggregation, so it can avoid the generation of multi-fractal aggregates [38].

Freshly emitted soot particles tend to be coated with other chemical components in the atmosphere by the coagulation and condensation of secondary aerosol compounds [39–41]. The closed-cell [42–44] structure is an example of where coating material not only covers the outer layers of soot aggregates but also fills the internal voids among primary spherules [45], which can greatly represent the thinly coated soot. However, thickly coated soot are commonly represented by a structure where soot aggregates are completely embedded in a sphere [46, 47]. In order to reflect the influences of morphology on the radiative properties in the whole atmosphere aging process, 3 types of morphologies were considered in this study: (a) bare soot particles, represented by fractal aggregates; (b) thinly coated soot particles, which composed of concentric monomers; (c) thickly coated soot particles, where the soot aggregates are embedded into other chemical components. The typical soot morphologies are shown in Fig. 1. Even though the real morphologies may be more complex, the morphologies considered in this study can greatly reflect the real morphologies and are more likely to be put into climate model. We generated the bare soot aggregates directly by tunable DLA algorithm. For thinly coated soot, the non-absorbing shell were generated by tunable algorithm, then the soot monomers with identical center as non-absorbing shell were added. The details of generations of thinly coated soot were described by Wu et al. [44]. For thickly coated soot, the non-absorbing sphere are covered over the soot aggregates, as the study of Cheng et al. [24]. When investigating the dependences of radiative properties on particle sizes for different fixed morphologies, we preserved the morphologies for different particle sizes by maintain the relative positions of monomers identical. We generated different morphologies under fixed equivalent volume radius by the way shown in Fig. 2. In this process, we keep the equivalent volume radius of soot-containing particles identical. The soot monomers radius were calculated using:

asoot_bare=RVNs3
asoot_coated=fsootRVNs3
where asoot_bare and asoot_coated represent the soot monomers radius of bare and coated soot aggregates respectively. When the equivalent volume radius is fixed, the soot monomers radius decreases by increasing Ns and reducing soot volume fraction. The morphological parameters assumed in this study are shown in Table 1.

 

Fig. 1 Morphologies considered in this study.

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Fig. 2 The way to generate different morphologies for the fixed RV.

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Tables Icon

Table 1. Morphological parameters of soot particles

2.2. Multiple-sphere T-matrix method

Recently, numerically exact multiple-sphere T-matrix (MTSM) method [48, 49] has been developed to calculate the arbitrary configurations of spheres without overlapping. Compared with other numerical methods, MSTM method calculates the radiative properties of randomly oriented particles analytically without numerical averaging over particle orientations, so it can calculate the radiative properties of particles with high efficiency. In this study, the MSTM version 3.0 [50] was used in this work. However, the calculations are based on the concept of random orientation particles, which is mathematically defined by Mishchenko et al. [51]. In atmosphere, it is reasonable to assume that the possibility of each particle direction is identical, which rigorously satisfies the definition of random orientation. The spheres positions which generated by tunable DLA algorithm are initialized as the input of MSTM version 3.0 at first. Combined with other parameters, such as refractive index, size parameter, and error tolerance, the absorption, scattering and extinction efficiencies and ASY can be obtained from the output file. Due to the fact that there are different configurations satisfy identical fractal law, therefore, the calculation results may be varied over a small range. Many studies attempted to reduce the deviation caused from random clusters by averaging the results over multiple realizations. For example, Wu et al. [52] averaged the radiative properties over 10 realizations and Dong at al. [53] averaged the radiative properties over 5 realizations. In this work, random-oriented radiative properties were averaged over 10 realizations to reflect its general properties.

3. Results

3.1. Radiative properties of soot particles under fixed RV

The radiative properties of soot particles were investigated for a visible wavelength at 0.55um, and the refractive index was assumed to be 1.95 + 0.79i [54]. The coatings were assumed to be organic carbon with a refractive index of constant 1.55 according to Chakrabarty et al. [55].

Figure 3 shows the radiative properties of bare soot particles under fixed RV. It indicates that the optical properties can be diverse even the RV is fixed. Cabs decreases with Ns and increases with Df for small particles but the opposite phenomenon is observed for large particles. When the particle size is small, absorbing material is fully exposed to the electromagnetic field, more compact morphology and less monomers number can result in growing contact among absorbing spheres, therefore, lead to larger electromagnetic field interactions among absorbing materials. As a result, Cabs decreases with Ns and increases with Df. While for large soot, given Ns, monomers radius is large. Therefore, the electromagnetic field is not able to penetrate deeply by the shielding effect of the outer layer of monomers. The increases of Ns and more fluffy morphology allow more absorbing materials exposed to light. Thus, larger Cabs is observed.

 

Fig. 3 Radiative properties of bare soot particles under fixed RV.

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The variation of Csca is also dependent on particle size. For small soot, intensifying scattering interaction between the spherules is observed as the soot aggregates become more compact. The results are consistent with the study of Liu et. al [21]. In addition, less Ns also leads to larger Csca as the aggreagtes also turn more compact when Ns is decreased. However, for large soot aggregates, when Ns is extremely small, Csca may be increased with Ns due to decreasing shielding effects of huge monomers.

ASY increases with Ns when Ns is less than a threshold value but changes slowly for more Ns. There are deferent dependences on Df for different particle sizes. For small soot, the lower Df result in lager ASY due to more asymmetrical structures. However, the contrary effects of Df are observed for large soot, which may be caused by the shielding effect of large monomers.

Figure 4 shows the influences of monomers number on the radiative properties of thinly coated soot particles under fixed RV. Thinly coated soot shares nearly the same dependence on primary particles number as that of the bare soot. This may be due to the fact that the thinly coated soot particles still present fractal characteristics. Differently, when Ns is more than a value, Cabs is always to decrease with Ns due to the fact that the actual absorbing material size is small compared to bare soot.

 

Fig. 4 Radiative properties of thinly coated soot particles under fixed RV, fsoot = 0.4.

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Figure 5 demonstrates the variations of radiative properties with fsoot for different Df. With different fsoot, the relative contents of soot are varied when RV is fixed. It deserves to be investigated for the reason that the information about the relative contents of coatings and soot is commonly unclear. Therefore, it is significative to understand how the contents of coatings influence the optical properties when the total particle size is known. Given identical RV, larger fsoot leads to stronger Cabs due to increases of absorbing materials. Csca is increases with fsoot. It indicates that non-absorbing materials may cause less scattering interaction compared to absorbing materials with identical volume. The dependence of ASY on fsoot is very small, this is due to the fact that the fractal structure is not changed.

 

Fig. 5 The variation of radiative properties of thinly soot particles with soot volume fractions under fixed RV, Ns = 200.

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Figure 6 shows how the radiative properties depend on fsoot for different Ns. When fixing RV, the radius of primary particles changes with Ns. The results show there are nearly identical variations with fsoot for different Ns. However, the effects of Ns are influenced by fsoot. For small particles, the effects of Ns on Cabs is small due to the fully exposure to light. However, there are a little increases when increasing Ns. The reason lies that less Ns could result more compact structure, which results in more electromagnetic field interactions among absorbing spheres. While for large soot, Cabs increases with Ns when coatings is thin but decreases if the soot is further coated. This can be explained as below. For large soot where the monomer is large with a identical Ns, the outer monomers will block the light deeply into monomers. More Ns may result in less shielding effects due to the decreases of monomers radius, so lead to more electromagnetic field interaction among absorbing spheres when the coatings is thin. Therefore, larger Cabs is caused. However, when the soot are further coated, the increasing Ns leads to smaller Cabs. This may be due to the fact that the actual soot size is small.

 

Fig. 6 The variation of radiative properties of thinly soot particles with soot volume fraction under fixed RV, λ = 0.55um, Df = 2.2.

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The effects of Ns on the radiative properties of thickly coated soot particles are shown in Fig. 7. Similar to bare soot and thinly coated soot, the effects of Ns is relative small when Ns is over a threshold value. Thus, it is feasible to simplify the thickly coated soot as a model with less Ns but by no means core-shell sphere because the optical properties changes obviously with Ns if Ns is less than the threshold value.

 

Fig. 7 The effects of primary particles number on the radiative properties of thickly coated soot particles under fixed RV, Df = 2.5.

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3.2. Sensitivity of morphologies on radiative properties

Figures 89 show the sensitivity of Df on radiative properties of bare and thinkly coated soot aggregates. The symbol “R” represents the relative errors of radiative properties of soot with different parameters and “&” is the abbreviation of “and”. For bare and thinly coated soot aggregates, the effects of Df on Cabs is small for small particles, where the relative errors among different Df are within 2.5%. However, for large soot, the effects Df on Cabs is obvious. This phenomenon can be explained from physical insights. When the particle is small, the whole particle is nearly fully exposed to the electromagnetic field. Therefore, the changes of Df leads little variation in electromagnetic interaction among absorbing materials. However, when the soot is large, given identical Ns, the monomer radius is large. The soot is difficult to be fully exposed to the electromagnetic field. The changes of compact degree can result in large variation in shielding effects of large monomers, therefore, large variations of Cabs are observed. In addition, compared with bare soot, the effects of Df on Cabs is smaller for thinly coated soot, where the relative errors between different Df is below 9%. While for bare soot, the relative errors between Df = 2.2 and Df = 2.5 can reach to about 18%. Csca and ASY is more sensitive to Df for small soot.

 

Fig. 8 Relative errors of radiative properties computed with bare aggregates for different Df.

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Fig. 9 Relative errors of radiative properties computed with thinly coated aggregates for different Df, fsoot = 0.4.

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Figure 10 shows the sensitivities of Ns on radiative properties of bare and thinkly coated soot aggregates. For both bare and thinly coated soot, the effects of Ns on Cabs is insensitive when Ns is over a threshold value. The relative errors of Cabs between Ns = 800 and Ns = 500 as well as between Ns = 500 and Ns = 300 are below 1% for bare soot, and below 2.5% for thinly coated soot. The results are consistent with the study of Kahnert [28], who demonstrated that Cabs is insensitive to monomer radius when the monomer radius are within 15–25um. However, when Ns is further decreased, the relative errors of different Ns may be increased. For example, the relative error between Ns = 100 and Ns = 300 can reach to 5% when RV = 0.2784um for bare soot. The reason may be due to the blocking effects of large monomers. For large soot, when the coatings are thin, the relative error between Ns = 100 and Ns = 300 is relative small compared to bare soot, which is below 2%. This may be due to the decreases of actual absorbing materials. However, when the soot is further coated, the relative errors are increased, which reach to 9%.

 

Fig. 10 Relative errors of radiative properties computed with bare and thinly coated aggregates for different Ns, Df = 2.2.

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Relative errors of Csca between Ns = 800 and Ns = 500 are below 5%. However, the relative errors between Ns = 300 and Ns = 100 can be above 15%. It demonstrate again that the Csca is insensitive to Ns unless when the Ns is above a threshold value. However, the ASY is more sensitive to Ns for small soot. This is because the main factor affects ASY of large soot may be the shielding effects of large monomers.

Figure 11 shows the sensitivities of radiative properties to fsoot for thinly coated soot. The Cabs is always rather sensitive to fsoot. Therefore, when given the total particle size, the contents of different components should be carefully considered. Csca is more sensitive to fsoot for small particles. However, ASY is insensitive to fsoot, and the relative errors between different fsoot are below 1.5%, which indicates the thinly coated soot can be calculated as a homogeneous structure for ASY.

 

Fig. 11 Relative errors of radiative properties computed with thinly coated aggregates for different fsoot, Df = 2.2.

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Figure 12 shows the sensitivities of Ns on optical properties of thickly coated soot. The effects of Ns on Cabs and Csca is small when Ns is large. For Cabs, the relative errors between Ns = 200 and Ns = 300 and between Ns = 100 and Ns = 200 is below 1% and 2.5% respectively, and the relative errors of Csca are also below 2.5%. However, when the Ns further decreases, the errors are large. For Ns = 25 and Ns = 100, the relative error of Cabs can reach to about 18% when RV = 0.0464um and the relative error of Csca can reach to about 10% when RV = 0.2784um. ASY is insensitive to Ns due to the unchanged overall spherical structure, and the relative errors of ASY for different Ns are below 2.25%.

 

Fig. 12 Relative errors of radiative properties computed with thickly coated aggregates for different fsoot, Df = 2.5.

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4. Summary and conclusions

In this study, a numerical investigation was conducted to understand the morphological effects on radiative properties of soot particles using MSTM method. We have investigated the morphological effects under different fixed RV. We keep the RV identical, so the soot monomers radius changes for different Ns and fsoot. Our results demonstrate that the effects of different morphologies on the scattering, and absorption properties of soot particles. The radiative properties are significantly affected by morphologies even the particle sizes are fixed. Therefore, we should consider the model errors when using simplified model. However, at a specified range, there are many insensitive parameters under different aging status.

For soot in different aging status, under fixed size, the effects of Ns is insensitive on Cabs when Ns is larger than a threshold value. Therefore, it is possible to simplify the real morphologies as a model with less Ns but by no means single core-shell sphere because there are large changes when Ns is extremely small, which may be due to the shielding effects of large monomers. For bare and thinly coated soot aggregates, Cabs is insensitive to Df when the RV is small, where the relative errors of Cabs for different Df are within 2.5%. However, the sensitivity of Df is obvious for large soot due to the shielding effects of large monomers, and the relative errors for different Df can reach to 18% for bare soot. Compared to bare soot, the effects of Df is small for thinly coated soot. In addition, the effects of fsoot on Cabs is obvious.

Compared to small Ns, the effects of Ns on Csca is also relative low for large Ns. Relative errors of Csca between Ns = 800 and Ns = 500 are below 5% but the relative errors between Ns = 300 and Ns = 100 can be above 15%. The effects of Df on Csca is more obvious for small soot when the Ns is fixed. This is because the main factor affects Csca of large soot may be the shielding effects of large monomers.

For bare and thinly coated soot, ASY is more sensitive to Ns for small particles. However, the effects of Ns on ASY is negligible for thickly coated soot where the relative errors for different Ns are below 2.25%. The reason may be that the overall spherical structure is unchanged. Compared to small soot, the effects of Df is smaller for large soot when fixed Ns. This may be caused by the shielding effects of large monomers. For thinly coated soot, ASY is insensitive to fsoot due to the unchanged fractal structure and the relative errors between different fsoot are below 1.5%.

The aims of study are to understand how the morphologic parameters influence the radiative properties under fixed RV and investigate the sensitivities of morphological parameters on optical properties of soot particles. It may be helpful for the model simplification. For an example, as shown in Fig. 11, for thinly coated soot, the ASY seems to be insensitive to fsoot, so it may be proper to reconstruct the ASY using an aggregate with a homogeneous fractal structure for simplification. In addition, as demonstrated in Fig. 3 and Fig. 4, for both bare and thinly coated soot, Cabs changes slowly with Ns when Ns is beyond a threshold value. Therefore, an equivalent volume structure with less Ns can be used to reconstruct the Cabs. Our study may also improve the understanding of the influences of morphology on radiative properties of soot aerosols.

Funding

National Key Research and Development Plan (Grant No. 2016YFC0800100 and 2017YFC0805100); National Natural Science Foundation of China (NSFC) (Grant No. 41675024 and U1733126); Fundamental Research Funds for the Central Universities (Grant No. WK2320000035).

Acknowledgments

We particularly thank Dr. D. W. Mackowski and Dr. M. I. Mishchenko for the MSTM code and the constructive suggestions of reviewers. We also acknowledge the support of supercomputing center of USTC.

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29. S. China, B. Scarnato, R. C. Owen, B. Zhang, M. T. Ampadu, S. Kumar, K. Dzepina, M. P. Dziobak, P. Fialho, J. A. Perlinger, J. Hueber, D. Helmig, L. R. Mazzoleni, and C. Mazzoleni, “Morphology and mixing state of aged soot particles at a remote marine free troposphere site: Implications for optical properties,” J. Geophys. Res. 42(4), 1243–1250 (2015).

30. A. F. Khalizov, H. X. Xue, L. Wang, J. Zheng, and R. Y. Zhang, “Enhanced light absorption and scattering by carbon soot aerosol internally mixed with sulfuric acid,” J. Phys. Chem. A 113(6), 1066–1074 (2009). [CrossRef]   [PubMed]  

31. Z. Y. Wu, C. L. Song, G. Lv, S. Z. Pan, and H. Li, “Morphology, fractal dimension, size and nanostructure of exhaust particles from a spark-ignition direct-injection engine operating at different air-fuel ratios,” Fuel 185, 709–717 (2016). [CrossRef]  

32. U. O. Koylu, G. M. Faeth, T. L. Farias, and M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100(4), 621–633 (1995). [CrossRef]  

33. H. G. E. Hentschel, “Fractal dimension of generalized diffusion-limited aggregates,” Phys. Rev. Lett. 52(3), 212–215 (1984). [CrossRef]  

34. R. Thouy and R. Jullien, “A cluster-cluster aggregation model with tunable fractal dimension,” J. Phys. A-Math. Gen. 27(9), 2953–2963 (1994). [CrossRef]  

35. A. V. Filippov, M. Zurita, and D. E. Rosner, “Fractal-like aggregates: Relation between morphology and physical properties,” J. Colloid Interface Sci. 229(1), 261–273 (2000). [CrossRef]   [PubMed]  

36. K. Skorupski, J. Mroczka, T. Wriedt, and N. Riefler, “A fast and accurate implementation of tunable algorithms used for generation of fractal-like aggregate models,” Physica A 404, 106–117 (2014). [CrossRef]  

37. M. Wozniak, F. R. A. Onofri, S. Barbosa, J. Yon, and J. Mroczka, “Comparison of methods to derive morphological parameters of multi-fractal samples of particle aggregates from tem images,” J. Aerosol Sci. 47, 12–26 (2012). [CrossRef]  

38. M. H. Jensen, A. Levermann, J. Mathiesen, and I. Procaccia, “Multifractal structure of the harmonic measure of diffusion-limited aggregates,” Phys. Rev. E 65(4), 046109 (2002). [CrossRef]  

39. T. Tritscher, Z. Juranyi, M. Martin, R. Chirico, M. Gysel, M. F. Heringa, P. F. DeCarlo, B. Sierau, A. S. H. Prevot, E. Weingartner, and U. Baltensperger, “Changes of hygroscopicity and morphology during ageing of diesel soot,” Environ. Res. Lett. 6(3), 034026 (2011). [CrossRef]  

40. J. P. Schwarz, R. S. Gao, J. R. Spackman, L. A. Watts, D. S. Thomson, D. W. Fahey, T. B. Ryerson, J. Peischl, J. S. Holloway, M. Trainer, G. J. Frost, T. Baynard, D. A. Lack, J. A. de Gouw, C. Warneke, and L. A. Del Negro, “Measurement of the mixing state, mass, and optical size of individual black carbon particles in urban and biomass burning emissions,” Geophys. Res. Lett. 35(13), L13810 (2008). [CrossRef]  

41. S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013). [CrossRef]   [PubMed]  

42. K. N. Liou, Y. Takano, and P. Yang, “Light absorption and scattering by aggregates: Application to black carbon and snow grains,” J. Quant. Spectrosc. Radiat. Transf. 112(10), 1581–1594 (2011). [CrossRef]  

43. J. Luo, Y. M. Zhang, and Q. X. Zhang, “A model study of aggregates composed of spherical soot monomers with an acentric carbon shell,” J. Quant. Spectrosc. Radiat. Transf. 205, 184–195 (2018). [CrossRef]  

44. Y. Wu, T. H. Cheng, X. F. Gu, L. J. Zheng, H. Chen, and H. Xu, “The single scattering properties of soot aggregates with concentric core-shell spherical monomers,” J. Quant. Spectrosc. Radiat. Transf. 135, 9–19 (2014). [CrossRef]  

45. A. W. Strawa, K. Drdla, G. V. Ferry, S. Verma, R. F. Pueschel, M. Yasuda, R. J. Salawitch, R. S. Gao, S. D. Howard, P. T. Bui, M. Loewenstein, J. W. Elkins, K. K. Perkins, and R. Cohen, “Carbonaceous aerosol (soot) measured in the lower stratosphere during polaris and its role in stratospheric photochemistry,” J. Geophys. Res. 104(D21), 26753–26766 (1999). [CrossRef]  

46. X. L. Zhang, M. Mao, Y. Yin, and B. Wang, “Absorption enhancement of aged black carbon aerosols affected by their microphysics: A numerical investigation,” J. Quant. Spectrosc. Radiat. Transf. 202, 90–97 (2017). [CrossRef]  

47. T. H. Cheng, Y. Wu, and H. Chen, “Effects of morphology on the radiative properties of internally mixed light absorbing carbon aerosols with different aging status,” Opt. Express 22(13), 15904–15917 (2014). [CrossRef]   [PubMed]  

48. D. W. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011). [CrossRef]  

49. M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, “Scattering and radiative properties of semi-external versus external mixtures of different aerosol types,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 139–147 (2004). [CrossRef]  

50. D. W. Mackowski, “MSTM Version 3.0: April 2013,” http://www.eng.auburn.edu/~dmckwski/scatcodes/ (2013).

51. M. I. Mishchenko and M. A. Yurkin, “On the concept of random orientation in far-field electromagnetic scattering by nonspherical particles,” Opt. Lett. 42(3), 494–497 (2017). [CrossRef]   [PubMed]  

52. Y. Wu, T. H. Cheng, L. J. Zheng, and H. Chen, “Models for the optical simulations of fractal aggregated soot particles thinly coated with non-absorbing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 182, 1–11 (2016). [CrossRef]  

53. J. Dong, J. M. Zhao, and L. H. Liu, “Morphological effects on the radiative properties of soot aerosols in different internally mixing states with sulfate,” J. Quant. Spectrosc. Radiat. Transf. 165, 43–55 (2015). [CrossRef]  

54. T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006). [CrossRef]  

55. R. K. Chakrabarty, H. Moosmuller, L. W. A. Chen, K. Lewis, W. P. Arnott, C. Mazzoleni, M. K. Dubey, C. E. Wold, W. M. Hao, and S. M. Kreidenweis, “Brown carbon in tar balls from smoldering biomass combustion,” Atmos. Chem. Phys. 10(13), 6363–6370 (2010). [CrossRef]  

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  30. A. F. Khalizov, H. X. Xue, L. Wang, J. Zheng, and R. Y. Zhang, “Enhanced light absorption and scattering by carbon soot aerosol internally mixed with sulfuric acid,” J. Phys. Chem. A 113(6), 1066–1074 (2009).
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    [Crossref]
  32. U. O. Koylu, G. M. Faeth, T. L. Farias, and M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100(4), 621–633 (1995).
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  38. M. H. Jensen, A. Levermann, J. Mathiesen, and I. Procaccia, “Multifractal structure of the harmonic measure of diffusion-limited aggregates,” Phys. Rev. E 65(4), 046109 (2002).
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    [Crossref]
  41. S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
    [Crossref] [PubMed]
  42. K. N. Liou, Y. Takano, and P. Yang, “Light absorption and scattering by aggregates: Application to black carbon and snow grains,” J. Quant. Spectrosc. Radiat. Transf. 112(10), 1581–1594 (2011).
    [Crossref]
  43. J. Luo, Y. M. Zhang, and Q. X. Zhang, “A model study of aggregates composed of spherical soot monomers with an acentric carbon shell,” J. Quant. Spectrosc. Radiat. Transf. 205, 184–195 (2018).
    [Crossref]
  44. Y. Wu, T. H. Cheng, X. F. Gu, L. J. Zheng, H. Chen, and H. Xu, “The single scattering properties of soot aggregates with concentric core-shell spherical monomers,” J. Quant. Spectrosc. Radiat. Transf. 135, 9–19 (2014).
    [Crossref]
  45. A. W. Strawa, K. Drdla, G. V. Ferry, S. Verma, R. F. Pueschel, M. Yasuda, R. J. Salawitch, R. S. Gao, S. D. Howard, P. T. Bui, M. Loewenstein, J. W. Elkins, K. K. Perkins, and R. Cohen, “Carbonaceous aerosol (soot) measured in the lower stratosphere during polaris and its role in stratospheric photochemistry,” J. Geophys. Res. 104(D21), 26753–26766 (1999).
    [Crossref]
  46. X. L. Zhang, M. Mao, Y. Yin, and B. Wang, “Absorption enhancement of aged black carbon aerosols affected by their microphysics: A numerical investigation,” J. Quant. Spectrosc. Radiat. Transf. 202, 90–97 (2017).
    [Crossref]
  47. T. H. Cheng, Y. Wu, and H. Chen, “Effects of morphology on the radiative properties of internally mixed light absorbing carbon aerosols with different aging status,” Opt. Express 22(13), 15904–15917 (2014).
    [Crossref] [PubMed]
  48. D. W. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
    [Crossref]
  49. M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, “Scattering and radiative properties of semi-external versus external mixtures of different aerosol types,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 139–147 (2004).
    [Crossref]
  50. D. W. Mackowski, “MSTM Version 3.0: April 2013,” http://www.eng.auburn.edu/~dmckwski/scatcodes/ (2013).
  51. M. I. Mishchenko and M. A. Yurkin, “On the concept of random orientation in far-field electromagnetic scattering by nonspherical particles,” Opt. Lett. 42(3), 494–497 (2017).
    [Crossref] [PubMed]
  52. Y. Wu, T. H. Cheng, L. J. Zheng, and H. Chen, “Models for the optical simulations of fractal aggregated soot particles thinly coated with non-absorbing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 182, 1–11 (2016).
    [Crossref]
  53. J. Dong, J. M. Zhao, and L. H. Liu, “Morphological effects on the radiative properties of soot aerosols in different internally mixing states with sulfate,” J. Quant. Spectrosc. Radiat. Transf. 165, 43–55 (2015).
    [Crossref]
  54. T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
    [Crossref]
  55. R. K. Chakrabarty, H. Moosmuller, L. W. A. Chen, K. Lewis, W. P. Arnott, C. Mazzoleni, M. K. Dubey, C. E. Wold, W. M. Hao, and S. M. Kreidenweis, “Brown carbon in tar balls from smoldering biomass combustion,” Atmos. Chem. Phys. 10(13), 6363–6370 (2010).
    [Crossref]

2018 (1)

J. Luo, Y. M. Zhang, and Q. X. Zhang, “A model study of aggregates composed of spherical soot monomers with an acentric carbon shell,” J. Quant. Spectrosc. Radiat. Transf. 205, 184–195 (2018).
[Crossref]

2017 (3)

M. I. Mishchenko and M. A. Yurkin, “On the concept of random orientation in far-field electromagnetic scattering by nonspherical particles,” Opt. Lett. 42(3), 494–497 (2017).
[Crossref] [PubMed]

X. L. Zhang, M. Mao, Y. Yin, and B. Wang, “Absorption enhancement of aged black carbon aerosols affected by their microphysics: A numerical investigation,” J. Quant. Spectrosc. Radiat. Transf. 202, 90–97 (2017).
[Crossref]

D. T. Liu, J. Whitehead, M. R. Alfarra, E. Reyes-Villegas, D. V. Spracklen, C. L. Reddington, S. F. Kong, P. I. Williams, Y. C. Ting, S. Haslett, J. W. Taylor, M. J. Flynn, W. T. Morgan, G. McFiggans, H. Coe, and J. D. Allan, “Black-carbon absorption enhancement in the atmosphere determined by particle mixing state,” Nat. Geosci. 10(3), 184–188 (2017).
[Crossref]

2016 (2)

Z. Y. Wu, C. L. Song, G. Lv, S. Z. Pan, and H. Li, “Morphology, fractal dimension, size and nanostructure of exhaust particles from a spark-ignition direct-injection engine operating at different air-fuel ratios,” Fuel 185, 709–717 (2016).
[Crossref]

Y. Wu, T. H. Cheng, L. J. Zheng, and H. Chen, “Models for the optical simulations of fractal aggregated soot particles thinly coated with non-absorbing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 182, 1–11 (2016).
[Crossref]

2015 (4)

J. Dong, J. M. Zhao, and L. H. Liu, “Morphological effects on the radiative properties of soot aerosols in different internally mixing states with sulfate,” J. Quant. Spectrosc. Radiat. Transf. 165, 43–55 (2015).
[Crossref]

S. China, B. Scarnato, R. C. Owen, B. Zhang, M. T. Ampadu, S. Kumar, K. Dzepina, M. P. Dziobak, P. Fialho, J. A. Perlinger, J. Hueber, D. Helmig, L. R. Mazzoleni, and C. Mazzoleni, “Morphology and mixing state of aged soot particles at a remote marine free troposphere site: Implications for optical properties,” J. Geophys. Res. 42(4), 1243–1250 (2015).

T. H. Cheng, Y. Wu, X. F. Gu, and H. Chen, “Effects of mixing states on the multiple-scattering properties of soot aerosols,” Opt. Express 23(8), 10808–10821 (2015).
[Crossref] [PubMed]

C. He, K. N. Liou, Y. Takano, R. Zhang, M. L. Zamora, P. Yang, Q. Li, and L. R. Leung, “Variation of the radiative properties during black carbon aging: theoretical and experimental intercomparison,” Atmos. Chem. Phys. 15(20), 11967–11980 (2015).
[Crossref]

2014 (3)

K. Skorupski, J. Mroczka, T. Wriedt, and N. Riefler, “A fast and accurate implementation of tunable algorithms used for generation of fractal-like aggregate models,” Physica A 404, 106–117 (2014).
[Crossref]

Y. Wu, T. H. Cheng, X. F. Gu, L. J. Zheng, H. Chen, and H. Xu, “The single scattering properties of soot aggregates with concentric core-shell spherical monomers,” J. Quant. Spectrosc. Radiat. Transf. 135, 9–19 (2014).
[Crossref]

T. H. Cheng, Y. Wu, and H. Chen, “Effects of morphology on the radiative properties of internally mixed light absorbing carbon aerosols with different aging status,” Opt. Express 22(13), 15904–15917 (2014).
[Crossref] [PubMed]

2013 (5)

S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
[Crossref] [PubMed]

C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Response to comment on ’radiative absorption enhancements due to the mixing state of atmospheric black carbon’,” Science 339(6118), 393 (2013).
[Crossref] [PubMed]

M. Z. Jacobson, “Comment on ’radiative absorption enhancements due to the mixing state of atmospheric black carbon’,” Science 339(6118), 3932013.

M. Kahnert, T. Nousiainen, and H. Lindqvist, “Models for integrated and differential scattering optical properties of encapsulated light absorbing carbon aggregates,” Opt. Express 21(7), 7974–7993 (2013).
[Crossref] [PubMed]

T. C. Bond, S. J. Doherty, D. W. Fahey, P. M. Forster, T. Berntsen, B. J. DeAngelo, M. G. Flanner, S. Ghan, B. Karcher, D. Koch, S. Kinne, Y. Kondo, P. K. Quinn, M. C. Sarofim, M. G. Schultz, M. Schulz, C. Venkataraman, H. Zhang, S. Zhang, N. Bellouin, S. K. Guttikunda, P. K. Hopke, M. Z. Jacobson, J. W. Kaiser, Z. Klimont, U. Lohmann, J. P. Schwarz, D. Shindell, T. Storelvmo, S. G. Warren, and C. S. Zender, “Bounding the role of black carbon in the climate system: A scientific assessment,” J. Geophys. Res. 118(11), 5380–5552 (2013).

2012 (4)

C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Radiative absorption enhancements due to the mixing state of atmospheric black carbon,” Science 337(6098), 1078–1081 (2012).
[Crossref] [PubMed]

M. Kahnert, T. Nousiainen, H. Lindqvist, and M. Ebert, “Optical properties of light absorbing carbon aggregates mixed with sulfate: assessment of different model geometries for climate forcing calculations,” Opt. Express 20(9), 10042–100582012.
[PubMed]

C. Liu, R. L. Panetta, and P. Yang, “The influence of water coating on the optical scattering properties of fractal soot aggregates,” Aerosol Sci. Technol. 46(1), 31–43 (2012).
[Crossref]

M. Wozniak, F. R. A. Onofri, S. Barbosa, J. Yon, and J. Mroczka, “Comparison of methods to derive morphological parameters of multi-fractal samples of particle aggregates from tem images,” J. Aerosol Sci. 47, 12–26 (2012).
[Crossref]

2011 (3)

K. N. Liou, Y. Takano, and P. Yang, “Light absorption and scattering by aggregates: Application to black carbon and snow grains,” J. Quant. Spectrosc. Radiat. Transf. 112(10), 1581–1594 (2011).
[Crossref]

T. Tritscher, Z. Juranyi, M. Martin, R. Chirico, M. Gysel, M. F. Heringa, P. F. DeCarlo, B. Sierau, A. S. H. Prevot, E. Weingartner, and U. Baltensperger, “Changes of hygroscopicity and morphology during ageing of diesel soot,” Environ. Res. Lett. 6(3), 034026 (2011).
[Crossref]

D. W. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
[Crossref]

2010 (3)

R. K. Chakrabarty, H. Moosmuller, L. W. A. Chen, K. Lewis, W. P. Arnott, C. Mazzoleni, M. K. Dubey, C. E. Wold, W. M. Hao, and S. M. Kreidenweis, “Brown carbon in tar balls from smoldering biomass combustion,” Atmos. Chem. Phys. 10(13), 6363–6370 (2010).
[Crossref]

M. Kahnert, “On the discrepancy between modeled and measured mass absorption cross sections of light absorbing carbon aerosols,” Aerosol Sci. Technol. 44(6), 453–460 (2010).
[Crossref]

D. A. Lack and C. D. Cappa, “Impact of brown and clear carbon on light absorption enhancement, single scatter albedo and absorption wavelength dependence of black carbon,” Atmos. Chem. Phys. 10(9), 4207–4220 (2010).
[Crossref]

2009 (1)

A. F. Khalizov, H. X. Xue, L. Wang, J. Zheng, and R. Y. Zhang, “Enhanced light absorption and scattering by carbon soot aerosol internally mixed with sulfuric acid,” J. Phys. Chem. A 113(6), 1066–1074 (2009).
[Crossref] [PubMed]

2008 (2)

L. Liu, M. I. Mishchenko, and W. P. Arnott, “A study of radiative properties of fractal soot aggregates using the superposition t-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 109(15), 2656–2663 (2008).
[Crossref]

J. P. Schwarz, R. S. Gao, J. R. Spackman, L. A. Watts, D. S. Thomson, D. W. Fahey, T. B. Ryerson, J. Peischl, J. S. Holloway, M. Trainer, G. J. Frost, T. Baynard, D. A. Lack, J. A. de Gouw, C. Warneke, and L. A. Del Negro, “Measurement of the mixing state, mass, and optical size of individual black carbon particles in urban and biomass burning emissions,” Geophys. Res. Lett. 35(13), L13810 (2008).
[Crossref]

2007 (1)

Q. Y. Xie, H. P. Zhang, Y. T. Wan, Y. M. Zhang, and L. F. Qiao, “Characteristics of light scattering by smoke particles based on spheroid models,” J. Quant. Spectrosc. Radiat. Transf. 107(1), 72–82 (2007).
[Crossref]

2006 (2)

J. C. Chow, J. G. Watson, J. L. Mauderly, D. L. Costa, R. E. Wyzga, S. Vedal, G. M. Hidy, S. L. Altshuler, D. Marrack, J. M. Heuss, G. T. Wolff, C. A. Pope, and D. W. Dockery, “Health effects of fine particulate air pollution: Lines that connect,” J. Air Waste Manag. Assoc. 56(10), 1368–1380 (2006).
[Crossref] [PubMed]

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

2005 (3)

T. C. Bond and H. L. Sun, “Can reducing black carbon emissions counteract global warming?” Environ. Sci. Technol. 39(16), 5921–5926 (2005).
[Crossref] [PubMed]

M. O. Andreae, C. D. Jones, and P. M. Cox, “Strong present-day aerosol cooling implies a hot future,” Nature 435(7046), 1187–1190 (2005).
[Crossref] [PubMed]

L. Liu and M. I. Mishchenko, “Effects of aggregation on scattering and radiative properties of soot aerosols,” J. Geophys. Res. 110(D11), 211 (2005).
[Crossref]

2004 (2)

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[Crossref]

M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, “Scattering and radiative properties of semi-external versus external mixtures of different aerosol types,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 139–147 (2004).
[Crossref]

2003 (1)

T. L. Anderson, R. J. Charlson, S. E. Schwartz, R. Knutti, O. Boucher, H. Rodhe, and J. Heintzenberg, “Climate forcing by aerosols - a hazy picture,” Science 300(5622), 1103–1104 (2003).
[Crossref] [PubMed]

2002 (3)

Y. J. Kaufman, D. Tanre, and O. Boucher, “A satellite view of aerosols in the climate system,” Nature 419(6903), 215–223 (2002).
[Crossref] [PubMed]

S. H. Chung and J. H. Seinfeld, “Global distribution and climate forcing of carbonaceous aerosols,” J. Geophys. Res. 107(D19), 4407 (2002).
[Crossref]

M. H. Jensen, A. Levermann, J. Mathiesen, and I. Procaccia, “Multifractal structure of the harmonic measure of diffusion-limited aggregates,” Phys. Rev. E 65(4), 046109 (2002).
[Crossref]

2000 (1)

A. V. Filippov, M. Zurita, and D. E. Rosner, “Fractal-like aggregates: Relation between morphology and physical properties,” J. Colloid Interface Sci. 229(1), 261–273 (2000).
[Crossref] [PubMed]

1999 (1)

A. W. Strawa, K. Drdla, G. V. Ferry, S. Verma, R. F. Pueschel, M. Yasuda, R. J. Salawitch, R. S. Gao, S. D. Howard, P. T. Bui, M. Loewenstein, J. W. Elkins, K. K. Perkins, and R. Cohen, “Carbonaceous aerosol (soot) measured in the lower stratosphere during polaris and its role in stratospheric photochemistry,” J. Geophys. Res. 104(D21), 26753–26766 (1999).
[Crossref]

1998 (1)

M. P. Menguc and S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci 36(12), 1569–1593 (1998).
[Crossref]

1997 (3)

S. Aggarwal and V. Motevalli, “Investigation of an approach to fuel identification for non-flaming sources using light-scattering and ionization smoke detector response,” Fire Saf. J. 29(2–3), 99–112 (1997).
[Crossref]

S. Manickavasagam and M. P. Menguc, “Scattering matrix elements of fractal-like soot agglomerates,” Appl. Opt. 36(6), 1337–1351 (1997).
[Crossref] [PubMed]

H. Luck, “Remarks on the state of the art in automatic fire detection,” Fire Saf. J. 29(2–3), 77–85 (1997).
[Crossref]

1995 (1)

U. O. Koylu, G. M. Faeth, T. L. Farias, and M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100(4), 621–633 (1995).
[Crossref]

1994 (1)

R. Thouy and R. Jullien, “A cluster-cluster aggregation model with tunable fractal dimension,” J. Phys. A-Math. Gen. 27(9), 2953–2963 (1994).
[Crossref]

1984 (1)

H. G. E. Hentschel, “Fractal dimension of generalized diffusion-limited aggregates,” Phys. Rev. Lett. 52(3), 212–215 (1984).
[Crossref]

1908 (1)

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys.-Berlin 330(3), 377–445 (1908).
[Crossref]

Aggarwal, S.

S. Aggarwal and V. Motevalli, “Investigation of an approach to fuel identification for non-flaming sources using light-scattering and ionization smoke detector response,” Fire Saf. J. 29(2–3), 99–112 (1997).
[Crossref]

Aiken, A. C.

S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
[Crossref] [PubMed]

Alfarra, M. R.

D. T. Liu, J. Whitehead, M. R. Alfarra, E. Reyes-Villegas, D. V. Spracklen, C. L. Reddington, S. F. Kong, P. I. Williams, Y. C. Ting, S. Haslett, J. W. Taylor, M. J. Flynn, W. T. Morgan, G. McFiggans, H. Coe, and J. D. Allan, “Black-carbon absorption enhancement in the atmosphere determined by particle mixing state,” Nat. Geosci. 10(3), 184–188 (2017).
[Crossref]

Allan, J. D.

D. T. Liu, J. Whitehead, M. R. Alfarra, E. Reyes-Villegas, D. V. Spracklen, C. L. Reddington, S. F. Kong, P. I. Williams, Y. C. Ting, S. Haslett, J. W. Taylor, M. J. Flynn, W. T. Morgan, G. McFiggans, H. Coe, and J. D. Allan, “Black-carbon absorption enhancement in the atmosphere determined by particle mixing state,” Nat. Geosci. 10(3), 184–188 (2017).
[Crossref]

Altshuler, S. L.

J. C. Chow, J. G. Watson, J. L. Mauderly, D. L. Costa, R. E. Wyzga, S. Vedal, G. M. Hidy, S. L. Altshuler, D. Marrack, J. M. Heuss, G. T. Wolff, C. A. Pope, and D. W. Dockery, “Health effects of fine particulate air pollution: Lines that connect,” J. Air Waste Manag. Assoc. 56(10), 1368–1380 (2006).
[Crossref] [PubMed]

Ampadu, M. T.

S. China, B. Scarnato, R. C. Owen, B. Zhang, M. T. Ampadu, S. Kumar, K. Dzepina, M. P. Dziobak, P. Fialho, J. A. Perlinger, J. Hueber, D. Helmig, L. R. Mazzoleni, and C. Mazzoleni, “Morphology and mixing state of aged soot particles at a remote marine free troposphere site: Implications for optical properties,” J. Geophys. Res. 42(4), 1243–1250 (2015).

Anderson, T. L.

T. L. Anderson, R. J. Charlson, S. E. Schwartz, R. Knutti, O. Boucher, H. Rodhe, and J. Heintzenberg, “Climate forcing by aerosols - a hazy picture,” Science 300(5622), 1103–1104 (2003).
[Crossref] [PubMed]

Andreae, M. O.

M. O. Andreae, C. D. Jones, and P. M. Cox, “Strong present-day aerosol cooling implies a hot future,” Nature 435(7046), 1187–1190 (2005).
[Crossref] [PubMed]

Arnott, W. P.

R. K. Chakrabarty, H. Moosmuller, L. W. A. Chen, K. Lewis, W. P. Arnott, C. Mazzoleni, M. K. Dubey, C. E. Wold, W. M. Hao, and S. M. Kreidenweis, “Brown carbon in tar balls from smoldering biomass combustion,” Atmos. Chem. Phys. 10(13), 6363–6370 (2010).
[Crossref]

L. Liu, M. I. Mishchenko, and W. P. Arnott, “A study of radiative properties of fractal soot aggregates using the superposition t-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 109(15), 2656–2663 (2008).
[Crossref]

Babenko, V. A.

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[Crossref]

Baltensperger, U.

T. Tritscher, Z. Juranyi, M. Martin, R. Chirico, M. Gysel, M. F. Heringa, P. F. DeCarlo, B. Sierau, A. S. H. Prevot, E. Weingartner, and U. Baltensperger, “Changes of hygroscopicity and morphology during ageing of diesel soot,” Environ. Res. Lett. 6(3), 034026 (2011).
[Crossref]

Barbosa, S.

M. Wozniak, F. R. A. Onofri, S. Barbosa, J. Yon, and J. Mroczka, “Comparison of methods to derive morphological parameters of multi-fractal samples of particle aggregates from tem images,” J. Aerosol Sci. 47, 12–26 (2012).
[Crossref]

Bates, T. S.

C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Response to comment on ’radiative absorption enhancements due to the mixing state of atmospheric black carbon’,” Science 339(6118), 393 (2013).
[Crossref] [PubMed]

C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Radiative absorption enhancements due to the mixing state of atmospheric black carbon,” Science 337(6098), 1078–1081 (2012).
[Crossref] [PubMed]

Baynard, T.

J. P. Schwarz, R. S. Gao, J. R. Spackman, L. A. Watts, D. S. Thomson, D. W. Fahey, T. B. Ryerson, J. Peischl, J. S. Holloway, M. Trainer, G. J. Frost, T. Baynard, D. A. Lack, J. A. de Gouw, C. Warneke, and L. A. Del Negro, “Measurement of the mixing state, mass, and optical size of individual black carbon particles in urban and biomass burning emissions,” Geophys. Res. Lett. 35(13), L13810 (2008).
[Crossref]

Bellouin, N.

T. C. Bond, S. J. Doherty, D. W. Fahey, P. M. Forster, T. Berntsen, B. J. DeAngelo, M. G. Flanner, S. Ghan, B. Karcher, D. Koch, S. Kinne, Y. Kondo, P. K. Quinn, M. C. Sarofim, M. G. Schultz, M. Schulz, C. Venkataraman, H. Zhang, S. Zhang, N. Bellouin, S. K. Guttikunda, P. K. Hopke, M. Z. Jacobson, J. W. Kaiser, Z. Klimont, U. Lohmann, J. P. Schwarz, D. Shindell, T. Storelvmo, S. G. Warren, and C. S. Zender, “Bounding the role of black carbon in the climate system: A scientific assessment,” J. Geophys. Res. 118(11), 5380–5552 (2013).

Bergstrom, R. W.

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

Berntsen, T.

T. C. Bond, S. J. Doherty, D. W. Fahey, P. M. Forster, T. Berntsen, B. J. DeAngelo, M. G. Flanner, S. Ghan, B. Karcher, D. Koch, S. Kinne, Y. Kondo, P. K. Quinn, M. C. Sarofim, M. G. Schultz, M. Schulz, C. Venkataraman, H. Zhang, S. Zhang, N. Bellouin, S. K. Guttikunda, P. K. Hopke, M. Z. Jacobson, J. W. Kaiser, Z. Klimont, U. Lohmann, J. P. Schwarz, D. Shindell, T. Storelvmo, S. G. Warren, and C. S. Zender, “Bounding the role of black carbon in the climate system: A scientific assessment,” J. Geophys. Res. 118(11), 5380–5552 (2013).

Bond, T. C.

T. C. Bond, S. J. Doherty, D. W. Fahey, P. M. Forster, T. Berntsen, B. J. DeAngelo, M. G. Flanner, S. Ghan, B. Karcher, D. Koch, S. Kinne, Y. Kondo, P. K. Quinn, M. C. Sarofim, M. G. Schultz, M. Schulz, C. Venkataraman, H. Zhang, S. Zhang, N. Bellouin, S. K. Guttikunda, P. K. Hopke, M. Z. Jacobson, J. W. Kaiser, Z. Klimont, U. Lohmann, J. P. Schwarz, D. Shindell, T. Storelvmo, S. G. Warren, and C. S. Zender, “Bounding the role of black carbon in the climate system: A scientific assessment,” J. Geophys. Res. 118(11), 5380–5552 (2013).

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

T. C. Bond and H. L. Sun, “Can reducing black carbon emissions counteract global warming?” Environ. Sci. Technol. 39(16), 5921–5926 (2005).
[Crossref] [PubMed]

Boucher, O.

T. L. Anderson, R. J. Charlson, S. E. Schwartz, R. Knutti, O. Boucher, H. Rodhe, and J. Heintzenberg, “Climate forcing by aerosols - a hazy picture,” Science 300(5622), 1103–1104 (2003).
[Crossref] [PubMed]

Y. J. Kaufman, D. Tanre, and O. Boucher, “A satellite view of aerosols in the climate system,” Nature 419(6903), 215–223 (2002).
[Crossref] [PubMed]

Bui, P. T.

A. W. Strawa, K. Drdla, G. V. Ferry, S. Verma, R. F. Pueschel, M. Yasuda, R. J. Salawitch, R. S. Gao, S. D. Howard, P. T. Bui, M. Loewenstein, J. W. Elkins, K. K. Perkins, and R. Cohen, “Carbonaceous aerosol (soot) measured in the lower stratosphere during polaris and its role in stratospheric photochemistry,” J. Geophys. Res. 104(D21), 26753–26766 (1999).
[Crossref]

Cappa, C. D.

C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Response to comment on ’radiative absorption enhancements due to the mixing state of atmospheric black carbon’,” Science 339(6118), 393 (2013).
[Crossref] [PubMed]

C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Radiative absorption enhancements due to the mixing state of atmospheric black carbon,” Science 337(6098), 1078–1081 (2012).
[Crossref] [PubMed]

D. A. Lack and C. D. Cappa, “Impact of brown and clear carbon on light absorption enhancement, single scatter albedo and absorption wavelength dependence of black carbon,” Atmos. Chem. Phys. 10(9), 4207–4220 (2010).
[Crossref]

Carvalho, M. G.

U. O. Koylu, G. M. Faeth, T. L. Farias, and M. G. Carvalho, “Fractal and projected structure properties of soot aggregates,” Combust. Flame 100(4), 621–633 (1995).
[Crossref]

Chakrabarty, R. K.

R. K. Chakrabarty, H. Moosmuller, L. W. A. Chen, K. Lewis, W. P. Arnott, C. Mazzoleni, M. K. Dubey, C. E. Wold, W. M. Hao, and S. M. Kreidenweis, “Brown carbon in tar balls from smoldering biomass combustion,” Atmos. Chem. Phys. 10(13), 6363–6370 (2010).
[Crossref]

Charlson, R. J.

T. L. Anderson, R. J. Charlson, S. E. Schwartz, R. Knutti, O. Boucher, H. Rodhe, and J. Heintzenberg, “Climate forcing by aerosols - a hazy picture,” Science 300(5622), 1103–1104 (2003).
[Crossref] [PubMed]

Chen, H.

Y. Wu, T. H. Cheng, L. J. Zheng, and H. Chen, “Models for the optical simulations of fractal aggregated soot particles thinly coated with non-absorbing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 182, 1–11 (2016).
[Crossref]

T. H. Cheng, Y. Wu, X. F. Gu, and H. Chen, “Effects of mixing states on the multiple-scattering properties of soot aerosols,” Opt. Express 23(8), 10808–10821 (2015).
[Crossref] [PubMed]

Y. Wu, T. H. Cheng, X. F. Gu, L. J. Zheng, H. Chen, and H. Xu, “The single scattering properties of soot aggregates with concentric core-shell spherical monomers,” J. Quant. Spectrosc. Radiat. Transf. 135, 9–19 (2014).
[Crossref]

T. H. Cheng, Y. Wu, and H. Chen, “Effects of morphology on the radiative properties of internally mixed light absorbing carbon aerosols with different aging status,” Opt. Express 22(13), 15904–15917 (2014).
[Crossref] [PubMed]

Chen, L. W. A.

R. K. Chakrabarty, H. Moosmuller, L. W. A. Chen, K. Lewis, W. P. Arnott, C. Mazzoleni, M. K. Dubey, C. E. Wold, W. M. Hao, and S. M. Kreidenweis, “Brown carbon in tar balls from smoldering biomass combustion,” Atmos. Chem. Phys. 10(13), 6363–6370 (2010).
[Crossref]

Cheng, T. H.

Y. Wu, T. H. Cheng, L. J. Zheng, and H. Chen, “Models for the optical simulations of fractal aggregated soot particles thinly coated with non-absorbing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 182, 1–11 (2016).
[Crossref]

T. H. Cheng, Y. Wu, X. F. Gu, and H. Chen, “Effects of mixing states on the multiple-scattering properties of soot aerosols,” Opt. Express 23(8), 10808–10821 (2015).
[Crossref] [PubMed]

Y. Wu, T. H. Cheng, X. F. Gu, L. J. Zheng, H. Chen, and H. Xu, “The single scattering properties of soot aggregates with concentric core-shell spherical monomers,” J. Quant. Spectrosc. Radiat. Transf. 135, 9–19 (2014).
[Crossref]

T. H. Cheng, Y. Wu, and H. Chen, “Effects of morphology on the radiative properties of internally mixed light absorbing carbon aerosols with different aging status,” Opt. Express 22(13), 15904–15917 (2014).
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China, S.

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S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
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D. T. Liu, J. Whitehead, M. R. Alfarra, E. Reyes-Villegas, D. V. Spracklen, C. L. Reddington, S. F. Kong, P. I. Williams, Y. C. Ting, S. Haslett, J. W. Taylor, M. J. Flynn, W. T. Morgan, G. McFiggans, H. Coe, and J. D. Allan, “Black-carbon absorption enhancement in the atmosphere determined by particle mixing state,” Nat. Geosci. 10(3), 184–188 (2017).
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L. Liu, M. I. Mishchenko, and W. P. Arnott, “A study of radiative properties of fractal soot aggregates using the superposition t-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 109(15), 2656–2663 (2008).
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C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Response to comment on ’radiative absorption enhancements due to the mixing state of atmospheric black carbon’,” Science 339(6118), 393 (2013).
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C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Response to comment on ’radiative absorption enhancements due to the mixing state of atmospheric black carbon’,” Science 339(6118), 393 (2013).
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C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Response to comment on ’radiative absorption enhancements due to the mixing state of atmospheric black carbon’,” Science 339(6118), 393 (2013).
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J. C. Chow, J. G. Watson, J. L. Mauderly, D. L. Costa, R. E. Wyzga, S. Vedal, G. M. Hidy, S. L. Altshuler, D. Marrack, J. M. Heuss, G. T. Wolff, C. A. Pope, and D. W. Dockery, “Health effects of fine particulate air pollution: Lines that connect,” J. Air Waste Manag. Assoc. 56(10), 1368–1380 (2006).
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T. Tritscher, Z. Juranyi, M. Martin, R. Chirico, M. Gysel, M. F. Heringa, P. F. DeCarlo, B. Sierau, A. S. H. Prevot, E. Weingartner, and U. Baltensperger, “Changes of hygroscopicity and morphology during ageing of diesel soot,” Environ. Res. Lett. 6(3), 034026 (2011).
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M. H. Jensen, A. Levermann, J. Mathiesen, and I. Procaccia, “Multifractal structure of the harmonic measure of diffusion-limited aggregates,” Phys. Rev. E 65(4), 046109 (2002).
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A. W. Strawa, K. Drdla, G. V. Ferry, S. Verma, R. F. Pueschel, M. Yasuda, R. J. Salawitch, R. S. Gao, S. D. Howard, P. T. Bui, M. Loewenstein, J. W. Elkins, K. K. Perkins, and R. Cohen, “Carbonaceous aerosol (soot) measured in the lower stratosphere during polaris and its role in stratospheric photochemistry,” J. Geophys. Res. 104(D21), 26753–26766 (1999).
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C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Response to comment on ’radiative absorption enhancements due to the mixing state of atmospheric black carbon’,” Science 339(6118), 393 (2013).
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C. D. Cappa, T. B. Onasch, P. Massoli, D. R. Worsnop, T. S. Bates, E. S. Cross, P. Davidovits, J. Hakala, K. L. Hayden, B. T. Jobson, K. R. Kolesar, D. A. Lack, B. M. Lerner, S. M. Li, D. Mellon, I. Nuaaman, J. S. Olfert, T. Petaja, P. K. Quinn, C. Song, R. Subramanian, E. J. Williams, and R. A. Zaveri, “Radiative absorption enhancements due to the mixing state of atmospheric black carbon,” Science 337(6098), 1078–1081 (2012).
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K. Skorupski, J. Mroczka, T. Wriedt, and N. Riefler, “A fast and accurate implementation of tunable algorithms used for generation of fractal-like aggregate models,” Physica A 404, 106–117 (2014).
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J. P. Schwarz, R. S. Gao, J. R. Spackman, L. A. Watts, D. S. Thomson, D. W. Fahey, T. B. Ryerson, J. Peischl, J. S. Holloway, M. Trainer, G. J. Frost, T. Baynard, D. A. Lack, J. A. de Gouw, C. Warneke, and L. A. Del Negro, “Measurement of the mixing state, mass, and optical size of individual black carbon particles in urban and biomass burning emissions,” Geophys. Res. Lett. 35(13), L13810 (2008).
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A. W. Strawa, K. Drdla, G. V. Ferry, S. Verma, R. F. Pueschel, M. Yasuda, R. J. Salawitch, R. S. Gao, S. D. Howard, P. T. Bui, M. Loewenstein, J. W. Elkins, K. K. Perkins, and R. Cohen, “Carbonaceous aerosol (soot) measured in the lower stratosphere during polaris and its role in stratospheric photochemistry,” J. Geophys. Res. 104(D21), 26753–26766 (1999).
[Crossref]

Sarofim, M. C.

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Z. Y. Wu, C. L. Song, G. Lv, S. Z. Pan, and H. Li, “Morphology, fractal dimension, size and nanostructure of exhaust particles from a spark-ignition direct-injection engine operating at different air-fuel ratios,” Fuel 185, 709–717 (2016).
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Zamora, M. L.

C. He, K. N. Liou, Y. Takano, R. Zhang, M. L. Zamora, P. Yang, Q. Li, and L. R. Leung, “Variation of the radiative properties during black carbon aging: theoretical and experimental intercomparison,” Atmos. Chem. Phys. 15(20), 11967–11980 (2015).
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J. Luo, Y. M. Zhang, and Q. X. Zhang, “A model study of aggregates composed of spherical soot monomers with an acentric carbon shell,” J. Quant. Spectrosc. Radiat. Transf. 205, 184–195 (2018).
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C. He, K. N. Liou, Y. Takano, R. Zhang, M. L. Zamora, P. Yang, Q. Li, and L. R. Leung, “Variation of the radiative properties during black carbon aging: theoretical and experimental intercomparison,” Atmos. Chem. Phys. 15(20), 11967–11980 (2015).
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A. F. Khalizov, H. X. Xue, L. Wang, J. Zheng, and R. Y. Zhang, “Enhanced light absorption and scattering by carbon soot aerosol internally mixed with sulfuric acid,” J. Phys. Chem. A 113(6), 1066–1074 (2009).
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Figures (12)

Fig. 1
Fig. 1 Morphologies considered in this study.
Fig. 2
Fig. 2 The way to generate different morphologies for the fixed RV.
Fig. 3
Fig. 3 Radiative properties of bare soot particles under fixed RV.
Fig. 4
Fig. 4 Radiative properties of thinly coated soot particles under fixed RV, fsoot = 0.4.
Fig. 5
Fig. 5 The variation of radiative properties of thinly soot particles with soot volume fractions under fixed RV, Ns = 200.
Fig. 6
Fig. 6 The variation of radiative properties of thinly soot particles with soot volume fraction under fixed RV, λ = 0.55um, Df = 2.2.
Fig. 7
Fig. 7 The effects of primary particles number on the radiative properties of thickly coated soot particles under fixed RV, Df = 2.5.
Fig. 8
Fig. 8 Relative errors of radiative properties computed with bare aggregates for different Df.
Fig. 9
Fig. 9 Relative errors of radiative properties computed with thinly coated aggregates for different Df, fsoot = 0.4.
Fig. 10
Fig. 10 Relative errors of radiative properties computed with bare and thinly coated aggregates for different Ns, Df = 2.2.
Fig. 11
Fig. 11 Relative errors of radiative properties computed with thinly coated aggregates for different fsoot, Df = 2.2.
Fig. 12
Fig. 12 Relative errors of radiative properties computed with thickly coated aggregates for different fsoot, Df = 2.5.

Tables (1)

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Table 1 Morphological parameters of soot particles

Equations (4)

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N s = k 0 ( R g a ) D f
R g 2 = 1 N s i = 1 N s l i 2
a s o o t _ b a r e = R V N s 3
a s o o t _ c o a t e d = f s o o t R V N s 3

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