Relating the single particle soot photometer (SP2) signal response to soot maturity

Abstract Light absorbing carbonaceous aerosols produced from combustion span over a range of physicochemical properties. Soot is the most recognized species in this category and its formation process involves gradual maturation from amorphous young soot with a high hydrogen-to-carbon-ratio toward mature soot aggregates. In this work, the optical response of a single particle soot photometer (SP2) to electrical mobility size selected soot of different maturity produced by a mini-CAST soot generator is investigated. The results show that for soot of a specific mobility diameter, the laser-induced incandescence (LII) signal appears earlier and with a higher LII peak height for increasing soot maturity. The experimental observations are supported by simulations using a numerical model for the LII process. Furthermore, the effect of systematically varying the SP2 laser power on the detection of soot of different maturity using LII is explored. This work can be seen as a step toward the aim of using the SP2 instrument to identify soot particles of different maturity in the atmosphere. Graphical Abstract


Introduction
Light absorbing carbonaceous (LAC) aerosols play an important part in the Earth's radiative balance, both directly via absorption of solar radiation and indirectly by influencing cloud properties (Szopa et al. 2021).Atmospheric LAC species are produced by a range of natural and anthropogenic sources under different conditions.Large variations in LAC nanostructure, composition, and absorption properties exist, and complicates the task of quantifying the LAC climate impact (Andreae and Gelencs� er 2006;Corbin et al. 2019;Kirchstetter, Novakov, and Hobbs 2004;Liu et al. 2020).While the atmospheric community uses the term black carbon (BC) to describe the most well-known and strongly absorbing subset of LAC, the combustion community often refers to these particles as mature soot (Michelsen et al. 2020).It is however important to recognize that other LAC species may absorb in the near-infrared and therefore caution is advised when attributing visible or near-infrared light absorption exclusively to mature soot (Corbin et al. 2019).
Fractal soot aggregates are produced during high temperature combustion in what can be described as a maturation process.The first incipient particles are formed from gaseous soot precursors and grow to form aggregates from individual so-called primary particles (Michelsen et al. 2020).In this process, the nanostructure evolves from amorphous to more ordered with increasing carbon-to-hydrogen (C/H) ratio and size of graphitic sp2-bonded structures.Simultaneously, the soot absorption properties change and several studies have shown that the soot absorption efficiency and its wavelength dependence are coupled to maturity (Bond and Bergstrom 2006;Johansson et al. 2017;L� opez-Yglesias, Schrader, and Michelsen 2014;Olofsson et al. 2015;T€ or€ ok, Mannazhi, and Bengtsson 2021).Mature soot absorbs efficiently in the visible to near-infrared wavelengths, while less mature young soot has a stronger spectral dependence and weaker absorption efficiency (Johansson et al. 2017;L� opez-Yglesias, Schrader, and Michelsen 2014;Michelsen et al. 2015;Migliorini, Thomson, and Smallwood 2011;Olofsson et al. 2015).The soot maturity, in turn, depends on the burning conditions related to the thermal and chemical environment in which the soot is formed (Alf� e et al. 2009(Alf� e et al. , 2010;;Russo and Ciajolo 2015;Wal and Tomasek 2004).
Pulsed nanosecond laser induced incandescence (LII) has long been one of the main techniques for soot diagnostics in flames, often for measurements of soot concentrations and primary particle sizes/distributions (Michelsen et al. 2015;Schulz et al. 2006).Such in-situ measurements using high temporal as well as spatial resolution have largely contributed to the understanding of soot formation in combustion processes.More recently, LII has also been used for investigations regarding soot absorption properties (Johansson et al. 2017;L� opez-Yglesias, Schrader, and Michelsen 2014;T€ or€ ok, Mannazhi, and Bengtsson 2021).Specifically, the evaluation of absorption efficiency and its wavelength dependence by varying the laser pulse energy and measuring the LII signal response (so-called fluence curve analysis) has provided insights into how the soot absorption properties are related to maturity (T€ or€ ok, Mannazhi, and Bengtsson 2021).
The application of a 1064 nm continuous wave (CW) Nd:YAG laser in the single particle soot photometer (SP2) enables studies of LII and light scattering from individual particles.When single soot particles pass through the laser beam, they absorb and heat up to incandesce.The emitted thermal radiation (referred to as the LII signal) is detected as a function of time in two different wavelength bands, and the peak intensity is used to indirectly determine the single particle refractory black carbon (rBC) mass (Moteki and Kondo 2010).Simultaneously, the elastically scattered laser light is recorded and can be used to determine the optical particle size, laser beam profile and to detect non-refractory coatings (Gao et al. 2007;Laborde et al. 2013).
Over the last decades, the SP2 has been used in lab and ambient studies to retrieve rBC properties and mixing state (see e.g., Liu et al. 2014;Moteki, Kondo, and Adachi 2014;Schwarz et al. 2006;Yuan et al. 2021;Zanatta et al. 2023), although detection and identification of other near-infrared absorbing species capable of undergoing incandescence have also been investigated.One of the first SP2 applications involved the determination of particle composition from twocolor pyrometry (Stephens, Turner, and Sandberg 2003), and more recent work addresses the detection of for example iron oxides (Lamb 2019;Moteki et al. 2017;Yoshida et al. 2016).Notably, the SP2 has been reported to be able to detect organic-rich flame generated soot (Gysel et al. 2012) and tar brown carbon (BrC) (Corbin and Gysel-Beer 2019), which demonstrates the potential of using the SP2 instrument for the detection and identification of LAC species other than mature soot.
In this work, the aim is to investigate if the time resolved LII signal measured by the SP2 instrument can be related to the soot maturity of mobility size selected particles.Measurements were performed on mobility size selected young and mature soot from a mini-CAST soot generator (Jing 2009).The soot produced by the mini-CAST has been characterized in terms of maturity in many previous studies (Le et al. 2019;Malmborg et al. 2019;Malmborg et al. 2021;T€ or€ ok, Mannazhi, and Bengtsson 2021;T€ or€ ok et al. 2018, 2022).Specifically, the timing and intensity of peak LII signals relative to the laser intensity profile are studied for soot of various maturity.A numerical model for the LII process is used to simulate the SP2 LII signal from the laser-particle interaction to investigate whether the features of the experimental results can be qualitatively reproduced.Furthermore, we explore the effect of laser power on the SP2 detection by varying the laser power while sampling soot of specific mobility diameters.

Clarification of terminology
Many SP2-studies target atmospheric aerosol scientists, rather than the combustion community.These two communities use, for example, different terminology to accommodate their different interests.Soot in the combustion community represents the carbonaceous particles formed during incomplete combustion (from the first incipient particles to the aggregated soot with high carbon content, see Michelsen et al. 2020), and we rely on this definition in our work.
The term "soot maturity" is rarely used in the atmospheric community, and in our work, we use the nomenclature defined in Michelsen et al. (2020).In the combustion community, this term refers to the soot formation process in the flame, namely the evolution of soot properties (e.g., nano structural, chemical, optical) from the formation of the first incipient particles to the mature soot aggregate.In the intermediate stages, partially graphitized/matured soot particles are found.Partially mature soot particles may exhibit various degrees of graphitization internally (for example, the surface may undergo growth in the flame, whereas the bulk exhibits a higher degree of graphitization).With this definition, partially mature soot could be described as a subset of what the atmospheric community refers to as brown carbon (BrC, see the definition of Brown Carbon in Michelsen et al. 2020) but the term is strictly related to the soot formation process.

Experimental setup
The experimental setup used in this study is depicted in Figure 1.Soot particles of different maturity were generated using a mini-CAST soot generator 5201 C (Jing 2009) and diluted by a porous tube diluter (PTD) and ejector diluter before entering the SP2.The PTD was operated at different flows but the ejector diluter was operated with the same setting throughout the campaign.The SP2 and mini-CAST apparatuses and characteristics of the soot that our study encompasses are described in further detail in the following two sections.A differential mobility analyzer (DMA 3082, TSI) was used to select particles of different mobility diameters upstream of the SP2.A condensation particle counter (CPC 3775, TSI) was placed in parallel with the SP2 downstream of the DMA.Particle number size distributions were obtained by operating the DMA and CPC as a scanning mobility particle sizer (SMPS).To study the effect of varying laser power on the SP2 detection of the differently mature soot, the DMA was set to a fixed size (electrical mobility) and the SP2 pump laser current was varied to systematically vary the intracavity laser power.

Soot generation
Soot of different maturity was generated from a mini-CAST soot generator 5201 C (Jing 2009), by using different flow conditions for the gas supply.The mini-CAST contains a propane/air diffusion flame, which is quenched at a fixed height above the burner.By increasing the nitrogen dilution flow and thus the flame height, the quenching of the flame at a certain height results in the probing of younger soot in the exhaust stream of the soot generator.Hence by systematically varying the gas flows feeding the diffusion flame, the characteristics of the soot can be varied.In this work, OP1, OP5, and OP6 soot were studied, and some of the soot characteristics and flame operating conditions are listed in Table 1.
Soot produced by the mini-CAST soot generator has been investigated in several previous papers.It has been shown that the conditions for a lower operating point (OP) number produce more matured soot with less organic content and lower absorption Ångstr€ om exponent (AAE) (Le et al. 2019;Malmborg et al. 2019;T€ or€ ok et al. 2018).Their bonding structure and morphology were characterized by Raman spectroscopy and HRTEM (Le, Henriksson, and Bengtsson 2021;Le et al. 2019;Malmborg et al. 2019), while the optical/absorption properties were studied by laser-induced incandescence (T€ or€ ok, Mannazhi, and Bengtsson 2021;T€ or€ ok et al. 2018).Specifically, in two recent papers (T€ or€ ok, Mannazhi, and Bengtsson 2021;T€ or€ ok et al. 2022) we showed that OP6 soot has brown soot character after evaporation of the organics coating, absorbing approximately with half the efficiency of OP1 soot.Also, in another study, it was shown that the carbon nanostructure of OP6 soot is different from OP1 soot, as the distribution of vaporization fragments from these soot types was clearly different when laser vaporized in a soot particle aerosol mass spectrometer (SP-AMS) after evaporation of the organic fraction (Malmborg et al. 2019).Note that the soot characteristics in Table 1 refers to polydisperse (and not mobility size-selected) mini-CAST soot at different operating points.

Description of the single particle soot photometer (SP2)
In the SP2 instrument, single particles travel through a continuous wave (CW) 1064 nm (Nd:YAG) laser beam carried by a sample flow constrained by a particle free sheath flow.The results of interaction of laser light and particles are monitored using four detectors: two channels detecting scattering and two channels detecting incandescence (described further below).The first scattering signal is detected by an avalanche photodiode (APD) and can be used for optical particle sizing in the diameter range of 200-400 nm.The waveform of the time-resolved scattering signal of non-absorbing particles corresponds to the spatial laser intensity distribution that a particle is exposed to (the laser beam profile).The particle position in the laser beam is estimated by using a second scattering detector denoted the "split detector" or position sensitive detector (PSD), which was first introduced by Gao et al. (2007).At a certain physical position across the laser beam, referred to as the split point, the scattering signal is inverted and crosses zero.
Absorbing particles, like soot, that traverse the laser beam absorb light at 1064 nm and heat up until the point of vaporization (after the evaporation of nonrefractory constituents) on the timescale of microseconds.At the high vaporization temperature of soot, >�3400 K (Olofsson et al. 2015) the emitted thermal radiation is detected at two wavelength bands by two photomultiplier tubes (PMT's).The broadband detector for the SP2 used in this study covers the range 400-650 nm, whereas the narrowband detector encompasses 610-650 nm.Unless otherwise stated, the LII peak intensities and temporal signals in this work refer to the broadband channel.
The peak height of the incandescence signal is to a first approximation proportional to the mass of rBC in individual particles.This mass estimation has been shown to be independent of mixing state and morphology (Moteki and Kondo 2007;Slowik et al. 2007).In general, the SP2 can determine the rBC mass between 0.3 and 117 fg corresponding to volume equivalent diameters of 70-500 nm (assuming a density of 1.8 g/ cm 3 ).Below 0.9 fg, the detection efficiency is reduced below 100% (Laborde et al. 2012), although the detection of smaller aggregates can be enhanced if the laser fluence is increased (Liu et al. 2017;Schwarz et al. 2010).At a given laser power, the lower detection limit mainly depends on the soot surface-to-volume ratio, which for small aggregates means that heat losses by conductive cooling prevent the soot from reaching its vaporization temperature (Schwarz et al. 2010).However, total aggregate mass might not be a sufficient criterion for detection.In case of low effective density and very small primary particle size (5-10 nm, see Gysel et al. 2012 and references therein) the SP2 detection may be significantly impaired.
Another criterion that needs to be fulfilled for detectable incandescence in the SP2, given that the laser power is high enough (Schwarz et al. 2010), is a sufficiently high material vaporization temperature.The LII peak intensity depends on T a , where a � 4 is related to the soot particle emissivity (Michelsen 2003), and T is temperature.Hence, such strong temperature dependence implies large changes in LII signal for even rather small changes in particle vaporization temperature.Less mature soot has been observed to have a lower sublimation temperature (Olofsson et al. 2015) which should lead to lower signal intensity than for mature soot with comparable soot mass.

Preparation of the SP2
The SP2 was prepared according to the recommendations of Laborde et al. (2012).The scattering detector was calibrated using polystyrene latex spheres (PSL) particles.By using the elastic light scattering signal from 269 nm PSL's, the laser beam profile can be obtained.The incandescence detectors were calibrated using mobility selected Aquadag V R particles (aggregates of irregular flakes of graphite in a suspension) and recalculated to a fullerene soot equivalent following Laborde et al. (2012).As the LII peak height is proportional to mass for a specific calibration material, the mass measured by the SP2 of less mature OP6 soot cannot be related to OP1 soot mass for example.

The laser-induced incandescence technique
The LII technique for soot detection is based on the heating of the particles to 3500-4000 K, at which the thermal radiation, i.e., the LII signal, is detected (Michelsen et al. 2015;Schulz et al. 2006).The method has been used for decades based on pulsed nanosecond lasers, where a rapid heating during a few nanoseconds is followed by a slower cooling process lasting for around a microsecond.The physical processes during the heating and cooling have been successfully reproduced using a heat and mass transfer model, and simulated LII signals can often reproduce experimental data efficiently, see for example Bladh et al. (2006).
In comparison with the pulsed LII technique, the LII signal that results from a soot particle passing through the SP2 intracavity laser beam is much more complex to describe.The major difference is that the propagation of the particle through the intracavity laser beam in the SP2 instrument has a duration of tens of microseconds, which is around a factor of 1000 longer than the interaction time for the pulsed LII technique.It means that the soot particle will be exposed to heating by laser light during much longer time, which in turn means that the soot with increasing temperature in greater occurrence will undergo nano structural changes.These structural changes involve thermal annealing, thereby leading to carbonization and graphitization, and at sufficiently high temperature vaporization/sublimation followed by particle shrinking.Another effect of the nano structural changes at high temperatures is that the optical absorption efficiency increases.
In the present work, we have adapted the LII model from our previous works (T€ or€ ok, Mannazhi, and Bengtsson 2021;T€ or€ ok et al. 2022) to the present measurement situation with a longer interaction time.The same material parameters for soot were used as in T€ or€ ok, Mannazhi, and Bengtsson 2021.Additional information about the model is found in Section S2 and Table S2 (model parameters) in the online supplementary information (SI).While we initially have good knowledge of the model parameters for soot, such as the absorption efficiency E(m, k) (defined in the SI Section S2), no information is available about how soot material properties (optical and thermal) change during the long interaction time while propagating through the laser beam.Hence, this complex situation makes simulation results uncertain, yet they can be used for qualitative comparison with the experiments with the best agreement to be expected at the beginning of the soot propagation across the laser beam.

Data analysis
In our analysis of the SP2 signals we are specifically interested in the peak height and timing of the LII signal (t max LII ) for soot of different maturity and mobility diameters.The SP2 can discriminate singly charged particles as its signals are proportional to particle mass, and hence we focus on the single charged particles only (i.e., excluding the larger multiply charged particles produced in the DMA).The peak incandescence timing relative to the time at maximum laser intensity (t max laser ) is defined as Dt ¼ t max LII − t max laser .To calibrate the timing of the soot traversing the laser beam, the LII signal was related to the scattering signal from the split detector.
In this study the signal detection in the SP2 was triggered primarily on the scattering channel and secondly on the incandescence channel.When these signals surpass their baseline thresholds the temporal signals from a user defined number of pre-trigger points are saved.However, this triggering approach also means that temporal LII signal from individual particles is not well constrained with regard to signal timing at a physical position in the laser beam.To overcome this issue, the split detector signal provides information on the physical position of the particle relative to the laser beam, and thus it is possible to calibrate the temporal signals relative to the laser beam to make timing comparable.Although the use of single particle split signals (especially for less mature soot) was impeded by the signal-to-noise ratio being low, forming a median signal response for each OP soot and mobility diameter proved to work.We thereby assume that although single particle timing is not well constrained, the median signal for a specific OP soot and aggregate size should represent the major features in the SP2 response (see Figures S5b and c).The median signals were then adjusted to a common time base by aligning the split points with the split point of 269 nm PSL.In this way, the temporal signals are pinned to the laser intensity profile, and the timing of the signals is comparable between different OP soot and aggregate sizes.The number of traces of singly charged particles that were used to form the median response is shown in Figure S4.
To estimate the uncertainty in our method with regards to timing, we examine 269 nm PSL (purely scattering) single particle split points and found that the median of the single particle split points and the median signal split point agreed within 0.4 ms (see Figures S5a-c in the SI).Due to the time resolution of the SP2 data and our method for determining the median split point, we estimate this uncertainty to ±0.4 ms.
Estimating the uncertainty related to timing from monodisperse PSL particles, however, misses some of the uncertainties related to soot characteristics.We assume that the variability of soot characteristics and maturity is larger for the less mature soot than the mature soot, due to the generation procedure in the mini-CAST where quenching occurs across the diffusion flame.This translates into larger variability in the timing of less mature soot which is not quantified in this work.

Effect of soot maturity on the temporal LII signal
The SP2 instrument measures signals from scattering and laser-induced incandescence for single particles passing through the laser beam.In Figures 2a and b, examples of the median LII signal (obtained from the broadband channel 400-650 nm) for soot of three different maturities; OP1, OP5, and OP6, of the same mobility diameter are shown (169 nm in Figure 2a and 209 nm in 2b).It should be noted that the time scale can be seen as a spatial dimension as well, as it shows the LII signal evolution for soot propagating across the spatial laser intensity profile (shaded region in Figure 2).For both 169 and 209 nm, the LII signal from the most mature soot (OP1) rises earlier as well as peaks earlier than the corresponding signal from the least mature soot (OP6).This can partly be understood from the weaker absorption for less mature soot that needs longer transport through the beam to experience the corresponding rise in temperature as the mature soot.A second observation is that the peak heights for less mature soot are lower than for the mature soot, of the same mobility diameter, which will be discussed later in relation to Figure 3.
To contrast differences in the response of the SP2 instrument to soot with different absorption properties, a set of three variables were chosen: (i) the median broadband LII peak signal, (ii) its timing relative to the maximum laser intensity (Dt), and (iii) the soot mobility diameter.In Figure 3a, the relation between these parameters is presented for soot (OP1, OP5, and OP6) in the size range 169-400 nm.The soot of equal mobility diameter is grouped by lines.A Dt corresponding to 0 ms implies that the LII peak coincides with the maximum laser intensity, whereas a Dt < 0 means that the LII signal peaks before the maximum laser intensity is reached.The main observation is that the more mature the soot is, the earlier peak incandescence is reached, and the magnitude of the median LII peak increases with aggregate size and degree of maturity.Worth noting from the results in Figure 3a is that for example OP1 soot with size 260 nm and OP5 soot with size 400 nm have similar peak height.In a polydisperse mix of soot particles of varying maturity, these would appear to have identical rBC masses as measured by the SP2, unless for example the time delay is considered.In Figure 3b, where the LII peak height is normalized to the highest OP1 soot peak height for each given size, it is clear that the peak timing depends more on soot maturity than mobility size in the investigated range.Furthermore, OP1 and OP5 soot display Dt that are constrained within relatively narrow time intervals for  each OP case, regardless of aggregate size.This contrasts with the more variable Dt of the least mature OP6 soot.A possible explanation for the greater variability of OP6 soot properties is the generation procedure of soot in the mini-CAST, where quenching of the diffusion flame occurs at a fixed flame height.For the OP1 condition, flame quenching occurs at a height where the soot particles have more similar characteristics, while for the OP6 condition, flame quenching occurs at a height where the soot properties are less mature on the centerline in comparison with the particles at the edge of the sooting region.
No obvious effect of aggregate size on Dt can be seen for mature OP1 soot in Figure 3a.In the work of Bambha and Michelsen (2015) a size dependent difference in signal timing was found for mature soot of aggregate sizes 126, 195, and 250 nm, where the smallest aggregates were delayed the most (0.8 ms compared to the largest).In our work, such effect could be overshadowed for several reasons: (i) the choice of singlecharge peak heights included in forming the median signal (see Figure S4), (ii) the width of the single charge peak, and/or (iii) the uncertainties related to timing (discussed in the Method).
LII signals are to a first approximation proportional to mass for mature soot particles of various sizes.In Figure 3a, the LII peak of OP6 soot is about 30-40% of that of mature OP1 soot.For OP5 soot, the peak height is about 40-50% of that for OP1 soot for the same mobility sizes.A study was made to see if any difference in effective particle density or shape could explain this.The effective densities of OP1 and OP6 soot aggregates were measured with an Aerosol Particle Mass analyzer (APM).In the range 150-300 nm, the OP1/OP6 soot mass ratio (from fitting a power law) was found to vary between 1.02 and 1.11 (see Figure S6a in the SI) for particles with the same mobility diameter.Furthermore, the mass mobility exponents (Park, Kittelson, and McMurry 2004) of OP1 and OP6 were calculated to 2.01 and 2.13 (where 3 would indicate a spherical shape, see Figure S6b).Thus, OP1 soot and OP6 soot are fractal aggregates of similar shape.In Cross et al. (2010), the SP2 response in terms of LII peak height was found to be independent of shape for fresh, fractal soot, and restructured soot, which indicates that shape may have a small effect on the LII peak height.A similar result was found in Bambha and Michelsen (2015) where the peak height was unaffected by compaction (although the peak was shifted to appear slightly earlier).Hence, the difference in effective density or shape could only to a limited extent explain the lower LII peak height of the least mature soot.
Other explanations for the features of the less mature soot signal can be found in the underlying laser-soot interaction processes.The soot particles traversing the laser beam undergo substantial changes already well before the LII peak signal is reached, which also may differ between the immature and the mature soot.During the particle heating by the laser light non-refractory constituents on the particles will be evaporated, and structural modifications will take place.Organic molecules will evaporate, amorphous structures will tend to be partly graphitized and thermally annealed, soot density will increase, the hydrogen content will decrease, and particles will start to vaporize at temperatures above 3400 K.These processes are complex to predict in theoretical models on time scales thousand times longer than for ns-pulsed LII, for which numerical models successfully have predicted experimental LII signals.
Using ns-pulsed LII, it has been shown that the properties of soot may change by annealing if it is heated to high temperatures (Apicella et al. 2019;Cenker and Roberts 2017;Migliorini et al. 2020;T€ or€ ok et al. 2022;Vander Wal, Ticich, and Stephens 1998;Vander Wal and Choi 1999).Subsequently, the soot absorption efficiency will be enhanced, and the soot will exhibit characteristics of more mature soot.Double ns-pulse LII experiments on mini-CAST soot (T€ or€ ok et al. 2022) showed that thermal annealing from the first pulse resulted in an increased value of the absorption function and an enhanced peak LII signal for OP6 soot.In the SP2, where the laser-particle interaction time is about 20 ms, the soot is heated and remains at high temperatures for more than a thousand times longer compared to the 10 ns pulses used in conventional LII.It can therefore be speculated that the absorption efficiency of OP5 soot and OP6 soot approaches that of OP1 during the particle propagation across the intracavity laser beam.Annealing in the SP2 has been demonstrated by Sedlacek et al. (2018) for materials with a low starting degree of graphitization (nigrosin, tar BrC, and HULIS surrogates) if the laser fluence is sufficient.For uncoated samples of light-absorbing organic aerosol surrogate materials and laboratory generated tar balls, Sedlacek et al. (2018) found that the LII onset times were delayed in comparison to a reference material (carbon black soot).This delay was attributed to the time needed for SP2 induced annealing to produce detectable rBC, which likely is relevant for the less mature soot in our work.Moteki and Kondo (2008) on the other hand did not observe laserinduced annealing of nigrosine, possibly due to insufficient laser fluence.The laser-induced annealing in SP2 has also been suggested to be responsible for the (in some cases) observed incandescence of tar balls in the work by Corbin and Gysel-Beer (2019).
Soot composition and evaporation of volatile soot constituents during laser heating could also influence the LII peak height and timing.In Gysel et al. (2012), an organic-rich "mini-CAST brown" soot was produced.The characteristics (e.g., effective density) and mini-CAST setpoint are different from that of our OP6 soot, but like our results in Figure 3, they found a difference in the mass quantification by the SP2.In their work, they found that the average mass for the 125 nm "mini-CAST brown soot" at the 1.2 fg APM setpoint, was as low as 0.45 fg rBC (determined by the SP2), despite 100% counting efficiency in the range 125-500 nm.The results from previous studies clearly show that the composition of OP6 soot is different from that of OP1 (see section Soot generation, in the Method), and given the results in Gysel et al. (2012) it is likely that composition influences the peak height of our OP6 soot.In atmospheric applications of the SP2, evaporation of volatile coatings delays the onset of the LII relative to the scattering of the total particle including coating, as it takes time and energy to evaporate such volatiles before the soot core incandesces (Gao et al. 2007;Moteki and Kondo 2007;Schwarz et al. 2006).Increasing coating thickness relative to the soot core size has been shown to further increase this delay (Moteki and Kondo 2007;Slowik et al. 2007).Previous characterization of OP6 showed that it contains a larger fraction of organic carbon and PAHs compared to OP1 (see Table 1 and T€ or€ ok et al. 2018).Malmborg et al. (2019) found that for OP6, the mass ratio of PAH to OA (organic aerosol) measured with a soot particle aerosol mass spectrometer (SP-AMS) was substantially reduced after furnace treatment at 500 � C, whereas for OP1 it remained close to zero with and without heat treatment.Although the time scales and mechanisms for furnace and laser-induced heating are different, it can be assumed that the organic compounds will evaporate in the SP2 laser and thus contribute to mass loss.In Figures S7 and S8, the normalized median LII and scattering signals for OP1, OP5, and OP6 soot are shown.In comparison to OP1 and OP5 soot, the time resolved scattering signal of the least mature OP6 soot suggests that evaporation before incandescence may occur, as the scattering signal features resemble evaporation of a coating for internally mixed soot (Moteki and Kondo 2007).

Effect of laser power on the temporal LII signal
Laser-induced incandescence signals increase strongly with temperature.Hence, a higher laser power in the beam leads to a faster temperature increase and thereby a faster rise of the LII signal.Also, a soot particle with higher absorption efficiency leads to a faster signal increase for the same reason.Studying the effect of laser power on the SP2 LII signal for soot of different maturity (and absorption efficiencies) is therefore of interest.In this study, soot particles of a fixed mobility diameters and maturity were sampled, and LII signals were studied for various settings of the SP2 pump laser current (related to the YAG power voltage measured by the output coupler in the cavity, see discussion in Section S7 and Figure S9 in the SI).
In Figure 4a, the normalized peak LII intensities for OP1 (88 and 250 nm) and OP6 (145 nm) soot for the broadband incandescence channels are shown as a function of YAG power voltage.It should be noted that the pump laser current set point or YAG power voltage is not necessarily directly proportional to the actual intracavity laser power as it for example depends on alignment and quality of the optics (see discussion in the SI Section S7).Below 2.5 V we were unable to detect and form acceptable median signals as the split signal was too low for 88 nm OP1 soot.The corresponding YAG power voltage were 1.7 V for 250 nm mature aggregates and 2.9 V for 145 nm OP6 soot.For the less mature OP6 soot we have included data from each setpoint whereas for the mature OP1 soot, median LII signals of each second pump laser setpoint are shown.The default setting throughout the rest of the campaign was about 5 V (2350 mA).
For the mature OP1 soot, the effect of aggregate size can be seen.The laser power for which the LII peak signal height reaches a plateau and becomes independent of laser power is lower for the larger aggregates compared to the smaller ones.Likely, this is the result of the larger surface-to-volume ratio of the smaller aggregates, probably due to smaller primary particles, which increases the importance of conductive cooling in relation to absorptive heating.Lastly, the laser powers tested here did not initiate substantial mass loss of OP1 soot before the LII peak was reached (i.e., no decrease in LII peak height for increasing laser power).For less mature 145 nm OP6 aggregates, the plateau with regards to LII peak height is more variable (Figure 4a).The YAG power voltage for which this plateau is reached is similar to that of 88 nm mature soot aggregates (see S8 and Figure S10 in the SI for the non-normalized LII peak heights), but rather than an effect of size or shape (Figure S6b), this is likely the result of the weaker absorption efficiency of OP6 soot related to its partial matureness.
In Figure 4b, the broadband LII peak timing relative to the laser intensity maximum (Dt) as a function of YAG power voltage is shown.For mature OP1 soot, an increasing laser power implies shifting the LII peak to occur earlier in the laser beam, as the absorption and heating of the soot is faster.Except for the highest laser power setpoints, 145 nm OP6 soot follows a similar trend.As we only investigate one size of OP6 soot, it is hard to speculate on the reasons for the behavior at higher laser power.For mature OP1 soot, there is no obvious difference in timing between 88 nm and 250 nm aggregate if the laser power is sufficient to form reasonable median signals.

Modeling of the temporal LII signal
The temporal SP2 LII signals of OP1, OP5, and OP6 soot of different mobility diameters presented in the previous section indicated a difference in both LII peak timing and peak signal intensity.In this work, a model developed previously in our laboratory was used to investigate the origin of this difference in signal response (Bladh, Johnsson, and Bengtsson 2008).This model, developed for nanosecond pulsed LII, was applied here to the measurement situation in the SP2 instrument where the particles are exposed to laser radiation for a much longer time.The model implemented in MATLAB was run for the SP2-experimental conditions (laser power, laser wavelength, detection wavelength band).Modeling of the LII signal for OP1 soot and OP6 soot was carried out using previous estimations of E(m, 1064 nm) ¼ 0.33 and 0.16, respectively (T€ or€ ok, Mannazhi, and Bengtsson 2021).The definition of E(m, 1064 nm) as well as additional information about the LII model and input parameters can be found in the SI Section S2.
In Figure 5, the experimental laser profile as well as experimental and modeled temporal LII signals for OP1 and OP6 soot are shown, where the experiments were made for 169 nm size-selected particles.The experimental and modeled beam profile and LII signals are normalized to the LII signal from OP1 soot.The modeled LII signals are made for two different primary particle sizes; 22 nm in Figure 5a and 16 nm in Figure 5b, as discussed later in this section.
A first observation in Figure 5a is that the LII model to a large extent reproduces the main characteristics of the experimental results of the LII peak.The experimental observation of a delayed peak LII signal for OP6 soot compared to the mature OP1 soot is evident in the modeled signals.Another observation that there is a qualitative agreement in, is the lower LII peak height of OP6 compared to OP1 soot, although with a much lower peak height for the modeled LII signal.
A direct comparison between modeled and experimental results is not as straightforward as it might seem from Figure 5.It is important to be aware that the LII model with the implemented mechanisms described in the SI Section S2, works best to describe the early stages of heating of the soot particle as it enters the laser beam.As discussed in the Method section, numerous processes take place at increasing temperatures for which the time dependence is currently not feasible to predict.While LII models for pulsed nanosecond LII can re-produce time-resolved experimental LII signals adequately, this is not the case for the SP2 instrument where processes, such as thermal annealing, evaporation, and particle shrinking will occur on a time scale that is three orders of magnitudes longer.Considering these large uncertainties in morphological and chemical processes during particle heating, the agreement between experimental and modeling results in Figure 5 can be regarded as satisfactory.
The only difference in the modeling of the temporal LII signals in Figure 5 is the primary particle size, 22 nm in Figure 5a and 16 nm in Figure 5b.The choice of 22 nm particle size in the modeling in Figure 5a is because this was the mean value of primary particle sizes in the distribution derived from the analysis of transmission electron micrographs (TEM) from polydisperse OP1 soot, in Karlsson et al. (2022).However, after size selection using the DMA in the present experiments there is no direct information about the primary particle size and the best value to assume is 22 nm.The corresponding data for the mean primary particle size of OP6 soot was 16 nm (calculated from TEM images of OP5 in Karlsson et al. 2022), and this case is presented in Figure 5b.Also here is a reservation that the size selection using the DMA results in a different average primary particle size.When now comparing the modeling in Figures 5a and b, it can be noticed that independent of primary particle size there is a qualitative agreement both regarding the LII peak height and delay for OP6 soot in comparison with OP1 soot.However, the smaller modeled primary particle size leads to a slightly larger delay of the LII peak as well as a smaller LII peak height.
To summarize, the modeling shown in Figure 5 clearly shows that a lower absorption efficiency of the soot leads to a time delay of the LII signal peak.The absorption efficiency is often expressed as E (m), thus a function of the complex refractive index m, where the absorption efficiency is correlating with the imaginary part of the refractive index (see details in the SI, section S2).The effect of a smaller imaginary part at near-infrared wavelengths (lower absorption efficiency) on incandescence timing has been observed in a study by Yoshida et al. (2016).Hematite, with a comparably smaller imaginary part, was there shown to heat slower with a delayed incandescence in comparison to for example magnetite, fullerene soot, Taklamakan Desert dust, and Icelandic dust.

Implications for atmospheric measurements and outlook
This laboratory study on freshly emitted mini-CAST soot shows that the time-resolved LII signal is clearly related to soot maturity.The question is if this observation can be used for the detection of maturity for the soot cores of particles in the atmosphere using the SP2 instrument.During their lifetime in the atmosphere, the emitted soot particles will undergo morphological transformations (e.g., Corbin, Modini, and Gysel-Beer 2023) from hydrophobic soot agglomerates to compacted soot cores embedded in hygroscopic coatings, which means that the particles can grow to form droplets at typical atmospheric relative humidities (see e.g., Eriksson et al. 2017).The LII signal of compacted soot (where the coating was removed by a thermodenuder) has for example been shown to be delayed in comparison to fresh soot (Bambha and Michelsen 2015) which likely complicates the identification of the maturity of the soot core of atmospheric aerosol particles.Some of the issues related to field campaigns could potentially be solved by the use of a thermodenuder to remove volatile coatings and an instrument to sizeselect the particles before entering the SP2 instrument.By registering the LII peak intensity and the time delay between the LII peak signal and the laser intensity maximum, the results in Figure 2 suggest that the maturity can be estimated with our method.Averaging the SP2 signals as in our work will however not be possible due to the myriad of soot sources in ambient air.Alternative approaches that work for identification on a single particle level must therefore be explored, preferably in a controlled lab environment.Adding a thermodenuder to coated and fresh soot of different maturity and studying the SP2 LII signal characteristics would also provide useful information toward the ultimate goal of determining soot maturity in the ambient air.As T€ or€ ok et al. (2018) showed that OP6 soot is still "brown" despite thermodenuding (in terms of AAE), it would be interesting to see which characteristics of the OP6 LII signal that would be preserved and which would not.Lastly: although it may be questionable if OP6 soot is representative of atmospheric BrC (Maricq 2014), our results show that flame soot with a different composition than mature soot (e.g., diesel soot-like) can be detected and identified with the SP2.
The signatures of less mature soot identified in our work may be combined with other SP2 signal features of less graphitized LAC species.The time resolved scattering cross section of tar balls was for example used to identify them separately from soot (Corbin and Gysel-Beer 2019).Possibly, other signature signal features of less mature soot than those explored in this work may be used for differentiation, such as the ratio between the broadband and narrowband LII channel.Moreover, the supervised machine learning approach as deployed by Lamb (2019) to classify iron oxide aerosols from SP2 signal signatures may also be interesting for the detection of less graphitized species in ambient air.
In this work, we studied the LII signal behavior for soot with different absorption efficiencies for various laser powers, and observed different characteristics regarding LII signal behavior, as shown in Figure 4.It may be suggested that cycling the laser power when monitoring ambient LAC aerosols-thermodenuded (to remove atmospheric coating) and size selectedcould be a way to estimate the number fraction of less efficient absorbers that are capable of yielding detectable incandescence (such as tar balls from marine-engine exhaust Corbin and Gysel-Beer 2019 or wildfires Chakrabarty et al. 2023).

Conclusions
A single particle soot photometer SP2 was used to investigate the LII signal response to soot of varying maturity from a mini-CAST soot particle generator.Also, the difference in peak LII signal intensity and timing for soot of the same mobility diameter and the effect of SP2 laser power on the temporal LII signal were explored.A theoretical model for the LII process was used for numerically calculating time-resolved LII signals to support the experimental results.
Our main findings are: � The measured peak LII signal is increased and appears earlier with increasing maturity for soot of the same mobility diameter.� The mobility size had only a weak influence on the time delay of the peak LII signal, at least for the more mature soot particles.� The minimum SP2 laser power to achieve a signal with sufficient signal-to-noise ratio is higher for the less mature soot in comparison with mature soot.� Qualitative temporal agreement was achieved between the experimental LII signals and modeled LII signals.This statement should be seen in view of the complexity of modeling the temporal LII signal response, as physicochemical processes, such as thermal annealing and evaporation of volatiles, change the soot particle characteristics during the transport through the laser beam.These processes were not modeled in the present work due to a lack of input variables to represent the processes occurring in the SP2 soot-laser interaction.

Figure 1 .
Figure1.Experimental setup for the measurement of the effect of soot maturity on the SP2 response.The mini-CAST soot generator produces soot aggregates of different maturity.The differential mobility analyzer (DMA) selects soot particles of a fixed mobility diameter generated by the mini-CAST before sampling with the single particle soot photometer (SP2) in parallel with a condensation particle counter (CPC).

Figure 2 .
Figure 2. Temporal median LII signals for OP1, OP5, and OP6 soot of mobility diameter (a) 169 nm and (b) 209 nm.The median laser profile is shown for comparison (shaded region).The vertical line represents the peak laser intensity at time t max laser.The time scale is relative to the maximum laser intensity.A color version of this figure can be viewed online.

Figure 3 .
Figure 3.The median LII signal (broadband) peak height and its relation to peak timing for soot of different mobility diameters and maturity (OP1, OP5, and OP6).The error bars indicate the 10-90 percentile.(a) The absolute value of the median signal peak LII intensity as a function of peak timing.(b) Normalized LII signal intensities within each size group for the three types of soot as a function of peak timing.Total number of data points were 7, 7, and 9 for OP1, OP5, and OP6 soot, respectively, although markers may overlap.A color version of this figure can be viewed online.

Figure 4 .
Figure 4.The effect of varying the laser power on the LII peak height and timing relative to the laser intensity maximum.(a) The normalized peak LII intensity for the broadband (400-650 nm) incandescence channel as a function of YAG power voltage for two types of soot, OP1 (diamonds and squares) and OP6 (circles), of three different sizes (88, 145, and 250 nm).The whiskers indicate the 10-90 percentile.(b) The broadband LII peak timing relative to the laser intensity maximum as a function of pump laser current.A color version of this figure can be viewed online.

Figure 5 .
Figure 5.Comparison of measured and modeled temporal LII signals.Model calculations are done with E (m, 1064 nm) ¼ 0.33 for OP1 and 0.16 for OP6.The model calculations have been done with primary particle size d ¼ 22 nm (a) and 16 nm (b).The laser profile is shown for comparison.The arrows indicate the peak timing of the modeled LII signals.Note that the experimental and modeled beam profile and LII signals are normalized to the LII signal from OP1 soot.A color version of this figure can be viewed online.

Table 1 .
Mini-CAST operating parameters and soot characteristics for different operating points (OP's).A lower OP number indicates higher maturity.