2.3.1 Online soot aggregate characterization

Online soot aggregate property measurements mean that the soot particles for characterization were taken from the same aerosol flow as for IN experiments. Thus, the characterized soot particle population is identical to ice- or water-activated soot INPs or CCN. Considering that a HINC RH scan at a fixed T takes ∼40 min, during which the fresh soot might become compacted to some extent (see Fig. 3), soot samples were always replaced with fresh soot for every sample RH ramp during the IN experiments. Soot samples agitated for 2 weeks were used to produce compacted soot aerosols. Both fresh and compacted 60, 100, 200 and 400 nm soot particles were sampled. In order to monitor the changes in the particle morphology and its influence on soot IN ability, the particle size and mass distribution of size-selected soot were measured synchronously with IN experiments. The single particle mass of a size-selected soot aerosol sample was derived from the CPMA mass scan measurements running with a CPC (Model 3787, TSI Inc., 1.5 L min⁻¹). Simultaneously, the size distribution of monodisperse soot particles was scanned by the SMPS setup operating with a CPC (Model 3776, TSI Inc.) in high-flow mode (1.5 L min⁻¹) for 60 and 100 nm or in low-flow mode (0.3 L min⁻¹) for 200 and 400 nm soot particles. Both the CPMA and SMPS raw data scans were fitted by a bimodal lognormal distribution model. The uncertainty in particle mass and mobility diameter was derived from the standard deviation of the mode mass from the CPMA scans and mode mobility diameter from SMPS scans from at least 20 to 100 runs per sample. The mass-mobility exponent D_f was obtained by plotting the single particle mass as a function of the particle mobility diameter and by fitting the data with a power function. Equation (A1) in Appendix A is used to fit mass-mobility data. In addition, the size distributions of polydisperse fresh and compacted soot particles were also measured and presented in Appendix A. The proportion of double-charged particles is less than ∼25 % and ∼29 % for the 60 and 100 nm size-selected particles, respectively, and approximately smaller than 20 % for 200 and 400 nm (see Figs. A2 to A5). In order to take TEM images for soot aggregate morphology analysis, soot aggregates were deposited on 400 mesh Cu girds with a formvar/carbon support film (TED, PELLA, INC.), utilizing the ZEMI setup (Mahrt et al., 2018). The sample grids were visualized at a magnification value of 75k.

2.3.2 Offline soot particle characterization

Bulk soot sample property measurements, termed offline measurements in Fig. 1 including Ar, N₂ and water vapor gas physisorption isotherm measurements, were not conducted simultaneously with IN experiments. Soot powder samples for these offline measurements were prepared in the same way as for online measurements. Therefore, different standard methods and analysis approaches are used to characterize soot cavity characteristics. In the following, we describe the different gas physisorption measurements used and associated analysis models applied.

Gas physisorption measurements: N₂, Ar and water vapor

Gas physisorption measurements can be used to evaluate particle structural and surface properties by measuring the interaction characteristics of bulk particulate samples with respect to probe gas pressure levels. Different probe gases have their advantages and disadvantages of addressing specific particle properties. N₂ is widely used for physisorption measurements to characterize porous material PSD in the literature (Jelinek and Kovats, 1994; Kruk et al., 1997; Galarneau et al., 1999; Hayati-Ashtiani, 2011; Kupgan et al., 2017). Some studies reported that the results from N₂ physisorption measurements might be biased due to its quadrupolar nature and the interaction with the substance surface functional groups, which affects the orientation of the molecule adsorbed. For instance, pore structure diameters for porous material derived from N₂ isotherms can be substantially underestimated (Jelinek and Kovats, 1994; Kruk et al., 1997; Lowell et al., 2004). More recently, Ar has become a more favored noble gas in some laboratory studies (Gardner et al., 2001; Thommes et al., 2012; Sing, 2014b) as a result of its single atomic shape and its inertness with the substrate surface polarities. Thus, we performed both N₂ and Ar isotherm measurements to compare the differences of soot porosity results derived from both measurements. The DVS measurement, which has the advantage of reflecting the interaction ability of soot with water vapor, was also conducted to understand soot IN activities at low T with supersaturated water vapor. However, quantitative water vapor isotherm data analysis requires the soot–water contact angle, which is not well constrained in the literature. Thus, contact angle assumptions are made for approximate calculations in this study. By comparing the results of these three measurements, morphology differences between fresh and compacted soot particles and the influence on soot particle IN activities are discussed.

The Ar and N₂ adsorption and desorption isotherms for soot samples were measured at 77 and 87 K, respectively, at varying adsorbate gas pressure. Before the measurement, all samples were outgassed for 2 h at 573 K under vacuum. The raw data are presented as the volume of the adsorptive gas adsorbed per gram of sample at standard temperature and pressure (STP) corresponding to each relative pressure ($p/p_{\mathrm{0}}$) condition, which is indicated by the ratio of adsorptive vapor pressure (p) to the adsorptive vapor saturation pressure (p₀).

Before the DVS measurement, soot samples were dried for 4 h at 573 K and then cooled down to ambient T under vacuum. The measurement was conducted at 298 K by a gravimetric dynamic method measuring the mass of water vapor adsorbed or desorbed by the soot sample under varying $p/p_{\mathrm{0}}$ (or RH) conditions, assuming a quasi-equilibrium state of the soot sample under this vapor pressure. The initial sample mass is used as a reference for following mass measurements. For each sample, an adsorption isotherm was obtained from $p/p_{\mathrm{0}}=\mathrm{5}\mathit{\%}$ to 90 % with a step of 10 %, and then a desorption isotherm down to $p/p_{\mathrm{0}}=\mathrm{5}\mathit{\%}$ with the same $p/p_{\mathrm{0}}$ resolution was also measured. Finally, the sample mass change (Δ m) in percentage as a function of $p/p_{\mathrm{0}}$ can be obtained, representing the amount of water adsorbed or released per gram of soot sample under various $p/p_{\mathrm{0}}$ conditions.

Table 1Soot sample characterization results.

^a Information from the manufacturer. ^b Calculated from the SMPS-CPMA particle size and mass measurement results by using Eq. (A1). ^c N₂S_BET is calculated by the formulation presented in Appendix B. ^d Defined as a two-dimensional void encompassed by primary particle clusters per aggregate and derived from TEM image analysis. The total number of soot aggregates analyzed is shown in the parentheses, respectively.

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PSD analysis

Sorption isotherms can be used to calculate the PSD, which is of interest for describing the structure of carbon black aggregates. In the following we apply the term “pore” to describe the cavity structures in the soot aggregate. The corresponding term “pore radius” is hereby defined as a radius equivalent to the cylindrical pore half-width that leads to the same vapor pressure reduction due to the inverse Kelvin effect. The PSD results reflecting soot cavity characteristics as a function of pore size can be derived from the desorption isotherms by applying the Kelvin equation with specific assumptions. The Kelvin equation is given as the following:

where r_k is the pore radius required for capillary condensation induced by the inverse Kelvin effect, γ_sl denotes the interfacial tension between the solid and liquid phases, v_s is the adsorptive molar volume, θ is the contact angle between the soot surface and the adsorptive gas which can be taken as 0^∘ for N₂ and Ar, and R is the ideal gas constant with the value of 8.314 J mol⁻¹ K⁻¹. The application of the Kelvin equation for PSD analysis relies on the following assumptions. (1) The equation is valid over the complete pore size range addressed. (2) The pores are rigid and of a cylindrical structure. (3) The capillary filling or desorption of each pore does not depend on its location within the pore network inside the aggregate. (4) The adsorption or desorption on the pore walls proceeds exactly in the same way as on the corresponding open surface.

Liquid can condense in mesopores (2–50 nm) when N₂ or Ar saturation ratios are above the BET range ($p/p_{\mathrm{0}}>\mathrm{0.15}$ or 0.1), due to capillary effects according to the Kelvin equation. This condensation step is reversible with decreasing $p/p_{\mathrm{0}}$, which refers to the desorption branch of the isotherms and is in equilibrium state. By applying the Brunauer–Joyner–Holanda (BJH) approach (Barrett et al., 1951; Lowell et al., 2004), the PSD can be calculated from the desorption branch of the respective sorption isotherm. A more detailed description of the PSD results determination by the BJH approach can be found in the International Union of Pure and Applied Chemistry (IUPAC) recommendation for calculation of the distribution of mesopores (Thommes et al., 2015). The BJH approach calculates the pore size from the Kelvin equation at each $p/p_{\mathrm{0}}$ value, and the cumulative adsorbed gas volume corresponding to a pore size value can also be retrieved. However, the desorption step includes the desorption from the adsorbent surface in addition to a release of N₂ or Ar from pores, and these surface desorbates are irrelevant to pore structures during the desorption process. To distinguish between the liquid released from pores and that which is desorbed from the material surface, the De Boer thickness equation was applied (Thommes and Cychosz, 2014; Thommes et al., 2015). With the BJH method, pore radius from 1 to 200 nm can be calculated, but values close to the limits have to be interpreted carefully. At the lower limit, inter-molecular forces lead to an enhanced condensation of liquid. Therefore, the pore radius below 10 nm calculated by the Kelvin equation is an underestimation of the real pore radius by approximately 30 % (Lowell et al., 2004). The upper limit of 400 nm is defined by the highest $p/p_{\mathrm{0}}\approx \mathrm{0.99}$ that can be reached during the measurement. Due to the irregular geometry of carbon black aggregates, the intra-aggregate cavity volume among primary particles cannot be clearly distinguished from the outer-aggregate volume between primary particle clusters. Therefore, the pore volume at the highest pore radius is uncertain. Regardless of the limitation of the BJH method, the calculated PSD results can be used to compare different types of soot and to investigate the effect of particle compaction on the spatial pore density of soot aggregates in this study.

Figure 4The effective density (ρ_eff) of 400 nm (a), 200 nm (b), 100 nm (c) and 60 nm (d) size-selected fresh and compacted FW200 and PR90 soot particles at each IN experiment T (x axis). The error bar is propagated from the particle mass and mobility diameter measurement uncertainties.

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Figure 5TEM images for 400 nm fresh and compacted FW200 and PR90 soot aggregates at a magnification value 75k. The red circle is used to indicate intra-aggregate voids with sizes of tens of nanometers.

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Analogously to the BJH method applied for N₂ and Ar isotherms, a PSD analysis approach can be formulated for DVS data on the basis of the Kelvin equation as well. The DVS isotherm PSD analysis method is based on the theory proposed by Wheeler (1951) and more recently formulated by Shkol'nikov and Sidorova (2007) and is also similar to the approach applied by Mahrt et al. (2020b). A six- or seven-order polynomial function is used for the extrapolation of the discrete isotherm data points into a polynomial expression instead of a three-order polynomial stepwise fitting for every three data points used by Mahrt et al. (2020b). The desorption branch in water vapor sorption measurement was used to derive the PSD as this branch is more associated with the equilibrium gas–liquid phase transition. Because soot–water contact angle was not measured, three contact angle values including 0, 45 and 75^∘, representing surface wettability from hydrophilic to hydrophobic, were used to cover the possible values for soot samples in this study. With a contact angle value assumption, pore radius can be calculated as a function of $p/p_{\mathrm{0}}$, according to Eq. (2). Under each water vapor $p/p_{\mathrm{0}}$ condition, the mass of water vapor is measured in the DVS measurement. Subtracting the amount of water sticking on the material surfaces and wall area, water volume can be calculated which is equivalent to the pore volume. Hence, the pore volume distribution can be determined as a function of pore radius. A detailed formulation of this approach is provided in Appendix B.

Figure 6Average of three AF curves as a function of RH_w and RH_i from the 1 µm OPC channel for 400 nm fresh and compacted FW200 and PR90 soot particles at different T. For 243 and 238 K the AF curves represent water droplet formation (see text Sect. 3.2.1 for details). Black solid lines represent water saturation conditions according to Murphy and Koop (2005). Black dashed lines denote the expected RH values for solution droplet homogeneous freezing at each T (Koop et al., 2000). The grey shading shows the possible variation range in RH that aerosol in HINC can encounter for the calculated homogeneous freezing RH values at each T.

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3.2.1 Fresh and compacted soot particle activation fraction curves

The AF curves for fresh and compacted FW200 and PR90 soot with different particle sizes are presented in Figs. 6 to 9, respectively. Our soot particles only show water droplet formation at T> HNT and nucleate ice at T< HNT. Evidence of soot–water droplet formation at T> HNT is presented in Figs. C1 to C4, showing that OPC signals from the 5 µm channel are absent for T=243 and 238 K. Since droplet growth rates are much lower than those of ice crystals due to the difference between RH_i and RH_w, any ice crystals nucleating onto the soot particles at T<233 K would be able to grow up to 5 µm in HINC and be detected by the OPC. This is also consistent with the results reported by Lacher et al. (2017) and Mahrt et al. (2018). For T< HNT, 200 and 400 nm compacted FW200 and 400 nm compacted PR90 soot particles generally can reach a higher AF value under the same T and RH condition compared to the fresh particles, suggesting compaction enhanced IN activities at T< HNT and soot–water interactions for T> HNT. Aggregate compaction also promotes 100 nm FW200 soot activation at T≥233 K as shown in Fig. 8. However, the rest of the AF curves for small-sized (60 and 100 nm) particles do not show significant differences between compacted and fresh FW200 or PR90 soot. Overall, compacted soot particles with larger sizes are more effective INPs in the cirrus regime compared to the uncompacted ones. We attribute the soot particle IN activity below RH_hom at T< HNT to the PCF process. In the following, we compare the differences in soot particle IN between fresh and compacted soot particles produced from both BC materials.

Figure 8Average of three AF curves as a function of RH_w and RH_i from the 1 µm OPC channel for 100 nm fresh and compacted FW200 and PR90 soot particles at different T. For 243 and 238 K the AF curves represent water droplet formation (see text Sect. 3.2.1 for details). Black solid lines represent water saturation conditions according to Murphy and Koop (2005). Black dashed lines denote the expected RH values for solution droplet homogeneous freezing at each T (Koop et al., 2000). The grey shading shows the possible variation range in RH that aerosol in HINC can encounter for the calculated homogeneous freezing RH values at each T.

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Figure 9Average of three AF curves as a function of RH_w and RH_i from the 1 µm OPC channel for 60 nm fresh and compacted FW200 and PR90 soot particles at different T. For 243 and 238 K the AF curves represent water droplet formation (see text Sect. 3.2.1 for details). Black solid lines represent water saturation conditions according to Murphy and Koop (2005). Black dashed lines denote the expected RH values for solution droplet homogeneous freezing at each T (Koop et al., 2000). The grey shading shows the possible variation range in RH that aerosol in HINC can encounter for the calculated homogeneous freezing RH values at each T.

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FW200. For 400, 200 and 100 nm compacted FW200 soot particles, our results are in good agreement with Mahrt et al. (2018), who studied the IN activity of the same BC material with the same sizes but utilized a fluidized bed aerosol generator (FBG) to produce soot aerosol samples. It is very likely that the beads and rotating motion of the transition belt in the FBG setup can also result in soot aggregate compaction, which has a similar compaction effect on the fresh soot to that induced by Teflon bar mechanical agitation in this study. However, fresh soot particles without physical aging may have a loose structure. As shown in Fig. 6, 400 nm compacted FW200 soot particles are more effective INPs than the fresh sample, as the compacted particles require a lower RH to reach the same AF value at T<233 K. We ascribe this to an enrichment in small mesopores for compacted FW200 soot particles. After agitation, macropores (>50 nm in width) and larger mesopores (>20 nm in width) among fresh soot aggregates might be compacted into smaller mesopores which induce an inverse Kelvin effect and lead to capillary condensation under RH conditions well below water saturation conditions, thereby promoting PCF activation according to the soot–PCF framework (Marcolli et al., 2021). Given that physical agitation is the only modification to soot samples, the enhancement of IN ability must result exclusively from the changes in morphology (resulting in mesopore enrichment) induced by soot aggregate compaction. At T=233 K, 400 nm fresh and compacted FW200 soot particles show comparable AF values at RH_w<94 %, but FW200fresh AFs are lower than that of FW200comp at RH_w<94 %, as shown in Fig. 6c. This is also because FW200comp soot contains more mesopores relevant to PCF activation compared to the fresh sample, showing that 400 nm FW200comp reaches higher AFs than the fresh particles, because the 400 nm FW200fresh sample may reach its limit for PCF-relevant mesopores, whereas a larger fraction of FW200comp sample has more mesopores, satisfying the PCF process when reaching at the same AF level at RH_w=94 % for 233 K. At T> HNT, the enriched mesopores by aggregate compaction can also promote water droplet formation for 400 nm soot particles, as shown in Fig. 6a and b, in which compacted soot can form more water droplets than the fresh one under the same RH and T condition. This promoted soot–water interaction ability also results from the pore structure enrichment induced by aggregate compaction, considering that mesopores can make contributions to soot–water uptake by facilitating water capillary condensation (Persiantseva et al., 2004; Popovicheva et al., 2008a, b). The IN activities of 200 nm FW200 soot particles are similar to those of 400 nm FW200, but smaller-sized soot samples (60 and 100 nm) only freeze homogeneously (see Figs. 7 to 9) at T< HNT. At T> HNT, these small-sized soot particles (<400 nm) form water droplets only above water saturation conditions. We believe that small-sized aggregates (100 and 60 nm) do not possess enough mesopores of the right size or structure due to the limited number of primary particles making up these small aggregates, resulting in a limited intra-aggregate void volume.

Figure 10Onset saturation values (at AF =0.1 %) with respect to ice (S_i) as a function of T and soot particle size (indicated in each panel) for fresh and compacted FW200 and PR90 soot samples. Black dashed lines denote the homogeneous freezing conditions for solution droplets at T< HNT, according to Koop et al. (2000). Blue dashed lines denote the homogeneous freezing conditions for solution droplets at T< HNT, according to Schneider et al. (2021). Grey dotted lines represent constant water saturation conditions calculated based on Murphy and Koop (2005). Red dashed lines indicate the 1 µm size water droplet survival conditions for T> HNT, where the phase of the particle >1 µm can be either ice or liquid water. The S_i uncertainty caused by the temperature uncertainty (±0.1 K) of the HINC chamber is indicated as error bars. Each data point was derived from the AF curves in Figs. C1 to C4 (see Appendix C), in which each AF curve is an average of at least three individual RH ramps.

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PR90. Size-selected 400 nm PR90 soot particles show similar but less pronounced IN enhancement after compaction, in comparison to FW200 soot. At T≤228 K below HNT, PR90comp soot particles reach a higher AF value under the same T and RH condition compared to PR90fresh, which means PR90comp are more active INPs. This is also because compacted PR90 soot contains mesopores of relevant properties (size and structure) to promote PCF activation. However, there is no difference between the PR90comp and PR90fresh soot at T=233 K (see Fig. 6c). This is because of the homogeneous freezing dependence on T and the limitation of ice embryo growth with such a small mesopore volume in PR90 soot. In addition, the homogeneous freezing nucleation rate decreases exponentially with increasing T (Ickes et al., 2015). Additionally, the small PSD (see Sect. 3.4) in PR90 soot aggregates limits the volume of supercooled water engaging in porewater homogeneous freezing. Both inhibit the PCF process by leading to a small homogeneous freezing rate (Ickes et al., 2015; Vali et al., 2015; Koop and Murray, 2016). On the other hand, the pore volume in PR90 soot aggregate may be too small for the volume of water to freeze on the timescale of our experiments (∼10 s) or to allow the ice embryo to grow outside of the pore. David et al. (2020) reported a similar case where silica particles with smaller mesopores (2.8 or 3.3 nm) are less active INPs via PCF than those particles with larger mesopores (9.1 nm) at 233 K. At T> HNT, PR90comp 400 nm soot particles do not tend to be more effective CCN than PR90fresh, suggesting the enrichment of small mesopores caused by agitation has a limited influence on promoting PR90 soot–water interaction abilities. Smaller-sized (<400 nm) PR90 soot particles do not show a significant difference for IN ability between aggregates with and without compaction but require homogeneous conditions to form ice crystals (Figs. 7 to 9) at T< HNT. At T> HNT, small-sized (<400 nm) PR90 soot particles form water droplets at RH_w>105 %, which implies their hydrophobic surface and low water interaction ability.

There are also differences between FW200 and PR90 IN activities. Firstly, PR90 soot particles are less active INPs compared to FW200, as shown by the fact that the same-sized fresh or compacted PR90 soot particles require a higher RH than that of FW200 soot with the same compaction level to reach the same AF value at the same T. According to the PCF mechanism (Marcolli, 2014; Marcolli et al., 2021), this probably results from the differences in soot sample properties, including sample PSD and soot–water contact angle, both of which are determinators for the PCF mechanism. Thus, the PR90 soot PCF process occurs under higher saturation conditions and requires low T if PR90 soot is originally less porous than FW200 and/or of a lower surface wettability. Secondly, aggregate compaction-induced IN promotion for PR90 soot is not as significant as for FW200 soot. As can be seen from Fig. 7, soot aggregate compaction can exert IN enhancement for 200 nm FW200 soot particles but not for PR90 soot particles. This is also determined by the intrinsic nature of the soot sample and may suggest that aggregate compaction-induced mesopore enrichment for PR90 soot is not as strong as for FW200 soot or may simply be due to a higher contact angle of PR90 at T> HNT, where PR90 soot particles are poorer CCN and require higher RH conditions to form droplets than FW200 soot with the same sizes, also suggesting a paucity of pore structures and a low water interaction ability of PR90 soot.

3.2.2 Fresh and compacted soot particle onset ice nucleation results

In this section, the IN ability of fresh and compacted FW200 and PR90 soot particles will be compared in terms of their onset ice saturation (S_i) results, and the IN dependence on particle size will be discussed. The onset S_i value is a measure to evaluate the IN ability of INPs, using the threshold S_i value required for the INP to reach a prescribed AF value (0.1 %) at a fixed T. The onset S_i values for each soot sample particle at different T are presented in Fig. 10, derived from the AF curves of the 1 µm OPC channel in Figs. 6 to 9 in which each curve is an average of three RH ramp experiments. In Figs. C5 to C8, we show the size dependence for the sample type compared to Figs. 6 to 9, where we show different samples for a given size.

FW200. From Fig. 10a, soot aggregate compaction decreases the onset S_i value for 400 nm FW200comp soot particles by at least 0.08 compared to the fresh sample when T<233 K in the cirrus regime. As shown in Fig. 10b, the onset S_i for 200 nm FW200 can be decreased by as much as 0.15 when T<233 K. In particular, there is also a reduction in the onset S_i value at T=233 K for 200 nm FW200comp soot particles showing a smaller S_i value compared to 200 nm fresh FW200 soot particles, which means that soot aggregate compaction can even promote, albeit by a small S_i reduction, 200 nm FW200comp to nucleate ice. Both compacted and fresh 100 nm FW200 soot particles are still more competitive INPs than the solution droplets freezing homogeneously at T≤223 K (see Fig. 10c). However, the onset condition values for fresh and compacted particles are overlapped, which means limited IN enhancement for 100 nm compacted particles, as discussed before. Finally, 60 nm FW200 soot particles cannot facilitate ice crystal formation below homogeneous conditions proposed by Koop et al. (2000) at T< HNT, showing that the error bars are across the homogeneous freezing line even at the lowest T=218 K. If we consider the homogeneous freezing conditions of sulfate particles proposed by Schneider et al. (2021), 60 and 100 nm soot particles are active INPs via PCF at T≤223 K, as their S_i values are below the corresponding RH_hom condition (blue dotted line, Fig. 10). At T> HNT all data points lie within error bars and above the 1 µm water droplet limit line (the limit above which we cannot distinguish between ice and water solely based on the 1 µm OPC channel) for both compacted and fresh FW200 soot of all sizes, suggesting compaction does not have pronounced effects on FW200 soot droplet activation activities. Kanji et al. (2020) suggested that soot particles are poor INPs in immersion-mode freezing at T> HNT and can only form water droplets under these conditions. These results are also consistent with the findings reported by Friedman et al. (2011), Mahrt et al. (2018) and Falk et al. (2021), in which the authors noted that soot particles do not nucleate ice for T> HNT.

PR90. In general, PR90 soot requires a higher onset S_i value than FW200 soot with the same compaction level to reach the same AF =0.1 % at T< HNT, indicative of less active IN abilities. Nonetheless, soot compaction significantly enhances 400 nm PR90 soot IN at T≤228 K, similarly to that of FW200 soot discussed above. In Fig. 10a, 400 nm compacted PR90 soot onset S_i values can be reduced by more than 0.1, in contrast to the fresh particles. Fresh and compacted 200 nm PR90 soot still can compete with homogeneous freezing at T=218 and 223 K as the S_i values are smaller than the RH_hom condition, but the error bars intercept with the homogeneous freezing threshold calculated according to Koop et al. (2000) as depicted in Fig. 10b. PR90 soot particles with or without compaction of sizes 60 and 100 nm only freeze homogeneously at T< HNT even considering the higher limit of homogeneous freezing proposed by Schneider et al. (2021), also suggesting that the agitation process does not promote PR90 soot IN, as shown by onset value error bars being in touch at all T (see Fig. 10c and d). At T> HNT, all sizes of fresh and compacted PR90 soot particles form water droplets under similar RH conditions at S_w>1.05, suggesting soot particle structure compaction does not influence PR90 soot–water droplet formation, as discussed previously.

In brief, aggregate compaction can enhance soot particle IN ability significantly by lowering the onset S_i values required for PCF activation at T< HNT in the cirrus regime and showing a clear size dependence. Firstly, soot aggregate compaction-induced IN enhancement shows a size dependence, suggesting that this compaction effect on soot IN ability is more pronounced for large soot particles (>200 nm) and that physical agitation might not compact the small soot aggregate morphology as effectively as for large soot aggregates to induce IN enhancement. The size dependence effect is observed for the IN of soot particles with the same compaction level, showing that large particles require a lower onset S_i value than smaller ones at the same T, which coincides with the results reported by Mahrt et al. (2018) and Nichman et al. (2019) and also what is generally known about mineral dust ice nucleation (Archuleta et al., 2005; Welti et al., 2009; Kanji and Abbatt, 2010). This is because large soot aggregates have a higher probability of possessing the mesopores of the right size for the PCF mechanism. Large soot aggregates contain a larger number of primary particles and are more susceptible to a primary particle network change caused by external forces, whereas small soot aggregates contain a limited number of primary particles and are more analogous to the fresh soot basic unit which is much closer to primary particle clusters or a single primary particle. Thus, large soot aggregates better present the aggregate compaction effect on ice nucleation. The PCF activation has a positive relation to the number of mesopores, implying that the PCF activation requires sufficient mesopores with the right characteristic for capillary condensation and ice nucleation within the mesopores. Furthermore, an individual mesopore even with the appropriate pore size for PCF probably plays a limited or implicit role in the event. For instance, dynamic molecular simulation results suggest that a single 3 nm pore in a silica slab does not facilitate ice formation, whereas ice crystal can grow quickly in an array of pores with the same width under the same simulation environment (David et al., 2019), suggesting that a bridging effect from the pore network promotes the growth of pore ice to a macroscopic ice crystal. In this study, experiments for 60 nm FW200 and PR90 soot are performed to extend a lower size limit for the investigation of soot particle IN activities in the cirrus regime since sub-100 nm particles are often observed in the upper troposphere (Petzold and Schröder, 1998; Twohy and Gandrud, 1998; Cziczo and Froyd, 2014). According to Zhang et al. (2020), there might be a size threshold between 100 and 400 nm for soot particles to be active INPs under cirrus cloud conditions. However, it is difficult to define such a threshold size for soot particles to trigger the PCF mechanism under cirrus conditions. As can be seen from the aforementioned discussion, the IN ability dependence on size is different for FW200 and PR90 soot in this study, showing that PR90 is more dependent on its size than FW200 soot as 200 nm PR90 soot onset results are close to the homogeneous freezing line, whereas those of 200 nm FW200 soot are well below the RH_hom limit. Last but not least, our IN results for 60 and 100 nm FW200 soot particles suggest that the freshly emitted aviation soot particle majority with a small mobility size (≤100 nm) could act as INP candidates in the cirrus cloud regime if they have properties (pores and surface wettability) similar to FW200 soot, and the homogeneous freezing limit considered is analogous to that proposed by the homogeneous freezing parameterization of Schneider et al. (2021).

3.4.1 Pore size distribution retrieved from Ar and N₂ isotherms

According to the BJH approach, the PSD results for soot samples can be analyzed from Ar and N₂ isotherms, which are independent of the contact soot–water angle. Based on Ar and N₂ physisorption measurement isotherms provided in Figs. D1 and D2, the calculated PSD results as a function of pore radius are presented in Fig. 12. The PSD results generally show that physical agitation shifts soot mesopore size distribution to smaller size ranges in comparison to the fresh samples. Compacted FW200 soot PSD derived from Ar BJH changes to a markedly smaller distribution mode from ∼27 (21 nm, N₂ BJH) to ∼7 nm (13 nm, N₂ BJH) compared to the fresh soot (see Fig. 12a). Analogously to FW200 soot, PR90 soot Ar PSD peak decreases from ∼14 down to ∼6 nm after compaction (see Fig. 12b). N₂ BJH analysis for compacted PR90 soot shows a PSD reduction from ∼16 to ∼7 nm compared to fresh PR90 soot. In general, the shift in PSD to small pore sizes for compacted soot samples suggests that small mesopores with radii approximately <10 nm can be appreciably enriched after agitation, which would favor the PCF process, thereby enhancing soot IN via PCF. The mesopore enrichment contributes to compacted soot particle IN ability enhancement because the smaller the mesopore size is, the lower the RH is that will be required to trigger the PCF mechanism at the same T. For example, the Ar PSD result for FW200 soot, presenting a larger mesopore size distribution for pore radius from ∼3 to ∼12 nm, directly supports onset results in Fig. 10, as shown where 200 and 400 nm FW200comp soot shows ice nucleation at much smaller RH reaching the onset AF value (0.1 %) at the same T as the FW200fesh soot. According to the PCF process (Marcolli, 2014), 400 nm FW200 soot particles with a 60^∘ water contact angle assumption (Marcolli et al., 2021) need ∼4 nm mesopores to present onset S_i=1.24 at 228 K (Fig. 10a) in order to induce capillary water condensation. If the contact angle is assumed to be 45^∘, the mesopore should be around 6 nm. From Fig. 12a, FW200comp soot contains more mesopores around 4–6 nm than the fresh sample, explaining that 400 nm FW200comp soot can show such a low onset S_i value, whereas 400 nm fresh FW200 soot containing fewer 4–6 nm mesopores requires higher onset S_i at the same T. In general, the increased mesopore availability around 10 nm contributes to the enhanced IN ability of compacted soot particles because of the pore morphology changes upon aggregate structure compaction.

However, both fresh soot samples contain more larger-sized pore structures than compacted soot by showing a cross in the PSD curves of fresh and compacted soot sample derived from the same gas sorption technique. Fresh FW200 soot has more mesopores $>\sim \mathrm{12}$ nm (Ar PSD) or $>\sim \mathrm{18}$ nm (N₂ PSD) than the compacted soot sample, and the similar case for PR90 soot is about $>\sim \mathrm{9}$ nm (Ar PSD) or $>\sim \mathrm{11}$ nm (N₂ PSD). These pore structures are too large to trigger inverse Kelvin effects under the same RH condition as required by smaller mesopores (<10 nm), making them PCF-irrelevant. For example, a 12 nm mesopore in a 400 nm FW200 soot aggregate with a water contact assumption 60^∘ requires S_i=1.38 at 233 K to induce capillary water condensation according to the Kelvin equation, which is already higher than the onset S_i value for 400 nm fresh (1.36) and compacted (1.34) FW200 soot particles shown in Fig. 10a. Hence, these large mesopores in fresh soot particles do not contribute to the IN activity. Besides, fresh soot samples also contain more pore structures larger than 50 nm in comparison to the compacted soot (see Fig. 12), which is consistent with their larger cumulative pore volumes (Table 1). These larger pore structures are probably intra-aggregate voids (macropores >50 nm) among primary clusters or outer-aggregate voids as shown in TEM images (Fig. 5), which can be filled by Ar and N₂ near the saturation condition during sorption measurements.

Gas sorption measurements also manifest the structural difference between soot samples and the derived PSD dependence on a gas agent (Ar and N₂). Comparing the PSD results between FW200 and PR90 soot with the same physisorption measurement, there is a difference to be noted even though they reveal similar mesopore size change effects exerted by agitation. The FW200 soot PSD curve can reach a much higher peak and contains a larger quantity of mesopores than PR90 soot with the same compaction level, supporting FW200 soot being more active in PCF activation than PR90 soot (Sect. 3.2). A higher porosity level of FW200 soot than PR90 soot is also proven by its larger cumulative pore volume from BJH analysis (see Table 1). In addition, the agitation can lead to a more significant Ar PSD change to fresh FW200 soot than to fresh PR90 soot, showing compacted FW200 soot Ar PSD peak-mode reduction from ∼27 to ∼7 nm, whereas the case for PR90 soot is from ∼14 to ∼6 nm and with a smaller cumulative pore volume change (see Table 1). This results from the difference in the soot sample original primary particle network. Likely, PR90 soot, comprising a small fraction of volatile content (∼1 %), may have a tight primary particle connectivity. Compared to PR90 soot, FW200 soot may have looser and less intimate primary particle connections, providing a higher probability of primary particle rearrangement when the physical force is imposed. For example, Marcolli et al. (2021) used the concept of overlap coefficient for primary particles to depict the tightness of primary particle connection, which has an important influence on the mesopore sizes of soot aggregates. Furthermore, the pore structure in FW200 soot aggregates is not as stable as that in PR90 soot aggregates, also resulting from its lower carbonization (Table 1). Therefore, agitation-induced aggregate compaction generates more smaller mesopores for FW200 soot than for PR90 soot. Furthermore, compacted PR90 soot has a comparable amount of mesopore structures in the size range ∼6–7 nm to that of fresh FW200 soot, both showing a volume-based PSD value of ∼1000 mm³ g⁻¹ nm⁻¹ in this pore size range. This explains the comparable IN ability of 400 nm PR90comp and FW200fresh at T≤228 K. Again, it implies that originally hydrophobic soot can be active INPs if it contains sufficient mesopores relevant to PCF activation. Finally, Fig. 12 shows a divergence between Ar and N₂ PSD results for the same soot sample, suggesting the PSD result is dependent on the probe gas nature. As introduced in Sect. 2.3.2, the quadrupole moment of N₂ affects the orientation of the molecule during the sorption process (Thommes et al., 2012), thereby influencing isotherms measured and the PSD results. Nonetheless, these measurements allow one to conclude the same fact that the physical agitation shifts the PSD mode of fresh soot to small sizes and leads to significant medium mesopore enrichment and IN enhancement for compacted soot.

3.4.2 Pore size distribution retrieved from water vapor isotherms

In this section, we present the calculated soot sample PSD results by applying the Kelvin equation-based formulation in Appendix B to corresponding DVS isotherms, assuming different soot–water contact angle values for soot samples. The contact angle ranging from 0 to 180^∘, and from completely wettable to non-wettable, can be understood as a measure of surface wettability (Pruppacher and Klett, 1997; Lohmann et al., 2016). Reasonable assumptions for FW200 and PR90 soot need to be made by comparing similar water isotherms to the other soot samples with reported soot–water contact angle values in the literature. For instance, Persiantseva et al. (2004) used the sessile drop technique to measure the contact angle of water droplets on different soot pellets covering a broad range of wettability in conjunction with water vapor isotherms. The authors reported that the water contact angle on the aircraft combustor produced soot surface spans from 60 to 80^∘. By comparing the isotherm characteristics, their study can serve as a good reference for soot–water contact angle estimates in this study because we collected similar types of isotherms. Also note that the contact angle of different soot samples can vary in a broad range. For example, Shin et al. (2010) found that the hydrophobic graphene contact angle can be up to approximately 91 ± 1^∘ tested by using a charge coupled device (CCD) camera. However, Kireeva et al. (2009) reported that the soot–water contact angle can be as low as 28^∘ for hydrophilic black carbon. Moreover, the water contact angle for INPs even with the same material might show a distribution as a result of surface heterogeneity. For example, both Welti et al. (2012) and Marcolli et al. (2007) found that a distribution of contact angles describes the mineral INPs' IN ability better than a single contact angle value arbitrarily used for IN parameterization. Considering the heterogeneity and complex surface properties of soot particles, to ease the discussion, different contact angle values are assumed to describe averaged soot particle wettability and to simplify data analysis. In this study, three contact angle values (0, 45 and 75^∘) for both FW200 and PR90 soot samples were used for the PSD formulation for DVS analysis. According to DVS isotherm analysis in Sect. 3.3, a low contact angle (45^∘) may fit the FW200 real surface better, whereas a higher contact value (75^∘) for PR90 might be suitable for its more hydrophobic surfaces. Marcolli et al. (2021) used a contact angle mean value 60^∘ for FW200 soot in the PCF–soot framework study, which is also within the contact angle assumption range in this study. In brief, these three contact angle values can cover the possible contact angle range of these soot samples and present the role of contact angle in soot–water interaction activities. The corresponding soot PSD results with different soot–water contact angle assumptions are presented in Fig. 13.

The PSD analysis in Fig. 13 demonstrates that small mesopores generated after compaction are responsible for stronger water interaction abilities of compacted soot compared to fresh soot. PSD curves with the 0^∘ contact angle assumption are used as a perfect case for soot samples and to serve as a PSD benchmark. Assuming a 45^∘ contact angle for FW200 soot, the PSD curve for FW200comp stays above FW200fresh in the radius range from approximately 2 to 14 nm in Fig. 13a (dotted lines), suggesting compacted FW200 soot contains more PCF-relevant mesopores which are required to be smaller than ∼10 nm at T< HNT (Marcolli, 2014, 2020). PR90comp soot mainly contains pore structures smaller than ∼17 nm, as shown by the PSD curve (dashed line) in Fig. 13b calculated with a soot–water contact angle 75^∘. However, PR90fresh soot shows less mesopore abundance in the pore size range from 2 to 9 nm as its PSD curve stays below that of PR90comp soot. It is just the paucity in this pore size range that leads to the poor IN ability of PR90 fresh soot particles. Additionally, the PSD curves retrieved from DVS isotherms showing a monotonic decrease with increasing pore size are different from PSD curves derived from $\mathrm{Ar}/{\mathrm{N}}_{\mathrm{2}}$ measurements in Fig. 12 showing a unimodal distribution as a function of pore radius. This originates from contact angle dependence of soot–water interaction and is also because of the different nature of the probe gas.

Figure 13The PSD as a function of pore size (r_p) for fresh and compacted (a) FW200 and (b) PR90 soot with contact angle assumptions θ=0, θ=45 and $\mathit{\theta }=\mathrm{75}{}^{\circ }$ indicated by solid, dotted and dashed lines corresponding to DVS isotherms shown in Fig. 11.

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Overall, PSD results for FW200 soot derived from DVS measurements coincide with the N₂ or Ar PSD results to imply that physical agitation-induced soot compaction results in the increment of small mesopores required for the PCF activation and thereby promotes compacted soot being more active INPs. We believe soot PSD results derived from DVS measurements are more relevant to soot particle IN activities as they both are associated with soot–water interaction activities. In particular, mesopore abundance is a more important predictor of soot particle IN via the PCF mechanism. As discussed in Sect. 3.2, both soot particle IN and compaction-induced IN enhancement show size dependence. We suggest that the size dependence is in fact mesopore abundance dependence as a function of aggregate size. In this context, each mesopore can be viewed as a local PCF-active site. Only when the mesopore number density reaches a critical amount can the aggregate nucleate ice under a PCF-favored T and RH condition. For example, the PSD results in Fig. 13a can explain why 400 nm FW200comp soot AF increases with a larger slope than that of the fresh soot particles at 233 K as presented in Fig. 6. According to the soot PCF mechanism (Marcolli, 2014), cylindrical mesopores with a radius smaller than ∼9 nm are relevant to PCF at T=233 K and RH_w<94 %, assuming a 45^∘ contact angle for FW200 soot. The PSD results in Figs. 12a and 13a for FW200 soot both suggest that FW200comp soot has more mesopores smaller than 9 nm in comparison to FW200fresh soot.

Similarly, the mesopore increment for compacted PR90 soot (see Fig. 13b) also explains its enhanced water interaction ability and promoted IN activity. Particularly, the reason for that compaction can promote PR90 soot IN significantly at 228 K but not at 233 K can also be explained by its PSD results. With a soot–water contact angle assumption 75^∘, PR90 soot shows the existence of small mesopores between ∼2 and ∼17 nm (Fig. 13b). Though these mesopores are small enough to induce capillary condensation but are too small to provide enough space for the ice embryo to grow out of the pore at 233 K or to nucleate ice in a small volume of water on the short timescale of our experiments (∼10 s), i.e., the PCF activation is limited by ice crystal growth at T=233 K or freezing rate. For example, Marcolli et al. (2021) reported that a three-membered-ring pore in a tetrahedral primary particle packing is smaller in pore volume than a four-membered-ring pore in a cubic packing and is more likely to have the ice growth limitation scenario. This can be the possible case for PR90comp soot. The second possible scenario is the limitation of a low homogeneous freezing rate for supercooled porewater because the supercooled porewater homogeneous freezing rate is both T and the porewater volume dependent. Based on the parameterization for homogeneous freezing in confined structures (Ickes et al., 2015; Marcolli, 2020), calculation can be made to show some evidence. For example, 400 nm PR90comp soot particles with a 75^∘ water contact angle show onset S_i=1.31 at T=228 K, suggesting its 3 nm mesopore is responsible for porewater capillary condensation. However, assuming a cylindrical pore with a radius of 3 nm and a height 400 nm, supercooled porewater homogeneous freezing at 228 K takes ∼0.1 s, whereas it takes ∼25 s at 233 K which is longer than the particle residence time in the HINC chamber in this study. Therefore, PR90comp soot shows a strong T dependence and a PCF suppression from T=228 to 233 K. Again, linking the PSD results analyzed from DVS measurements for FW200 and PR90 soot to the IN results, both low soot–water contact angle and mesopore abundance exert advantages for FW200 soot in PCF activation and contribute to its higher IN effectiveness compared to PR90 soot.