Mechanisms of soot-aggregate restructuring and compaction

Abstract Soot aggregates form as open, fractal-like structures, but aged atmospheric particles are often observed to be restructured into more-compact shapes due to internal mixing (“coating”). This compaction has a major effect on the radiative properties of the aggregates, and may also influence their aerosol-cloud interactions, toxicity, and deposition in human lungs. Recent laboratory studies have presented conflicting arguments on whether this compaction occurs during condensation or during the evaporation of coatings. In this three-part study, we combine theory and experiments to explain these conflicting results. First, we review the surface-science literature and identify explicit mechanisms for condensation-compaction as well as evaporation-compaction. We also identify a mechanism for avoiding compaction during condensation, based on heterogeneous nucleation theory and the kinetic barriers to capillary formation. Second, we review the soot-restructuring literature and find clear evidence for both condensation- and evaporation-compaction, with condensation-compaction being the norm. Third, we present new experimental results where the capillary forces due to anthracene coatings were “switched on” or “switched off” by using solid or liquid phases during coating addition and removal. Consequently, we demonstrate condensation-compaction, evaporation-compaction, and no compaction, for the same soot source. Overall, our study indicates that soot particles will typically undergo compaction when internal mixing occurs by the condensation of liquid coatings, while compaction may be avoided when internal mixing occurs through coagulation or the gas-to-particle formation of solid or highly viscous coatings. Copyright © 2022 American Association for Aerosol Research


Introduction
Globally, soot particles are predicted to absorb comparable amounts of solar radiation as carbon dioxide, with the exact absorption amount depending on the concentration of soot particles and their mixing with other particulate material (PM) (Ramanathan and Carmichael 2008;Bond et al. 2013). However, describing the radiative properties of soot BC as a function of atmospheric lifetime remains a major challenge Jacobson 2013;Cappa et al. 2013) due to variability in the morphologies of the BC spherules which comprise soot (Yon et al. 2014;Radney et al. 2014) and the various possible configurations of soot with other internally-mixed material (Adachi, Chung, and Buseck 2010;Liu and Mishchenko 2018). A key issue is whether the spherules comprising soot aggregates are arranged in extremely open, fractal-like structures (Eggersdorfer and Pratsinis 2014) or more compact, spheroidal shapes ). This change of structure strongly influences their optical properties (Qiu, Khalizov, and Zhang 2012;Scarnato et al. 2013;Radney et al. 2014;Hu et al. 2022;Kelesidis et al. 2022).
The open and compact limits of soot spherule morphology are defined by the normally distinct processes of aggregate formation and of internal mixing. Soot aggregates, like other flame-synthesized aggregates, are formed by the diffusion-limited clustering of spherules (Eggersdorfer and Pratsinis 2014) with diameters roughly 10 À 80 nm spherules (Corbin et al. 2019), which produces open-structured aggregates (Eggersdorfer and Pratsinis 2014) as observed at or near combustion source. However, electron microscopy of atmospherically aged soot often shows these spherules to be highly compacted (Xiong and Friedlander 2001;Abel et al. 2003;Shi et al. 2003;Buseck 2013;China, Salvadori, andMazzoleni 2014, China et al. 2015b;Bhandari et al. 2019), apparently due to internal mixing with non-refractory material (often referred to as "coating", whether occurring due to condensation or coagulation).
Historically, it has been widely believed that soot particles were compacted by capillary forces upon the condensation of coatings (K€ utz and Schmidt-Ott 1992;Zhang et al. 2008;Qiu, Khalizov, and Zhang 2012;Khalizov et al. 2013). This belief generally relied on indirect evidence, due to the difficulty of measuring the structure of a soot particle while it remains coated. In contrast to this common belief, Ma et al. (2013a) directly observed that soot particles could remain open in structure after coating by water. The same particles were compacted after evaporation of the water coating. In the Ma et al. (2013a) experiments, restructuring therefore occurred during evaporation, not condensation. Although Ma et al. (2013a) did not recommend that their observations should be extrapolated to all atmospheric and combustion systems, many authors have since begun to model coated soot particles as open in structure (Dong, Zhao, and Liu 2015;Heinson, Liu, and Chakrabarty 2017;Wu et al. 2016Wu et al. , 2017Wang et al. 2017;Luo et al. 2018;Liu, Yon, and Bescond 2016;Lefevre et al. 2019;Luo et al. 2021;Zheng and Wu 2021;Romshoo et al. 2021). Other authors still model restructuring as occurring upon condensation, in both numerical work (Fierce et al. 2016;Wu et al. 2017;Luo et al. 2018;Kahnert 2017;Kanngießer and Kahnert 2018;Luo, Zhang, and Zhang 2020) and the interpretation of measurements Rissler et al. 2013;Peng et al. 2016;Zhang et al. 2018;Cappa et al. 2019;Fierce et al. 2020;Yuan et al. 2021;Hu et al. 2022;Gao et al. 2022). Meanwhile, subtle but clear experimental evidence that condensation does lead to soot restructuring has not been fully acknowledged (Section 3 of this work).
The morphology of soot aggregates influences their light absorption and physical properties, as relevant to climate, health impacts and other contexts. Fractal-like soot aggregates scatter up to 30 % more light (Scarnato et al. 2013;Radney et al. 2014), and the optical properties of a coated soot particle which remains open in morphology are significantly different from a compacted one (Scarnato et al. 2013;Kelesidis et al. 2022). Experimentally, the relative absorption enhancement caused by coatings on soot is often measured by comparing the absorption properties of coated and denuded soot Lack et al. 2012); this comparison would be biased if the denuded soot was compacted but the coated soot was not. In terms of health impacts, fractal-like aggregates may deposit in the human lung at a different rate than compacted ones (Scheckman and McMurry 2011;Rissler et al. 2012). The humid environment of the human lungs may potentially trigger compaction for hygroscopic soot particles, influencing their size and surface area, and therefore their health impacts. In a 1975 study, Chamberlain et al. (1975) directly observed the compaction of soot aggregates after inhalation and exhalation of engine exhaust by human volunteers. Yet Brauer et al. (2001) reported two examples of fractal-like soot found in the lungs of lifetime residents of Mexico City during autopsy. In addition, scrubbers used in exhaust aftertreatment have been observed to cause soot restructuring (Lieke et al. 2013); understanding this behavior would inform engine aftertreatment system design. Finally, the restructuring of synthetic nanoparticle aggregates is a useful procedure in materials science (Kelesidis et al. 2018).
Overall, there is a strong need to progress toward consensus on the causes and mechanisms of sootaggregate restructuring, as well as to provide a conceptual framework from which the morphological effects of atmospheric aging, cloud processing and human respiration may be predicted. The contribution of the present manuscript toward this goal are to (1) synthesize literature from nucleation, surface and capillary science to identify explicit restructuring mechanisms, based on the processes of phase nucleation, capillary condensation, and droplet formation, (2) critically review the available literature on soot aggregate restructuring for evidence of these four modes, (3) present new experiments designed to resolve some of the conflicts in the literature, using solid or liquid anthracene coatings, and liquid oleic acid.

Review of physical mechanisms required for compaction
Aggregate compaction by condensation must proceed via the (i) nucleation and (ii) growth of a liquid phase, resulting in (iii) the torquing of aggregate monomers due to attractive capillary forces caused by surface tension. These 3 steps have not previously been discussed in the context of the literature on phase nucleation, capillary condensation, and droplet formation. We critically review this literature in the present section. Our review provides a basis for the understanding and classification of the experimental studies on aggregate restructuring reviewed in Section 3.

Nucleation and growth of the liquid phase
Bulk, pure liquid phases may grow when the vapor pressure, p, exceeds the equilibrium vapor pressure over a flat surface, p 0 , at a saturation ratio S ¼ p=p 0 : Bulk liquid surfaces may grow at S slightly greater than 1, while droplets require S > 1 due to their positive curvature (Lamb and Verlinde 2011). In contrast, nanoscopic quantities of liquid may condense when S ( 1 via the processes discussed in this section. The formation of these nanoscopic phases is generally limited by energy barriers. These energy barriers are important to the process of soot compaction, because they lead to different condensation pathways occurring under different physical conditions. We therefore begin our discussion from the perspective of these barriers. Liquid condensation onto insoluble surfaces is generally initiated by the nucleation of molecular clusters onto active sites on the surface to form small patches of liquid (Laaksonen 2015;Laaksonen, Malila, and Nenes 2020). These small patches have been observed using atomic force microscopy for both high (Cao et al. 2011) and low (Xu, Cao, and Heath 2010) contact angles, and we refer to them collectively as nanodroplets.
If the areal density of nanodroplets formed on an insoluble particle is high enough, the nanodroplets may coalesce to form a film (Laaksonen, Malila, and Nenes 2020); the required density is lower at lower contact angles. If a film forms between two nearby surfaces (e.g., of two touching soot spherules), then fluctuations in the film-air interface may lead to the sudden coalescence of a capillary phase (Crassous, Charlaix, and Loubet 1994;Restagno, Bocquet, and Biben 2000). The lifetime of the metastable film phase is the capillary-formation timescale, and can be extremely long, as evidenced by the hours required for equilibrium in pore adsorption processes (Bocquet et al. 1998;Restagno, Bocquet, and Biben 2000;Ferry et al. 2002). However, this lifetime decreases exponentially with increasing temperature (Restagno, Bocquet, and Biben 2000). Once formed, the capillary phase grows slightly more slowly than if it were diffusion limited (Kohonen, Maeda, and Christenson 1999).
At a critical point, S crit > 1, nanodroplets, films and capillaries may activate into droplets and grow without any remaining energy barriers. This droplet activation may proceed via nanodroplet activation (NDA), film activation, or capillary activation (Laaksonen, Malila, and Nenes 2020). The majority of vapor or "coating" volume will condense at this stage. Crucially, activation may occur before the equilibration of capillary phases, due to the abovementioned long capillary-equilibration timescales.
We note that nucleating substances are often observed to be liquid rather than solid, even below the macroscopic melting point. This phenomenon is attributable to the lower free energy of a liquid-solid interface versus a solid-solid interface (Christenson 2001) as well as the fact that interfacial energy leads to a melting point depression for nanoscopic quantities of matter, as discussed below.
In summary, depending on the nucleation rate and growth rate of the respective phases (which themselves depend on the liquid-particle contact angle, density of active sites, and temperature), vapor may condense onto soot particles at S < 1 as nanodroplets, films, or capillaries. At S > 1, activation of these nanodroplets, films, or capillaries into droplets may result in different shapes of metastable liquid phases. These liquid phases may exert unbalanced capillary forces on soot particles, as described in the next subsection.

Mechanisms of soot compaction during condensation
During the condensational growth of capillaries at S < 1 or droplets at S crit > 1, the liquid phase may exert capillary forces on the soot monomers and cause restructuring of the aggregate. These forces will generally be attractive, and must be asymmetric about the point of contact between spherules for compaction to occur. In general, spherule movements due to capillary forces are expected to be extremely rapid (( 1 second; Narhe and Beysens 2006) relative to the rate of condensation, so we do not focus our discussion on timescales in this section. Rather, we discuss specific mechanisms of condensation-induced compaction, focusing on mechanisms for which direct experimental evidence exists in the literature. All three of the following mechanisms rely on capillary condensates and capillary forces, and we therefore refer to them collectively as capillary compaction (CC) mechanisms.
The first and second mechanisms we identify are related to the formation of capillary menisci between two soot spherules (Butt and Kappl 2009). They both may occur at the step labeled "capillary formation" in Figure 1a. The first CC mechanism occurs during the initial formation of a capillary condensate, when the capillary suddenly forms from the connection of neighboring films (Section 2.1). This initial connection generates a force about two orders of magnitude larger than the equilibrium capillary force (Crassous, Charlaix, and Loubet 1994) and is therefore not well described by equilibrium-force considerations (Butt and Kappl 2009).
The second CC mechanism occurs during the growth of capillary phases and films. This growth is accompanied by an advancing liquid-solid-gas interface: the contact line. During condensation, this contact line may advance more quickly in one region of the surfacependular ring than another due to physical heterogeneities on the soot surface, such as variations in curvature, atomic-scale discontinuities or bumps in the graphitic nanostructure (Toth et al. 2019) or chemical heterogeneities due to surface functional groups (Figueiredo et al. 1999;Matuschek et al. 2007;Corbin et al. 2015). These heterogeneities mean that the equilibrium contact angle h will vary across the soot spherule surface (Gao and McCarthy 2006), and may also lead to contact line pinning (Fadeev and McCarthy 1999;Gao and McCarthy 2006). Pinned contact lines grow via small "jumps" or molecular avalanches (Sch€ affer and Wong 2000), which may cause sudden changes and asymmetric torque on the touching spherules.
The effects of pinned contact lines and heterogeneous contact angles on capillary forces can be illustrated by considering the growth of the capillary phase. After the capillary phase forms from the coalescence of nearby films, it may grow until reaching its equilibrium shape: a pendular ring (Butt and Kappl 2009; Figure 1a illustrates the cross-section of an imperfect pendular ring at the label "capillary formation"). During the growth of a pendular ring, both pinned contact lines and heterogeneous contact angles would lead to a greater capillary attraction on one side of the pendular ring than the other, resulting in torque on the touching spherules. This mechanism may also be relevant if a partial pendular ring forms between film coalescence and the formation of a pendular ring. In the real world, asymmetric pendular rings are likely the norm. Even in controlled laboratory studies using polished ruby spheres, Pitois, Moucheront, and Chateau (2000) only achieved perfect pendular rings after several cycles of capillary formation. We note that this second CC mechanism is dependent on the rate of capillary growth (Eral, 't Mannetje, and Oh 2013;Shi et al. 2018) as well as whether or not the touching spherules are already in motion. Our first and second CC mechanisms are consistent with an earlier, apparently intuitive, suggestion by K€ utz and Schmidt-Ott (1992) which was modeled by Schnitzler, Gac, and J€ ager (2017).
A third CC mechanism was also modeled by Schnitzler, Gac, and J€ ager (2017). In this mechanism, two non-neighboring soot spherules were connected by a capillary phase, which led to an attractive force. While we did not find direct evidence for this bridgecapillary compaction mechanism in the literature, such a phase could potentially form if NDA occurs on Figure 1. Compaction mechanisms for soot in the context of the activation barriers (inset circles) involved in forming the liquid phase. These mechanisms are based on the experimental observations reviewed in Section 2 and are generally sensitive to both time (kinetic limitations) and vapor saturation (thermodynamic limitations). Yellow and blue colors indicate liquids with low and high contact angles, respectively. Dark-red arrows indicate evaporation, which is only depicted for the case where compaction was avoided during condensation. Green curved arrows show torque due to compaction forces. In the inset circles, surface heterogeneities that may act as adsorption sites are depicted by the jagged line. For NDA, the critical droplet diameter prior to activation is drawn at a scale that represents an approximate critical diameter, assuming a 30 nm diameter soot spherule. two different spherules and the activated droplets subsequently coalescence. Alternatively, a capillary bridge could form when pendular capillary rings or adsorbed films grow to engulf the particles which they connect, creating an attractive capillary force between three neighboring spheres. This engulfment mechanism was explored theoretically by Crouzet and Marlow (1995) for a pair of spheres. The only experimental evidence we have identified for this engulfment hypothesis is provided by the two-dimensional analogy observed directly by Narhe and Beysens (2004). Overall, the only experimental evidence we have identified for bridge-capillary compaction is that of the soot-restructuring study by (Chen et al. 2018, discussed in Section 3.2.3). Both of these capillary-bridge mechanisms would occur during the step labeled "droplet activation" in Figure 1a.
We have proposed that bridge-capillary compaction may proceed after droplets nucleate by NDA on two (or more) spherules. This would require extremely high supersaturations, to overcome the energy barriers to activation simultaneously for multiple nanodroplets. At less extreme supersaturations, NDA would proceed via the activation of one nanodroplet per aggregate. In this scenario, contact between the growing liquid phase and the soot monomers is minimal, and there is no opportunity for capillary forces to act. Therefore, soot particles coated by NDA are unlikely to be compacted ( Figure 1b). This conclusion also extends to the scenario of coating by coagulation, which is discussed further in Section 3.5.6 and Section 5.
Overall, our framework contrasts with the alternative framework proposed by Chen et al. (2018), which focused on the competition between condensational growth rates on curved surfaces versus capillaries. This competition may come into play in some scenarios, though it is less likely to be crucial during atmospheric aging, and does not cover all literature cases reviewed below. In our framework, condensation is limited by the energy barriers to phase formation, not by condensation rates.

Mechanisms of soot compaction during evaporation
The restructuring of a coated aggregate upon evaporation of a liquid coating (droplet-evaporation compaction, DEC) occurs due to the attachment of the liquid surface to the aggregate. From the perspective of a single spherule, this scenario is analogous to that of an isolated particle at a liquid-gas interface, for which the theory is well developed (Butt, Graf, and Kappl 2003, 123). Compared to condensation compaction, the situation is much simpler because it does not involve the nucleation of a new phase. At equilibrium, such an isolated spherule would be freely floating in the liquid phase due to the balance of buoyant and surface forces. For contact angles h > 0, a small "cap" defined by the contact angle will protrude from the liquid interface (Ref. 229 in Butt, Graf, and Kappl 2003). During the evaporation of a relatively large droplet, the isolated spherule would be pulled inwards by the capillary force of the retreating liquid-air interface. If the spherule was part of an aggregate, this retreating interface would eventually come into contact with two or more spherules. At this critical point, two or more spherules would be pulled inwards, and the aggregate would begin to experience a net compacting force, causing evaporation-compaction ( Figure 1c). This has been exploited in materials science (Manoharan, Elsesser, and Pine 2003;Lauga and Brenner 2004). For contact angles > 90 , this force is still present (Lauga and Brenner 2004); the only effect of the high contact angle is that more than half of the spherule area moves to the gas interface (Butt, Graf, and Kappl 2003; in a bulk liquid, the spherule would appear to float higher). For evaporation-compaction to be the dominant restructuring mechanism, the soot aggregate must first be incorporated into a droplet without undergoing substantial compaction. We discuss scenarios for this in Section 3.

Review of experimental demonstrations of aggregate restructuring mechanisms
Dozens of studies have either focused on or commented on the restructuring of soot after exposure to condensable vapors. In this section, we review these studies in light of the restructuring mechanisms identified above and summarized in Figure 1. For completeness, we also include here those relatively few studies which have investigated the restructuring of aerosol aggregates or agglomerates other than soot. We find that the literature is consistent with the identified mechanisms, with no exceptions that are relevant to atmospheric science. For completeness, we also discuss here those exceptions and some related topics.
3.1. Background: Electron microscopy, mobility size, and shape factor Before reviewing the literature in earnest, we briefly introduce two of the most common techniques for compaction measurements. The first technique, electron microscopy, is invaluable, but requires low-pressure conditions (vacuum or near vacuum) for analysis, which triggers the evaporation of volatile coatings. The electron beam itself may also trigger evaporation, which hinders the imaging of coated soot aggregates. Additionally, the labor intensive nature of microscopy means that such studies typically report measurements on tens or hundreds of particles, rather than the orders of magnitude more measured by the second common technique. The second common technique, mobility diameter d mob measurements, measures the migration velocity of particles in an electric field. The resulting d mob is the product of the shape factor v and the sphericalequivalent diameter of the particle, after correcting for the non-continuum nature of the gas phase (Equation (S1)). The shape factor v describes the ratio of the drag force on the particle to the drag force on an equivalent-volume sphere, and can be calculated from measurements of particle mass and mobility if the particle's material density is known (the calculation is detailed in Section S1). The shape factor v ¼ 1 for spheres (e.g., liquid particles). For a d mob ¼ 300 nm soot particle, v can be as large as 2 or 3 (Sorensen 2011, and our Figure 4). Following extensive compaction, v is about 1.5 for moderately large soot particles (Ghazi and Olfert 2013, our Figure 4;and Corbin and Sipkens, in prep.), although this limit is smaller for aggregates containing smaller numbers of spherules.

Evidence for capillary compaction
3.2.1. Context: Use of the mobility diameter d mob to infer compaction A large number of studies have reported a decrease in the mobility diameter d mob of soot aggregates after the condensation, and sometimes both condensation and evaporation, of liquid coatings (e.g., K€ utz and Schmidt-Ott 1992;Burtscher 1995, Weingartner, Burtscher, andBaltensperger 1997;Gysel 2003;Zhang et al. 2008;Khalizov et al. 2009;Xue et al. 2009;Pagels et al. 2009;Miljevic et al. 2010;Tritscher et al. 2011;Bambha et al. 2013;Ghazi and Olfert 2013;Peng et al. 2016;Leung et al. 2017b;Pei et al. 2018;Chen et al. 2016Chen et al. , 2018Enekwizu, Hasani, and Khalizov 2021). Many of these studies interpret changes in the mobility diameter d mob as clear evidence of compaction. Only a few of these studies, discussed here, provide clear evidence for capillary compaction, as distinct from evaporation.
Because d mob is not a direct measurement of compaction, its use to infer compaction may hypothetically lead to biases. For example, it may be hypothesized that d mob may change upon condensation due to a change in v rather than a change in size. However, Leung et al. (2017b) showed unequivocally that a decrease in d mob is due to condensation-compaction and is not a measurement artifact. Leung et al. (2017b) formed p-xylene SOA at extremely low relative humidity (RH < 12%), where it is known to form a glassy solid as well as high RH (20% to 85%) where it is expected to be liquid (Song et al. 2016). Leung et al. (2017b) then showed that d mob decreased with the addition of small amounts of liquid SOA, but increased with the addition of small amounts of solid SOA. Therefore, the liquid condensation must have caused compaction. This result is consistent with the anthracene results discussed in Section 4, however, we note that solid SOA is glassy (J€ arvinen et al. 2016) while solid anthracene is crystalline, which may lead to differences in the final shape of the coated particles. Miljevic et al. (2010) observed that freshly-produced soot particles compacted when bubbled through a variety of organic liquids, but not when bubbled through water. These results are particularly important because of two details of the bubbling technique, which stand in contrast to the more-common alternative of exposing the soot particles to supersaturated vapors.

Capillary compaction below saturation
First, bubbling was done at room temperature, which means that the temperature-dependent rate of capillary formation (Section 2) was not enhanced relative to atmospheric conditions. Soot particles spent a relatively short time (about 1 second) in the bubbler, although subsequent changes during the additional seconds of transport to the measurement system may have occurred (Enekwizu, Hasani, and Khalizov 2021).
Second, the vapor pressure within a bubble is slightly below saturation, due to the inverse Kelvin effect (relatively small at large diameter of most bubbles). Since compaction occurred below saturation, and since capillary menisci condense well below saturation, this corroborates the capillary-condensation mechanism described above and suggests a role of contact angle (which governs capillary formation).
We also note that, when Miljevic et al. (2010) switched from bubbling candle soot through hexane to bubbling through water, the soot did not undergo compaction. This observation is consistent with the Ma et al. (2013a) study discussed below, and illustrates the key role of contact angle. The high water-soot contact angle would have prevented capillary condensation from occurring.
Further evidence for capillary compaction is provided by the studies of Chen et al. (2016Chen et al. ( , 2018 and Enekwizu, Hasani, and Khalizov (2021). Chen et al. showed that a sub-monolayer volume of PAHs coated onto soot could cause substantial compaction, while Enekwizu, Hasani, and Khalizov (2021) detected compaction near room temperature, at saturation ratios S < 1 of triethylene glycol (a polar organic compound). At these sub-monolayer and sub-saturation conditions, only capillary condensation could have occurred. Therefore, these experiments provide clear evidence for capillary condensation, as also concluded by those authors. Chen et al. (2018) presented a study of several different coating materials which we interpret here as illustrating the difference between capillary-compaction by menisci (first two mechanisms in Section 2.2) and by capillary bridges (third mechanism in Section 2.2). In Chen et al. (2018), a first group of compounds (Group A) caused sudden compaction with minute coating volumes (d mob decreased to 80% of its initial value for coatings $ 5% of initial particle volume), while a second group (Group B) required much larger coating volumes to be compacted (d mob decreased to a similar endpoint for coatings 10-48% of initial volume). These trends cannot be explained by differences in surface tension (as noted by Chen et al. (2018)) nor by contact angle alone, since the two groups contained compounds with a range of polarities.

Capillary compaction above saturation
The one consistent difference between Groups A and B in Chen et al. (2018) is that the Group A compounds had vapor pressures at 25 C ranging from 0.18 to 2.00 Pa, whereas Group B compounds had vapor pressures ranging from 10 À7 to 10 À4 Pa. Consequently, Chen et al. (2018) exposed soot particles to Group B compounds at much higher experimental temperatures (! 50 C) compared with Group A. This difference in temperature altered the coating volume, as pointed out by Chen et al. (2018). Crucially, it also created much higher transient saturation ratios. According to the calculations of Chen et al. (2018), the Group-B temperatures resulted in maximum saturation ratios of S max > 20: At these extreme saturation ratios, multiple nanodroplets may have activated and grown too quickly for capillary menisci to nucleate, leading to bridge-capillary compaction. (As with all studies that both add and remove liquid coatings, it is also possible that further compaction occurred during coating removal, via the DEC mechanism. Our experimental results, presented Section 4, removed solid coatings and isolated the capillary and DEC mechanisms.) If Groups A and B of Chen et al. (2018) represent different condensation-compaction mechanisms due to different experimental conditions, then some experimental results must be interpreted with caution. Specifically, changes in soot structure with coating volume should not be parameterized and extrapolated from laboratory studies using high-S max systems (i.e., systems with heated sample reservoirs). On the other hand, the final change in mobility diameter (maximum compactness) achieved between studies is consistent, as expected ): this was similar at high S max in Groups A and B, and was consistent with the below-saturation studies discussed in the previous subsection.
In their discussion and subsequent work (Ivanova, Khalizov, and Gor 2021;Enekwizu, Hasani, and Khalizov 2021), Chen et al. (2018) focused on the competition between the Kelvin effect and vapor supersaturation. As their data set also varied S max substantially, it is not clear whether this competition played a key role relative to phase-formation barriers. Additional data to constrain this hypothesis would be valuable.

Evidence for evaporation-compaction and nanodroplet activation (NDA)
Three studies have indicated evidence for evaporation compaction. Two of these data sets demonstrate only subtle evidence, while the third presents direct evidence. The subtler evidence from Leung et al. (2017b) and Chen et al. (2016), using glassy SOA and anthracene respectively, showed that d mob increased for thin coatings but decreased when these coatings were denuded, presumably after due to melting in the denuder. The glassy SOA case was discussed above; the anthracene result is returned to below in Section 4.3 and Figure 5.
The third study provides the most direct evidence, by observing the morphology of water-coated soot after injecting it into bulk water and measuring the particle fractal dimension by static light scattering (Ma et al. 2013a). Ma et al. (2013a) found that this fractal dimension remained low within the water droplets (less than 1.94), corresponding to an open morphology. They also demonstrated that the same soot particles underwent compaction during water evaporation using transmission electron microscopy (TEM) and by measuring a mass-mobility exponent of 2.79 (see Sorensen 2011 and Olfert and Rogak 2019 for a detailed discussion of the mass-mobility exponent).
The soot particles studied by Ma et al. (2013a) did not take up water below S ¼ 1.2. This shows that they were hydrophobic. Hydrophobicity implies a high contact angle (h > 90 ) as expected (Persiantseva, Popovicheva, and Shonija 2004). Therefore, film formation would be unlikely and capillary condensation would not have occurred. Rather, water will have condensed via NDA (Figure 1), as described in Section 2. There are two reasons why the results of Ma et al. (2013a) should not be extrapolated to atmospheric science. First, such high S do not normally occur in the atmosphere, where most particles activate at S < 1.01 (Schmale et al. 2018). Second, atmospheric soot typically becomes rapidly oxidized or coated with small amounts of hydrophilic material (e.g., Vakkari et al. 2014) which are observed to result in water condensation at much lower S than for hydrophobic soot (Mikhailov et al. 2006;Xue et al. 2009). Surface oxidation may also occur (Matuschek et al. 2007;Corbin et al. 2015) to lower S crit without involving coatings. Atmospherically realistic condensates like secondary organic aerosol have been shown to condense readily onto soot, without requiring extreme supersaturations (Qiu, Khalizov, and Zhang 2012;Schnitzler et al. 2014;Guo et al. 2016;Leung et al. 2017b), due to low contact angles and the presence of organics with a broad range of volatilities (Tr€ ostl et al. 2016). Thus, the work of Ma et al. (2013a) represents a specialized system in which the phenomenon of evaporationcompaction could be demonstrated.
We note that Ma et al. (2013a) attempted to explore the role of h on their results by oxidizing their soot samples in a furnace. They flowed soot particles through a furnace at 300, 600, and 700 C. However, as shown in a later study using the same system (Ma, Zangmeister, and Zachariah 2013b), at these temperatures soot oxidation results in a decrease of particle mass due to volume oxidation by O2, in contrast to the surface oxidation that occurs at higher temperatures (Kelesidis and Pratsinis 2019). This decrease of particle mass is evident in the oxidation results of Ma et al. (2013a) and makes the quantitative interpretation of their data difficult. Nevertheless, it is clear that this furnace treatment did not have the expected result of rendering the soot particles hydrophilic, since the maximum saturation ratio required to activate particles after furnace oxidation was even higher after the furnace (S > 1.5) compared to before (S > 1.2). This may be due to the loss of polar functional groups at the soot surface (Matuschek et al. 2007), which would be active sites for NDA.

Related aggregate restructuring topics
The preceding discussion focused on studies providing clear evidence for the restructuring mechanisms relevant to soot coating in the atmosphere. For completeness, the present subsection discusses other noteworthy studies on related topics.

Role of surface tension and viscosity
Schnitzler, Gac, and J€ ager (2017) reported a correlation between the surface tension of a variety of organic coatings (including glycerol, ethylene glycol, furfural, oleic acid, and o-xylene) and the amount of compaction these coatings caused on soot particles. This observation stands in contrast to that of Chen et al. (2018), who observed large differences in compaction for different restructuring mechanisms (discussed in detail above) and no correlation with coating surface surface tension. From these two studies, we conclude that the extent of restructuring depends first on the restructuring mechanism, and second on coating properties such as surface tension.
From the perspective of coating viscosity, the data of Leung et al. (2017b) provide valuable insights. Leung et al. (2017b) observed soot compaction by SOA at relative humidities between 20% and 80%. The viscosity of SOA at 20% RH is approximately 5 orders of magnitude lower than at 80% humidity (Song et al. 2016), so the Leung et al. (2017b) data indicate that restructuring is possible across a broad range of viscosities. Their data do suggest small differences in compaction for SOA coatings formed between 20-40% RH and 60-85 % RH. These differences were similar in magnitude ($ 10% change in d mob ) as those observed by Schnitzler, Gac, and J€ ager (2017) where coating surface tension was varied, indicating a minor effect in the context of this review.

Evidence from effective-density measurements
of soot The effective density of soot is widely used to estimate the mass of particles for which d mob is known. Olfert and Rogak (2019) reviewed a large number of studies and showed that the effective-density trends in uncompacted soot with d mob are similar for many engines and laboratory flames. We note that Olfert and Rogak (2019) observed a slightly higher effective density for compression-ignition engines than for other sources, suggesting that those soot particles may have undergone partial compaction due to condensation in the exhaust of those engines. This may suggest that some degree of compaction occurred in those engines, since condensation is most rapid for smaller particles and since those engines emit a larger fraction of volatile material. Care should therefore be taken when applying the effective-density fit of Olfert and Rogak (2019) to soot samples where compaction may have occurred. A detailed discussion of the effective density of compacted soot is presented in Corbin and Sipkens (manuscript in preparation). Bambha et al. (2013) reported that soot restructuring could be reversed by laser-heating. They coated soot by condensation, then used a pulsed 1064 nm laser to heat the soot and cause coating evaporation. Since condensation-compaction is to be expected for this soot-oleic-acid system, this implies that the soot particles underwent decompaction due to the laser heating process, perhaps due to the nucleation of bubbles at the soot surface (in analogy to the heterogeneous nucleation of bubbles at liquid-solid interfaces during boiling). Such bubbles would remain attached to the soot surface in order to minimize their Gibbs energy, and may lead to decompaction of the soot structure during their growth. Bambha et al. (2013) also stated that they observed compacted soot in the electron microscope after coating, but they were unable to image the particles before coatings evaporated. Such images would constitute evidence for condensation-compaction, if they could be produced without any interference of the evaporating droplet.

Metal nanoparticles and sintering
Aggregates of metal nanoparticles are known to sinter (partially coalesce without liquefying) at temperatures well below the melting point, and this leads to aggregate compaction (Kleinwechter, Friedlander, and Schmidt-Ott 1997;Schmidt-Ott 1988;Friedlander 2000). The same is true for metal-oxide nanoparticles (Kelesidis et al. 2018). This process is attributable to melting-point depression (Section S4) and not capillary forces. Conversely, the strong inter-particle bonds of strongly sintered aggregates (Friedlander 2000) can prevent condensation-compaction (Kelesidis et al. 2018). The fact that compaction has been observed for the wide variety of soot sources cited herein, without exception, indicates that such inter-particle bonds are weaker than typical capillary forces for soot. Weingartner, Burtscher, and Baltensperger (1997) and Mikhailov et al. (1997) observed the compaction of spark-generated carbon nanoparticles at S < 1 due to water and benzene vapor exposure, respectively. These spark-generated nanoparticles have significantly different properties to soot due to their unique and rapid formation pathway (Gysel et al. 2012, and citations therein). Their contact angles with different liquids and inter-particle bonds are different to soot, so they are not discussed in the soot section above.

Carbon nanoparticles other than soot
3.4.6. Can soot compaction be avoided during condensation? A small number of laboratory studies have implied that soot compaction during condensation can be avoided in some cases. These studies are reviewed in the following discussion, and are attributed to either soot-substrate adhesion forces or to statistical anomalies. Caution should therefore be exercised when interpreting these studies as generally representative.
A salient example of avoided compaction is provided by Cross et al. (2010). This study presented a single electron micrograph of a laboratory soot particle that was not compacted despite being sampled during a coating-denuding experiment using dioctyl sebacate. The authors suggested that this processing had failed to compact the soot. However, studies using the in-situ d mob technique, which measured orders-ofmagnitude more particles, have consistently reported compaction of soot by the exact same compound (Ghazi and Olfert 2013;Chen et al. 2018). The most likely explanation is that the single particle measured by Cross et al. (2010) was not representative of the overall particle ensemble. This example is particularly important because it was possible to reproduce the experiment and revise the initial conclusions, unlike most atmospheric studies.
Another category of exceptions is studies where soot particles were sampled onto microscopy grids before coatings were condensed. These studies have included electron (Huang et al. 1994;Ebert, Inerle-Hof, and Weinbruch 2002;Zuberi et al. 2005), X-ray (Zelenay et al. 2011), and atomic force (K€ ollensperger et al. 1998) microscopy. Of those studies, only K€ ollensperger et al. (1998) claimed to observe restructuring on the microscopy grid. In these on-grid condensation experiments, soot-substrate adhesion forces, which are substantial (Friedlander, Jang, and Ryu 1998;Rocca et al. 2013) may exceed compaction forces, preventing both condensation-compaction and evaporation-compaction. In contrast, studies where soot is restructured in the aerosol phase before being sampled for microscopy analysis can provide valuable insights into morphology, both in the laboratory (studies cited above) and in the atmosphere (Section 5).
3.4.7. Does soot compaction occur during uptake into bulk liquids, or during coagulation? A few studies have provided evidence that compaction can be partly or fully avoided during soot uptake into bulk liquids. Ma et al. (2013a), discussed in detail above, measured a low fractal dimension for soot that was incorporated into bulk water after activation as soot-in-water droplets. Using electron microscopy, Rocca et al. (2013) observed that soot particles in the lubricating oil of a diesel engine were only partly compacted. Finally, Brauer et al. (2001) observed noncompacted soot in the lungs of lifelong Mexico City residents. The observations of Brauer et al. (2001) are significant and suggest that soot particles entered the lungs as freshly emitted, hydrophobic soot, did not nucleate water during inhalation, and deposited onto the respiratory system. These uncompacted particles may have been more toxic due to their higher active surface area, and potentially different interactions with human macrophages.
These observations of avoided compaction during uptake into bulk liquids indicate that the direct contact of aggregates with air-liquid interfaces is not sufficient to cause compaction. Therefore, the process of coagulation between soot aggregates and liquid droplets is also unlikely to cause compaction. Conversely, partial evapration-compaction may occur in the scenario that the liquid droplet partially wets an aggregate and is then evaporated. This scenario may occur during cloud processing or laboratory experiments.

Uncompacted soot in the atmosphere
The evidence reviewed above suggests that soot particles coated primarily by condensation (gas-to-particle addition of liquid coatings) will undergo substantial compaction. However, soot particles may become internally mixed by other mechanisms, such as deposition (gas-to-particle addition of solid or extremely viscous glassy coatings), or coagulation (diffusive collision of soot particles with other particles and subsequent adhesion). The question of what fraction of soot particles in the atmosphere remains uncompacted upon mixing has substantial implications for the light-absorption properties of soot, and is discussed in detail later in this manuscript (Section 5).

Summary of soot compaction review
Our review of the soot compaction literature has illustrated that: capillary condensation generally leads to soot compaction, capillary compaction is slightly less efficient in experiments where very high saturation ratios (S > 1.2) do not allow enough time for capillary formation, capillary compaction can be avoided when highcontact-angle vapors, such as water, condense by nanodroplet activation (NDA) instead of capillary activation, capillary compaction can be avoided or reduced for extremely viscous (glassy) glassy or solid coatings of atmospheric relevance, capillary compaction can be avoided or reduced when soot mixes by coagulation with other particles, or impaction with a bulk liquid, evaporation compaction will act on soot particles within evaporating droplets, when those droplets shrink below the size of the soot aggregate, and is important only when capillary compaction is avoided during the preceding incorporation of the aggregate into the droplet, for atmospherically relevant systems, changes in coating mechanisms play a larger role than changes in coating surface tension or viscosity, unique compaction trends and mechanisms have been observed for non-soot materials (spark-generated aggregates, sintered-metal aggregates, etc.) and during special processes such as heating by pulsed lasers.

Experimental study
In this Section we present the results of a series of experiments designed to separately study condensation and evaporative compaction. In these experiments, we controlled the phase of an organic coating during its addition or removal, so that capillary forces could be switched on or off. We performed most experiments using anthracene, and some with oleic acid. The results demonstrate that both condensation and evaporation can cause soot restructuring, and represent the first data set in which both of these mechanisms have been demonstrated for the same soot source and coating material.

Compaction pathways
Our experiments are summarized in Table 1, which also introduces the labels used in the subsequent discussion. The five rows of Table 1 represent five pathways by which coatings can be added and removed. Each pathway is defined by the addition-removal of two phases as nanodroplets N, capillary liquids L, or solids S. For example, liquid-addition-solid-removal (i.e., condensation-sublimation) is referred to as pathway LS. During addition or removal, the CC or DEC restructuring mechanisms may occur, or may be avoided by NDA (Section 2), as illustrated in more detail in Figure 2.
We designed experiments to follow these pathways using anthracene based on its phase diagram ( Figure  S1) as further discussed in the SI. Due to the experimental difficulty of removing liquid anthracene coatings, we performed some additional experiments using oleic acid. The experiments were interpreted as follows. For Pathway LS, we performed experiments where coatings were added as liquids (condensed), then frozen prior to their removal as solids (sublimation). Since capillary forces cannot act during sublimation, we attribute any restructuring via Path LS to the condensation process. Path SL is the inverse of Path LS: coatings are added in the solid phase (deposition) then melted prior to their removal as liquids Table 1. Summary of coating addition/removal pathways and their corresponding compaction mechanisms. Mechanisms are defined in Figure 1 and Section 2. Pathways are explained in Figure 2 and Section 4.1. Figures 3-5 Figure 1. c n.a. ¼ not applicable.  Table 1 and illustrated in Figure 1 can be explored by adding and removing solid ("S") and liquid ("L") coatings. Blue and red arrows indicate liquid and solid phase coatings, respectively. Solid arrows indicate coating addition or phase transformation, open arrows coating removal. Red, blue, and orange coatings indicate solid, low-h liquid, and high-h liquid phases, respectively. Green arrows indicate opportunities for compaction (mechanisms shown in Figure 1). In our experiments, the nanodroplet-liquid (NL) pathway was not achieved due to the low contact angles between our coating materials (oleic acid and anthracene) with soot.
(evaporation), so, capillary forces can act only during coating removal. Path SS is a control experiment where no capillary forces are allowed to act: coatings are deposited and subsequently sublimated. Since capillary forces are not allowed to act, no restructuring should occur. Path LL both adds and removes coatings in the liquid phase, allowing capillary forces to act during both coating addition and removal. Finally, Path NL may allow droplets to form without capillary forces acting. Path NL was not reproduced in this study, as we focused on a single coating material to avoid changing the physical properties of our coatings between experiments.

Experimental methods
Our experimental setup ( Figures S2 and S3) was similar to that used in previous studies (e.g., Nguyen et al. 1987;Moteki and Kondo 2007;Chen et al. 2016). The present subsection therefore summarizes only the key experimental details of our experiments; complete details are given in the supplementary information (Section S3).
Soot was generated by a miniCAST 5201c soot generator (Jing Ltd., Switzerland) which consists of a partiallyquenched propane diffusion flame. We pre-selected aggregates of mature soot with mobility diameter of 300 nm before using coating apparatuses constructed inhouse to add anthracene or oleic acid coatings to the soot.
The coating apparatuses ( Figure S3) generally consisted of a heated section (using either a hot plate, oil immersion, or heating tape) followed by a cooling section (using either heat conduction to room air, additional insulation to slow cooling, or ice packs to accelerate cooling). Oleic acid coatings were added with the apparatus heater set between 94 and 140 C. Anthracene coatings were added with the apparatus heater set between 95 and 202 C. Above 202 C, the reservoir emptied too quickly for measurements to be practical. In some experiments, we pre-coated the walls of the second apparatus with anthracene in order to increase its vapor phase concentrations, which allowed us to avoid anthracene sublimation upon heating and to melt anthracene prior to its evaporation. The mass of added coatings was then measured using an Aerosol Particle Mass analyzer (APM, Model 3601, Kanomax Japan; Ehara, Hagwood, and Coakley 1996) as described further in the SI. The particle-mass measurements were converted to coated-particle volume V1 according to where V0 and m0 are the volume and mass of an uncoated soot particle, V OM is the volume of coating, m 1 ¼ ðm 0 þ m OM Þ is the total mass of a coated soot particle, q soot ¼ 1800 kg m -3 is the material density of soot (Ouf et al. 2019) and q OM is the material density of the organic coating. For unprocessed or denuded soot, m OM ¼ 0, so V 1 ¼ V 0 . For coated soot, V 1 =V 0 is the volume increase due to the coating. Shape factors were calculated by iteratively solving Equation (S1) with d mob ¼ 300 nm.
The primary denuder used in this work was a catalytic stripper (CS015, Catalytic Instruments GmbH, Rosenheim, Germany), which vapourizes and then oxidizes organic molecules at 350 C. In some experiments, this stripper was replaced with the activatedcharcoal thermodenuder described by Burtscher et al. (2001) or a second coating apparatus. Figure 3 shows d mob distributions measured during the experiments. The experiments used anthracene or oleic acid to investigate the compaction mechanisms from Section 2. Oleic acid was used for Path LL; anthracene was used for all others. The inset TEM images in Figure 3 depict aggregates sampled from each condition. Not all particles observed in the TEM were fully compacted after processing ( Figure S4); this may be due to variability between compaction events, soot-particle properties, or heterogeneity in the conditions of our processing apparatus. We rely on the much better sampling statistics of the mobility-sizedistributions for all of our conclusions below. Figure 3a shows results for the addition and removal of solid coatings via Path SS of Table 1 and Figure 2. The results show that Path SS, coating deposition-sublimation, resulted in no change to d mob : The lack of compaction for Path SS shows that capillary forces are necessary for compaction in general, and rules out the hypothesis that van der Waal's forces alone are sufficient. In Figure 3a, we intentionally presented conditions where a very large volume of solid coatings was added (10-fold the initial soot-particle volume) to ensure that the lack of observed compaction was not due to a lack of sufficient coating material.

Changes in mobility diameter
In Figure 3b, capillary forces were allowed to act since coatings were melted prior to their evaporation (Path SL). This resulted in a reduced final d mob and compacted particles, as confirmed by TEM. Combined with the results of Figure 3a (Path SS), this confirms that evaporation-compaction exclusively occurred in this experiment. The coating volume in Figure 3b was 10-fold the initial soot-particle volume.
In Figure 3c, the reverse of Figure 3b was measured. Liquid coatings were added by condensation, but frozen prior to their removal by sublimation (Path LS). This resulted in a reduced modal d mob and compacted particles, as confirmed by TEM. This confirms that condensation compaction occurred in Path LS.
Thus, the experiments shown in Figures 3a-c demonstrate that both condensation-compaction and evaporation-compaction may occur: aggregate compaction may be triggered by liquid condensation or liquid evaporation, but not solid deposition nor solid sublimation. This conclusion is corroborated by previous studies using anthracene in Section 4.3.
Finally, Figure 3d shows results for Path LL (coating condensation and evaporation). Compacted particles were observed after this experiment. Because the final modal d mob in Paths LS and LL are similar (purple lines in Figures 3c and d), most of the compaction in Path LL likely occurred during condensation, which occurred before evaporation. We used a smaller coating volume in Figure 3c and d (2-fold the initial soot-particle volume) because this was sufficient to cause compaction. Figure 4a shows the results of Figure 3 in terms of the change in modal d mob as a function of coating volume. That is, Figure 4a extends Figure 3 to a much larger number of comparable experiments in which the coating mass was varied. Data are shown for both anthracene and oleic acid coatings. Each group of data is labeled with two letters following Table 1: the first letter (S or L) indicates the coating phase during addition, the second letter (S or L) indicates the coating phase during removal. Curves are included to guide the eye. Error bars are included for sparse data and are omitted where multiple similar measurements provide an indication of measurement precision.

Coating volume effects
In Figure 4, the mode d mob was retrieved from fits to the data. When more than one mode was apparent due to heterogeneity in coating thicknesses (e.g., Figures 3a and b), the mode containing more particles was reported, for consistency with the denuded size distributions. Figure 4b plots the same data after conversion to shape factor v. Figure 4a shows that oleic acid condensation led to a decrease of d mob until the particle volume approximately doubled (V 1 =V 0 > 2), that is, until the particle contained equal volumes of coating and soot. For thin coatings, d mob was similar for coated and denuded particles. For these particles, the shape factor v (Figure 4b) was larger for denuded than for coated particles. In the context of Sections 2 and 3, this is interpreted as condensation compaction. Figure 4b shows that v decreased monotonically with increasing V 1 =V 0 for both coating materials. This v reached an asymptotic value of unity for oleic acid coatings, demonstrating particle sphericity. Sphericity is expected when the particle surface is liquid, and when aggregates are fully encapsulated. Importantly, v ¼ 1 was also reached for liquid-anthracene coatings. This was not observed for solid anthracene coatings, where v ¼ 1:2 was the asymptotic value. Slowik et al. (2007) achieved a similar asymptotic value (v ¼ 1:3) for solid anthracene ( Figure S5). Therefore, our measured shape factors support our assertion that we were able to deposit solid or liquid anthracene coatings by varying our experimental conditions. For all V 1 =V 0 , v is higher for denuded than for coated particles because a compact soot aggregate is not a smooth sphere ( Figure S4).
Because our coating apparatus did not allow us to finely control the amount of anthracene addition in experiments involving solid deposition, only a single data point is available for those cases. However, our conclusions from this limited data set are corroborated by the literature comparison below.
A unique implication of our data set relative to previous literature is that we observed smaller amounts of restructuring after condensation-compaction than after evaporation-compaction. This suggests that evaporation-compaction is even more efficient at restructuring than the capillary-compaction mechanisms. However, because we were only able to follow Path LL using oleic acid, and not anthracene, this difference may also reflect differences in surface tension (Schnitzler, Gac, and J€ ager 2017), contact angle, or morphology for the solid-coated particles.

Further validation experiments
To confirm that bulk anthracene sublimated upon heating in our apparatus, we performed an experiment where anthracene powder (as received) was heated in the coating-apparatus reservoir while the apparatus was kept open (in a fume hood) for observation. The crystals were heated continuously in air at roughly 1 C s À1 : We observed no visual changes until the apparatus reached 191 C, at which point the crystals began to shrink rapidly. As the temperature was The coating phase state during addition is indicated by the first (or single) capital letters S for solids and L for liquids. The coating phase during removal is indicated by the second capital letters. In our experiments, DEC results in more complete compaction than CC (compare LL and LS). In Panel b, The shape factor of 1 for thick L (liquid) coatings and 1.2 for thick S (solid) coatings confirms that these two phases were liquid (spherical) and solid (aspherical), respectively. Fewer data points were available for solid coatings due to the experimental difficulty of adding solid coatings.
increased to 220 C, fumes were observed without any indication of melting. A spatula placed within the fumes became coated with a matte film initially and millimetre-sized planar crystals later ( Figure S6). The initial matte film on the spatula may be related to the melting point reduction of nanoscopic quantities of anthracene ( Figure S7). Although our visual observation could not confirm this hypothesis, Lopatkin, Protsenko, and Skorobogatko (1977) have directly observed that thin films of anthracene condense as liquids at temperatures above 55 C and solids below this temperature. Lopatkin, Protsenko, and Skorobogatko (1977) studied films of thickness 10 nm to 16 lm with growth rates of 3 to 15 nm/s. Their conclusions are consistent with our melting-point depression calculations, discussed above and in the SI.
To ensure that the phase of condensing anthracene was not affected by residual OM from the flame, we pre-denuded the soot at 350 C before repeating the condensation (V 1 =V 0 $ 3:3) and condensationdenuding (at 200 C and 150 C) experiments. No change was observed in our results and the soot particles returned to their original mass (the mean ± standard deviation of measurements before and after denuding was 6:40 6 0:15 fg and 6:38 6 0:18 fg, respectively). We also ensured that anthracene oxidation was not relevant in our apparatus by repeating the experiment in nitrogen rather than synthetic air. The results were included in Figure 4 at V 1 =V 0 ¼ 2:55 and are fully consistent with the other results.

Discussion: Comparison with previous soot-anthracene studies
Two previous studies have reported data similar to Figure 4 for anthracene (Slowik et al. 2007;Chen et al. 2016). These data have been included in Figure  5. The purple diamonds in Figure 5 show the data of Slowik et al. (2007), who coated soot with anthracene at 52-85 C. As shown in Figure S7, this temperature is well below the melting point of even 3 nm anthracene spheres, so Slowik et al. (2007) most likely deposited solid coatings. Slowik et al. (2007) removed these coatings at 200 C, which is below the 216 C melting point of anthracene. Therefore, as also concluded by those authors, the anthracene coatings of Slowik et al. (2007) did not result in restructuring of soot; they followed Path SS of Figure Chen et al. (2016) indicate solid deposition, since mobility diameters increased upon coating. These three data sets are not plotted here in terms of shape factor v (as in Figure 3b) because soot monomer and aggregate sizes differed between studies.
factor v, because those two studies and our study used soot with different spherule diameters and aggregate mobility diameters. So, the initial and final v expected in the three studies is different, as shown systematically by Leung et al. (2017a). Regardless, we have reanalyzed the data of Slowik et al. (2007) in Figure S5 to show that they do illustrate the same trends observed here. For the data of Chen et al. (2016), shape factor changes are small since those authors focused on thin coatings (i.e., small volume growth factors in Figure 5).
Here it is worth repeating the statement by Chen et al. (2016) that complex mixtures are likely to have lower melting points (Peters et al. 1997;Marcolli, Luo, and Peter 2004). Nanoscopic quantities of material are also more likely to exist in the liquid phase (Section S4). Consequently, in combustion and atmospheric chemistry, coatings are most likely to condense as liquids. Important exceptions may include the scenarios where secondary organic aerosols reach very high viscosities due to low temperatures or humidity (Leung et al. 2017b;Koop et al. 2011;Schmedding et al. 2020) and where ice crystals may form without transitioning through cloud droplets on soot (Marcolli 2014;David et al. 2019).

Discussion: Atmospheric implications
If liquid condensation generally leads to the compaction of soot particles, as concluded by the reviews and experiments summarized above, then it may be expected that atmospheric soot particles coated by condensation are compact. In this context, the condensate may be secondary particulate matter (e.g., Adachi, Chung, and Buseck 2010), cloud water (Bhandari et al. 2019;China et al. 2015a), or semivolatiles co-emitted with the soot which condense as combustion emissions cool (Weingartner, Burtscher, and Baltensperger 1997;China, Salvadori, and Mazzoleni 2014). If atmospheric soot particles are observed not to be compact, they may have become internally mixed by the deposition of highly viscous (nonliquid or glassy) organic materials (Shrivastava et al. 2017) or by coagulation.
Coagulation is recognized as an important mixing mechanism for soot during photochemically inactive periods (e.g., at night) (Riemer, Vogel, and Vogel 2004;Fierce, Riemer, and Bond 2015) as well as in heavily polluted regions such as Eastern China, India, and Central Africa (He et al. 2016). Microscopy images provide unambiguous evidence for coagulation when soot is mixed with nonvolatile material such as dust (Xiong and Friedlander 2001). Other images strongly suggest coagulation, when soot particles appear to be attached to droplets of other material (e.g., Adachi, Chung, and Buseck 2010;Adachi and Buseck 2013;China et al. 2013, China, Salvadori, andMazzoleni 2014;Moteki, Kondo, and Adachi 2014), although coagulation can also result in other morphologies. In practice, both coagulation and condensation are likely to contribute to the internal mixing of atmospheric soot particles with coating materials. For example, a soot particle may coagulate with a much smaller particle and remain uncompacted but later undergo condensation-compaction due to the formation of secondary aerosol, the hygroscopic uptake of water by the coagulated material, or by activation into a cloud droplet.
It has been inferred from recent experimental work that approximately half of the measured soot particles were non-spherical (i.e., non-compacted) in the atmosphere over Beijing, based on tandem measurements of single-particle soot-particle mass and optical size after d mob classification (Hu et al. 2021). These measurements were shown to predict the light absorption enhancement due to coatings ( E abs ) in a simple empirical model which considered non-spherical particles as uncoated and spherical particles as core-shell coated soot particles (Hu et al. 2022). At the same time, negligible E abs has been observed in other studies despite substantial coating volume fractions (Cappa et al. , 2019. Fierce et al. (2020) proposed that this discrepancy was related to deviations from a core-shell configuration of coated soot, and showed that a laboratory-based model of these deviations better described the atmospheric data of Cappa et al. (2019). In particular, the Fierce et al. (2020) model explained half of the E abs discrepancy by accounting for heterogeneity in soot coating distribution between particles, and another quarter of the discrepancy by accounting for deviations from core-shell morphology. Fierce et al. (2020) estimated deviations from coreshell morphology based on laboratory experiments where soot was coated extremely quickly, either in coating apparatuses like ours ( Figure S3a) or in a potential aerosol mass (PAM) oxidation flow reactor (Forestieri et al. 2018). These apparatuses have residence times of less than 2 minutes, while atmospheric coatings take 2 hours to form even under the most favorable conditions (Vakkari et al. 2014). Therefore, atmospheric particles may deviate even further from core-shell mixtures than represented by the Fierce et al. (2020) model. Extending the approach of Fierce et al. (2020) to model atmospheric coagulation more directly may therefore be valuable in improving our predictions of the global climate effects of soot restructuring.
Since solid coatings do not cause restructuring, future work should also explore the potential of solid coating formation in the context of biomass-burning particles and secondary organic aerosols. In this context, care should be taken when interpreting indirect evidence of coating phase. For example, particle phase may be inferred from measurements of particle bounce (solids bounce, while liquids wet the surface) or chemical reactivity (solids react more slowly than liquids). For m-xylene SOA, bounce measurements have indicated a glass-to-liquid phase transition at 60-80% RH while reactivity measurements indicated a transition at 35-45% RH (Li et al. 2015). Since compaction is a physical process, the higher RH would be expected to be more relevant to soot restructuring. However, as discussed in Section 3, Leung et al. (2017b) observed a transition in soot restructuring by p-xylene-SOA at 20% RH, consistent with the pokeand-flow experiments of Song et al. (2016). The difference may be due to the melting-point depression of small amounts of SOA condensates, a difference in the composition of smaller (capillary) quantities of SOA, or some other mechanism.
Finally, we have not discussed the NDA mechanism in an atmospheric context because the necessary conditions of high supersaturation and high contact angle are unlikely to occur. For the typical case of organic condensates on soot, atmospheric SOA may also reach high supersaturations (S > 4 for the lowest-volatility compounds, Donahue et al. 2011), but chamber data have already provided clear evidence that liquid coatings condensed under environmental conditions result in soot compaction (Qiu, Khalizov, and Zhang 2012;Schnitzler et al. 2014;Guo et al. 2016;Leung et al. 2017b). For the extreme case of cloud formation onto un-aged soot particles (e.g., during contrail formation), laboratory experiments at 108% RH have shown that compaction still occurs (China et al. 2015a).

Summary
An understanding of soot compaction based on wellestablished, directly observed phenomena in surface science (Section 2) indicates that there are two mechanisms for condensation compaction (capillary and capillary-bridge) which may regularly occur in the environment under subsaturated conditions. A third mechanism, nanodroplet activation, requires extreme supersaturations and has been demonstrated in the laboratory, but not observed in natural systems. Soot aggregates coated in combustion systems or in the atmosphere are therefore expected to be compacted by the coating process. This compaction may be avoided by coagulation, by the addition of solid coatings, or (in the laboratory) by nanodroplet activation. If compaction is avoided, then coating evaporation also leads to compaction.
This framework of condensation-compaction and evaporation-compaction mechanisms resolves conflicting conclusions in the literature (Section 3) and was demonstrated in the laboratory (Section 4). Future modeling studies focused on atmospheric and climate science should assume that soot particles become compact when liquid condensation is the primary mechanism of internal mixing. The relative roles of internal mixing by liquid condensation versus coagulation or solid-coating formation should also be explored.

Funding
This work was funded by the ERC under grant ERC-CoG-615922-BLACARAT. Thanks are owed to Maarten Heringa for providing a component of the condensation apparatus, to Elisabeth M€ uller for TEM assistance, and to Louis Tiefenauer for the loan of the TEM sampler. We are grateful to Jay Slowik and Alexei Khalizov for their openness in sharing published data, to Ogochuwku Y. Enekwizu for stimulating discussions, to Timothy Sipkens for contributions to figures, and to the anonymous reviewers for their constructive feedback.

Author contributions
JCC conceived the study, initiated the experiments and critical reviews, and drafted the paper. RLM and MGB discussed initial results, co-designed subsequent experiments, and contributed substantially to data interpretation and to writing.