Effects of Mixing State on Black Carbon Measurements by Laser-Induced Incandescence

Abstract

Laboratory experiments and theoretical calculations were made to characterize the performance of a Single Particle Soot Photometer (SP2) manufactured by Droplet Measurement Technologies (DMT), which was designed to measure the mass and the mixing state of individual black carbon (BC) or elemental carbon (EC) particles, based on the laser-induced incandescence (LII) technique. In this study, graphite was used as a surrogate of EC. Graphite particles with mass equivalent diameters of 110–200 nm were layered with organic liquids (glycerol and oleic acid) to produce coated graphite with diameters up to 650–800 nm. These were sampled by the SP2 to measure the waveforms (i.e., time development) of the LII and scattering signals. The peak temperature and the peak LII signal of graphite particles were independent of the coating thickness or the coating material to within experimental errors. These results indicate that the mass of EC can be measured by using peak LII signal without interference by the coating conditions. It was also shown that the difference between the times of the scattering and LII peaks can be used as an indicator of coating on EC with thicknesses larger than about 100–200 nm. LII and scattering waveforms were calculated using a newly developed theoretical model that takes into account the physical processes controlling the temperature and evaporation rate of the coated graphite particle in the laser beam. The calculations reproduced the general features of observed waveforms of LII and scattering signals, providing a firm theoretical basis for the interpretation of the SP2 data.

1. INTRODUCTION

Elemental carbon (EC) is produced by incomplete combustion of carbon-based fuels, principally fossil fuels and biomass (e.g., Streets et al. 2003; Bond et al. 2004). Generally, EC is also referred to as black carbon (BC). EC has been identified as making important contributions to the radiative heating of the atmosphere (e.g., Haywood et al. 1997; Myhre et al. 1998; Jacobson et al. 2001). It can also contribute to climate forcing by changing snow and ice albedos (Hansen and Nazarenko 2004). EC particles have been shown to be agglomerates of spherical graphitic carbon with primary diameters of 15–50 nm. Usually, EC particles have organic carbon (OC) coatings upon emission (e.g., Seinfeld and Pandis 1998; Park et al. 2004a, 2004b). EC particles are further coated with various non-refractory compounds (inorganic and organic) by condensation and coagulation as they age in the atmosphere (e.g., Riemer et al. 2004). Size distributions of EC near emission sources (Tokyo) were measured by Kondo et al. (2006) using a calibrated Scanning Mobility Particle Sizer combined with a heated inlet. A majority of the EC mass concentration was in diameters between 50–200 nm, peaking at around 130 nm. Optical properties of EC, usually represented by the mass-normalized absorption cross section (m²/g), depend on how the EC is distributed by size. Furthermore, experiments (e.g., Schnaiter et al. 2005; Mikhailov et al. 2006) and theoretical calculations (e.g., Fuller et al. 1999) have shown that the absorption cross section increases strongly when EC particles are internally mixed (e.g., coated by non-refractory materials). Therefore it is important to measure the size distributions and mixing states of EC for an improved estimate of its climate impact of EC. The Single Particle Soot Photometer (SP2) (Droplet Measurement Technologies (DMT), Boulder, CO) was designed for measurements of the size-segregated concentration of EC by laser-induced incandescence (LII) using continuum laser (Stephens et al. 2003; Baumgardner et al. 2004; Schwarz et al. 2006). The scattering waveforms measured by the SP2 can be used to diagnose the mixing state of EC (Schwarz et al. 2006; Gao et al. 2006). Studies of the effect of internal mixing of EC particles on quantitative measurements by LII are limited because the majority of previous LII studies focus on measurements in the vicinity of combustion sources (e.g., burner flame, mobile exhaust) where EC is rarely internally mixed with non-refractory materials (e.g., Eckbreth 1977; Melton 1984; Michelsen 2003; Michelsen et al. 2003). In addition, prior to the SP2, all LII studies used pulsed lasers and required high concentrations of EC particles, in contrast to the particle-by-particle approach used in the SP2.

Some observational results of EC in the free troposphere using the LII technique have been reported (Baumgardner et al. 2004; Schwarz et al. 2006). Interpretation of these measurements necessitates an improved understanding of possible interferences from the coating by non-refractory materials on the LII response. Slowik et al. (2006) and Gao et al. (2006) first reported the relationship between the EC mixing state and the LII and scattering signals. According to Slowik et al. (2006), the EC particles were coated by either oleic acid (liquid) or anthracene (solid) to thicknesses of up to 100 nm. It was found that (1) the peak intensity of LII was independent of coating thickness, (2) the colour temperature of the LII did not change with coating, and (3) the waveform of the scattering signal changed with the increasing coating thickness. For applications of the SP2 instrument to atmospheric measurements, data for a wider range of coating thickness are desired.

The objective of this study is to fully characterize and interpret the relationships between the LII and scattering signals of the SP2 instrument and the properties of the non-refractory coating on EC particles. We used commercially available graphite particles as a surrogate of EC and have developed a new system using a Tandem Differential Mobility Analyzer (TDMA) for aerosol coating to generate layers of known size. We have also developed a new theoretical model that calculates time-dependent LII signals of the particle consisting of absorbing core and non-absorbing shell. The model calculations are used for the interpretation of some representative experimental data.

2. DMT-SINGLE PARTICLE SOOT PHOTOMETER (SP2)

2.1. Instrument Configuration

The operational principle of the SP2 has been described in previous studies (Stephens et al. 2003; Baumgarder et al. 2004; Schwarz et al. 2006; Slowik et al. 2006; Gao et al. 2006). The schematic diagram of the SP2 is depicted in Figure 1.

FIG. 1 Schematic diagram of the single-particle soot photometer (SP2). Although the axis of the aerosol jet is perpendicular to the plane containing the APDs and the beam of the YAG laser, it is drawn in parallel for simplicity.

An air jet containing sample aerosol intersects an intense (∼ 1 MW cm^{− 2}), Nd:YAG, intra-cavity, continuous laser beam (λ = 1064 nm) pumped by a diode laser. The laser is in a TEM00 mode, with a Gaussian intensity distribution (Stephens et al. 2003; Schwarz et al. 2006). Aerosol particles elastically scatter light in the laser beam and, if they contain light absorbing material at the wavelength of the incident light, like EC, they are also heated as they absorb the laser radiation and eventually incandesce and vaporize due to evaporation at high temperatures. The mass of EC with diameters between about 150–1000 nm is derived by measuring the intensity of the LII signal from individual particles. Non-light absorbing aerosols, such as sulfate, nitrate, and organics, elastically scatter laser light without evaporation during laser irradiation. The size of non-light absorbing aerosol with diameter of 250–1000 nm can be measured by the intensity of scattering. EC particles coated by non-light absorbing material scatter laser light more efficiently than uncoated EC due to the larger scattering cross section (Slowik et al. 2006). We can constrain the chemical composition of an incandescing particle based on the temperature at the point of peak LII intensity because it is a proxy of the boiling point of the composition (Stephens et al. 2003; Baumgardner et al. 2004; Schwarz et al. 2006). Scattering signals, in comparison with the LII signals, are also used for assessing the coating state of EC particles (Schwarz et al. 2006; Gao et al. 2006).

The laser beam power is monitored by a detector that measures a small fraction of the light that passes through the output coupler with an efficiency of 15 part per million (ppm). The light detection system consists of four detectors; one for scattered light, two for LII, and one for redundancy. Each detector system consists of an avalanche photo-diode (APD) (Perkin Elmer C30916E), a complex lens to focus light onto the APD, and optical filters. The broadband and narrowband LII channels are equipped with band pass filters for wavelength regions of λ = 350–800 nm (Schott KG5) and λ = 630–800 nm (Schott KG5 and RG630), respectively. The scattering channel uses a low pass filter that rejects light at λ < 850 nm (Schott RG850). The solid angle Δ Ω (str) of light collection for the lens system is calculated as

for the θ of 15° < θ < 75° and ϕ of 60° < ϕ < 120°, as shown in Figure 2.

FIG. 2 Spherical coordinates of the laser cavity of the SP2. The θ -plane contains the APDs and the beam of the YAG laser. The ϕ-plane contains the aerosol jet and it is perpendicular to the beam of the YAG laser.

The ϕ -plane is parallel to the aerosol jet and perpendicular to the laser beam. The laser beam and four detectors are located in the θ-plane. The amplified voltage signal is digitized by an A-D converter at a sampling rate of 5 MHz (i.e., time resolution of 0.2 μ s) for each channel. The duration of the light pulse is equal to the transit time of a particle in the laser beam, which is typically about 10 μ s. The time resolution of 0.2 μ s for sampling is adequate for recording the temporal evolution of LII and scattering intensities of single particles.

2.2. Formulation of the LII and Scattering Signals

First of all, we give formulations of SP2 signals for systematic interpretation of experimental data and modeling results presented in this paper. The output signals (V) for the broadband and narrowband LII channels, S _bb(t) and S _nb(t), respectively, at a time t are expressed as a function of a particle diameter (D _p ), emissivity (ϵ, particle temperature (T), responsivity of the APD (η), and mathematical constants (s _bband s _nb). In the case of a spherical particle, S _bb(t) and S _nb(t) are written as

where subscripts bb and nb refer to the broadband and narrowband channels, respectively. S, s, and η are given in the units of V, V A^{− 1}, and A W^{− 1}, respectively. R(λ) denotes wavelength-dependent transmittances of the optical filter. D _p , ϵ, and T are functions of t. The Planck function B(T, λ) expresses irradiance (W m^{− 2}nm^{− 1}) at wavelength λ emitted from a blackbody surface at temperature T

where h, c, and k _b are the Planck constant, speed of light, and Boltzmann constant, respectively. s _bb and s _nb are expressed as

where C is the light collection efficiency that should be determined via calibration. C is ∼ 1 for well-aligned conditions. A denotes the amplification factor (V A^{− 1}) of the detection signal. For glassy carbon particles (Alfa Aesar, Ward Hill, MA, USA), the intensity of fluorescence at the wavelength of C₂ Swan bands was observed to be negligibly small as compared to that of LII (Schwarz, J. P., private communication, 2006). As can be seen from Equation (2a) and Equation (2b), the intensity of the LII signal is proportional to D _p ². However, Slowik et al. (2006) and Schwarz et al. (2006) showed that the peak intensity of the LII signal measured by the SP2 was linearly proportional to the EC mass. This might be due to the linear dependence of emissivity on D _p , as detailed below. In any case, EC mass is measured by using the LII peak-EC mass relationship determined from calibration. The peak height of the LII signal of the broadband channel (S _bb ^peak) was used to quantify the EC mass for the present study (section 4.2).

The blackbody temperature of an incandescing particle is determined by the ratio of the LII intensity at different wavelengths. LII signals from broadband (S _bb) and narrowband (S _nb) channels represent radiances at λ = 350–800 nm and λ = 630–800 nm, respectively. The S _bb/S _nb ratio is expressed as follows.

The C _bb/C _nb ratio was determined from the S _bb/S _nb ratio obtained by observing incandescent light from a tungsten-halogen lamp at 3100 K (LS-1, Ocean Optics, Inc., Fla, USA) emitted from the point where light-absorbing particles incandesce. For this purpose, the light from the lamp was transmitted into the chamber using an optical fiber. The wavelength-dependent spectral emissivity (λ = 350–800 nm) of the tungsten at T = 2800 K by Weast (1988) was used for numerical calculation of Equation (5). Very weak temperature dependence of emissivity at 2800 K < T < 3100 K was taken into account for the extrapolation from 2800 K to 3100 K. The C _bb/C _nb ratio was 1.35 during the experiment reported in this paper.

Assuming that ϵ is independent of wavelength within the region of λ = 350–800 nm, Equation (5) can be approximated by the liner relationship

where the constants a and b depend on R _bb(λ), R _nb(λ), and η (λ); a = 0.4757 and b = 5.053 × 10^{− 4} K^{− 1}. By using Equation (6), particle temperature T can be determined independent of the absolute value of ϵ, if ϵ is independent of λ · The particle temperature at the peak of the LII signal (hereafter, denoted as T ^peak) was used to estimate the chemical composition of the particle (e.g., metals, EC) (Stephens et al. 2003; Baumgardner et al. 2004; Schwarz et al. 2006).

Possible errors in determining T caused by the assumption of constant ϵ are assessed for the case of spherical graphite particles. Figure 3a shows spectral emissivities of spherical graphite particles for several diameters calculated using a Mie-scattering code of Bohren and Huffman (1983). The spectral hemispherical emissivity of a flat surface (i.e., infinite particle diameter) was calculated according to Modest (2003), and is also shown for reference. We used the spectral refractive index of graphite by Borghesi and Guizzetti (1991) for these calculations. The refractive index of graphite depends only weakly on λ for λ = 350–800 nm (Borghesi and Guizzetti 1991). The ϵ depends on the size parameter of the particle (π D _p /λ) (Bohren and Huffman 1983). Because of this effect, ϵ depends on λ more strongly for smaller D _p as seen in Figure 3a. ϵ is proportional to D _p for D _p /λ ≪ 1 and independent of D _p for π D _p /λ ≫ 1. For π D _p /λ ≪ 1, the LII intensity of Equation (2a) is proportional to D _p ³, consistent with the observed S _bb ^peak -EC mass linear relationship discussed above. Relationships between S _bb/S _nb and T for particles with different diameters, including a flat surface, are calculated by Equation (5) using these ϵ values and are shown in Figure 3b.

FIG. 3 (a) Spectral emissivity of graphite particles: dependence on particle diameter. (b) Relationship between detected intensity ratio of broadband to narrowband channel and temperature: dependence on particle diameter. Average values of measured S _bb/S _nb at incandescence peak for graphite particles with diameters of 110 and 200 nm are also shown.

The S _bb/S _nb values measured for graphite particles with mass equivalent diameters (D _me) = 110 and 200 nm are also shown for reference. The uncertainty of emissivities due to non-sphericity of the graphite particles (discussed in section 3.1) are not quantified. For D _p > 200 nm, the dependence of ϵ on λ is weak and therefore the S _bb/S _nb−T relationship does not depend on D _p . For D _p < 200 nm, ϵ depends more strongly on λ, leading to deviations of the S _bb/S _nb-T relationship from that for D _p > 200 nm. For D _p = 110 nm, the deviation amounts to ∼ 700 K. It is noted that the observed S _bb/S _nb ratios decrease somewhat with the increase in diameter. Therefore, dependencies of the predicted S _bb/S _nb-T relationship and the observed S _bb/S _nb ratios need be considered in estimating T.

The output signal (V) of the scattered light S _sc is expressed as

where dC _s /dΩ is the differential scattering cross section (m² str⁻¹) of the particle. s _sc (V A⁻¹) is

where η is the responsivity of the APD for scattering, C _sc is the light collection efficiency for the scattering channel, determined by calibration using polystyrene latex (PSL) spheres of known scattering cross section, A _sc is the amplification factor (V A⁻¹) for the scattering channel, and R _sc is the transmittance of the optical filter. Integration of θ in Equation (1) is performed for 15° < θ < 75° (forward scattering), 105° < θ < 165° (backward scattering). The scattering channel is designed for the detection of the scattered light at λ = 1064 nm and the RG850 filter on this channel blocks interference of LII at λ < 850 nm, as discussed in section 2.1. To estimate possible interference of LII at λ > 850 nm on the scattering channel, we measured the S_sc/S_bb ratio for thermal radiation at 3100 K using a tungsten-halogen lamp. From the measured ratio, interference of LII on S _sc at T = 3000–4000 K for a graphite particle with D _p = 100–200 nm was estimated to be smaller than 3%. For the proper tuning of the SP2, the cross sectional intensity profile (on the ϕ -plane in Figure 2) of the laser beam was measured by recording the peak height of S _sc(t) (S _sc ^peak) of mono-disperse PSL particles injected through the aerosol jet at many different radial positions, by horizontally scanning the position of the aerosol jet on the ϕ-plane. The measured laser beam profile, I (W m⁻²) was Gaussian (TEM00 mode) expressed as

where r is the radial coordinate and r = 0 corresponds to the center of the laser beam. The standard deviation σ _r was measured to be 210 ± 10 μm from the measured S _sc ^peak as a function of r. The aerosol jet was tuned so as to be positioned at the center of the laser beam. After this tuning, the peak height of S _sc ^peak was used for sizing scattering aerosols and observing coating state of EC. For the purpose of determining intensity I ₀, the laser beam profile was assumed to be concentrically symmetric. Assuming that the transmittance of the laser coupler is 15 ppm and measuring laser power outside the cavity, the peak amplitude I ₀ was determined to be 0.65 MW cm⁻² under normal operating conditions. In considering the time development of the LII and scattering signals in section 5, we need to express the temporal variation of the laser beam intensity incident on the aerosol particle as a function of t. For this purpose, the velocity of a particle that transits the laser beam (v _p ) was estimated by dividing the full width of half maximum (FWHM) of the laser beam by the FWHM of the scattered pulse by a PSL particle. v _p was measured to be 48 ± 7 m s⁻¹, independent of particle size for particle diameters of D _p = 250–700 nm. The time evolution of the laser beam intensity incident on the aerosol particle is expressed as follows, by substituting r with v _p t in Equation (9)

where t = 0 in Equation (10) is the time when the particle is located at the center of laser beam.

3. LABORATORY EXPERIMENTS

3.1. Characterization of Graphite Particles

Colloidal graphite particles were used as a surrogate for EC in order to investigate the effects of mixing state on incandescence and scattering signals obtained by the SP2. The thermo-chemical and optical properties of graphite particles are better understood than those of other materials, including glassy carbon and flame-generated soot. However, the morphology (shape of individual particles; aggregate or non-aggregate) of graphite particles is poorly known. Knowledge of particle morphology is important for the coating experiment, because irreversible changes in the morphology of soot occur by condensation of liquid compounds (Mikhailov et al. 2006). In addition to this, mass equivalent diameters (D _me) need to be measured so as to uniquely define the volume of compounds that coat the non-spherical particles.

First of all, we measured the shapes of a representative sample of graphite particles using a transmission electron microscope (TEM). For this purpose, graphite particles were generated by atomizing a 50 mL ethanol solution in which 0.1 g of colloidal graphite (stock# 41773, Alfa Aesar, Inc., Ward Hill, MA, USA) was dispersed. After atomization, the graphite particles were passed through a thermo-denuder (inner diameter = 9 mm and total length = 1.2 m) consisting of a heated tube maintained at 400°C and an activated charcoal tube, as shown in Figure 4.

FIG. 4 Schematics of the laboratory experiment for collecting the TEM samples ([1]) and measuring the mass-mobility relationship ([1]+[2]) of colloidal graphite particles.

The air flow rate was maintained at 5–12 cm³ s⁻¹. The thermo-denuder removed ethanol and the dispersing agent (isopropanol) contained in colloidal graphite. Then, the graphite particles were size-selected by a differential mobility analyzer (DMA; TSI model 3081). Both size-selected and unselected graphite particles were collected on collodion films with a Cu-grid for TEM analysis downstream and upstream of the DMA, respectively. The TEM images of the collected particles were obtained by a JEM-400 TEM (JEOL Ltd., Japan) operated at 400 kV at the Center of Advanced Technology of Aoyama Gakuin University in Kanagawa, Japan. Figure 5a shows the TEM image of the graphite particles with mobility diameter (D _mob) of 200 nm. Figure 5b is the image of size-unselected particles.

FIG. 5 TEM images of colloidal graphite (Alfa Aesar, Inc, Stock# 41773) particles collected on collodion films with Cu-grid. (a) Collected downstream of the DMA with a transmission mobility diameter of 200 nm. (b) Collected downstream of thermo-denuder prior to sizing by DMA.

As shown by these images, graphite particles were non-spherical. However, they were not branched-aggregates, unlike combustion-generated soot. Therefore, graphite particles will change their shapes very little with the condensation of volatile compounds.

Secondly, we measured D _me using the DMA-APM (Aerosol Particle Mass analyzer) system (e.g., McMurry et al. 2002) shown in Figure 4. The APM measured masses of graphite particles that were mobility size selected by the DMA. For these measurements, the flow rates of the sample air and the sheath air of DMA were maintained at 5 and 100 cm³s⁻¹, respectively. This sheath/sample flow ratio leads to a D _mob-transmission width of 5%. The D _mob values were set to 150, 200, and 250 nm. Detailed descriptions of the APM are given elsewhere (Ehara et al. 1996; McMurry et al. 2002). APM model 302 (KANOMAX, Inc., Osaka, Japan) was used for this study. The radius of the inner (r ₁) and outer (r ₂) electrodes of the APM model 302 are 50 mm and 52 mm, respectively. The rotational speed (ω) of the APM cylinder was varied between 3000 and 4000 rpm, and the voltage of the electrode (V _APM) was scanned from 25 to 900 V, depending on D _mob (150–250 nm). During the APM voltage scan, the number concentration of particles downstream of the APM was measured by using a condensation particle counter (CPC; TSI model 3022A) to obtain mass distribution of the particles. The central mass m _cen is calculated by equating the centrifugal force and electric forces accelerating a particle in the annular gap

where n, e, and r denote the charge number of the particle, elemental charge and the mean distance from the rotational axis to the center of the annular gap (r = (r ₁+ r ₂)/2), respectively.

Figure 6 shows the number concentrations of graphite particles as a function of m _cen for D _mob = 150, 200, and 250 nm.

FIG. 6 Mass spectra of colloidal graphite particles with mobility diameters of (a) 150 nm, (b) 200 nm, and (c) 250 nm.

The peaks of the masses for these D _mob values were 1.65, 4.20, and 8.94 fg, respectively. D _me was calculated by using the mass-D _mob relationship, assuming that the bulk density of graphite at room temperature is 2.26 g cm⁻³ (Michelsen 2003). The D _me for particles with D _mob = 150, 200, and 250 nm were derived to be 112, 153, and 196 nm, respectively.

3.2. Experimental Setup

This study uses a core-shell model (Figure 7) for quantitative expression of the mixing state of coated particles. As discussed in section 2.2, a particle can be identified as EC by the T _peak and the mass is measured by the S _bb ^peak essentially for uncoated EC particles. However, effects of the coating on EC on T _peak and S _bb(t) are poorly understood, especially when thickness exceeds 100 nm. We conducted laboratory experiments to quantify possible interference of the coating on these parameters. For this purpose, we used a simple apparatus by which core particles were coated by low vapor pressure liquid compounds, as depicted in Figure 8.

FIG. 7 Model of internally mixed particle of core-shell morphology: Definition of core diameter (D _c ) and particle diameter (D _p ).

FIG. 8 Schematic diagram of the coating apparatus.

Core particles (PSL or graphite) were generated by an atomizer (Model 3076 (PSL) and Model 9302 (graphite), TSI, Inc., Shoreview, MN, USA). They were introduced to a Pyrex test tube partially filled by liquid organic material; glycerol (B.P. = 290°C) and oleic acid (B.P. = 360°C) were used for the present study. These organic liquids were vaporized by heating to about 100°C then re-condensed onto the core particles. The flow rate of air containing the core particles was 12 cm³ s⁻¹, and the number concentration of the particles was maintained at about 10³ particles cm⁻³. We first used PSL as core particles in order to characterize the performance of the coating apparatus. A core diameter (D _c ) of 150 nm was chosen for this test. The size distributions of the coated particles were measured with a Scanning Mobility Particle Sizer (SMPS) consisting of a TSI model 3081 DMA and a TSI model 3022A CPC. Figure 9 shows the measured size distributions as a function of the particle diameter (D _p ) for two oil bath temperatures.

FIG. 9 Size distributions of oleic acid-coated PSL particles: Dependence on oil bath temperature of the coating apparatus.

The initial size distribution of PSL (D _c = 150 nm) is also shown for reference. The size distribution of the coated particles was adjusted by controlling the oil bath temperature. It was found that coated particles with D _p < 800 nm were generated by maintaining the oil bath temperature at 70 ± 5°C and 100 ± 5°C for glycerol and oleic acid, respectively. At these oil bath temperatures, particles with diameters smaller than 150 nm were not observed, indicating that new particle formation by homogeneous nucleation of the organic vapor did not occur. We generated graphite particles coated by organic materials with fixed D _c and D _p using the system, schematically shown in Figure 10.

FIG. 10 Schematics of the laboratory experiment for measuring LII and scattering signals of SP2 for organic-coated graphite particles.

These graphite particles were size selected by the DMA 1 (TSI model 3081). D _mob of selection were 150, 200, and 250 nm in this study. For graphite particles, we defined the graphite core diameter as D _c = D _me (= 112, 153, and 196 nm) calculated from D _mob, as discussed in section 3.1. For simplicity, we used approximate D _c values of 110, 150, and 200 nm, which differ from the above values by 2%. The mono-disperse graphite particles with a diameter of D _c were introduced to the apparatus for coating by glycerol or oleic acid. Before being sampled by the SP2, the coated particles were size selected (D _p ) again by the second DMA (DMA 2, TSI model 3081), which was operated at an aerosol flow rate of 6 cm³ s⁻¹. Sheath/sample flow ratios of DMA 1 and DMA 2 were maintained at 9–18, depending on the selection diameter. In this range of sheath/sample flow ratios, the size transmission width of the DMA is estimated to be narrower than ±6%. It was found that the size distribution and number concentration of coated particles did not change within the measurement uncertainties during transport through the 3.8 mm inner diameter copper tubes between DMA 2 and SP2. Coated particles with D _c = 110, 150, and 200 nm and D _p < 800 nm were measured by the SP2. For uncoated graphite particle, D _p is defined as D _p = D _c . Doubly charged particles were easily discriminated from singly charged particles and were rejected because both D _c and D _p of doubly charged particles were about twice as large as those of singly charged particles. In previous studies, coated particles with fixed D _p were generated by controlling the vapor pressures of condensable gases or the residence time of core particles within the vapor (Cruz and Pandis 1998; Hansson et al. 1998; Joutsensaari et al. 2001; Katrib et al. 2004). For the present study, D _p was directly controlled by the DMA with a good accuracy, as described above. It should be noted that both glycerol and oleic acid are resistant to pyrolysis. Possible effects of pyrolysis on LII signals would be smaller than those for organic compounds that pyrolyze without vaporization (e.g., sugar, humic acid).

4. EXPERIMENTAL RESULTS

4.1. Waveforms of LII and Scattering Signals

Figure 11 shows the measured S _bb(t) and S _sc(t) for individual glycerol-coated graphite particles with D _c = 150 nm and D _p = D _c , 300, 400, and 500 nm. The coating thicknesses defined as Δ D _p = D _p − D _c , were 0, 150, 250, and 350 nm, respectively. Here, we introduce the symbol S _sc ^peak to denote the maximum value of S _sc(t). For Figure 11, we selected the data with average S _bb ^peak and S _sc ^peak (within 5% of the average values for 10³ particles sampled). The absolute times when the incandescing particles encounter the laser beam cannot be determined; t = 0 in Figure 11 does not necessarily correspond to the time when the particle was located at the center of the laser beam. As shown in Figure 11, S _bb ^peak did not significantly depend on D _p as discussed in more detail in section 4.4. However, the width (FWHM) of S _bb(t) decreased by 50% with an increase in D _p from D _c (Figure 11a) to 500 nm (Figure 11d). The decrease of the width is likely due to faster sublimation of graphite at larger Δ D _p as discussed in section 5.2. The S _sc ^peak strongly depended on D _p as did the time difference (Δ t) between the time (t _S ) of the S _sc(t) = S _sc ^peak and the time (t _I ) of S _bb(t) = S _bb ^peak, as shown in Figure 11c. For a thin coating with Δ D _p = 150 nm, S _sc(t) showed a single peak near t _I with Δ t = 0–1 μs, similarly to the uncoated particles with Δ D _p = 0 nm (Figure 11a and Figure 11b). In this case, the scattering peak was due to the scattering by uncoated graphite, after the coating completely evaporated.

FIG. 11 D _p dependence of waveforms of LII and scattering signals of glycerol-coated graphite particle of D _c = 150 nm. The times for peaks of LII (t _I ) and scattering (t _S ) are also shown. (a) D _p = D _c (uncoated graphite), (b) D _p = 300 nm, (c) D _p = 400 nm, and (d) D _p = 500 nm.

For ΔD _p = 250 nm (D _p = 400 nm), a scattering peak was observed at t = t _S (1), 3–4 μs prior to t _I as shown in Figure 11c. For this Δ D _p , evaporation rate of the coated materials was slower and the scattering cross section of coated particle was larger than that for Δ D _p = 150 nm. The first scattering peak at t = t _S (1) is due to the scattering by the coated material. S _sc (t) also showed a second peak at t = t _S (2), close to t _I , indicating that this peak was due to scattering by the core. For Δ D _p = 350 nm, only the first scattering peak was observed, with S _sc ^peak several times higher than that for Δ D _p = 250 nm (Figure 11d). In this case, the second peak by the core was not seen because it was much weaker than the first peak. Figure 12 shows the S _bb(t) and S _sc(t) measured for oleic acid-coated graphite particles with D _c = 150 nm and with (a) D _p = 300 nm and (b) D _p = 400 nm.

FIG. 12 Waveforms of LII and scattering signals of oleic acid-coated graphite particles of D _c = 150 nm. (a) D _p = 300 nm and (b) D _p = 400 nm. The times for peaks of LII (t _I ) and scattering (t _S ) are also shown.

In contrast to glycerol coating, even for Δ D _p = 150 nm, the scattering peak by the coated material was observed at t = t _S (1) (Figure 12a). The first scattering peak at t = t _S (1) was smaller than the second peak at t = t _S (2). Furthermore, for Δ D _p = 250 nm, S _sc ^peak for oleic acid coating was about 2 times larger than that for glycerol coating. Refractive indices of glycerol and oleic acid differ only by about 1% (Table 1b and Table 1c), leading to only 5% difference in the scattering cross sections. It is likely that the larger S _sc ^peak for oleic acid was due to the slower evaporation. The slower evaporation of oleic acid may be due to its higher boiling point.

TABLE 1b The parameters and functions of glycerol used in LII modeling

Symbols	Parameter	Values used	Units	Reference
M v	Molecular weight of vapor	0.0921 (C3H8O3)	kg/mol
P	Vapor pressure	log 10 P = 9.6118 − 1948.7(T − 140.2)^− 1	Pa	Japan Oil Chemists' Society 2001
Δ H v	Enthalpy of vaporization	37308 T ^2(T − 140.2)^−2	J/mol	Calculated from P(T)
c	Specific heat	1495 + 3.457T − 1.221 × 10^− 3 T ^2	J/kgK	Omel'chenko 1962
ρ	Bulk density (liquid)	1.55 × 10^3 − 0.959T	kg/m^3	Japan Oil Chemists' Society 2001
D va	Vapor-Air binary diffusion coefficient	4.34× 10^− 5 T ^1.75/P total[Pa]	m^2/s	Fuller et al. 1966
—	Refractive index	1.475 − 0.0i	–	The Chemical Society of Japan 1993

TABLE 1c The parameters and functions of oleic acid used in LII modeling

Symbols	Parameter	Values used	Units	Reference
M v	Molecular weight of vapor	0.2825 (C18H34O2)	kg/mol
P	Vapor pressure	log 10 P = 11.9667 − 4531.99(T + 15.886)^− 1	Pa	Stull 1947
Δ H v	Enthalpy of vaporization	86764T ^2(T + 15.886)^− 2	J/mol	Calculated from P(T)
c	Specific heat	423.8 + 5.02T	J/kgK	Japan Oil Chemists' Society 2001
ρ	Bulk density (liq.)	1.08× 10^3 − 0.644T	kg/m^3	Japan Oil Chemists' Society 2001
D va	Vapor-Air binary diffusion coefficient	2.01× 10^− 5 T ^1.75/P total[Pa]	m^2/s	Fuller et al. 1966
—	Refractive index	1.458 − 0.0i	—	Japan Oil Chemists' Society 2001

4.2. Time Delay of LII Peak

As discussed in section 4.1, the time delay of the LII peak (Δ t = t _I −t _S ) is an indicator of coating state. For thin-coated graphite particles, it is difficult to routinely extract information of coating state from the first scattering peak with sufficiently high signal-to-noise ratios when the S _sc(t) signal is weak, although with visual inspection, it will be possible to use the information of the first peak, at least in laboratory studies. The fluctuation of the S _sc(t) for ambient EC particles was larger than that for graphite particles probably because of the presumably irregular shapes of ambient EC. Thus, the practical use of the first scattering peak is more limited for ambient EC if the first scattering peak was comparable or smaller than the second peak. Therefore, in the present study, we defined Δ t = t _I −t _S only for the largest scattering peak (S _sc ^peak) in the S _sc(t) signal. Figure 13a shows Δ t as a function of D _p for D _c = 110, 150, and 200 nm.

FIG. 13 Scattering peak-to-LII peak time delay (Δ t) for organic-coated graphite particles of D _c = 110, 150, and 200 nm. Each data point is average value of 10³ particles. (b) Scattering peak-to-LII peak time delay (Δ t) for internally mixed ambient EC of D _c = 150, 200, and 250 nm. Each data point is the average value of 10³ particles.

For each D _c , Δ t showed a discontinuous increase with the increase in D _p . If the scattering peak by uncoated graphite (second peak) is larger than that by coated graphite particle (first peak), Δ t is close to zero (0-1 μ s) as in the case of (D _c , D _p ) = (150 nm, 300 nm) shown in Figure 12a. If two scattering peak heights become equal, Δ t changes discontinuously by definition. This transition in Δ t was observed for organic-coated graphite for each D _c as shown in Figure 13a where Δ t was 0–1 μ s (short-Δ t) for thin-coating and 3–4 μ s (long-Δ t) for thick-coating. For D _c = 110 nm, as an example, transition of Δ t occurred at Δ D _p = 170 nm (D _p = 280 nm) for glycerol and Δ D _p = 120 nm (D _p = 230 nm) for oleic acid. Here, the threshold Δ D _p for Δ t-transition, denoted as Δ D _p * hereafter, was defined as Δ D _p , where the short-Δ t and long-Δ t were observed with the same frequency. For D _c = 110–200 nm, the transition from short-Δ t to long-Δ t occurred at Δ D _p * ∼ 150–250 nm for glycerol-coated graphite and at Δ D _p * ∼ 100–150 nm for oleic-acid coated graphite. For oleic-acid, the Δ D _p * values were smaller than glycerol by about 50 nm, because of the slower evaporation rate mentioned in section 4.1. The Δ D _p * gives a measure of the minimum detectable thickness of coating on the graphite.

The Δ D _p * was also measured for EC particles coated by non-refractory compounds in ambient air in the suburbs of Tokyo, Japan in the summer of 2004. For this measurement, the D _p of coated EC particles was selected by DMA (Model 3081, TSI inc.) after drying the aerosol flow by using a diffusion dryer (Model 3062, TSI inc.). The D _c of the EC particles was defined as mass equivalent diameter with a bulk density of 1.77 g/cm³ (Park et al. 2004b). The mass of EC particles was measured by using calibrated S _bb ^peak-EC mass relationship obtained by sampling ambient EC particles. For this calibration, the EC mass was selected by using a system consisting of an inlet heated at 400°C, a DMA, and an APM (Kondo et al. 2006). The results for D _c = 150, 200, and 250 nm are shown in Figure 13b.

The Δ D _p * of the coated EC in ambient air was about 100–200 nm, similar to that of organic-coated graphite particles for D _c = 110–200 nm, and the values of short-Δ t and long-Δ t were 0–1 μ s and 3–4 μ s, respectively. These observations, together with the laboratory experiments demonstrate that the Δ t is an indicator of coating on EC with Δ D _p > about 100–200 nm for D _c = 150–250 nm.

We also examine the dependence of the Δ D _p -Δ t relationship on laser power with laboratory experiment. For D _c = 110 nm and Δ D _p = 290 nm, and for D _c = 150 nm and Δ D _p = 350 nm, the long-Δ t values decreased (increased) by only about 0.5 μ s with changes of laser power by +(−)40% from normal operating values (i.e., I ₀ = 0.47–0.85 MW/cm²). For uncoated or thin-coated graphite with D _c = 110–200 nm, the short-Δ t was stable from 0–1 μ s, depending little on the change of the laser power. For field measurements, the laser power was tuned to within ± 15% of the normal operating values (0.65 ± 0.1 MW/cm²). This ± 15% variability should not influence the Δ D _p * values derived above.

4.3. Dependence of T _peak and S _bb ^peak on Coating

The peak temperatures (T ^peak) of coated graphite particles were determined from the measured S _bb ^peak/S _nb ^peak using the S _bb/S _nb-T relationship shown in Figure 3b. Figure 14a and Figure 14b show T ^peak of coated graphite with D _c = 110 and 200 nm, as a function of D _p .

FIG. 14 D _p dependence of particle temperature at the time of the LII peak for organic-coated graphite particles of (a) D _c = 110 nm and (b) D _c = 200 nm.

Each data point represents the average value of data from about 10³ particles and the vertical bars represent 1σ. For uncoated graphite with D _c = 200 nm and Δ D _p = 0 nm, the T _peak was 3800 ± 300 K (± 1σ). The average T _peak value changed only to within ± 3% for glycerol and oleic acid-coated particles with Δ D _p ≤ 450 nm (D _p ≤ 650 nm). Similarly, for uncoated particles with D _c = 110 nm and 150 nm (not shown), T ^peak were 3100 ± 500 K and 3500 ± 200 K, respectively, and changed only to within 10 and 5% by coating with Δ D _p ≤ 500–600 nm. The observed changes in the average T ^peak up to ∼ 200 K with the increase in coating with Δ D _p up to 500–600 nm were much smaller than the difference of the boiling points between graphite (4100 K) and metals; the B.P. of iron, niobium, and aluminum are 3130 K, 5010 K, and 2790 K, respectively (Gale and Totemeier 2004). These results indicate that graphite can be discriminated from other metals by using T _peak, independent of coating on graphite with Δ D _p ≤ 500–600 nm. For graphite particles with D _c ∼ 200 nm, the constant emissivity assumption is generally valid, as discussed in section 2.2 (see also Figure 3b) and the T ^peak value for D _c = 200 nm was about 3800 K in this study. This value is consistent with the T ^peak of various carbon particles (including graphite) reported by Schwarz et al. (2006) (∼3700–4300 K) estimated by using λ -independent emissivity.

Figure 15a and Figure 15b show the measured S _bb ^peak of coated graphite of D _c = 110 and 200 nm as a function of D _p . The S _bb ^peakwas stable to within ± 10% for Δ D _p ≤ 450–550 nm. Similar results were obtained for D _c = 150 nm with Δ D _p ≤ 650 nm (not shown). Schwarz et al. (2006) and Slowik et al. (2006) reported the S _bb ^peak of flame-generated EC did not change with coating of oleic acid or anthracene up to 100 nm thickness. The present experiments, together with their results, indicate that the EC mass-S _bb ^peak relationship has no interference from coatings with Δ D _p up to ∼600 nm.

FIG. 15 D _p dependence of peak intensity of LII signal of organic-coated graphite particles of (a) D _c = 110 nm and (b) D _c = 200 nm.

4.4. Waveforms of Very Thick-Coated Graphite

For very thick-coated graphite particles, high intensities of S _sc(t) lasted even after the decay of S _bb(t) (Type A), depending on Δ D _p . Figure 16(a) is an example of the Type A particle for glycerol-coated graphite particle with (D _c , D _p ) = (150 nm, 600 nm). The width of S _sc(t) of the Type A particles was much larger than that for the particles discussed in section 4.1 (Type B) as shown in Figure 16b.

FIG. 16 Waveforms of LII and scattering signals of thick-coated graphite: (a) Type A and (b) Type B signal for glycerol-coated graphite particles with D _c = 150 nm and D _p = 600 nm.

The type A and the type B were clearly separated by the FWHM of the Gaussian-fitting of S _sc(t). Type A (B) particles were defined as those with FWHM larger (smaller) than 6 μ s. Another feature of the Type A particles is that S _sc(t) had two peaks. The fraction of Type A particles increased with the increase in D _p , as shown in Figure 17.

FIG. 17 Count fractions of Type A signals of organic-coated graphite particles with D _c = 110, 150, and 200 nm plotted versus D _p .

At a D _p of about 400 nm (500 nm) for oleic acid (glycerol) coating, the fraction of Type A rapidly increased irrespective of D _c at 110–200 nm. For oleic acid coating, the fraction of Type A particle started to increase at D _p about 150 nm smaller than that for glycerol. The difference in the heat transfer properties (e.g., thermal diffusivity) may cause this difference.

The S _sc(t) for Type A particles can be explained by the breakup of an internally mixed particle (Gao, R. S., private communication, 2006). We consider a coated particle in which the graphite core is eccentrically positioned and hypothesize that: (1) the evaporation rate of coating material in the laser beam is faster on the surface closer to the graphite core than the surface on the opposite side, because the heat flux supplied by thermal conduction from the graphite core is larger; the first peak of the S _sc(t) (Figure 16a) occurs in this period, (2) the coated particle breaks up into a graphite particle and a remaining organic particle, and (3) the graphite particle immediately heats up to vaporization temperature and incandesces. The organic particle no longer evaporates and continues to move inward with respect to the Gaussian laser beam, resulting in the second peak of the S _sc(t) (Figure 16a). In this case, the position of the second scattering peak is considered to be the center of the Gaussian beam.

5. MODEL

5.1. Model Description

In this section, we discuss important features of the observed S _bb(t) and S _sc(t) of organic-coated graphite particles by comparing them with theoretical calculations. A time-dependent LII model was developed to analyze the dependence of S _bb(t) and S _sc(t) on D _c , D _p , and coating material. There are a number of studies on the modeling of the physical processes (e.g., temporal development of temperature and evaporation rate) controlling the LII signal for uncoated soot or graphite (Schulz et al. 2006, and references therein). LII and scattering signals obtained by the SP2 have been modeled by Stephens et al. (2003), accounting for only uncoated graphite particles.

This is the first study of modeling of the LII and scattering signals of internally mixed particles. Here, details of the LII model used in this study are described. Energy transfer processes that determine the internal energy of a coated graphite particle are the heating of the particle by light absorption and cooling by (1) heat conduction to ambient air, (2) radiative emission (incandescence), and (3) evaporative heat loss. First, changes in temperature, T(t), are calculated from energy conservation. The evaporation rate of particles is calculated assuming equilibrium vapor pressures at the particle surface followed by diffusion of the vapor to the surrounding air. T(t) and D _p (t) are calculated by solving the simultaneous equation for energy and mass conservation at each time step. Equating the rate of change of the internal energy to the sum of the rates of heating and cooling, we obtain energy conservation equation

T and T _∞ are the temperatures of the particle and ambient air, respectively. T _∞ was fixed at 300 K, close to the temperature of the SP2 chamber. ϵ _tot is the total emissivity of the particle which is assumed to be unity. σ_SB is the Stephan-Boltzmann constant and m denotes the mass of the particle. The thermo-chemical, thermo-physical, and optical parameters used in the equations are listed in Table 1a, Table 1b, and Table 1c for graphite, glycerol and oleic acid, respectively. The temperature dependencies of these parameters were considered except for refractive indices. C _p in Equation (12) is the total heat capacity of the particle

where ρ and c are the bulk density and the specific heat of the material, respectively. Subscripts c and s denote core and shell, respectively. Q _abs is a light absorption efficiency of the core-shell particle, which depends on D _c , D _p , and refractive indices of the core and shell. Q _abs was calculated by a Mie-scattering code for a concentrically stratified sphere (BHCOAT, Bohren and Huffman 1983). I(t) is the energy flux of the laser beam incident on the particle given as Equation (10). The factor of 2 in the first term on the right-hand side (RHS) of Equation (12) is due to heating by the laser beam incidents on the particle from two opposite directions in the laser cavity (e.g., Pinnick et al. 2000). The Knudsen number (Kn = 2l _MFP/D _p ) for the particle size range relevant to this study (i.e., D _p ∼ 10–1000 nm) is about Kn ∼ 0.1–10 at the temperature and pressure of the surrounding air (300 K, 1 atm), indicating that mass and heat transfer have to be based on formulations applicable to the transition regime between Knudsen regime (Kn > ∼10) and continuum regimes (Kn < ∼0.01). Here, l _MFP is the mean free path of air molecules and was fixed at 65.1 nm (300 K and 1 atm). The harmonic interpolation method (Sherman 1963; Liu et al. 2006) is adopted to calculate heat and mass flux in the transition regime. According to the interpolation method, flux q _v (i. e., mass, heat, and momentum) in the transition regime can be expressed as

where q _k and q _c are the fluxes of the Knudsen regime and continuum regime, respectively. Assuming that the thermal conductivity and the specific heat of air are equal to those at temperature of the surrounding air (T _∞), the heat transfer coefficient h _N for the transition regime is given by

using Equation (14) (McCoy and Cha 1974; Melton 1984), where λ_air(T _∞) is the thermal conductivity of air at 300 K, which was set to be 0.0262 W/mK (Jaluria and Torrance 2003). Details of the derivation of Equation (15) from (14) are described by Liu et al. (2006). G is the geometry-dependent transfer factor,

where γ is the specific heat ratio of air, which was fixed at 1.40 (at 300 K), and α is the thermal accommodation coefficient between graphite and air. We used a value of α = 0.26, measured for graphite-N₂ at temperatures of 1220–1270 K (Leroy et al. 1997). Calculations with α = 0.9 were also made because α was reported to increase with surface roughness and contamination (Devienne 1967). For glycerol-air and oleic acid-air, α was assumed to be unity due to the lack of data. The mass loss rate is expressed according to the mass conservation law (Snelling et al. 2000).

Here, N _A is the Avogadro constant and F _v is the outward molecular flux in the transition regime that was calculated by Equation (14)

where F _k and F _c are the molecular fluxes of the Knudsen and continuum regimes, respectively. F _k in Equation (18) is expressed as

The evaporation coefficients β for graphite (glycerol and oleic acid) in Equation (19) were fixed at 0.8 (1.0) in the absence of the experimental data. Assuming that the vapor is an ideal gas, the molecular concentration n _v is calculated as

When the particle surface is graphite, the vapor pressure of C₃ is estimated by the Clausius-Clapeyron equation

For a particle surface composed of glycerol or oleic acid, the vapor pressure is estimated by Antoine's empirical function of equilibrium vapor pressure,

Parameters A, B, and C in Equation (22) are referenced from the Japan Oil Chemists' Society (2001) (glycerol) and Stull (1947) (oleic acid). Molecular flux in the continuum regime is

D _va is the diffusion coefficient of mixed gas, where

Equation (24) is an empirical expression for the gas-phase binary diffusion coefficient of Fuller et al. (1966). In Equation (24), T, M _v and M _A, and P _total, are given in units of K, kg/mol, and Pa, respectively. In Equation (24), T _p and pressure in the SP2 chamber are used as T and P _total, respectively. υ is the parameter (without dimensions) for each atom in a molecular constituent (Fuller et al. 1966). υ is 16.5 for C, 1.98 for H, 5.48 for O. For air, (Σ υ)_A is 20.1.

TABLE 1a The parameters and functions of graphite used in LII modeling

Symbols	Description	Values used	Units	Reference
M v	Molecular weight of vapor	0.036 (C 3)	kg/mol	Wainner 1999 Leider et al. 1973
P	Vapor pressure	P r exp [Δ H v (T − T r )/(RTT r )]	Pa
P r	Reference pressure	1.013 × 10^5	Pa
T r	Reference temperature	3915	K	Leider et al. 1973 Wainner 1999
ΔH v	Enthalpy of sublimation	6.58T ^−0.536× 10^6	J/mol	Leider et al. 1973 Wainner 1999 Michelsen 2003
c	Specific heat (solid)	Same as Eq. (5) of Michelsen 2003	J/kgK	Fried and Howard 2000
ρ	Bulk density (solid)	2.30× 10^3 − 7.31× 10^−2 T	kg/m^3	Michelsen 2003 Fried and Howard 1999
D va	Vapor-Air binary diffusion coefficient	6.20× 10^−5 T ^1.75/P total [Pa]	m^2	Fuller et al. 1966
—	Refractive index	Wavelength dependent	—	Borghesi and Guizzetti 1991

Rewriting Equation (17), the rate of D _p change is given by

To calculate T(t) and D _p (t), two simultaneous first-order ordinary differential equations, (12) and (25), were solved by the 4th-order Runge-Kutta method (Press et al. 1992). S _bb(t) was calculated by Equation (1a) and Equation (3a) using the derived T(t) and D _p (t). C _bb in Equation (3a) was assumed to be unity because of lack of better information. Similarly, S _sc(t) was calculated by Equation (7) using the calculated D _p (t) and I(t). Errors due to uncertainties in the input parameters (thermal accommodation and evaporation coefficients of the coating material) are not quantified.

Several simplifications have been made to describe the physical process in the present model. Processes controlling the time development of particle temperature and evaporation of coated graphite particle are more complex than the expressions described above. First of all, heat transfer (i.e., conduction, convection) inside particle should be considered, because thermal conductivities of volatile compounds are generally smaller than those of graphite by orders of magnitude; hence, the homogeneous temperature assumption used in most of the previous LII models for graphite or soot (Stephens et al. 2003; Schulz et al. 2006, and references therein) will be unrealistic for coated graphite particles. Secondly, phase transitions of the coating materials during the laser heating of the graphite core are complicated. In addition to the vaporization on the particle surface, a liquid-to-gas phase transition in the coating material may occur on the surface of graphite core due to the rapid heating. As a result, bubbles may form inside the particle leading to explosive desorption of coating material from graphite. In fact, Ueno and Shoji (2001) reported the generation of bubbles and shockwaves in water caused by rapid vaporization induced by nanosecond pulsed laser heating of a water-metal interface. Finally, the graphite core is not generally located concentrically inside the internally mixed particle. The temperature distribution in the coated particle will depend on the position of the core. An eccentrically positioned heat source can cause a break up of the particle, as discussed in section 4.4. In the present study, we attempt to obtain the general features of LII and scattering waveforms by using the simplified model without including these complexities.

5.2. Predicted Waveforms of LII and Scattering

The calculated S _bb(t), S _sc(t), T(t), and D _p (t), corresponding to the experimental conditions (Figure 11 and Figure 12) are shown in Figure 18. Figures 18a and c show results for uncoated graphite with D _c = 150 nm for α = 0.26 and 0.9. Figures 18b and d show results for graphite coated with glycerol or oleic acid with (D _c , D _p ) = (150 nm, 400 nm) for α = 0.26. For coated graphite, only the results for α = 0.26 are shown because the dependence of temperature and diameter on α is generally unaltered by coating on graphite. It can be seen that the shape, especially the widths, of the calculated S _bb(t) and S _sc(t) generally agree with those observed (Figure 18 and Figure 11), although the absolute time is unknown for the observations. The most notable point is that the first scattering peak of the coated particle increases with the increase in Δ D _p from 0 to 250 nm (Figure 18c and Figure 18d), similar to the observations (Figures 11 and 12). The mechanism causing the observed shape (i.e., width, relative position of peaks) of S _sc(t) and S _bb(t) for coated graphite can be interpreted based on the model results, as detailed below.

FIG. 18 Calculated results for organic-coated graphite particles. Time development of particle diameter and temperature for (a) uncoated graphite with (D _c , D _p ) = (150 nm, D _c ) and (b) glycerol or oleic acid-coated graphite with (D _c , D _p ) = (150 nm, 400 nm). LII and scattering waveforms for (c) uncoated graphite with (D _c , D _p ) = (150 nm, D _c ) and (d) glycerol or oleic acid coated graphite with (D _c , D _p ) = (150 nm, 400 nm). For uncoated graphite particles, calculated results with different thermal accommodation coefficients α are shown to demonstrate the dependence of the calculated results on α.

The laser intensity I(t) increases with t, although D _p (t) and scattering cross section decreases due to evaporation. Eventually S _sc(t), which is proportional to the product of I(t) and the scattering cross section (Equation (7)), reaches a local maximum value. The non-refractory coating of graphite delays the heating of graphite because of the heat loss caused by coating evaporation, as can be seen from the calculated T(t). Therefore, incandescence occurs at locations further inside the laser beam. The evaporation of the graphite particle occurs faster due to stronger I(t), leading to a narrower shape of S _bb(t), explaining the observed feature discussed in section 4.1. The calculated Δ t for a glycerol-coated graphite particles is plotted as a function of D _p in Figure 19 for D _c = 110–200 nm.

FIG. 19 Calculated scattering peak-to-LII peak time delay (Δ t) for glycerol-coated graphite particles of D _c = 110, 150, and 200 nm plotted versus D _p .

The calculated short-Δ t and long-Δ t were about 1 μ s and 3–4 μ s, respectively in agreement with the observations. This agreement is a direct consequence of the relative peak position of S _bb(t) and S _sc(t). The calculated Δ D _p * was 100–150 nm, in moderate agreement with the experimental data, although the slight decrease in the calculated long-Δ t with the increase in Δ D _p was not observed. This strongly supports the interpretation of the experimental data, discussed in sections 4.1–4.2.

There are some discrepancies between experimental data and the model. As shown in Figure 18a, the T(t) and D _p (t) are quite sensitive to the assumed value of α . This dependence is a result of the dominance of conductive cooling compared to evaporative and radiative heat loss, i.e., conduction contribute ∼60%, evaporation ∼ 35% and radiation ∼5% for –10 μ s < t < −5 μs). The onset of evaporation is faster for α = 0.26 than that for 0.9 because the increase in evaporative heat loss compensates for the decrease in conductive heat loss. In Figures 18a and c, peak temperature changed from 3800 K to 4200 K and S _bb ^peak increased by a factor of 1.5 as α decreased from 0.9 to 0.26. For coated graphite, the model predicted that T ^peak and S _bb ^peak systematically increase with Δ D _p and that they depend significantly on the coating material, in contradiction to the observed results discussed in section 4.2. In addition to this, the calculated S _sc ^peak for glycerol is higher than that for oleic acid, again in contradiction to the observations. The assumptions included in the model discussed in section 5.1 may partly contribute to these discrepancies.

6. SUMMARY AND CONCLUSIONS

We made laboratory experiments to evaluate the relationship between the key parameters measured by the SP2 and EC mixing states. These parameters are peak temperature (T _peak), peak LII intensity (S _bb ^peak), and the time delay of the LII peak (Δ t), which are directly related to the determination of the mass of individual EC particles and their mixing states. The measurements were made using graphite particles with core diameters (D _c ) of 110–200 nm coated with organic species (glycerol and oleic acid) with thicknesses (Δ D _p ) of 100–650 nm. The T _peak and S _bb ^peak were observed to depend little on the coating thickness and were close to those for uncoated graphite. The experimental results provide a strong basis to use T _peak for constraining chemical composition of incandescing particles and to use S _bb ^peak for measurement of the mass of EC contained in individual particle by the SP2, free of influence by coatings of non-refractory components.

Significant increase in Δ t was detectable for coated particles with Δ D _p above certain thresholds (Δ D _p *) with sufficiently higher scattering signal levels by coated materials. The increase in Δ t occurred abruptly at Δ D _p *, which depended on the core diameter and coating materials to some extent; Δ D _p * ∼ 100–200 nm for D _c = 110–200 nm. Similar results were obtained for EC particles in ambient air sampled in the suburbs of Tokyo. These results demonstrate that mixing states of EC particles in ambient air can be classified into two categories using the discrete levels of Δ t; thin-coated EC (Δ D _p < Δ D _p *) or thick-coated (Δ < eqid26 > D _p *) EC.

These experimental data were interpreted by using a newly developed theoretical model taking into account physical processes controlling the temperature change and evaporation rate of the coated graphite and assuming homogeneous particle temperature, an equilibrium phase transition at the particle surface, and a concentrically stratified spherical morphology. The features of the waveforms of incandescence and scattering signals of coated graphite particles were in general well reproduced by this model, strongly supporting the validity of the physical interpretation of the SP2 data given in this study.

Acknowledgments

This work was supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), the Japanese Science and Technology Agency (JST), and the global environment research fund of the Japanese Ministry of the Environment (C-051). We are indebted to S. Nakamura for taking TEM images of colloidal graphite particles. We thank Y. Komazaki, N. Takegawa, Y.Miyazaki, M. Koike, and M. Watanabe for assistance in the experiments and giving us useful comments. We also thank D.W. Fahey, J. P. Schwarz, R. S. Gao, J. R. Spackman, G. L. Kok, and D. G. Baumgardner for very stimulating discussions and sharing their works prior to publication.