Estimating viscosity of individual substrate-deposited particles from measurements of their height-to-width ratios

Abstract Airborne particles alter the radiative forcing of climate and have further consequences on air visibility, atmospheric chemistry, and human health. Recent studies reported the existence of highly viscous semisolid and even solid amorphous organic aerosol (OA) particles. Particle viscosity has an impact on the heterogeneous chemistry, gas-particle partitioning, and ice nucleation properties. Consequently, variations in particle viscosity must be considered when predicting the atmospheric impact of OA. Here, we use scanning electron microscopy (SEM) and scanning transmission X-ray microscopy (STXM) to estimate the viscosity of individual particles deposited on substrates based on their characteristic height-to-width ratios, which are affected by changes in morphology upon deposition. The height-to-width ratios obtained from SEM and STXM exhibit a strong correlation, demonstrating that both imaging approaches can be applied separately for viscosity assessment of the substrate-deposited particles. While these metrics are largely qualitative, this method enables rapid assessment of particle viscosity ranges, distinguishing between semisolid (>1010 Pa·s), viscous (104–108 Pa·s), and liquid (10°–101 Pa·s) particles within ensembles of ambient particles collected for microscopy studies. Copyright © 2023 American Association for Aerosol Research Graphical Abstract


Introduction
Over the last decade, numerous field and laboratory studies reported that atmospheric organic aerosol (OA) particles may exhibit highly viscous (semisolid) and even amorphous solid (glassy) phase states (Zobrist et al. 2008;Mikhailov et al. 2009;Virtanen et al. 2010).These distinct particle phases alter gasparticle partitioning of individual OA components, which exhibit different timescales depending on particle viscosity and volatility variations (Shiraiwa and Seinfeld 2012).While low viscosity (liquid) particles quickly respond to changes in the atmospheric gasphase composition, highly viscous (solid and semisolid) particles are kinetically more stable and require longer mixing times to reach multiple-phase equilibrium (Mikhailov et al. 2009;Koop et al. 2011;Krieger, Marcolli, and Reid 2012;Shiraiwa et al. 2013).The dynamics of gas-particle partitioning and atmospheric chemistry of OA strongly depend on the diffusional mixing time within individual particles (Bones et al. 2012).However, direct measurements of diffusion characteristics representative of mixing between various components inside sub-micrometer OA particles are not feasible.Consequently, the diffusion mixing inside atmospheric particles is commonly inferred from experimentally determined particle viscosity values, using the Stokes-Einstein equation, which quantitatively describes the diffusion-viscosity relationship (Shiraiwa and Seinfeld 2012;Marshall et al. 2016;Maclean et al. 2017;Shiraiwa et al. 2017;Evoy et al. 2019;Ullmann et al. 2019;Ingram et al. 2021).
Reaction mechanisms and kinetics of OA oxidation by gas-phase species are greatly affected by particle viscosity, which limits mass transport of reactants and products.These transport limitations are essential when predicting the chemical composition of aerosols evolving in the atmosphere (Shiraiwa et al. 2011;Zhou et al. 2013;Steimer et al. 2015;Berkemeier et al. 2016;Hosny et al. 2016;Marshall et al. 2016;Huang et al. 2018;Galeazzo et al. 2021;Maclean, Smith, et al. 2021).Additionally, particle viscosity impacts the photochemistry of OA components by slowing the photolysis rates in glassy and viscous semisolid particles (Lignell, Hinks, and Nizkorodov 2014;Wong, Zhou, and Abbatt 2015;Hinks et al. 2016;Galeazzo et al. 2021).Furthermore, because of the plasticizing effects of water (Zobrist et al. 2011), particle viscosity is very sensitive to variations in ambient relative humidity (RH).Thus, viscosity is of crucial importance for predicting particle behavior as cloud condensation nuclei (CCN) and as ice nucleating particles (INP) (Bones et al. 2012;Lienhard et al. 2015;Price et al. 2015;O'Meara, Topping, and McFiggans 2016;Ye et al. 2016;Yli-Juuti et al. 2017;Evoy et al. 2021;Maclean, Li, et al. 2021;Maclean, Smith, et al. 2021).In ambient air, viscosity of OA particles decreases under high RH conditions, accelerating the rate of water uptake and enhancing their CCN propensity.At low temperatures of high altitudes, particles transition into solid glass beads that facilitate their INP propensity.The phase state of OA particles may alter the formation of clouds and their lifecycles, with consequences to the indirect impact of aerosols on climate (Baker 1997;Lohmann and Feichter 2005;Baker and Peter 2008;Rosenfeld et al. 2014).Therefore, viscosity variations need to be considered when investigating airborne OA particles and predicting their impact on the atmosphere.
Various experimental techniques have been developed to measure the viscosity of OA particles, as discussed in a recent review article (Reid et al. 2018).Novel methods, such as optical tweezers, bead mobility, and poke-flow imaging have been employed to infer particle viscosity and investigate its dependence on aerosol chemical composition and ambient conditions (i.e., RH and temperature) (Power et al. 2013;Renbaum-Wolff, Grayson, and Bertram 2013;Renbaum-Wolff et al. 2013;Power and Reid 2014;Grayson et al. 2015;Bzdek, Collard, et al. 2016;Bzdek, Power, et al. 2016;Song et al. 2016;Sellier et al. 2019).However, these innovative approaches require relatively large sample volumes and either utilize particles larger than approximately 10 lm or bulk OA samples.Other validated techniques, such as particle rebound and shape-factor relaxation, have been applied for viscosity assessment of sub-micron (<1 lm) particles (Virtanen et al. 2010;Saukko, Kuuluvainen, and Virtanen 2012;Bateman, Belassein, and Martin 2014;Bateman, Bertram, and Martin 2015;Zhang et al. 2015;Rothfuss andPetters 2016, 2017), which are more relevant to atmospheric studies.Recently, atomic force microscopy (AFM) has been employed to infer the phase state and viscosity of sub-micron species on a per-particle basis (Lee, Ray, and Tivanski 2017;Ray et al. 2019;Lei, Olson, et al. 2022;Lei, Zhang, et al. 2022).Despite introducing advanced and sophisticated experimental approaches to measure particle viscosity, these techniques are labor-intensive, time-consuming, and provide limited particle statistics.Therefore, additional analytical methods are needed for quick and facile assessment of the viscoelastic properties of relevant atmospheric particles.
In previous studies, microscopic imaging of individual particles has been employed to obtain information about the viscosity of particles deposited on substrates (O'Brien et al. 2014;Wang et al. 2016;Fraund et al. 2020;Tomlin et al. 2020).Substratedeposited particles deform upon impaction, and the extent of deformation depends on their viscoelastic properties, among other factors (i.e., terminal velocity, surface tension, and adhesion forces) (Kirpes et al. 2022;Tackman et al. 2023).Low degree of deformation is expected when solid particles impact a rigid surface, while liquid-like particles will flatten on the substrate (Ivosevic, Cairncross, and Knight 2006).Consequently, the viscosity of collected particles can be inferred from their height-to-width (H/W) ratios.Scanning electron microscopy (SEM) and scanning transmission X-ray microscopy (STXM) have been used for qualitative assessment of particle viscosity by categorizing particles as solid (spherical), viscous (dome-shaped), and liquid-like (flat) particles.However, an evaluation of this method using standards with known viscosities has not been performed.In this work, we present the first systematic approach to infer particle viscosity of aerosolized standards using the H/W metrics.Additionally, we establish a quantitative relationship between height (H) values measured by SEM and total carbon absorption (TCA) values measured by STXM, enabling comparison of results obtained by each of these two methods.

Experimental methods
Particles composed of selected saccharide chemical standards with predictable viscosities were prepared and sampled following procedure detailed in the online supplementary information (SI) Note 1.Briefly, saccharide particles were aerosolized from aqueous solutions and directed into two CaSO 4 -filled drying tubes, where they were dried to achieve specific RH conditions of 40, 65, and 76% measured at the point of outflow.The RH conditions were controlled by adjusting the flow rate and adding or removing CaSO 4 desiccant, as needed.The saccharide standards used in these experiments included sucrose, glucose, maltose, trehalose, and raffinose.The viscosity of generated particles at each RH level was calculated using previously reported parameterization (Song et al. 2016).The calculated viscosity of particles generated at different RH settings range between 10 0 and 10 10 Pa�s, tabulated in SI Table S1.The particles laden outflow was directed into the inlet of a MOUDI-100 cascade impactor.The particle samples were collected on hydrophobic TEM copper grids (Carbon Type-B film, 400 Mesh) placed on the sixth, seventh, and eighth stages of the impactor with nominal aerodynamic cutoff sizes of 0.56, 0.32, and 0.18 lm, respectively.Additionally, samples of real-world particles collected in recent field studies were also included in this work.Specifically, we imaged solid environmental nanoplastic (EnvNP) particles (Morales et al. 2022) and low-viscosity liquid OA particles of biomass burning organic aerosol (l-BBOA) emitted from laboratory burns of grass biofuel conducted in a test facility (Pandey, Shetty, and Chakrabarty 2019).
Substrate-deposited particles were imaged using an SEM operated at high vacuum (2.04 � 10 −5 Torr).A secondary electron detector (Everhart-Thornley detector, ETD) was used for image acquisition.The samples substrates were gripped at 45 � angle by the sample holder and the microscope stage was additionally rotated by 35 � to achieve a final tilt angle of 80 � for particle imaging.Specific SEM parameters used to minimize beam damage and optimize image acquisition are specified in SI Note 2. From the SEM images, characteristic H and W dimensions of individual particles were measured using ImageJ software 1.52a (http://imagej.nih.gov/ij,Java1.8.0_112).For each of the samples, H and W values were recorded for 50-100 particles collected on each of the sixth, seventh, and eighth stages of the cascade impactor.Additional particle viscosity assessment was conducted on a perparticle basis using STXM instrument operated under environment of approximately 500 Torr of He (Kilcoyne et al. 2003).Unlike SEM imaging, direct measurements of the H values of individual particles are not feasible with STXM, as it images 2D projection areas of particles.Instead, particle-specific optical depth (OD) values are calculated on a per-pixel basis using the Beer-Lambert Law (OD E ¼ −ln(I/I 0 )) ¼ mqt) within the contours of particle areas and reported as total carbon absorption (TCA) values, derived as: where OD E is optical density at a given X-ray energy E (OD 320 and OD 278 are those at energies of the carbon post-edge (320 eV) and pre-edge (278 eV), respectively); I is the intensity of light transmitted through a particle and I 0 is the intensity of incoming light (background); m is the mass absorption coefficient of carbon, q is density of the specimen, and t is the optical thickness.From STXM images, the W dimension of particles is calculated from their 2D projection areas as an area equivalent circle diameter.
Particle-specific TCA versus W measurements have been used for the qualitative empirical assessment of particle viscosity, based on the assumption that viscous spherical particles exhibit higher TCA values compared to flat, liquid-like particles (O'Brien et al. 2014;Wang et al. 2016;Fraund et al. 2020;Tomlin et al. 2020).

Results and discussion
SEM imaging parameters were carefully selected to minimize beam damage, as detailed in SI Note 2. It should be noted that for saccharide particles, prolonged exposure to the electron beam can induce changes in particle shape, leading to inaccurate H and W measurements. Figure 1 illustrates typical morphologies of the substrate-deposited particles imaged at an angle h ¼ 10 � .The observed "flat," "dome-shaped," and "spherical" morphologies of individual particles are a result of their deformation upon impaction.However, the observed morphology reflects a combined effects of particle viscoelastic properties, surface tension and particle-substrate adhesion forces.H and W dimensions serve as two characteristics metrics of particle morphology that can be directly measured from the SEM images.While values of W are independent of the imaging angle (h) and can be obtained through direct measurements, the observed heights (H obs ) measured from particle images are different from the intrinsic heights (H) that can be calculated using Equation (2) for a given imaging angle h: H ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Geometry derivations leading to Equation ( 2) are based on the approximation of dome-shaped particles by the idealized morphology of symmetric half-spheroids, as discussed in SI Note 3. It follows that H obs ¼H for spherical particles and H obs > H for dome-shaped particles.
The graphical part of Figure 1a illustrates a limiting case specific to the imaging angle h, where observed height H obs corresponds to the distance between opposing edges of a low-dome particle for which the intrinsic height H becomes imperceptible from the observer's viewpoint.This geometric limit defines the lowest H obs /W ¼ Sin(h) that can be used to quantitatively assess the intrinsic height H of a particle.In the case of a h ¼ 10 � imaging angle, the meaningful range is 0.17 < H obs /W < 1.0, and the range narrows for larger imaging angles (SI Figure S4).The accuracy of H obs to H conversion decreases for particles with H obs /W ratios approaching 0.17.Essentially, particles prepared from all saccharide standards showed H obs / W ratios above 0.20 (SI Figure S5). Figure 2 summarizes measured H versus W values for all saccharide particles collected on stage 7 of the cascade impactor.Particularly, experimental values for the highly viscous (10 10 Pa�s) spherical particles cluster tightly along the H/W � 1 line and they are clearly distinguishable from all other particles.The least viscous liquid-like particles tested in this study (10 0 -10 1 Pa�s) exhibit ratios of 0.14 < H/W < 0.28, while particles with intermediate viscosities (10 4 -10 8 Pa�s) exhibit higher ratios of 0.28 < H/W < 0.4.The H/W ranges representative of the three principal viscosity classifications are in agreement with the values reported in previous study using atomic force microscopy (Ray et al. 2019), with minor inconsistency inherent to the application of different techniques.In our study, no discernible differences in H/W ratios were observed between particles with different viscosities within the intermediate range.Therefore, while the intermediate viscosity particles exhibit H/W ratios distinct from the semisolid (spherical) and the liquid-like (flat) cases, more accurate assessment of their viscosity is challenging.A plausible reason for this observed indifference is that combined effects of the substrate wetting by particles, associated adhesion, and surface tension forces are likely those that influence shape of the substrate-deposited particles stronger than their viscosity values.Further evidence supporting this conclusion was inferred from morphological transformations of spherical raffinose particles (10 10 Pa�s) observed after storage for 2 days, as depicted in SI Figure S6.Specifically, the initially spherical particles gradually transformed into dome shapes with H/W values comparable to those reported for particles with intermediate viscosity (10 4 -10 8 Pa�s).These observations suggest that particle viscosity higher than approximately 10 10 Pa�s is likely necessary to preserve the original spherical morphology over an extended period of time.For instance, environmental nanoplastic (EnvNP) particles detected in our recent study (Morales et al. 2022), for which higher viscosity of approximately 10 12 Pa�s was estimated, exhibited no observable changes in their spherical morphology even after prolonged storage for weeks and months.These observations are consistent with characteristic e-folding times of equilibration for approximately 1 mm particles projected as seconds, minutes, hours, days, and months for particles with the viscosity values of 10 1 , 10 3 , 10 5 , 10 7 , and 10 9 Pa�s, respectively (Shiraiwa et al. 2011).The time-of-flight of particles in the cascade impactor prior to deposition is in the order of milliseconds, and their residence time inside the impactor during sampling is minutes.Therefore, particles with viscosity lower than 10 4 Pa�s are substantially soft and may change their morphology under the flow of accelerated air during sampling, particles with viscosity 10 5 to 10 8 Pa�s may change their morphology after hours to days of storage, and only particles with viscosity higher than 10 8 Pa�s are unlikely to change even after months of storage.Additional reasons for particle transformation may include effects of substrate wetting which can be experimentally evaluated from systematic observations of shapes and morphology of particles deposited onto different types of substrates.
A similar trend in the morphology-viscosity relationship was also observed for saccharides standard particles collected on stage 8 of the cascade impactor (SI Figure S7).In these samples, the H/W ratios corresponding to liquid-like (10 0 Pa�s) and viscous (10 4- 8 Pa�s) particles overlap within the range of 0.2-0.5 with average H/W of 0.28 and 0.33, respectively.This makes it more ambiguous to distinguish between the liquid-like and viscous cases.The overlapping ranges of H/W ratios are a result of the higher linear velocity (higher kinetic energy) of particles impacting the lower (8 th ) stage of the impactor (Marple, Rubow, and Behm 1991), leading to greater deformation upon the impact.For that reason, particles deposited on the upper stage 6 (lower kinetic energy) experience less deformation upon the impact, which results in the indistinguishable H/W ratios corresponding to liquidlike and viscous particles (SI Figure S8).Therefore, the interpretation of measured H/W values as a metric of particle viscosity should be approached cautiously, always considering the specific deposition (impaction) conditions.When sampled by MOUDI, particles deposited on stage 7 provide the most informative H/ W ratios for viscosity assessment.Figure 2 indicates that viscosity of particles with the width sizes between 0.3 and 2.0 mm can be evaluated from the samples collected on stage 7.
SEM-based H values were compared to STXMbased TCA measurements to evaluate the correlation between both analytical approaches for particle viscosity assessment.Because of the gradual change of spherical particles into dome-shaped during storage, saccharide particles with different viscosities exhibit similar appearances after few days of storage.However, EnvNP particles detected in our recent studies (Morales et al. 2022), for which higher viscosity of 10 12 Pa�s was estimated, showed no observable changes in particle morphology and were thus preferred for viscosity assessment using STXM.Figure 3 illustrates SEM-based H and STXM-based TCA measurements for two additional samples representing limiting cases: semisolid spheres (EnvNP) and flat particles (l-BBOA).The measurements acquired from SEM and STXM highlight variations in aspect ratio between EnvNP and l-BBOA, corresponding to significant differences in their viscoelastic properties.The morphological differences between these two samples are confirmed by SEM tilted images, and H obs /W and H/W measurements shown in SI Figure S9.The TCA values obtained in this study for l-BBOA are in agreement with the TCA values of liquid-like laboratorygenerated particles reported in previous studies (O 'Brien et al. 2014), which highlights the reliability of STXM for inferring the viscosity of ambient particles.To establish the relationship between SEM and STXM measurements for particle viscosity assessment, the TCA values from STXM were correlated with H values determined from SEM imaging.The observed overlap between the two data sets suggests that both imaging techniques can be separately applied to infer viscosity from the morphology of particles deposited on substrates.Equation ( 3) presents an empirical relationship between H and TCA as: This equation accounts for all inconsistencies between SEM and STXM methods, which can be correlated to each other when experimental settings follow the image acquisition approach discussed in this study.It is important to note that measured TCA values are influenced by intrinsic properties of particles, such as mass absorption coefficient of carbon (m) and density (q), which may differ for particles composed of substantially different carbonaceous materials (e.g., graphitic carbon, polymers, SOA mixtures, singlecomponent organic standards).Furthermore, TCA values measured for mixed inorganic-organic particles will likely underestimate their viscosity due to the limited amount of absorbing material.Consequently, assessment of particle viscosity using STXM can only be considered for particles composed primarily of organic compounds.Considering these caveats and based on the previously reported TCA data shown in Figure 3 (O' Brien et al. 2014), viscosity values of 10 4 -10 8 Pa�s are estimated for the typical field collected OA, while viscosity values of 10 0 -10 1 Pa�s are common for the liquid-like SOA generated in laboratory environmental chambers.Our findings support results from previous study (Tomlin et al. 2020), where TCA measurements were used to classify organic particles and amorphous biological fragments collected onboard research aircraft as semisolid (10 2 -10 12 Pa�s) and solid (>10 12 Pa�s), respectively.This highlights the applicability of spectro-chemical imaging methods to study the viscoelastic properties of carbonaceous particles with non-spherical morphologies.

Conclusions
This study presents the application of SEM imaging to infer the viscosity of individual particles based on their measured H/W ratios, offering a simple and rapid method to distinguish between three basic viscosity ranges: "solid," "viscous," and "liquid-like."The method provides a semi-quantitative approach and has limited potential for precise measurements of particle viscosity because of the combined effects of various forces that influence the shape of substratedeposited particles.Nevertheless, this imaging method offers a practical and unique opportunity to assess the viscosities of individual real-world OA particles without the need for specialized and sophisticated measurements.

Figure 1 .
Figure 1.Left panels: SEM tilted-angle images illustrating three distinguishable morphology types of particles: (a) flat, (b) domeshaped, and (c) spherical.Right panels: Schematic representation of the observed particle height, H obs , for each of the three particle types.

Figure 2 .
Figure 2. Height and width measurements of saccharide particles representing three general viscosity ranges mapped with respect to their H/W ratios.Dashed lines indicate the average H/W values representative of different viscosity ranges.