Observations of a Correlation Between Primary Particle and Aggregate Size for Soot Particles

Abstract

For decades, soot has been modeled as fractal-like aggregates of nearly equiaxed spherules. Cluster–cluster aggregation simulations, starting from a population of primary particles, give rise to structures that closely match real aerosols of solid particles produced in flames. In such simulations, primary particle size is uncorrelated with aggregate size, as all aggregates contain primary particles drawn from the same population. Aerosol measurements have been interpreted with this geometric model. Examination of transmission electron micrographs of soot samples from various sources shows that primary particle sizes are not well mixed within an aerosol population. Larger aggregates tend to contain larger primary particles and the variation in size is much larger between aggregates than within aggregates. The soot sources considered here are all substantially not well-mixed (aircraft jet engine, inverted diffusion flame, gasoline direct injection engine, heavy-duty compression ignition engine). The observed variations in primary particle size can be explained if soot aggregates are formed and grew by coagulation in small zones of the combustion chamber, prior to dilution and transport (with minimal coagulation) to the sampling system.

Copyright 2014 American Association for Aerosol Research

INTRODUCTION

Soot particles are normally aggregates of primary particles. Soot radiative and transport properties are influenced by its morphology. Transmission electron microscopy (TEM) is the most common method used for direct characterization of the morphology of soot aggregates (Medalia and Heckman 1969; Samson et al. 1987; Brasil et al. 1999; Gaddam and Vander Wal 2013; Kuribayashi et al. 2013; Seong et al. 2014). Primary particle diameter (d_p), aggregate maximum length and width, projected area equivalent diameter (d_a), and gyration radius (R_g) can be measured from two-dimensional images produced by TEM. Three-dimensional morphology parameters, e.g., number of primary particles in individual aggregates (N_p) and spatial arrangement of the monomers, are commonly inferred from these 2D images (Rogak et al. 1993; Brasil et al. 1999; Park et al. 2004; Tian et al. 2007).

Primary particle diameter has a strong influence on measurable properties. Based on RDG-FA model, light scattering and absorption are proportional to the 6th and 3rd powers of d_p (Sorensen 2001), respectively. Soot active surface area (an important parameter for exhaust gas after-treatment devices and health studies) and mass are also proportional to the 2nd and 3rd powers of d_p, respectively. In our earlier work with others, (Ghazi et al. 2013) our group has shown that if d_p scales as dⁿ_A, the mass-mobility exponent of the particles will be increased by approximately n.

In most previous work, it was assumed that the average primary particle diameter is similar in all soot aggregates generated by a specific combustion source or at a specific operating condition (Dobbins and Megaridis 1991; Dobbins et al. 1994; Farias et al. 1996; Köylü 1997; Bushell and Amal 1998; Bushell and Amal 2000; Charalampopoulos and Shu 2002; Bond and Bergstrom 2006; Liu and Smallwood 2010). In other words, aggregates were assumed to be produced from equal-sized primary particles regardless of the size of the aggregates. This assumption has been used extensively in the generation of numerical aggregates and estimation of soot properties, where changes in the size of the particles in an ensemble of aggregates were only reflected by variations in the number of primary particles.

However, a few recent studies have reported the observation of very different average primary particle diameters in aggregates of different sizes. Barone and her coworkers (Barone et al. 2012) have reported images of aggregates with different primary particle sizes produced by a 2.0 L 4-cylinder DISI engine (see Figures 6 and 7 in Barone et al. 2012). A similar observation is reported for soot particles produced by a 0.55 L single-cylinder GDI engine (Lee et al. 2013). However, none of these studies has provided quantitative results for the variation of primary particle diameter with the size of the aggregates.

The effect of primary particle polydispersity on the fractal dimension of soot aggregates has been investigated before (Eggersdorfer and Pratsinis 2013), but by the nature of the simulation, it was assumed that large and smaller primary particles were equally likely to be present in aggregates of all sizes. As far as we know, this is consistent with previous experimental and theoretical treatments of primary particle polydispersity. This is, however, inconsistent with two widely known features of soot formation. First, in premixed systems, the primary particle size varies systematically with residence time and stoichiometry (Iyer et al. 2007). Second, in most engineered combustion systems, soot is formed only in a tiny fraction of the system volume, usually in turbulent conditions with large fluctuations in local stoichiometry and time spent in conditions favorable to soot formation. Particles formed in different combustion regions experience different formation and growth patterns, e.g., local equivalence ratio and residence time. The size of the primary particles and agglomerates forming in a combustion process depends on the interplay of complex formation and evolution mechanisms including nucleation, coagulation, surface growth, carbonization, oxidation, and sintering (Glassman 1988; Park and Rogak 2003; Park et al. 2005; Kholghy et al. 2013). Typically, surface growth and coagulation prior to carbonization lead to larger more spherical particles. Soot formation processes depend very strongly on both local equivalence ratio and local temperature.

Our group and collaborators have reported similar observations along with quantitative results for soot particles in different combustion sources. Results for the inverted burner have been peer reviewed (Ghazi et al. 2013) but for engine soot and aviation gas turbine, so far some results have been reported in conference proceedings (Tjong et al. 2012; Boies et al. 2013; Graves et al. 2013, 2014). The present work summarizes and compares results from these earlier studies.

Here, TEM results obtained from the analysis of thousands of aggregates and primary particles sampled from multiple operating conditions of three nonpremixed and one (imperfectly) premixed combustion environments are compiled. The variations of d_p in aggregates of different sizes, the effect of shielding on primary particle sizing from TEM images, and the variations in primary particle size are investigated.

EXPERIMENTAL SETUP FOR TEM SAMPLING

Soot samples from two types of reciprocating engines, a jet engine, and the inverted burner were collected on TEM grids using thermophoretic particle sampler (TPS).

Gasoline direct injection (GDI) engine: TEM samples taken from this engine (Ford 2.0 Liter, inline four cylinder) cover two types of fuel (gasoline blended with 0% and 30% ethanol) and four sets of operating conditions. Operating conditions include transient cold start and hot start tests, simulated highway cruise condition (2600 RPM and 40 lb.ft of torque), and a higher speed and lower torque setting (3000 RPM and 28 lb.ft). Exhaust was diluted using a TSI 379020A two-stage rotary disk diluter. Soot samples were collected from either denuded or undenuded streams. In total, 17 sets of soot samples were considered in TEM analysis of soot particles for this source.

High pressure direct injection (HPDI) natural gas engine: Particles were collected from a 15 L, six-cylinder, Cummins ISX engine operating with Westport Innovations HPDI natural gas combustion system. HPDI uses a diesel-pilot to ignite jets of natural gas; performance and emissions are closer to a diesel engine than a pilot-ignited fumigation engine. The engine was operated on a single cylinder (five cylinders were deactivated) at 15 different conditions. Engine speed, load, EGR, and fumigation were varied in these operating conditions. The exhaust gas was diluted with a ratio of approximately 10:1. In total, 14 sets of soot samples were considered for this engine.

Aviation gas turbine (JE): Soot particles were generated by a 120 kN thrust General Electric CFM56-5B4-2P turbofan engine at various engine speeds. All samples were collected downstream of a long (12 m)-heated tube at 160°C. In total, 11 sets of samples collected at engine speeds varying in the range of 1000 to 4500 rpm were considered for this engine.

Laminar inverted burner (IB): Soot samples were collected from an inverted burner fed with methane and operated at eight different global equivalence ratios. Detailed description of the experimental setup is described in (Ghazi et al. 2013). In total, eight sets of soot samples were considered for this burner.

TEM IMAGING AND IMAGE PROCESSING

TEM imaging was performed on the soot samples using a Hitachi H7600 transmission electron microscope operating at 80.0 kV and equipped with an AMT CCD camera. Images were taken at either high resolution or high contrast modes. Images considered in size characterization were collected under optimum optical focus with nominal resolution of 0.2 nm and typical magnifications in the range of 100,000–500,000 times using QuartzPCI software.

Images were taken at different locations on the center and around the grid. Human bias was also reduced by a random selection of the individual aggregates for imaging.

TEM images were analyzed using a semi-automatic MATLAB-based image processing program described in the online supplemental information (SI). Aggregate size was characterized using the binary images produced from the grayscale TEM images with the thresholding technique, and primary particle diameters were measured manually.

RESULTS AND DISCUSSION

Qualitative Observations

Sample TEM images of soot particles collected from the combustion sources considered in this research are illustrated in Figure 1. Each panel of this image corresponds to one combustion source operating in steady state. For each combustion source, aggregates with very different primary particle diameters are shown in this figure.

FIG. 1. Sample TEM images of aggregates with different primary particle sizes. All scale bars are 100 nm.

TABLE 1 Number of TEM images and particles considered

Source	# Of images produced	# Of aggregates analyzed	# Of primary particles analyzed
GDI engine	670	554	6516
HPDI engine	332	584	4030
Aviation gas turbine	351	292	1279
Inverted burner	144	180	>1608^a

^aThis number corresponds only to the primary particles counted in 89 (of 180) aggregates. Inverted burner samples were analyzed prior to other samples and intermediate image processing results are not available for all equivalence ratios.

In these images, an increase in primary particle size with aggregate size can be observed. However, considering the statistical uncertainties, the existence of such a correlation can only be verified by quantitative analysis of thousands of aggregates and primary particles. In addition, these images show that primary particle sizes may be more uniform in individual aggregates than an ensemble of the aggregates—but this too is to be verified statistically, as shown below.

Primary Particle and Aggregate Sizing

The total number of the TEM images produced, and number of the aggregates and primary particles measured for each combustion source are summarized in Table 1.

TEM results obtained from the analysis of these images are illustrated in Figure 2. Each point on this plot corresponds to the average diameter of primary particles and projected area equivalent diameter of one aggregate. Variations within individual aggregates are discussed in the next section. To avoid complexity, results obtained from different operating conditions of each combustion source are grouped together.

FIG. 2. The variation of average primary particle diameter (in individual aggregates) vs. aggregate-projected area equivalent diameter.

Although for each aggregate size range, a distribution of d_p is present, in general the average primary particle size increases with aggregate size. As further discussed in the SI, a constant average primary particle diameter for each of these combustion sources is a poor representation of data. For the GDI engine, the average d_p in individual aggregates increases from approximately 5 nm to 40 nm with aggregate projected area equivalent diameter increasing from 8 nm to 700 nm. Soot samples collected from HPDI engine, aviation gas turbine and inverted burner show similar trends. This confirms considerable increase in average primary particle size (for the cases investigated here, about four–six times increase in size) when aggregate size increases in an ensemble of aggregates (the aggregate size range is almost 10 times larger than primary particle size range). These differences are too large to be explained by artifacts of TEM resolution (image processing program used for these measurements enables operators to zoom on different sections of images for accurate measurements. Consequently, human detection errors are approximately similar for both large and small particles. Moreover, all images were produced at high magnifications providing resolutions better than 0.7 nm/pixel and much smaller than primary particle sizes). These differences cannot also be explained by the physical constraint that d_p cannot exceed d_a (most aggregates have many primary particles, so d_a » d_p). Similar trends were observed for most individual operating conditions, but in each case the scatter is too large to develop accurate correlations.

Primary Particle Polydispersity

The geometric standard deviation of primary particles for the whole ensemble of aggregates (σ_{g, p, ens}) is defined here as: [1] where N_{p, ens} and d_{pg, ens} are the total number and geometric mean diameter of all primary particles measured in an ensemble of aggregates, respectively. This measure of size variation does not consider whether primary particles may be connected within the same aggregate. For all aggregates from a sample, this measure of variation in an ensemble is in the range of approximately 1.25 to 1.7.

The polydispersity, the primary particles within individual aggregates (σ_{g, p, agg}), can be characterized by [2] where N_{p, j} and d_{pg, j} are the total number and geometric mean diameter of all primary particles in j^th aggregate. N_agg is total number of aggregates measured in each ensemble of particles.

As illustrated in Figure 3, primary particles are more uniform in individual aggregates than ensembles of aggregates. In the figure, each symbol is the result of analysis of the hundreds of images obtained for each combustion source and operating condition. This is consistent with the correlation of d_p with d_a shown in Figure 2.

FIG. 3. Geometric standard deviation of primary particle in ensembles of aggregates vs. individual aggregates. Each point on this graph corresponds to σ_(g,p,ens) and average σ_(g,p,agg) for an individual operating condition. Solid line shows 1:1 ratio for the x axis and the y axis.

A higher level of primary particle polydispersity in ensembles of soot particles is attributed to the heterogeneous distribution of combustion charges in macroscopic scales of the combustion domain. However, primary particles mainly form in microscopic scales where combustion charge is relatively homogeneous. Consequently, the observation of large aggregates composed of relatively uniform large primary particles might be correlated to the agglomeration of these monomers in microscopic rich (and hot) regions favorable for primary particle formation. Similarly, smaller aggregates composed of smaller primary particles are formed in small lean regions of the combustion.

Previous work on soot from the premixed McKenna burner (Oltmann et al. 2012) showed that sigma σ_g of the primary particles in ensembles of aggregates was about 1.15. Although the different sampling, microscopy, and analysis procedures in that work might make precise comparison with our work difficult, it is interesting that the premixed laboratory flame, with particles all sampled at a single residence time, show a far narrower primary particle size distribution than shown by any of the systems studied in our work.

Potential Sampling and Image Analysis Artifacts

Sampling and TEM imaging could produce several artifacts which we consider now. First, the sampler may produce unrepresentative samples. All samples discussed here were collected from a heated stream directed at a cold TEM sample grid. The main mechanism of deposition is thermophoresis, but impaction is significant for large particle. In particular, for the jet engine and inverted burner samples, velocities were large enough to result in oversampling of aggregates with large aerodynamic diameters (those larger than about 200 nm). Conceivably, this could bias large-aggregate sampling toward larger primary particles, but the other samples were collected with much lower velocities, and in any case, impaction cannot explain the observations related to Figure 3. For the HPDI and GDI samples, we have confirmed that TEM aggregate sizes are very close to those determined by mobility sizing, so samples are representative of the aerosol.

Several artifacts could arise in the microscopy. Operator bias in selecting aggregates for imaging might be a concern; we address this by imaging all particles in randomly located portions of the grid. Variations in magnification might make smaller primary particles less visible when imaging large aggregates, but in our work, images are produced at high magnification which provides resolutions better than 0.7 nm/pixel and smaller than primary particle sizes. Moreover, primary particle sizing in large aggregates was done by breaking aggregates into smaller sections, by zooming on different parts of the particles, which eliminates the effect of image magnification on the probability of the smaller primary particles being excluded from measurements.

Finally, we consider a fundamental projection artifact that might occur if smaller particles are more likely to be covered by large particles in images of large aggregates. We have investigated this effect using computer-generated aggregates with nonuniform primary particle size; these aggregates were donated by Eggersdorfer and Pratsinis (Eggersdorfer and Pratsinis 2013). This effect is investigated using 1200 aggregates numerically generated by hierarchical cluster–cluster agglomeration algorithm (Botet et al. 1984; Eggersdorfer and Pratsinis 2013). These aggregates consist of 16, 32, 64, and 128 (N_{p, act}) polydisperse primary particles with σ_{g, p, agg} = 1.4. For better simulation of polydispersity effect, the value assumed here for the geometric standard deviation of primary particles in individual aggregates is larger than what we measured for “individual” aggregates and is closer to values measured for “ensembles” of aggregates (σ_{g, p, ens}).

TEM images were simulated by projecting aggregates in three different orientations. Average diameter (d_{p, meas}), geometric standard deviation (σ_{g, meas}), and total number of the primary particles (N_{p, meas}) in individual aggregates which can be detected and measured were calculated from the simulated TEM images. We have not attempted a detailed simulation of the TEM image formation, resulting in a greyscale nonlinearly related to soot thickness. Instead, we use simplified algorithms to estimate what would be observable by normal operators.

As an extreme case, primary particles are assumed to be opaque. This means that the area of a monomer which is placed beneath other monomers cannot be observed in projected images (complete shielding). Moreover, if more than 50% of the area of the primary particle is completely shielded it is assumed that the monomer size cannot be measured. A second model assumes primary particles to be partially transparent and is further discussed in the SI.

Differences between the measured and actual N_p and d_p are measured by normalized parameters defined by Equations (4) and (5). Aggregate size is indicated by projected area-equivalent diameter d_a, normalized by the mean primary particle diameter d_p. Results obtained for ΔN_p and Δd_p are illustrated in Figures 4 and 5. Results acquired for these parameters and variations in σ_g are compared for the two shielding criteria in Figures S1–S3 [3] [4]

FIG. 4. Effect of shielding on the number of primary particles detectable on projected images.

FIG. 5. Effect of shielding on the average primary particle diameter in individual aggregates detectable on projected images.

As expected and shown in Figure 4, as the aggregate size increases, a larger fraction of the primary particles are shielded. Figure 5 shows that the size of the primary particles “measured” from projected images are slightly larger than actual values. This means that shielding results in slightly overestimation of the primary particle sizes from TEM images. However, even for large aggregates, this overestimation is about 2% of the actual size of the monomers. This small shielding effect is negligible comparing to four—six times changes in primary particle size with aggregate size, as illustrated in Figure 2. It confirms that the trends observed in Figures 2 and 3 are not artifacts caused by shielding of the smaller primary particles with larger ones.

CONCLUSIONS

Based on analysis of hundreds of TEM images from three nonpremixed and one (imperfectly) premixed combustion systems, there is a correlation between primary particle and aggregate size. It was shown that larger aggregates are mainly composed of larger primary particles. Moreover, the primary particles are more uniform in individual aggregates than in ensembles of aggregates. These results cannot be explained by the sampling, projection, and image analysis artifacts that we have considered.

These variations in primary particle size are consistent with the aggregates being formed in relatively homogenous microscopic regions; after formation and growth, aggregates from different regions, with different soot formation patterns and/or residence time, are mixed.

Many aerosol properties depend nonlinearly on both primary particle and aggregate size; therefore, it may not be appropriate to assume that all aggregates are formed from primary particles with the same size distribution. The correlation between primary particle size and aggregate size implies a need to adjust the traditional fractal model, because it would no longer be accurate to assume that aggregate mass is proportional to the number of primary particles.

It seems likely that the variations in primary particle size would be different for different sources, but the time involved in manual TEM analysis makes it difficult to provide quantitative measurements that can distinguish these sources.

SUPPLEMENTARY MATERIALS

Supplemental data for this article can be accessed on the publisher's website.

ACKNOWLEDGMENTS

M. Eggersdorfer and S. Pratsinis generously provided the numerically generated aggregates used here to investigate possible TEM projection artifacts. The authors would also like to thank Adam Boies (University of Cambridge), Greg Smallwood (NRC Canada), James Wallace (University of Toronto), Jason Olfert (University of Alberta), and Kevin Thomson (NRC Canada) for their contributions to the sampling campaigns.