Resolving the mechanisms of hygroscopic growth and cloud condensation nuclei activity for organic particulate matter

Hygroscopic growth and cloud condensation nuclei activation are key processes for accurately modeling the climate impacts of organic particulate matter. Nevertheless, the microphysical mechanisms of these processes remain unresolved. Here we report complex thermodynamic behaviors, including humidity-dependent hygroscopicity, diameter-dependent cloud condensation nuclei activity, and liquid–liquid phase separation in the laboratory for biogenically derived secondary organic material representative of similar atmospheric organic particulate matter. These behaviors can be explained by the non-ideal mixing of water with hydrophobic and hydrophilic organic components. The non-ideality-driven liquid–liquid phase separation further enhances water uptake and induces lowered surface tension at high relative humidity, which result in a lower barrier to cloud condensation nuclei activation. By comparison, secondary organic material representing anthropogenic sources does not exhibit complex thermodynamic behavior. The combined results highlight the importance of detailed thermodynamic representations of the hygroscopicity and cloud condensation nuclei activity in models of the Earth’s climate system.


Thermodynamic Modeling
The observed thermodynamic behaviors of biogenically-derived SOM were simulated using a coupled Flory-Huggins-Köhler model framework. The Flory-Huggins solution theory was originally developed for describing the interaction between long-chain polymers with solutions 1, 2 . The Flory-Huggins model uses volume fractions instead of molar fractions, because the solute and solvent molecules can be very different in size. It is formulated as a free energy function, from which chemical potential of each compound can be derived. The free energy function includes contributions from both the entropic term of ideal mixing, and the enthalpic term of non-ideal interactions. The enthalpic term can be described by the interaction parameter χ. The original Flory-Huggins model with a constant χ does not account for the concentrationdependent interaction of hydrogen bonding for organics in water. This effect can be taken into account using a concentration-dependent χ 3 .
Within the atmospheric sciences, Petters et al. 4 has coupled the Flory-Huggins theory to the Köhler theory to model the hygroscopic growth and cloud forming behaviors of atmospherically relevant oligomers and polymers. In the present work, this Flory-Huggins-Köhler framework has been further developed for modeling the thermodynamics of SOM with water. In brief, the original binary model was extended to a ternary form for modeling complex mixtures. Possible LLPS state and the composition for each liquid phase were calculated by minimizing the free energy. Surface tension of the gas-particle interface was calculated based on the predicted composition of particle surface. A minimum monolayer thickness of the outer shell phase was considered, similar to the treatment of organic film models in recent literature by Ruehl et al. 5 and Ovadnevaite et al. 6 , and the effect of partial surface coverage for surface tension was accounted.

Flory-Huggins Model for Water Activity
A detailed derivation for the ternary Flory-Huggins equations has been provided in ref. 7 , and only a synopsis is provided herein. The general form of the free energy density function f for an aqueous solution can be expressed as: where R is the gas constant, T is the absolute temperature, 0 v is the molar volume of water, i v is the molar volume of compound i, i φ is the volume fraction of compound i, is the ratio of molar volumes, and ij χ is the Flory-Huggins interaction parameter between compounds i and j. The first and second terms on the right-hand side represent the entropic and enthalpic contributions, respectively.
The chemical potential of compound i, µi, can be derived using the equation below: ( ) For a ternary mixture, the chemical potential for water (compound 0) can be written as 7 : For the binary case ( 1 φ φ = , and 2 0 φ = ), Eq. S3 can be reduced to: which is consistent with the binary Flory-Huggins equation in literature 4 . ϕ-dependent interaction parameter χ between water and SOM can be obtained from the sorption isotherm measured by the QCM using Eq. S5. The measured values of χ, as illustrated in Supplementary   Fig. 3, are parameterized as a function of ϕ using the equation below 4, 8 : The fitted values of ψ, ν, and β are listed in Supplementary Table 1. For the ternary case, it is assumed that small fractions of the α-pinene-and limonenederived SOMs are hydrophobic (a1 = ϕ1 / (ϕ1 + ϕ2) = 5-7%; Supplementary Table 1). This assumption is based on the experimental results that ~93% of the α-pinene-derived SOM is water soluble, and ~7% is water insoluble but methanol soluble, following the mass spectrometry analysis described in Kuwata and Lee 9 . We further assume that the interaction parameter of hydrophobic organic component with water has a large value χ01, while the interaction parameter between hydrophobic and hydrophilic components χ12 is relatively small (Supplementary Table  1). When the hydrophobic and hydrophilic components are treated as a single compound ( 1 2 φ φ φ = + ), the equivalent interaction parameter of total SOM with water can be derived by comparing Eq. S5 with Eq. S4: The interaction parameter χ02 between hydrophilic component and water can be calculated from the values of χ, χ01, χ12 and a1 (Supplementary Table 1).

Liquid-liquid Phase Separation
For a binary mixture, miscibility gap and co-existence of two liquid phases with different mixing ratios can occur when there is a strong interaction between solute and solvent 4 . Such behavior, however, is not predicted based on the χ values derived from experiments. For a multicomponent system, liquid-liquid phase separation (LLPS) states more generally occur when a separated two-phase configuration has a free energy lower than a miscible single-phase configuration. This general case of LLPS can be more applicable to the multicomponent laboratory SOM and ambient aerosol particles. In the present study, a minimal representation of the LLPS state requires a ternary system.
The LLPS algorithm, implemented in the present study in MATLAB, are similar to that presented in ref 10 . For a series of water-to-organic ratios, values of the free energy density function (Eq. S1) were calculated assuming a two-phase configuration. For each compounds, partition between two liquid phases was calculated by minimizing the total free energy using a Differential Evolution algorithm 10 . The initial guess was taken from the optimized results of the previous step, which had a similar water-to-organic ratio. To further minimize errors associated with initial guesses, calculations were performed for both increasing and decreasing water-toorganic ratios, and the results with lower free energy were taken. The algorithm found identical composition for the two phases when the single-phase configuration was stable. LLPS states can be identified by the significant different compositions between two phases resulted from the optimization. As a validation, water activities were calculated for both phases using Eq. S3, and the values were always identical for a fixed water-to-organic ratio.

Surface Tension and the Köhler Theory
The treatment of surface tension generally follows the method described in ref. 6  In the presence of LLPS, the organic-rich phase having a lower surface tension tends to occupy the shell of the particle to minimize the total free energy. For a growing droplet, however, the organic-rich phase may eventually not fully cover the droplet surface, because a minimum thickness δ, corresponding to a molecular single layer, is required. In the present study, a δ value of 0.3 nm was used (Supplementary Table 1). As an important adjustable parameter, the δ value used herein was comparable to the values used in recent literature 5,6 . For the partial coverage case, the effective surface tension σeff was computed as a surface-area-weighted mean of both phases.
Combining water activity aw derived from the Flory-Huggins model with the effective surface tension σeff, the Köhler curve can be expressed as: where Mw and ρw represent the molecular weight and material density of water, respectively. D is the wet diameter of the droplet, and S is the saturation ratio. Supersaturation can be calculated as ss = (S-1)×100%. The critical supersaturation sc is defined as the maxima of the Köhler curve. Aerosol Mass Spectrometer (HR-TOF-AMS). Analysis was based on the explicit approach described by Chen et al. 17 . c Values calculated from the O:C and H:C ratios using the method of Kuwata et al. 18 .

List of Supplementary Figures
Supplementary Figure 1. (a) Conceptual framework of hygroscopic growth of a secondary organic aerosol particle based on the assumption of solubility limits. The dry particle is composed of organic compounds with different degrees of solubility. The wet particle consists of an insoluble organic core and an aqueous shell with organics dissolved in water. (b) Conceptual framework of hygroscopic growth of an amorphous organic particle undertaken gradual deliquescence. Organics and water form one uniform amorphous phase at low RH. The concentration of a single organic compound may exceed its solubility limit. Liquid-liquid phase separation can occur at high RH for some types of secondary organic material. Organic-rich

Supplementary
Supplementary Figure 1 (A) Conceptual framework of hygroscopic growth of a secondary organic aerosol particle based on the assumption of solubility limits. The dry particle is composed of organic compounds with different degrees of solubility. The wet particle consists of an insoluble organic core and an aqueous shell with organics dissolved in water. (B) Conceptual framework of hygroscopic growth of an amorphous organic particle undertaken gradual deliquescence. Organics and water form one uniform amorphous phase at low RH. The concentration of a single organic compound may exceed its solubility limit. Liquid-liquid phase separation can occur at high RH for some types of secondary organic material.