Viscosity and phase state of aerosol particles consisting of sucrose mixed with inorganic salts

Research on the viscosity and phase state of aerosol particles is essential because of their significant influence on the particle growth rate, equilibration times and related evolution of mass concentration as well as heterogeneous reactions. So far, most studies of viscosity and phase state have been focused on 25 organic aerosol particles, yet data on how viscosity can vary when the organic materials are mixed with inorganic salts remain scarce. Herein, using a bead-mobility and a poke-and-flow technique, we quantified viscosities at 293 ± 1 K for binary mixtures of organic material/H 2 O and inorganic salts/H 2 O, as well as ternary mixtures of organic material/inorganic salts/H 2 O over the atmospheric relative humidity (RH) range. Sucrose as the organic species, and calcium nitrate (Ca(NO 3 ) 2 ) or magnesium nitrate 30 (Mg(NO 3 ) 2 ) as the inorganic salts were examined. For binary sucrose/H 2 O particles, the viscosities gradually increased from ~3 × 10 -2 to > ~1 × 10 8 Pa s as RH decreased from ~75% to ~25%. Compared with the results for the sucrose/H 2 O particles, binary Ca(NO 3 ) 2 /H 2 O and Mg(NO 3 ) 2 /H 2 O particles showed drastic enhancements to > ~1 × 10 8 Pa s at low RH close to the efflorescence RH. For ternary mixtures of sucrose/Ca(NO 3 ) 2 /H 2 O or sucrose/Mg(NO 3 ) 2 /H 2 O, with organic-to-inorganic mass ratios of 1:1, the 35 viscosities of the particles gradually increased from ~3 × 10 -2 to greater than ~1 × 10 8 Pa s for RH values from ~75% to ~5%. Compared to the viscosities of the Ca(NO 3 ) 2 /H 2 O particles, higher viscosities were observed for the ternary sucrose/Ca(NO 3 ) 2 /H 2 O particles, with values increased by about 1 order of magnitude at 50% RH and about 6 orders of magnitude at 35% RH. Moreover, we applied a thermodynamics-based group-contribution model, AIOMFAC-VISC, to predict aerosol viscosities for the 40 studied systems. The model predictions and viscosity measurements show good agreement within ~ 1 order of magnitude in viscosity. The viscosity measurements indicate that the studied mixed organic– inorganic particles range in phase state from liquid to semi-solid or even solid across the atmospheric RH range at a temperature of 293 K. These results support our understanding that organic/inorganic/H 2 O particles can exist in a liquid, semisolid, Data availability . Underlying material and related data for this paper are provided in the Supplement. Author contributions . MS and YS designed this study. MS and JBL setup and calibrated the viscosity 390 instrument. YS and MS conducted viscosity experiments and analyzed the data. JL and AZ conducted AIOMFAC-VISC model predictions. YS and MS prepared the manuscript with contributions from JL, JBL, AZ, ZJ, and MN.

. Moreover, both of these nitrate salts have a relatively low efflorescence RH in aqueous solutions, enabling viscosity measurements of crystal-free solutions from high RH down to at least 30 % RH. Using these binary and ternary mixtures, we explore how the viscosities vary as a function of RH and associated 115 aerosol compositions. Such viscosity studies can provide a better knowledge of the physicochemical properties of atmospherically relevant aerosol particles consisting of organic material and inorganic salts.
For ternary mixtures, solutions were prepared at an organic-to-inorganic dry mass ratio (OIR) of 1:1. This dry mass ratio was chosen since it is expected to reveal well the effects of mixing of substantial amounts The movement of the beads at 293 ± 1 K was recorded every 1 s with a CMOS camera (MSC-M 3.0 UCMOS, China) and then quantified at a target RH. The viscosity was calculated from the bead speeds using a calibration line, which produced bead speeds for the sucrose particles at different RH values (see  Figure S2 illustrates the mean bead speeds of each system as a function of the RH. When the bead speeds within a particle are too slow to be observed with this technique (i.e. below 155 ~10 -6 µm⋅m s -1 corresponding to ~10 2 Pa s, see Fig. S1 and S2), we used the poke-and-flow technique (Sect. 2.3). For example, the movement of the beads within Mg(NO3)2/H2O particles at ~35% RH was too slow to be readily observed (Fig. S2). Further information on the calibration and the bead-mobility technique is given in Sect. S1 in the Supplement.  Murray et al. (2012) developed the poke-and-flow technique for phase state determination, which was expanded for the quantification of viscosities > ~10 2 Pa s by Renbaum-Wolff et al. (2013a), Grayson et al. (2015), and Song et al. (2015). This technique uses a small hole on the top of the flow-cell to allow us to poke the particles on the hydrophobic substrate using a sterilized sharp needle (Jung Rim Medical 165 Industrial Co., South Korea). Using a micromanipulator (Narishige, model MO-152, Japan), the needle was controlled in the x-, y-, z-direction. The needle was passed through from the top to the bottom of a particle and then the needle was removed. After poking, the geometrical change of a deposited particle was observed and recorded by an optical microscope (Olympus CKX53 with 40× objective) with a CCD camera (MSC-M 3.0 UCMOS, China). All experiments were carried out at 293 ± 1 K. 170 Figure S3 shows an example of the geometrical changes in the sucrose/H2O, sucrose/Ca(NO3)2/H2O, and sucrose/Mg(NO3)2/H2O particles during pre-poking, poking, and post-poking. Before poking by the needle, the particles had a geometry of a spherical cap. After poking by a needle, a half-torus geometry with an inner hole in the particle was observed. As time progressed, the particle recovered by adopting its original geometry by filling of the hole to minimize the surface energy. The experimental flow time 175 (τ(exp, flow)) was obtained when the area of the inner hole just after poking (t = 0 s. Fig. S3) decreased to 1/4 of the initial inner hole area (Renbaum-Wolff et al., 2013a;Grayson et al., 2015Grayson et al., , 2016Song et al., 2019). Figure S4 shows the τ(exp, flow) at different RH for sucrose/H2O, sucrose/Mg(NO3)2/H2O, and sucrose/Ca(NO3)2/H2O particles. The τ(exp, flow) of the particles was converted to the lower limit to the viscosity using the equation reported in Sellier et al. (2015). Using the poke-and-flow technique, the upper 180 limit to viscosity is unknown in this work. For binary mixtures of inorganic salts/H2O, we were unable to determine the viscosity between 10 2 to 10 8 Pa s because the poke-and-flow technique is not accessible for droplets that are supersaturated with respect to a crystalline state of involved inorganic salts. We also measured the RH value and corresponding viscosity at which the particles cracked. When the particles cracked upon poking, without any detectable flow after a duration of > 5 h at a given RH, we defined a 185 lower limit to the viscosity of 1×10 8 Pa s based on the results of Renbaum-Wolff et al. (2013a), Grayson et al. (2015, 2016, and Song et al. (2019). Further details on these experiments can be found in Sect. S2 of the Supplement. 190 The Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients Viscosity model (AIOMFAC-VISC) is a thermodynamics-based group-contribution model for predicting the viscosity of aqueous organic mixtures (Gervasi et al., 2020). It is an extension module to the AIOMFAC model, which explicitly describes interactions among organic functional groups, inorganic ions, and water (Zuend et al., 2008(Zuend et al., , 2011. The AIOMFAC-VISC model offers predictive estimates of mixture viscosity covering the Briefly, a semi-empirical approach was introduced to predict the mixture viscosity of aqueous electrolyte solutions as a function of temperature, ion activities, and ionic strength. Model parameters for the aqueous ion interaction approach were simultaneously fitted to room temperature viscosity measurements 205 aggregated by Laliberté for many electrolyte solutions (Laliberté, 2007(Laliberté, , 2009). The training dataset for AIOMFAC-VISC did not include measurements for the nitrate salts investigated in this study. For aqueous electrolyte solutions, AIOMFAC-VISC predictions currently achieve an excellent level of accuracy, comparable to that of the fitted expressions by Laliberté (2007). Furthermore, to more accurately capture the water uptake behavior of sucrose as a function of equilibrium RH (i.e. water activity 210 of the solution), the version of AIOMFAC-VISC used to produce the viscosity predictions for the sucrosecontaining systems in this work includes an improved treatment of the ether-group-water interactions of sucrose. Thus, viscosity predictions in this study for aqueous sucrose differ slightly from those of the AIOMFAC-web model version.

AIOMFAC-VISC model
For the viscosities of ternary mixtures, a Zdanovskii-Stokes-Robinson (ZSR) type mixing rule is applied 215 to predict the viscosity of the ternary mixtures of organic material/inorganic salts/H2O. This mixing rule is here adopted for viscosity applications since the AIOMFAC-VISC model does presently not include explicit ion-organic interaction effects on viscosity (only on activity coefficients). Therefore, a mixing rule is required to combine the predictions of the viscosity contributions from the electrolyte-free subsystem (sucrose/H2O) and those from the organic-free aqueous electrolyte subsystem for the viscosity 220 estimation of the full mixture. Generally, the ZSR approach involves combining some physical property of two or more (binary) mixtures at the same RH, often to determine the water content of the whole multicomponent mixture (Zdanovskii, 1936(Zdanovskii, , 1948Stokes and Robinson, 1966 experimental conditions, the shown AIOMFAC-VISC predictions for the ternary systems use an OIR of 1:1, which constrains at each RH level the fractional contributions of mass (f1, f2) from each of the 225 subsystems, sucrose/H2O (1) or salt/H2O (2). The viscosity of the overall mixture is then obtained as ln( /°) = 1 ln( 1 /°) + 2 ln( 2 /°), with ° denoting unit viscosity (1 Pa s); see details in section S5 of the Supplement. Figure 1 shows the RH-dependent viscosities of sucrose/H2O particles obtained using the bead-mobility and poke-and-flow techniques. The viscosities of sucrose/H2O particles were determined to be between ~2 × 10 -1 and ~1 × 10 1 Pa s for RH values of ~85-69%, and between ~5 × 10 3 and ~2 × 10 6 Pa s for RH values of ~50 -37% (Fig. 1). The particles containing sucrose/H2O cracked at ~23% RH when poked 235 with a needle, and restorative flow did not occur over a time span of 5 h (Fig. 2a). Consequently, only a lower limit for the viscosity of ~10 8 Pa s was obtained (Renbaum-Wolff et al., 2013a;Grayson et al., 2015Grayson et al., , 2016Song et al., 2015aSong et al., , 2019. Figure 1 also includes results from previous studies for the viscosities of sucrose/H2O particles using different techniques such as bead-mobility, poke-and-flow, holographic optical tweezers, and fluorescence lifetime imaging microscopy (Hosny et al., 2013, Power 240 et al. 2013, Grayson et al., 2015, Song et al., 2015, 2016b. As shown in Fig. 1, the viscosities for the sucrose/H2O particles from this study and previous studies are consistent within ~ 1 order of magnitude at given RH values. Using the entire dataset, it suggests that the sucrose/H2O particle are in a liquid phase state for RH > ~65%, in a semi-solid phase state for ~25% < RH < ~65%, and in a semi-solid or solid phase state for RH < ~23%. determined at 293 ± 1 K upon dehydration using the bead-mobility and poke-and-flow techniques.  Wahab et al., 2006). The values of the viscosities of the particles at high RH are consistent with our results within ~ 1 order magnitude despite a limited number of data points due to the solubility limit restricting bulk solution measurements to the RH range above 260 70 %. In addition, Fig. 3 shows the viscosities of NaNO3/H2O particles measured by other groups (Haynes, 2015;Rovelli et al., 2019). The viscosities of the NaNO3/H2O particles were similar to those of the Ca(NO3)2/H2O particles for the RH range from ~30 to ~100 %.

Viscosities of particles consisting of sucrose/H2O
During the poke-and-flow experiments, the Mg(NO3)2/H2O or Ca(NO3)2/H2O particles cracked when poked with a needle at RH values of 30% and 5%, respectively. At these RH levels, noticeable restorative 265 flow did not occur for over 5 h ( Fig. 2b and c), which resulted in a lower estimated limit for the viscosity (~10 8 Pa s) at the given RH values. The RH value where the particles shattered is similar to the efflorescence RH (ERH) of Mg(NO3)2/H2O and, in case of Ca(NO3)2. The ERH of Mg(NO3)2/H2O is known to be ~30% at 298 K (Li et al., 2008;Wang et al., 2015b) and RH of crystallization for Ca(NO3)2/H2O is reported to be ~7% at 298 K (Liu et al., 2008). In this study, we optically observed an 270 ERH of 32.0 ± 2.5% for Mg(NO3)2/H2O particles (i.e. Fig. S5b), but we did not optically observe the ERH of Ca(NO3)2/H2O at 293 ± 1 K with decreasing RH (Fig. S5c) RH for the RH range from ~60 to 30% (Fig. 3). The difference in viscosities is likely due to the higher hygroscopicity of dissolved Mg(NO3)2 compared to Ca(NO3)2 (Guo et al., 2019). The Ca(NO3)2/H2O 280 particles were of a liquid phase state at RH > ~10%, and a semi-solid or solid phase state at RH < ~5%.
The Mg(NO3)2/H2O particles were of a liquid phase state at RH > ~35%, and a semi-solid or solid phases state at RH < ~30%. Based on the viscosity measurement, both inorganic particles underwent a phase change from liquid (<10 2 Pa s) to semi-solid or solid (>10 2 Pa s ) within a narrow RH range (Fig. 3) compared to the sucrose/H2O particles (Fig. 1). Indeed, this discontinuity in viscosity with decreasing RH 285 suggests a phase transition.
For sucrose/Mg(NO3)2/H2O particles, the viscosities ranged from ~7 × 10 -2 to ~1 × 10 1 Pa s for RH values 300 ranging from ~70 to ~35%, and from ~2 × 10 4 to ~2 × 10 5 Pa s for the RH ranging from ~17 to ~11% (Fig. 4c). The sucrose/Ca(NO3)2/H2O particles cracked at ~6% RH without flow over 5 h (Fig. 5b); and thus the lower limit of the viscosity was determined to be ~10 8 Pa s. These results imply that the sucrose/Ca(NO3)2/H2O particles are in a liquid phase state at RH > ~ 35%, a semi-solid phase state for 17% < RH < 11%, and a semi-solid or solid phase state at RH < ~6%. As shown in Figs. 4a and 4c, the RH, and ~6 orders of magnitude lower at 35% RH than the sucrose/Ca(NO3)2/H2O particles over the same RH range. Both particles experienced a phase state change from a liquid phase state to a semi-solid or even solid phase state with decreasing RH. Finally, although not confirmed by our measurements, it is possible that in one or both of these ternary mixtures a gel phase transition may occur upon sufficient 310 dehydration, as has been observed in mixtures of gluconic acid with CaCl2 (Richards et al., 2020). to the measurements in this study, note that AIOMFAC-VISC assumes that mixtures remain in a 320 metastable state to low water activity (or high solution concentration) and that solutes do not crystallize, which may explain the discrepancy among the model predictions and the measurements in the low RH region shown in Fig. 4b and 4d. Moreover, we note that the training of the AIOMFAC-VISC electrolyte solution model parameters did not include data from this study. The model predictions at RH levels below ~20% represent extrapolations of the model beyond the range of experimental data used in its training. 325 In AIOMFAC-VISC, the prediction of the temperature-dependent pure-component viscosity is based on the experimentally determined, yet uncertain glass transition RH. As such, we include error thresholds of ± 5% in the pure-component glass transition RH in Fig. 4 (Gervasi et al., 2020). Such uncertainty estimates are not necessary for aqueous electrolyte mixtures, so the AIOMFAC-VISC model sensitivity is shown instead, which is defined as the viscosity change due to a ± 2% change in the mass fraction of 1 order of magnitude from high RH to about 30 % RH (considering measurement uncertainty). In the case 335 of the ternary sucrose/Ca(NO3)2/H2O system, the model-measurement deviation increases to about 1.5 orders of magnitude in viscosity at 30% RH and lower, with AIOMFAC-VISC underestimating the measured viscosity. This result may be explained at least in part by the model predicting substantially lower viscosities for the binary aqueous Ca(NO3)2 system in this lower RH range, which affects the predictions for the ternary system via the deployed mixing rule. The good agreement between model and 340 measurements for the ternary sucrose/Mg(NO3)2/H2O system, even at low RH levels, may be interpreted as indicative of suppressed salt crystallization in the presence of sucrose, since no discontinuities in viscosity are observed (in contrast to the measurements for the binary salt particles). 345 Herein, we measured the RH-dependent viscosities at 293 ± 1 K for particles consisting of organic material/H2O, inorganic salt/H2O, and organic material/inorganic salt/H2O upon dehydration using the bead-mobility and poke-and-flow techniques. We selected sucrose as the organic species because previous studies have frequently applied it as a surrogate species of SOA and this organic offers favorable properties for measurements. Ca(NO3)2 and Mg(NO3)2 were selected as the inorganic salts for viscosity 350 measurements because these inorganic salts have been frequently observed from mineral dust and sea salt particles (Usher et al., 2003;Laskin et al., 2005;Sullivan et al., 2007). For the binary mixtures, the obtained viscosity of the sucrose/H2O particles agreed well with those reported in previous studies, i.e. mixture viscosities <10 2 Pa s at RH > ~65%, which corresponds to a liquid phase state; mixture viscosities of ~10 2 to 10 8 Pa s at RH values between ~65 and ~25%, which correspond to a semi-solid phase state; 355 and mixture viscosities > ~10 8 Pa s at RH < ~25%, which correspond to semi-solid or amorphous (or crystalline) solid phase states (Power et al., 2013;Grayson et al., 2016b;Song et al., 2016b;Rothfuss and Petters, 2017;Rovelli et al., 2019). Upon dehydration, we also quantified the viscosities of the inorganic salts. The viscosities of the Mg(NO3)2/H2O particles were to be < ~4 × 10 -2 Pa s for RH > ~35%, and > ~10 8 Pa s for RH < ~31%, whereas those of the Ca(NO3)2/H2O particles were < ~9 × 10 0 Pa s for RH > 360 ~10% and > ~10 8 Pa s for RH < ~10%. The particles containing either of these two inorganic salts cracked upon poking when the RH reached a value near the salt's ERH and/or the phase transition RH from a https://doi.org/10.5194/acp-2021-110 Preprint. droplet to a solid phase state. These inorganic particles exhibited a sudden enhancement in the viscosity when the particle effloresced. In contrast, sucrose/H2O particles showed a smooth enhancement in the viscosity with decreasing RH; this means that the viscosity of sucrose/H2O particles gradually approached 365 their glass transition RH. The AIOMFAC-VISC model prediction and viscosity measurements showed a good agreement within ~ 1 order of magnitude, especially at RH levels above 30%, where applicable. For sucrose/Ca(NO3)2/H2O particles and sucrose/Mg(NO3)2/H2O, predicted and measured viscosities showed good agreement over the whole RH range.

Conclusion and atmospheric implications
The phase states of aerosol particles have an impact on rate and potential for heterogeneous reactions as 370 well as consequences for the resulting mass concentration of aerosol particles. The uptake coefficient of gas phase oxidants depends on the phase states of aerosol particles (George et al., 2010;Xiao et al., 2011;Kuwata et al., 2012;Slade and Knopf, 2014;Davies and Wilson, 2015;Berkemeier et al., 2016;Li et al., 2020;Xu et al., 2020). For example, ozone uptake coefficients (γO3) decreased by an order of magnitude in a semi-solid phase state compared to a liquid phase state (Steimer et al., 2015). Moreover, the effective 375 mass concentration of aerosol particles can depend on the (assumed or modelled) phase state of aerosol particles (Shiraiwa and Seinfeld, 2012;Yli-Juuti et al., 2017;Kim et al., 2019). If a liquid aerosol phase state is assumed, the mass concentration may be overpredicted by up to one order of magnitude (Shiraiwa and Seinfeld, 2012). Based on the measurements and calculations, our results show that the studied aerosol particles consisting of organic material/inorganic salt/H2O range from liquid to semi-solid or solid 380 phase states depending on the RH. A caveat is that a single OIR of 1:1 and relatively simple aerosol systems were used compared to the multicomponent-multiphase particles likely occurring in the real atmosphere (Murphy et al., 2006;Jimenez et al., 2009;Song et al., 2010Song et al., , 2013Huang et al., 2015;Cheng et al., 2016). Additional investigations are required to further explore and quantify how the viscosities and phase states of mixed organic-inorganic particles vary with the OIR, temperature, and functional 385 group complexity.   K (Hosny et al., 2013, Power et al. 2013, Grayson et al., 2015, Song et al., 2015, 2016b and this study. The error bars in relative humidity (RH) were generated from the calibrated RH uncertainty and the standard deviation from grouped viscosity data (grouped by RH ranges) which included at least 3 data points. The error bars in viscosities were produced by 95% prediction bands of viscosities (Fig. S1).    (Abdulagatov et al., 2004;Wahab et al., 2006;Haynes, 2015) and this study. Also, viscosities of NaNO3/H2O from previous studies are included (CRC Handbook;Rovelli et al., 2019). Upward arrows represent a lower limit for the viscosities of the particles calculated by the experimental flow time and the equation reported in Sellier et al. (2015). The error bars in relative humidity (RH) were generated from 425 combined RH sensor uncertainty and the standard deviation from the grouped viscosity data by RH, which included at least 3 data points. The error bars in viscosities were produced by 95% prediction bands of viscosities (Fig. S1). Light blue region indicates a liquid phase, and light green region indicates a semisolid phase.