Morphology and Optical Properties of Numerically Simulated Soot Aggregates

Abstract

An understanding of soot aggregate optical properties is needed for the interpretation of optical measurements of soot. A modified cluster–cluster aggregation (MCCA) was used to numerically generate fractal aggregates containing 15–600 primary particles of

d_p = 30 nm diameter. For each size, the aggregates with fractal dimension D_f = 1.78 and 2.1 (with k_f = 2.24 and 2.26, respectively) were selected, and the scattering and absorption cross sections were calculated using the discrete dipole approximation (DDA). For uncoated aggregates, the optical properties of these numerically generated aggregates were compared with the Rayleigh–Debye–Gans (RDG) approximation. It was found that the differences in the optical cross sections obtained from the two methods were small. In addition, it was also found that the aggregates with similar fractal dimension and fractal prefactor exhibit small variations in the absorption and scattering cross sections. For aggregates with transparent coatings, DDA predicted larger absorption than the core-shell Mie model for volume-equivalent spherical particles. The coating-induced absorption enhancement increases with coating thickness from 10% for a 5-nm layer to about 50%–75% absorption enhancement for a coating thickness of 20 nm. The presence of the coating on the aggregates also results in an increase in the discrepancy between the scattering predicted by the DDSCAT and the equivalent core-shell Mie model with the scattering discrepancies become larger as the coating thickness increases (the scattering discrepancies increases from 65% to 75% and from 20% to 25% for aggregates with N = 200 and 15, respectively).

Copyright 2013 American Association for Aerosol Research

1 INTRODUCTION

Soot particles in the atmosphere have adverse impacts on global climate by absorbing solar radiation and accelerating global warming (Bond and Bergstrom 2006). The contribution of aerosols to climate forcing, however, is still not fully understood in part due to uncertainties in soot radiative properties. Furthermore, these properties are needed for quantitative measurement of soot using optical methods. The challenges arise due to the complex soot morphology, poorly characterized refractive index of soot, and the possibility of transparent coatings on the soot particles.

Large variations in soot refractive index contribute to difficulties in characterizing soot radiative properties (Bond and Bergstrom 2006). Published variations in soot refractive index may reflect its dependence on the optical wavelength and actual differences in soot nanostructure, but the discrepancies may

also result from errors in the geometric model of the soot aggregates that are used to interpret scattering and absorption

measurements.

Soot particles are usually aggregates of fine spheroidal “primary” particles. These clusters are often modeled as mass fractals. That is, the number of primary particles in the aggregate (N) and its radius of gyration (R_g ) are related as follows:

where k_f is the fractal prefactor, D_f is the fractal dimension, and a_p is the radius of the primary particle (a_p = d_p /2).

Real-world particles, such as those produced in engine combustion, may be covered by unburned or partially oxidized fuel and engine lubricants as well as other organic resins (Lammel and Novakov 1995). Medalia et al. (1983) and Stanmore et al. (2001) reported that soot emitted by diesel engine may be encapsulated with soluble organics with a mass fraction of up to 60%, depending on the engine-operating condition. The presence of the transparent coating complicates the calculation of the optical properties. It is believed that the coating affects the soot optical properties by (a) collapsing the aggregate and making it more compact, and (b) acting as a lens that focuses incoming light into the black carbon core of the particle. The two processes brought about by the coating process result in an increase in the light scattering by the particles. For light absorption processes, (a) and (b) have contradictory effects: the collapse of the aggregate results in a decrease in particle absorption, while the addition of the coating causes an increase in absorption (Gangl et al. 2008; Khalizov et al. 2008).

Soot aggregates covered with a thick coating may collapse to form compact structures. In this case, the optical properties can be accurately predicted using the concentric core-shell Mie model. The near-spherical geometry also makes traditional size measurements easier to interpret. As a consequence, the majority of experimental studies focused on compact soot (Schnaiter et al. 2004; Gangl et al. 2008; Bueno et al. 2011). Some aggregates such as those found in engine exhaust, however, may only be coated with a thin layer of organic (e.g., oil or fuel) and hence, they may still retain their fractal-like structure.

Sorensen (2001) provided an extensive review on the optical properties of aggregates. The light scattering is highly affected by the presence of the intracluster interaction between the primary particles in the aggregate, which in turn is highly influenced by the aggregate geometry. This means that scattering and absorption of fractal soot aggregates must be calculated using special approximation methods or advanced numerical models. In previous studies, the optical properties of this type of aggregates were often calculated by simple core-shell Mie model based on the diameter obtained from the scanning mobility particle sizer (SMPS). It is likely that this assumption will produce significant error in the estimated scattering and absorption.

Approximation methods such as Rayleigh–Debye–Gans (RDG) theory have been used for predicting the aggregate optical properties (Jullien and Botet 1987; Dobbins and Megaridis 1991; Köylü and Faeth 1993) since it is computationally efficient and can provide a reasonable estimation of the aggregate scattering (Sorensen 2001). The applications of RDG approximation, however, are usually limited for particles with refractive index near unity and the particle size must be significantly smaller than the wavelength (Bohren and Huffman 1983; Farias et al. 1996; Sorensen 2001).

Numerical methods that have been used in the study of soot aggregate optics include the T-matrix method (Mishchenko et al. 1996), method of moments (MoM) (Harrington 1987), generalized multisphere Mie (GMM) solution (Xu 1995, 1997), coupled electric and magnetic dipole (CEMD) method

(Mulholland et al. 1994), and discrete dipole approximation (DDA) (Draine and Flatau 1994). These numerical methods can be categorized as surface based (such as T-matrix or GMM) and volume based (such as DDA). Surface-based methods are usually faster while providing accurate estimation of the radiative properties of complex-shaped particles. However, they are usually only applicable for homogeneous aggregates composed of nonoverlapping spherical primary particles. For inhomogeneous particles such as soot aggregates covered with coating, volume-based numerical methods must be employed. In this study, the volume-based discrete dipole approach (i.e., DDA) was employed to solve the scattering and absorption problem due to its capability of calculating optical properties of objects with complicated

geometry such as coated aggregates. The main drawback of using the DDA approach is that it requires significant computer resources. Hence, the majority of studies and climate models represented coated soot by either using a simple core-shell sphere model (Schnaiter et al. 2003; Gangl et al. 2008) or applying an “effective medium” theory (Fuller et al. 1999; Yin and Liu 2010). A recent simulation study by Liu et al. (2012) utilizing the core-mantle generalized multiparticle Mie with primary particle point of contact in the coating layer, however, indicated that the latter simple approximation produces inaccurate results for coated aggregate due to the inaccurate model representation.

The main focus of this study is to investigate the optical properties of coated particles using numerically generated aggregates to model soot. The DDA is used to calculate the optical properties for a refractive index chosen to represent soot. The DDA is first used to estimate the optical properties of uncoated aggregate and the results are evaluated using the commonly used Rayleigh–Debye–Gans fractal aggregate (RDG-FA) model. Afterward, DDA is employed to estimate the optical properties of aggregates coated with nonabsorbing material with the purpose of evaluating the deviation between the scattering and the absorption cross sections of coated aggregate with respect to its volume-equivalent Mie core-shell sphere.

2 METHODOLOGY

2.1 Aggregate Simulation

The aggregates used in this study were generated by an algorithm similar to that used by Rogak and Flagan (1992). This “modified cluster–cluster aggregation” (MCCA) differs from the cluster–cluster aggregation (CCA) in that CCA simulates the aggregation of clusters with various (unknown) mass ratios (Kolb et al. 1983; Meakin 1983; Heinson et al. 2010) while MCCA specifies the mass ratio β of the colliding clusters. In MCCA, the growing cluster of N_i (initially N_i = 1; i.e., a cluster grows from a single primary particle) is located at the center of the control space. An added cluster (of size 1 or βN_i , whichever is larger) is then randomly placed near the boundary of the control space and allowed to travel following Brownian motion until it either collides with the growing cluster (the two clusters are then joined at the nearest point of contact) or strays far enough from the growing cluster and the simulation is restarted. The simulation is run until the number of primaries within the aggregate reaches the user-specified N. Two slightly different versions of MCCA (henceforth labeled as “current version” and “Rogak and Flagan (1992)”) were run for this study; in the end, the aggregates generated were very similar. Details on the MCCA algorithm are given in the online supplemental information (Section S1).

FIG. 1 Samples of aggregates generated using MCCA for different D_f .

Two sets of aggregates with D_f   = 1.78 and 2.1 were generated using both versions of MCCA with different values of the mass ratio β. These aggregates contain N = 15, 50, 100, 200, 400, and 600 primary particles. Ten aggregates were produced for each specific N and each MCCA version. A total of 120 aggregates were generated for each D_f . The sample aggregates are shown in Figure 1. A MATLAB program was then used to extract the aggregate geometrical properties such as the three-dimensional (3D) radius of gyration (R_g ), which can be determined from the locations of the primary particles (r_i ) within the aggregate:

TABLE 1 MCCA aggregate aspect ratio and fractal prefactor

Df	Aspect ratio*	kf (PCM)*
1.78	4.18 (± 1.66)	2.24 (± 0.16)
2.1	1.83 (± 0.24)	2.06 (± 0.07)
*The values inside the bracket represent the standard deviation. Table presents arithmetic averages for 120 aggregates ranging in size from 15 to 600.

where r _center is the aggregate center of mass. The availability of the exact geometry is the principle advantage of employing the numerically generated aggregates in investigating the relationship between the projected and the actual aggregate properties. In addition, the fractal dimension used to classify the aggregates was calculated based on the 3D pair-correlation method (PCM). From the aggregate coordinates, the pair correlation function C(l) can be calculated as follows:

with θ = 1 for l < r_ij < l + dl and 0 elsewhere, and r_ij is the distance between particles i and j. The fractal dimension is then obtained from the power-law fit of C(l) for a_p < l < R_g .

Table 1 shows the 3D aspect ratio (based on the principal axis; Fry et al. 2004, see the online supplemental information, Section S2). Table 1 also includes the fractal prefactors derived by using Equation (1) in conjunction with D_f derived from the PCM. The values of the k_f obtained with the PCM represent the average from 120 aggregates for each D_f .

We have also studied PC-MCCA aggregates produced in a prior study (Liu and Smallwood 2010). The PC-CCA method uses particle-cluster growth to generate a collection of small aggregates (i.e., N ≤ 30) that obey the statistical scaling law shown in Equation (1) for a specified k_f and D_f . Randomly selected aggregates from this collection were then joined to form larger aggregates using tunable CCA. Fractal aggregates containing N = 50, 100, 200, 400, and 600 primary particles were generated using the PC-CCA constrained to have k_f   = 2.3, D_f   = 1.78 and 2.1, and a_p = 15 nm, which are typical values for combustion-generated soot.

2.2 Discrete Dipole Approximation (DDA)

The DDA (or “coupled dipole”) uses the volume-integral equation method for discretization of Maxwell's equation and can provide a flexible approach for simulating the light scattering by arbitrarily shaped particles. DDSCAT requires a small interdipole separation (d) compared with (1) any structural lengths in the target and (2) the wavelength λ. For calculation of the total optical cross sections, the second criterion can be adequately satisfied if |m|kd < 1, where k = 2π/λ (Draine and Goodman 1993; Draine and Flatau 1994; Draine 2000). When the target is a strong absorber or a more accurate calculation of differential scattering cross section is needed, a more conservative criterion |m|kd < 0.5 should be applied (Draine 2000).

2.2.1 DDSCAT Features

In practice, the variations in DDSCAT implementations are attributed to different configurations of dipole geometry, different models used to relate the dipole polarizabilities to complex dielectric constant, and different iterative linear system solvers used. The main DDSCAT features chosen in this study are given in Table 2; further details are given in the online supplemental information (Section S3).

TABLE 2 DDSCAT parameters

	DDSCAT parameter
Feature	(Draine and Flatau 2008)
Model version	7.0
Dipole geometry	Cubic lattice
Dipole polarizability	Lattice dispersion relation (GKDLDR)
Iterative solver method	Biconjugate gradient with stabilization (PBCGS2)
Fast Fourier transform	Generalized prime factor algorithm for FFT (GPFA FFT)

The input parameter of the target geometry was set to ensure that the dipole distance d adheres to the conservative criterion |m|kd < 0.5. The detail discussion on the dipole distance is available in the online supplemental information (Section S3.2). For the uncoated aggregate, a default target generation “N_SPHERE” was employed, where the x, y, and z coordinates of the center of the primary particles and their radius were used as DDSCAT input.

The DDSCAT computation will provide absorption and scattering efficiencies (i.e., Q _ext, Q _abs, Q _sca). From these efficiencies, optical cross sections (i.e., C _ext, C _abs, C _sca) can be calculated as follows:

2.2.2 DDSCAT Accuracy

The accuracy of DDSCAT was tested on the scattering and absorption cross sections of concentric coated spheres, for which exact solutions are known. Calculations were performed for light with 532-nm wavelength, corresponding to light from an Nd:YAG laser used in many optical instruments. The distance between dipoles in the DDSCAT was set to be 2.5 nm. The diameter of the core spherical particle is assumed to be 135 nm and exhibits soot-like optical properties with refractive index, m _core = 1.6 + 0.6i. The nonabsorbing coating is assumed to have a refractive index m _coat = 1.46 + 0i [a value that has been used in past studies of soot coated with α-pinene (Schnaiter et al. 2003) and oleic acid (Slowik et al. 2007)]. It was found that the scattering and absorption cross sections predicted

by the DDSCAT are within 1.8% and 2.5%, respectively, of the Mie predictions (see the online supplemental information; Section S3).

3 RESULTS AND DISCUSSION

3.1 Optical Properties of Uncoated Particles

DDSCAT was applied to aggregates with D_f = 1.78 to D_f = 2.1 (95% confidence interval of ±0.012 and 0.007, respectively) for various values of N. The wavelength, refractive index, and dipole distance were the same as in the validation computations. All calculations use d_p = 30 nm, which corresponds to the primary particle size parameter x_p = πd_p/λ = 0.177. Orientation averaging was performed in DDSCAT by specifying the target orientations Φ = 0 to 180 (divided into 18 equal intervals),

Θ = 0 to 180 (divided into 9 equal intervals), and β = 0 to 90 (divided into 3 equal intervals) for a total of 486 orientations. The detailed explanation of the angles used in the orientation averaging is included in the online supplemental information (Figure S6). For each value of D_f and N, 20 different MCCA aggregates were used.

FIG. 2 Normalized aggregate scattering cross sections.

FIG. 3 Normalized aggregate absorption cross sections (GMM and DDSCAT results are indistinguishable at N = 400 and N = 600).

TABLE 3 The average and standard deviation of the optical cross section of the PC-CCA and MCCA as predicted by DDSCAT

	Df = 1.78				Df = 2.1
	C^a s /(N*C^p s )		C^a a /(N*C^p a )		C^a s /(N*C^p s )		C^a a /(N*C^p a )
N	PC-CCA	MCCA*	PC-CCA	MCCA*	PC-CCA	MCCA*	PC-CCA*	MCCA*
50	28.4 ± 0.6	26.8 ± 1.0	1.12 ± 0.01	1.13 ± 0.01	35.7 ± 0.7	35.3 ± 0.8	1.14 ± 0.01	1.12 ± 0.02
100	38.2 ± 0.7	37.1 ± 1.1	1.11 ± 0.01	1.10 ± 0.01	52.6 ± 1.2	50.8 ± 1.4	1.12 ± 0.01	1.11 ± 0.02
200	47.9 ± 1.1	46.8 ± 1.4	1.09 ± 0.01	1.08 ± 0.01	66.5 ± 1.4	65.2 ± 1.5	1.09 ± 0.01	1.08 ± 0.02
400	56.1 ± 0.7	55.7 ± 1.2	1.08 ± 0.01	1.07 ± 0.01	81.7 ± 1.1	80.6 ± 1.2	1.05 ± 0.01	1.06 ± 0.01
600	60.3 ± 0.9	61.2 ± 1.4	1.07 ± 0.01	1.06 ± 0.01	91.4 ± 1.3	91.5 ± 1.5	1.03 ± 0.01	1.03 ± 0.01
*A total of 40 aggregates were analyzed and an equal number of aggregates was generated using the two variations of MCCA described earlier.

Figure 2 summarizes the scattering cross section of the MCCA aggregates, as predicted by DDSCAT, along with predictions for other types of clusters and optical models. The aggregate scattering cross sections (C^a _s ) were normalized with the cross section of primary particles (C^p _s = 0.4463 nm²). The GMM points were previously published elsewhere (Liu and Smallwood 2010); these are based on the GMM model with aggregates generated by the PC-CCA algorithm. The widely used RDG-FA approximation (Dobbins and Megaridis 1991; Köylü and Faeth 1993) uses a simplified model of cluster geometry, considering only N and D_f : it does not use the actual complex aggregate shape. In addition, an RDG simulation was performed for the numerically generated aggregates (i.e., same MCCA aggregates used in the DDSCAT computation) using T-matrix program without multiple scattering. All methods predicted that scattering increases with D_f . Both DDSCAT and GMM predict higher scattering than the RDG calculations, particularly for small aggregates (i.e., N < 100). The discrepancy is smaller for large N, probably because the average density of a fractal aggregate decreases with N, making multiple scattering less important. Also, one expects an improvement in the accuracy of the RDG theory as the phase-shift parameter decreases with aggregate size (Sorensen 2001).

Figure 3 shows the normalized absorption cross sections for the same aggregates and models displayed in Figure 2. The aggregate absorption cross sections (C^a _s ) were normalized by the absorption cross section of primary particles

(C^p _a = 135.29 nm²). Both DDSCAT and GMM include the interaction between primary particles in an aggregate while RDG does not, so RDG predicts unit normalized absorption. DDSCAT and GMM predicted that the aggregate absorption initially increases with size for small aggregate, which can be attributed to the absorption enhancement induced by the aggregation of the primary particles. For large aggregates (i.e., N > 100), the absorption decreases with N. This decrease in the absorption is likely caused by the increase in the particle shielding within the aggregate, which mitigates the aggregation-induced effect. In general, the absorption enhancement observed in this study is consistent with the absorption calculations by Mulholland et al. (1994).

In order to evaluate the effect of cluster generation algorithm on optical properties, the same optical model (DDSCAT) was used for a set of MCCA and PC-CCA clusters (Table 3). The set of aggregates included five PC-CCA aggregates for each N and D_f . Aggregates generated from different growth algorithms had nearly identical absorption and scattering cross sections. This is consistent with prior computational studies (Liu and Mishchenko 2007; Liu and Smallwood 2010), which found that the aggregate geometrical configuration has insignificant effect on the orientation-averaged optical cross sections of soot aggregates provided that D_f and k_f are similar. This means that it is reasonable to use a small number of aggregates in the numerical calculations of orientation-averaged total scattering and absorption cross sections of random-oriented ensemble of aggregates. Kolokolova et al. (2006) observed that aggregates generated with either ballistic or diffusion-limited CCA may exhibit different scattering cross sections. This might be explained by differences in the fractal prefactors as described by

Heinson et al. (2010). Therefore, care is needed in generalizing the results of the present work.

3.2 Optical Properties of Coated Aggregates

Having characterized the simulated aggregates and verified the DDSCAT calculations for uncoated aggregates, we now turn to the chief contribution of this study, i.e., the prediction of optical properties for coated aggregates. We consider the case of thin coatings that do not affect the solid aggregate morphology, as illustrated in Figure 4. For clarity, the coating thickness δ is shown on an isolated primary particle.

FIG. 4 Lightly coated aggregate model.

In this study, the DDSCAT was applied to predict the scattering and absorption cross sections of coated aggregates and the results are compared with the coated sphere Mie model.

In the simulation, the nonabsorbing coating material was assumed to have m _coat = 1.46 + 0i, with the purpose of mimicking the organic coating used in the past experimental studies.

The Mie predictions were based on the core sphere with volume

where d_{p core} = 30 nm.

Figure 5 compares the absorption of coated aggregates with that of volume-equivalent spheres for δ = 5 nm. In DDSCAT, the dipoles for the coating form spherical shells that overlap (because the core primary particles are in contact); the extra dipoles in the overlap volumes were removed in order to provide a more accurate representation. Due to this overlap, the coating increases the particle volume by a factor of 1.8–1.9 relative to the uncoated core; neglecting the overlap would result in a volume of (40/30)³ = 2.37 times the core volume. The DDSCAT simulation was performed for 20 aggregates for each D_f and N combination. The standard error in the absorption ratio was less than 1.2% for each point. As shown by the circle symbol in Figure 5, the DDSCAT provided accuracy within 1% of the Mie theory for estimating the absorption for the concentric coated spherical particle with a core diameter of 30 nm and a coating thickness δ of 5 nm. For this case, the aggregate absorbs more light, especially for low D_f . For D_f = 1.78, the discrepancy between DDSCAT and the core-shell Mie model increases with size until N ∼ 100, and then decreases for N > 100. Bueno et al. (2011) observed a better agreement between the experimental data and the Mie model was for larger aggregates, which is consistent with the trend discussed above.

FIG. 5 Ratio of DDSCAT/Mie for coated aggregate absorption with d_p = 30 nm and δ = 5 nm.

FIG. 6 Ratio of DDSCAT/Mie for coated aggregate absorption for various coating thicknesses (aggregate N = 200 and D_f = 1.78).

For a specified size and fractal dimension (N = 200, D_f  = 1.78), the effects of coating thickness and refractive index on aggregate absorption and scattering are investigated further. The core primary particle diameter is 30 nm as before and the core refractive index, m _core = 1.6 + 0.6i. In addition to the baseline refractive index (m _coat = 1.46 + 0i), calculations are performed for m _coat = 1.65 + 0i (a plausible increase given the wide range of possible coating materials on aggregates). Thicker coatings, with a higher refractive index, increase the absorption of the aggregates relative to that of the volume-equivalent sphere as shown in Figure 6. The 20 uncoated core aggregates are represented by the points at the left-hand axis (D_p ≈ 175 nm); this shows that the Mie model and DDSCAT differ by only 5%. Further information on the absorption cross sections as predicted by the Mie core-shell sphere model can be found in the online supplemental information (Section S4).

FIG. 7 Ratio of DDSCAT/Mie for coated aggregate scattering for various coating thicknesses (aggregate N = 200 and D_f = 1.78).

FIG. 8 Ratio of DDSCAT/Mie for coated aggregate absorption for various coating thicknesses (aggregate N = 15 and D_f = 1.78).

For the same aggregates and coatings of Figure 6,

Figure 7 displays the normalized scattering. Even for uncoated aggregates, scattering is much lower than that of the volume-equivalent sphere, implying the importance of analyzing soot as an aggregate instead of a spherical particle for scattering-based soot measurement techniques. The discrepancies between the aggregate scattering predicted by the DDSCAT and the core-shell Mie model decrease when the transparent coating was first introduced. It is suspected that this is caused by the enhancement effect on the aggregate scattering due to the coating that initially suppressed the aggregate multiple scattering effects.

The effect of coating on the absorption for small aggregates (with N < 30) was also investigated. This type of aggregate is commonly observed in the engine exhaust. In this case, the core particles are specified to be aggregates with N = 15, D_f = 1.78, and m _coat = 1.46. It can be observed in Figure 8 that similar as before, the coating enhances the absorption of aggregates compared with its volume-equivalent sphere counterpart. For small aggregates, it should be noted that absorptions for uncoated aggregates are slightly less compared with its volume-equivalent spherical particles. In addition, it can be observed that the discrepancy between the absorption predicted by the DDSCAT and the equivalent core-shell Mie model is still growing even for the largest value of delta (δ). It is likely that this increasing trend will eventually reach a plateau at a thicker coating condition, just like in the large aggregate case.

Figure 9 shows the scattering for the same set of aggregates investigated in Figure 8. In general, there seems to be a decreasing trend in DDSCAT/Mie scattering ratio as the coating increases.

FIG. 9 Ratio of DDSCAT/Mie for coated aggregate scattering for various coating thicknesses (aggregate N = 15 and D_f = 1.78).

4 CONCLUSIONS

In this article, the optical properties of simulated coated and uncoated fractal-like aggregates have been investigated numerically. Essential groundwork includes careful characterization of the aggregate morphology and validation of the scattering/absorption calculations.

Fractal aggregates containing 15–600 primary particles of d_p  = 30 nm in diameter are numerically generated using an MCCA method. For each size, the aggregates with fractal dimension D_f  = 1.78 and 2.1 (with k_f = 2.24 and 2.26, respectively) were selected. The DDA (software package: DDSCAT version 7.0) has been used to estimate the optical properties for fractal aggregates produced from MCCA, using a refractive index representative of soot. For uncoated aggregates, the scattering and absorption predictions from DDSCAT and the RDG approximation were close. It was observed that aggregates with similar fractal properties (D_f and k_f ) exhibited small variation in the orientation-averaged scattering and absorption cross sections, which are the properties of practical interest.

Optical cross sections for both small (N = 15) and large

(N = 200) aggregates coated with nonabsorbing material were investigated. The DDSCAT aggregate model generally predicted higher absorption than the volume-equivalent core-shell Mie sphere. The increase in the coated aggregate absorption is influenced by the amount of the coating and the coating refractive index. It is observed that the influence of the coating refractive index on the coated aggregate absorption was relatively insignificant when the coating is thin (about 10% absorption enhancement at coating thickness δ = 5 nm), but became more important as the coating thickness increased (about 50%–75% absorption enhancement at coating thickness δ = 20 nm). Similarly, the presence of the coating on aggregates also generally results in an increase in the discrepancy (about 10% increase from uncoated aggregate to coated aggregate with δ = 20 nm) between the scattering predicted by the DDSCAT and the equivalent core-shell Mie model. It should be noted, however, that the increase in scattering discrepancy becomes less important considering that the discrepancies between uncoated aggregate and its volume-equivalent Mie sphere are already at 20%–60%, depending on the aggregate size. These findings highlight the importance of using a true aggregate model in estimating the optical properties of coated soot particles that are not fully

collapsed.

Acknowledgments

[Supplementary materials are available for this article. Go to the publisher's online edition of Aerosol Science and Technology to view the free supplementary files.]