The morphological information of BC is relatively complex, and usually, multiple parameters are used to jointly characterize the morphological evolution of BC. Parameters such as effective density (ρ_eff), fractal dimension (D_f), and dynamic shape factor (χ) are used to characterize the compactness of BC particles, and all these parameters can be calculated from data measured by online instruments. Additionally, some studies use parameters obtained from electron microscope identification, such as Roundness (RN), Convexity (CE), and Aspect Ratio (AR), to collectively characterize the morphological features of BC particles^［29-31］.

ρ_eff is used to characterize the compactness of a large number of small carbon spheres within particulate clusters. The greater the effective density, the more pronounced the compactness of BC particles. For example, field observation studies by Zhang et al. in North China have shown that as the proportion of non-BC components increases, the ρ_eff of the BC core increases from about 0.5 g/cm³ to 1.2 g/cm^3［32］.

in Equation (1), m is the mass of the particulate matter, and D_p is the electrical mobility diameter of the particulate matter.

D_f is a measure of the irregularity of particulate matter used to characterize cluster structures, and it is one of the key parameters for quantifying the structure of BC particulate matter, which can be used to distinguish the degree of irregularity between fresh and aged particles. When the fractal dimension D_f is close to 1, it indicates that the morphology of the particles is approximately a straight line; when the fractal dimension D_f is close to 3, it suggests that the particles are spherical^[33]. Studies have shown that the typical D_f value of aged urban environmental BC particles is around 1.82, ranging from 1.50 to 2.60^[16]. For different types of BC particles, the D_f ranges from 1.80 to 2.16, increasing in the following order: fresh < partially encapsulated < fully encapsulated BC particles^[33]. There are also significant differences in D_f among fresh BC particles from different sources. For example, the D_f of fresh diesel BC particles typically ranges from 2.2 to 2.4, within which the BC particle structures are all dendritic^[34]. Pang et al. measured the D_f of BC particles from different sources, and found a significant difference between the average D_f (1.66±0.17) of vehicle-emitted BC particles and those from biomass burning (1.75±0.18) and coal combustion (1.76±0.18). The average D_f (1.77±0.18) of BC particles in urban atmospheres is close to the D_f of biomass and coal combustion but much lower than that in rural atmospheres (D_f(1.85±0.13))^{[12, 35]}. Li et al.^[16] demonstrated that an accurate description of D_f can significantly improve the assessment of the optical effects of BC particles.

in Equation (2), d_p is the radius of fresh BC, where the number of BC carbon microsphere monomers is N, R_g refers to the rotational radius of BC (a particle size characterizing the features of cluster particles, which can be measured by techniques such as electron microscopy), k is a prefactor, and the values of D_f and k are determined by power function fitting of N with \mathrm{2}{R}_{\mathrm{g}}/d_{\mathrm{p}}.

χ is also used to characterize the irregularity of particles. If χ=1, it indicates that the particle is a standard sphere. The larger the χ, the more obvious its non-spherical characteristics are^{［32, 36］}.

among them, D_p is the electrical mobility diameter of the particles, D_ve is the volume equivalent diameter of the particles, D_m is the mobility diameter, and C_c represents the Cunningham correction factor for the corresponding particle size. The research by Guo et al.^［19］ shows that when BC particles are exposed to the OH oxidation products of m-xylene, \mathrm{\chi } decreases from around 1.5 to nearly 1.0, indicating that as the degree of aging increases, the morphology of BC particles transitions from an initially highly irregular structure towards a spherical shape.

Pei et al^［37］ also defined BC spatial ratios (internal space ratio, open space ratio), internal space modified dynamic shape factor, etc., in their study to characterize the BC structure.

Some other two-dimensional shape parameters, such as AR, RN, CE, etc., are used to characterize the sphericity of particles. These parameters can be obtained through electron microscopy^［38］.

in Equation (4), AR is the area ratio, L_max and W_max are the maximum length and width of the boundary, and in Equations (5) and (6), A_a is the projected area of BC particles. For spherical particles, AR=RN=1, while for non-spherical particles: AR>1 and RN<1. The values of RN and CE vary between 0 and 1, with larger values indicating that the BC particles are more compact. Chen et al.^[29] found that the CE and RN of fresh BC particles were 0.43±0.06 and 0.25±0.08, respectively. After being coated with pyrene, fluoranthene, and phenanthrene, the BC particles collapsed significantly, with CE increasing to 0.75~0.88 and RN increasing to 0.45~0.66.

During the initial aging process, vapors generated from gas-phase or heterogeneous reactions condense onto the surface of BC particles. Numerous studies have reported the collapse of BC particle branches during the condensation process, yet understanding of the collapse mechanism remains limited. The current perspective suggests that properties such as surface tension, polarity, and melting point of the coating materials are key factors influencing the deformation of BC particles.

Regarding the influence of surface tension, since the encapsulating material tends to minimize the surface area of the condensate to reduce surface energy during the condensation process on the surface of BC particles, this leads to a stretching effect on the carbon microspheres on both sides, and the greater the surface tension, the stronger the stretching effect, resulting in a more significant collapse of BC particles. However, some studies have shown that exposing BC particles to the vapor of saturated ethanol and dimethyl sulfoxide/water mixtures, despite a 2.5-fold difference in surface tension of the condensed material under these two conditions, results in a similar degree of collapse^［87］, indicating that surface tension alone cannot fully explain the collapse of BC particles. As for the influence of the melting point of the encapsulating material, Corbin et al.^［88］ suggested that the presence of encapsulating material in solid form on BC particles does not cause deformation, and its liquid form on the surface of BC particles is a necessary prerequisite for morphological evolution.

Regarding the impact of the polarity of encapsulating substances during the condensation process, studies have found that when the non-BC component is a non-polar substance, non-polar substances tend to adhere more easily to the surface of BC particles, causing the BC core to collapse^［89］, whereas this tendency is not as strong for polar encapsulating substances^［88］. This is mainly because the surface of fresh BC particles exhibits non-polar characteristics^［90］, which results in a lower contact angle with non-polar substances, making it easier for metastable liquid phases of different shapes to form between adjacent carbon spheres, leading to the collapse of BC particle branches through capillary forces. Recent research has proposed that the mechanism behind the collapse of BC particles during condensation is primarily determined by the polarity of the non-BC components. Non-polar substances exhibit a low contact angle with the surface of BC particles, allowing capillary condensation to occur between two adjacent carbon spheres, producing metastable liquid phases of different forms and inducing capillary forces that cause the collapse of BC particle branches, known as the capillary collapse mechanism^［88］. As shown in Figure 1a. This is the key factor behind the collapse of BC particles induced by non-polar substances during condensation. Some experiments have provided evidence of condensation-induced collapse. Chen et al. and Enekwizu et al.^［89］ encapsulated sub-monolayers of polycyclic aromatic hydrocarbons and triethylene glycol on BC particles under subsaturated conditions^［29-30］, where only capillary collapse could be triggered, providing further evidence for the capillary collapse^［29-30］. Evidence of condensation-induced collapse has also been demonstrated under subsaturated vapor conditions of non-polar substances in other experiments^［34,87］. This also explains that the polarity of substances is a key factor affecting the collapse of BC particle branches during the condensation process.

However, during the condensation process, when the non-BC component is a polar substance, the polar substance exhibits a high contact angle with BC particles, which means that a higher density of nanodroplets may be required to form a metastable phase. A high density of nanodroplets will require a higher concentration of saturated vapor. Therefore, in some laboratory studies, wrapping BC particles with low saturated vapor polar substances does not result in the observation of BC core collapse. For example, fresh BC particles show almost no collapse when exposed to water vapor under low saturation conditions^{［87, 91］}, because water is a polar liquid and exhibits a high contact angle with the surface of BC particles; a high contact angle does not cause capillary forces between adjacent carbon microsphere monomers. Brauer et al. reported two cases where dendritic BC particles were found during autopsies of residents in Mexico City^［92］, indicating that these fresh hydrophobic BC particles did not collapse as they entered the lungs. Another nanoactivation mechanism proposed by Corbin et al. (as shown in Fig. 1c) suggests that when the vapor concentration reaches the critical saturation ratio on a curved surface, metastable phases such as nanodroplets, thin films, and capillary phases may be activated into droplets and grow without any energy barrier^［88］. Thus, BC particles may undergo a nanodroplet activation process but without generating capillary forces, so the BC particles do not collapse. Under extreme supersaturation conditions, multiple nanodroplets on two or more carbon microspheres can overcome energy barriers and simultaneously activate into droplets, and these droplets connect two non-adjacent carbon microspheres through a capillary phase, thereby generating an attractive force. Alternatively, when pendant capillary rings or adsorption films grow to engulf the particles they connect, capillary bridges can form, generating mutually attractive capillary forces among three adjacent spheres. There is no direct evidence showing the capillary bridge collapse mechanism during actual measurements. Only in Chen et al.'s study was this theory speculated, where a group of compounds were exposed to an experimental temperature of 50°C, causing instantaneous collapse of BC particles. They believed that at the current temperature, the vapor of the encapsulating layer has a high transient saturation ratio, under such extreme supersaturation conditions, capillary nucleation cannot occur, i.e., capillary condensation does not happen^［30］. Multiple nanodroplets on the surface of carbon microsphere monomers might be simultaneously activated and rapidly grow to interconnect, forming capillary rings that engulf the carbon microspheres, possibly leading to the collapse of BC particles through the capillary bridge collapse mechanism^［30］.

Previous studies have suggested that the morphological evolution of BC particles during the condensation process significantly affects their optical properties, but the results of their light absorption properties are not consistent. For example, the mass absorption cross-section of a collapsed BC core can decrease by up to 30% compared to its fresh branched state^［27］. However, some studies suggest that the scattering cross-section of branched BC particles is smaller than that of a fully collapsed spherical BC core^［28］. In the actual atmosphere, BC particles mostly focus on the transition of mixed states and the increase in coating thickness (as shown in Figure 2), and multiple studies indicate that light absorption enhancement is highly correlated with the mixed state. BC particles coated by non-BC components can enhance light absorption through a lensing effect^［93-96］. There is limited research on the initial condensation process of non-BC components on the surface of BC particles regarding their optical properties. Peng et al. suggested that during the early aging stage of BC particles, when only a small amount of material is coated, BC collapses from a branched structure into an approximately spherical structure, which does not significantly increase the MAC of BC particles and may even show an initial increase followed by a decrease^［97-99］. This process implies a competitive relationship between the collapsing of BC branches and the lensing effect on the absorption during the early stages of aging^［97］. Currently, there are few reports on the optical properties of BC cores that do not collapse during the condensation process.

Additionally, studies have pointed out that during the aging process of BC, non-BC components may start aging at the end positions of BC branch structures rather than the main body of the branch-like structure. Therefore, when BC is completely encapsulated by non-BC components, the BC core is not always located at the center of the BC particles (as shown in Figure 3d)^[84]. The optical properties of BC particles with this eccentric structure differ somewhat from those of BC particles with an ideal core-shell structure. Laboratory measurement results from Liu et al. indicate that the initial aging situation at the ends of BC branches is similar to the scattering coefficient values and trends simulated by the externally mixed core-shell model, suggesting that the aging process of BC begins at the ends of its branches^[84]. When internally mixed and the BC core fully collapses, laboratory measurements and model simulations yield similar results. However, in the transition zone between external and internal mixing, there is a significant discrepancy between the measured scattering coefficients and the simulations. Cappa et al. observed that the light absorption enhancement of the coating layer in internally mixed BC particles in California was only about 6%, and the MAC values of the BC particle group did not show a significant increase with the increase in BC particle mass. This conclusion differs considerably from smog chamber results and MIE model calculations^[8]. They suggested that in the actual atmosphere, the BC core exists at the edge rather than the center of the particles. Thus, they proposed that BC particles with an eccentric core structure cause differences in light absorption capacity between observations and smog chamber and model simulations, questioning the applicability of MIE scattering theory in the real atmosphere. Huang et al.^[86], based on field observation data, found that the light absorption properties of these eccentrically structured particles would further decrease by 40%.

From the perspective of curvature, there are convex spherical surfaces on the surface of BC particles and grooves between two carbon spheres. According to the Kelvin effect, the sites for initial condensation of different substances may vary. Some studies suggest that non-BC components would first condense in the grooves between BC carbon spheres or uniformly adhere to the surface of carbon spheres^[30]. Therefore, it still needs further verification whether the aging of non-BC components starts from the ends of BC branches.

The aging of BC particles in the atmosphere involves encapsulation by various substances. When a certain relative humidity threshold is reached, the "salting-out effect" causes the particles to separate into two distinct liquid phases: typically, an outer organic phase and an inner inorganic aqueous phase. This phenomenon is referred to as the liquid-liquid phase separation of atmospheric particles, or simply phase separation^{［100-102］}. Recent studies have found that BC particles encapsulated by large amounts of organic and inorganic materials also undergo phase separation, which may alter the position of the BC core within the particle. Brunamonti et al.^［101］, based on laboratory observations of BC particle distribution in mixed solutions, first proposed that the BC core might migrate during phase separation, moving from the center of the particle to its surface (as shown in Figure 3a). Model calculations suggested that this migration increases the light absorption capacity of the BC core by 25%. Recent field observations have revealed that up to 73% of BC particles with a core-shell structure experience the migration of the BC core from the inorganic phase to the organic phase^［103］, indicating that the phase separation process of BC particles may be common in the atmosphere. Zhang et al.^［67］ used cryo-electron microscopy to analyze atmospheric particle samples and found that BC particles encapsulated by both inorganic and organic components undergo phase separation at relative humidity levels between 75% and 88%, accompanied by partial migration of the BC core and collapse of its branches. The study concluded that the migration of the BC core reduces light absorption by 28%~34%, challenging the traditional view that increased coating thickness leads to higher light absorption enhancement. The scattering cross-sections of these particles are 50% larger than those of uniformly mixed particles, but their absorption cross-sections can decrease by up to 20%^［16］.

In addition to the process of condensation on the surface of BC particles, other substances can also be fixed onto the surface of BC particles through the processes of collision or deposition. Laboratory studies have found that the processes of collision or deposition do not induce capillary forces, thus not causing the collapse of the BC core^［88］. Corbin et al.^［88］ achieved anthracene coating in a solid state deposition on the surface of BC particles by controlling the temperature. Although DMA measurements showed an increase in the size of the coated BC particles, electron microscope images revealed that the BC particles still maintained a fresh branched structure. Similar findings were observed in another study. Slowik et al.^［104］ used anthracene to coat BC particles and removed these coating layers by heating at 200 ℃, below anthracene's melting point of 216 ℃. The solid-state anthracene coating layer did not cause structural reorganization of the BC core. Chen et al.^［29］ coated BC particles with polycyclic aromatic hydrocarbons and observed significant reorganization under sub-nanometer coatings of pyrene, fluoranthene, and phenanthrene. They suggested that the polycyclic aromatic hydrocarbons were in a thin-film liquid state, with these liquid layers acting as lubricants reducing the force required to initiate reorganization. Conversely, thin layers of higher melting point polycyclic aromatic hydrocarbons (e.g., perylene, anthracene, and triphenylene) might remain solid at room temperature, causing less structural change to the BC core.

In the laboratory, it can be observed that there is no surface tension generated between carbon microspheres during the coalescence process under controlled conditions, so the controlled experimental conditions do not lead to the collapse of BC cores. However, the actual atmospheric environment is more complex, and the coalescence between different particles in heavily polluted areas may be an important mixing mechanism^［24］. Moreover, the coalescence has a certain randomness, which could involve fresh BC particles or aged BC particles coalescing with other aerosols. There is still a lack of research on the impact of changes in surface tension of different aerosols during the coalescence process on the morphology of BC cores and BC particles. Therefore, it remains unclear whether the coalescence process in the actual atmosphere can cause the collapse of BC cores. Additionally, BC particles can coalesce at various locations on other aerosols, thus the coalescence process also significantly affects the morphological evolution of BC particles. Recent observational studies have found that during the transport process dominated by coalescence, the BC cores in BC particles are mostly eccentric structures and the number of BC cores increases^［105］, these complex morphological structures bring some difficulties to accurately measuring optical properties. In recent years, some scholars have conducted simulation studies on the impact of irregular morphology on optical properties. Huang et al.^［86］ further parameterized the non-spherical structure of BC cores based on field observation data, and this morphology of BC particles reduces the light absorption enhancement of BC particles by 30% compared to core-shell simulations. Fierce et al.^［24］ compared the measured light absorption enhancement factor with the calculated light absorption enhancement factor based on the core-shell morphology assumption in laboratory studies and found that since the BC particles generated in the laboratory still exhibited irregular shapes, their light absorption values would be lower than those of core-shell structures. The modified core-shell MIE model improves the simulation performance of light absorption capacity but still cannot characterize the non-spherical morphological characteristics of BC particles in the actual atmosphere. Other optical models, such as Rayleigh-Debye-Gans fractal aggregate theory (RDG)^［106］, multi-sphere T-matrix method (MSTM)^［107］, and discrete dipole approximation (Discrete Dipole Approximation, DDA), etc., can be used to simulate the complex structure of BC particles. RDG and MSTM can use aggregates of multiple spheres to characterize the complex chain-like sphere structure of BC cores and use large-volume spheres to represent non-BC coatings, thereby establishing a model of BC particles with coatings. Li et al.^［108］ used the RDG model to simulate the scattering phase function of BC particles produced by biomass and fossil fuel combustion, and the simulation results were in good agreement with the nephelometer measurements. Liu et al.^［109］ found using MSTM simulation that the light absorption intensity of BC particles with non-absorbing coating layers can reach approximately 2. The shape of BC particles in the atmosphere is highly irregular and diverse, but the shape modeling of particles in RDG and MSTM can only calculate the scattering characteristics of aggregates composed of non-overlapping primary particles with special geometric shapes (such as spheres and spheres) and cannot flexibly simulate BC particles of various shapes in the atmosphere. DDA can perform optical simulations on BC particles of arbitrary shapes. In recent years, some scholars have estimated the optical properties of BC particles of different shapes based on the DDA algorithm. Feng Xue^［110］ used a simplified core-shell model to simulate the absorption enhancement, which overestimated the maximum by about 36% compared to observations, while the simulated absorption enhancement value using DDA was between 2 and 2.2, consistent with most observation results. Three-dimensional modeling methods have also been applied to describe the morphology of BC particles. Wang et al.^［25］ developed the SP-EMBS-DDA simulation tool using DDA combined with three-dimensional modeling methods, which can directly obtain the morphology and mixing structure of aged BC particles from SEM or TEM electron images, simulating the overall morphology of BC particles and the complex morphology of BC cores, describing the morphological structure of BC particles in the atmosphere and its changes in light absorption capacity as accurately as possible, and indicating that the light absorption enhancement of BC particles has a nonlinear relationship with the thickness of the secondary coating layer. However, compared with the other three models, the computational efficiency of the MIE theory is significantly higher, so the MIE model is widely used. Although numerous studies analyze the optical properties of aerosols using numerical simulation methods, the models established through numerical simulations in these studies still differ significantly from the mixing structure of single BC particles in the actual atmosphere. Detailed introductions to optical models and radiative forcing simulations can be found in Li et al.'s review^［16］.

The evaporation process of the coating layer on the surface of BC particles also largely affects the morphology of the BC core, namely, the restructuring process of the BC core as the liquid coating layer on the surface of BC particles evaporates, as shown in Figure 3d. In this process, the coating layer is generally a polar substance, and the polar substance exhibits a high contact angle with the surface of the carbon microspheres; substances with a high contact angle do not cause capillary forces between the carbon microspheres. During the evaporation process, individual carbon microspheres in a force-balanced state will experience inward movement due to the capillary force from the retreating liquid-air interface, and overall, the BC particles will be subjected to a net compressive force leading to collapse during evaporation, referred to as evaporative collapse. Some laboratory studies have provided evidence for the mechanism of evaporative collapse. Research by Leung et al.^[111] and Chen et al.^[29], using glassy SOA and solid anthracene respectively, shows that thin coatings lead to an increase in the migration diameter of BC particles, and when the coating is removed by heating, the migration diameter decreases, suggesting the collapse of BC particles during evaporation. Some studies propose that droplet evaporation in atmospheric processes may also lead to the collapse of BC particles. Ma et al.^[72] provided more direct observational evidence in their study; they found that fresh BC particles remained in a low fractal dimension, branch-like state within water droplets, and observed via TEM that the BC core collapsed somewhat during the evaporation of water vapor. However, in laboratory measurements, the evaporation process might be due to measurement errors caused by heating to remove the coating layer or by laser-induced high temperatures in electron microscopy. Corbin et al.^[88] also verified the mechanism of evaporative collapse by controlling temperature so that the anthracene coating layer was deposited on the surface of BC particles in a solid state (without surface tension), keeping the BC core in a branched shape, but after removing the coating layer by evaporation, microscopic images showed the collapse of the BC core. Without the heating process, the BC core may not collapse either. Additionally, Chen Chao^[112] used ETEM to observe in situ that BC particles coated with pure H₂SO₄ vapor (high contact angle) or humidified H₂SO₄ vapor (high contact angle) still maintained a branched structure. However, in Zhang et al.'s^[99] study, the BC core coated with pure sulfuric acid and humidified significantly collapsed, and the authors suggested it might be due to the reheating process of TDMA in the measurement system triggering the mechanism of evaporative collapse. The morphology of the BC core after artificially heating to remove the coating layer during instrument measurement cannot represent the actual morphology of the BC core, which in turn affects the calculation of its optical properties, also explaining to some extent why the optical properties calculated from laboratory measurements are greater than those observed in the field^[8,113-114]; therefore, it is recommended to observe the morphology of BC particles using means such as electron microscopy before heating to remove the coating layer in experimental studies.