Impact of nonionic surfactants on the water activity of binary and ternary aqueous solutions

Abstract

Atmospheric aerosol droplets have large surface-area-to-volume ratios, leading to bulk-to-surface partitioning. This partitioning affects both the surface tension and water activity of aerosol when strong surfactants are present. The Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model predicts the water activity of solutions containing mixtures of inorganic ions and organic species using a group contribution approach. However, AIOMFAC predictions for the water activity of solutions containing strong surfactants have not been validated against experimental measurements. Here, the water activities of solutions containing strong, nonionic surfactants and their mixtures with NaCl are compared against AIOMFAC model predictions. For molecules with a polyethylene glycol (PEG)-like tail, using the oxyethylene subgroup outperforms an alternative ether and alkyl subgroup approach for representing the repeating molecular substructure. This model–measurement comparison shows the importance of selecting appropriate subgroup descriptions to provide the most accurate predictions of water activity, which could improve predictions of cloud droplet activation.

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Introduction

Sea spray is one of the largest sources of aerosols to the atmosphere and plays a major role in marine cloud formation and light scattering above the world's oceans.¹ Sea spray aerosol contains sea salts, as well as organic molecules from the sea surface microlayer.^2–5 Often, these aerosols are enriched in organic content compared to the sea surface microlayer from where they were generated.^6–10 In the atmosphere, these aerosol particles will change composition to maintain equilibrium with their surroundings. For example, aerosol droplets may condense or evaporate water depending on the relative humidity (RH) of the surrounding air.¹¹ If the solute is nonvolatile (e.g., salts and surfactants), then the total concentration of solute changes during hygroscopic growth and evaporation, but the mole ratio of different solutes remains constant. At equilibrium, the RH is related to the water activity (a_w) of the condensed phase through a_w = RH/100%, for macroscopic systems and droplets larger than about 100 nm in diameter. When droplet size is sufficiently small for surface curvature effects to become important (<100 nm diameter), the Kelvin effect needs to be accounted for as part of the Köhler equation to more accurately describe the relation between water activity (of droplet bulk) and RH: ,¹² where σ is the droplet's surface tension, is the partial molar volume of water, r is the droplet radius, R is the gas constant and T is the temperature.

Surfactants have been identified in sea spray aerosol extracts in concentrations large enough to reduce the surface tension of macroscopic solutions.^8,13,14 Partitioned at the air–droplet interface, these surfactants can reduce the droplet's surface tension.^15–17 A reduced surface tension can impact the hygroscopic growth of aerosol and the supersaturation at which an aerosol droplet is activated into a cloud droplet by reducing the Kelvin term in the Köhler equation.^18–23

Understanding how surface-active organics partition in aerosol droplets has been a focus of recent works. A number of techniques have been developed to measure the surface tension of single aerosol droplets suspended in air.^24–30 These measurements have shown that the high surface-area-to-volume ratio of aerosol droplets can lead to bulk surfactant depletion and a size-dependent surface tension when strong surfactants are present.^15–18 Additionally, molecular dynamics simulations have been used to predict the surface tension in nanometer-sized droplets, which cannot be measured with current experimental methods.^31,32 This concentration and size-dependent surface tension can be predicted using a surfactant partitioning model.^24,33 Various partitioning models have been incorporated into Köhler theory to make predictions of critical supersaturation required for cloud droplet activation of surfactant-containing aerosol droplets.^{19,21,34–37} However, this surfactant bulk-to-surface partitioning also decreases the solute in the aerosol droplet bulk,^38,39 impacting the Raoult term in the Köhler equation.^21,40 Thus, reliable descriptions of water activity for mixtures of salts and surfactants are also necessary.

For mixtures where water activity is unknown, online thermodynamic models are commonly employed to determine activity coefficients of components in solutions and water activity. The Extended Aerosol Inorganics Thermodynamic Model (E-AIM) is capable of calculating the activity coefficients of aqueous solutions containing mixtures of inorganic ions and aqueous mixtures of ions with a small library of carboxylic acids.^41–44 If quantities such as the solubility product, Henry's law constant or vapor pressure, and a model to calculate the activity coefficient are known, users can also define additional organic solutes. The Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model uses a group contribution approach to predict the activity coefficients of a wide range of organics (e.g., alcohols, sugars, carboxylic acids, keytones, ethers, esters, and multifunctional aromatics) in aqueous solutions and their mixtures with an extensive list of inorganic ions.^45–47 Although the online version of the AIOMFAC model does not include any surfactants in its predefined list of example organic molecules, it is possible to describe their chemical structures using appropriate combinations of subgroups. AIOMFAC predictions for the activity coefficients of strong surfactants have been previously used in aerosol research.^21,48 While the predictions from AIOMFAC for small, soluble organics and multifunctional aromatics⁴⁷ as well as low molecular mass organosulfates⁴⁹ have been validated against laboratory measurements, model predictions have not previously been tested for strong surfactants. Validation of these model predictions is necessary to determine the accuracy of predictions for strong surfactants and their mixtures with salts.

In this work, we investigate the impact of nonionic surfactants on water activity using three model surfactant systems. We first measure the water activity of macroscopic aqueous surfactant solutions. We investigate the water activity of mixtures containing different mass ratios of NaCl to strong surfactant at a constant water mass ratio. Next, to mimic hygroscopic growth, we measure water activities of solutions containing a fixed mass ratio of NaCl to surfactant while increasing the water mass fraction. All water activity measurements are compared to predictions from the online version of AIOMFAC, allowing us to validate the model predictions for these strong nonionic surfactants. Finally, we estimate hygroscopicity parameters (κ) for the nonionic surfactants.

Methods

Chemicals

Nonionic surfactants Tween20 (Polysorbate 20, Boston Bioproducts Inc., 100%), Triton X-100 (PerkinElmer, or Sigma-Aldrich, laboratory grade, neat), and octyl-β-D-thioglucopyranoside (OTG, Thermo Scientific, 98+%) were used without further purification. NaCl (Fisher Chemical, certified ACS grade, or VWR, certified ACS grade) was used as a cosolute. Solutions were made with deionized (DI) water with a resistivity of 18 MΩ cm⁻¹. Binary (surfactant and water) and ternary (surfactant, NaCl, and water) solutions were made with mass fraction compositions using an analytical scale (±0.0001 g). Solutions were made in 10–30 mL volumes.

Water activity measurements

Water activity of 8 mL samples were measured using an Aqualab TDL 2 (precision of ±0.005 water activity units). The instrument underwent a multipoint calibration at 293 K using Aqualab water activity standards of 0.250 (13.41 m LiCl in water), 0.500 (8.57 m LiCl in water), 0.760 (6.00 m NaCl in water), and 1.000 (steam distilled water). Water activity standards were also used to verify instrument readings each day. Each sample was measured in triplicate, and average values are reported.

Estimation of water content in `pure' Tween20

Attenuated total internal reflection (ATR) infrared (IR) spectroscopy (Nicolet iS10 FTIR-ATR) was used to collect the IR absorbance of `pure' Tween20 as well as binary solutions with small mass fractions of water. The IR absorbance of the 1649.994 cm⁻¹ water bending vibration was used to obtain a standard addition calibration curve (Fig. S1). In order to convert water mass fraction to a concentration of water for the x-axis, we assume that the mixture is ideal and there is no change in volume upon mixing the two components. We also assume that the density of the mixture can be approximated as the density of pure Tween20 (1.1 g cm⁻³) due to its high mass fraction in the mixture, and its similarity to the density of water (0.998 g cm⁻³). The x-intercept of the calibration curve was found to be 6.88 ± 0.90 M, which corresponds to a water mass fraction of 0.1125 ± 0.0150.

Water activity predictions using AIOMFAC

The online Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model (version 3.12) was used to predict the water activity of solutions containing strong surfactants.^45–47,50 The AIOMFAC-web online model version treats any input mixture as being a well-mixed single-phase solution. However, strong surfactants form monolayers at the air–water interface.^51,52 We expect that this partitioning is negligible in the low surface-area-to-volume ratio of the macroscopic solutions investigated here (see SI text, bulk-to-surface partitioning section). Strong surfactants also undergo a pseudo-phase transition, forming micelles at the surfactant's critical micelle concentration (CMC). The model treats surfactant solutions as solutions consisting of only free surfactant species at all surfactant concentrations. In the online version of AIOMFAC, considering the representation of polyethylene glycol (PEG) and similar molecules, any effects of micelle formation are already implicitly folded into the parameters of the oxyethylene group. However, the AIOMFAC model does explicitly account for the binary interactions between water molecules and the functional groups constituting the organic surfactant molecules, the interactions between water and inorganic cations and anions (such as Na⁺ and Cl⁻), as well as the binary interactions between those ions and organic functional groups. In general, note that the AIOMFAC model's relative size and shape properties of functional groups and the group–group interaction treatment can account, to some extent, for nonideal mixing effects arising due to local non-random molecular/ionic structuring within a solution. Micelles can be considered an example of strong molecular-level solution structuring without forming a separate macroscopic phase.

Strong surfactants are not included in the list of predefined organic molecules. Instead, their structures were built by defining the subgroups of each molecule. OTG contains a sulfur atom, which is not currently included in any AIOMFAC organic subgroup (introduction of an organosulfate group is upcoming). We replace this sulfur atom with oxygen during subgroup selection due to their shared number of valence electrons and similarity in electronegativity. In other cases, e.g. thioglycosides or sulfones, such a substitution may introduce a notable bias or be inadequate. Tween20 and Triton X-100 have hydrophilic tails, which can be either described with CH₂ and CH₂O groups or the CH₂OCH₂ group, which was added to the online AIOMFAC to describe PEG oligomers.⁵⁰ An extended set of interaction parameters between the CH₂OCH₂ group and other functional groups in these surfactant molecules has recently been added to the online model based on an analogy approach (i.e., these parameters are estimated but not fitted to reliable thermodynamic data). The water activities of binary surfactant-water solutions were predicted using both descriptions of the hydrophilic tails. Details of these subgroup descriptions can be found in Fig. S2 and Table S1. All AIOMFAC calculations were run at 293 K.

Results and discussion

Sea spray aerosol droplets contain water, organics, and sea salts.^2,5 In this study, the water activities of binary solutions containing one of three strong nonionic surfactants, Tween20, Triton X-100, or OTG, or ternary solutions with NaCl were measured. These surfactants have a range of surface-active properties and oxygen-to-carbon (O : C) ratios that are in line with environmental surfactants.^10,13,53,54 In macroscopic solutions, these surfactants require tens of micromolar to millimolar concentrations to reduce the surface tension and can reduce the surface tension to 30–40 mN m⁻¹ at the CMC,^16,55 in line with surfactants characterized from sea spray aerosol, the sea surface microlayer^8,13,14 and fog samples.⁵⁶ Additionally, they are commonly used in laboratory experiments as model systems for the surface-active components of the sea surface microlayer.^54,57 NaCl was selected as a cosolute due to its abundance in sea spray aerosol.⁵⁸

First, the water activities of binary surfactant solutions were measured. For these macroscopic samples, water activity is equivalent to RH/100%. Fig. 1 shows the experimentally determined water activities as a function of water mass fraction for each surfactant system. The CMC of Tween20, Triton X-100 and OTG are 0.06 mM (w_water = 0.99993), 0.2 mM (w_water = 0.99987) and 9 mM (w_water = 0.99723), respectively^16,55 (Fig. S3 shows this data plotted on a log-scale to also show each surfactants CMC). Thus, it is expected that micelles or other nanostructures are present in every surfactant-containing solution measured.⁵⁹ Although micelles are likely present in the solutions, all measured samples appeared to be a single macroscopic phase. Tween20 and Triton X-100 are viscous liquids at room temperature, and the water mass fractions of the solutions were altered between 0 and 1. At room temperature, OTG is a solid. The most concentrated OTG sample (w_water = 0.21) was a waxy solid and had a water activity of 0.976. The next most concentrated sample measured (w_water = 0.31) was composed of a single macroscopic liquid phase. At water mass fractions between those of these two samples, coexisting solid and liquid phases were observed.

Fig. 1 Water activity of binary aqueous solutions containing strong nonionic surfactants, (a) Tween20, (b) Triton X-100, and (c) OTG. The solid line shows the predictions from the online version of AIOMFAC, and the data markers show the average of experimental measurements. In panel (c), the model line is shown in reduced opacity where it is hypothetical due to an observed macroscopic phase separations. Error bars in panel a show the uncertainty in water mass fraction propagated through from the linear regression used to estimate the amount of water in the `pure' Tween20 (Fig. S1), where they are larger than the data marker. The data markers are always larger than the standard deviation between measurements and the instrument read error (0.005 water activity units).

The water activity of `pure' Tween20 was found to be 0.3034 and reduced to 0.1170 following desiccation, indicating that the Tween20 contained an unknown amount of residual water. The amount of water in the Tween20 was estimated using a standard addition calibration curve built from the IR-absorbance of the 1649.994 cm<sup>−1</sup> bending vibrational mode of water (Fig. S1). Using this calibration curve, the mass fraction of water in `pure' Tween20 was found to be 0.1125 ± 0.0150. The mass fractions of Tween20 in each sample were then corrected using the mass fraction of residual water. Fig. S4 shows the comparison of the water activity measurements before and after correcting for the residual water mass fraction. The corrected mass fractions are shown in Fig. 1a.

Only relatively large surfactant mass fractions reduce the water activity. For Tween20 in Fig. 1a, a water activity of 1.0 is reached at a water mass fraction of about 0.5. In panel b, the water activity for aqueous Triton X-100 solutions reaches a water activity of 1.0 around a water mass fraction of 0.6. For OTG in panel c, the water activity only reaches 0.98 before its solubility limit is reached, and a water activity of 1.0 is reached when the water mass fraction reaches 0.66.

Water activities of approximately unity that remain unchanged until the surfactant mass fraction is increased to greater than 0.5 suggest that the solute is not strongly interacting with the water solvent and could be explained by a pseudo-phase separation (e.g., surfactant partitioning to the interface or forming micelles). Solute mass fractions of 0.2 or lower (often much lower) are commonly observed to be sufficient to measurably lower the water activity of an aqueous solution.^46,50,60,61 Due to the preferential partitioning of surfactants to the air–droplet interface, their concentration in the solution bulk can be depleted. The extent of bulk depletion depends on droplet size as well as surfactant concentration and surfactant strength.^16,38 For the 8 mL samples that were measured, bulk-to-surface partitioning is not expected to greatly impact the surfactant concentration in the sample bulk (see SI Text and Fig. S5).

Predictions for homogeneous solutions from the online AIOMFAC model are overlaid on Fig. 1 for each surfactant. Tween20 and Triton X-100 have hydrophilic tails with the same repeating subgroup as PEG. The online version of AIOMFAC has recently been updated to include interaction parameters between the oxyethylene group and most available organic subgroups, as well as ions. Previously, interaction parameters between the oxyethylene group and a few neutral AIOMFAC groups (water, hydroxyl, alkyl), as well as with NH⁺₄ and SO²⁻₄ ions, had been introduced into AIOMFAC based on model fits to experimental data.⁵⁰ The interactions between additional ions, including Na⁺ and Cl⁻, have recently been assigned based on an analogy approach, assuming the interaction between the ion and the oxyethylene group can be approximated by the interaction between the ether group and the same ion. This approach has been tested for PEG–NaCl mixtures, and the mean molal ion activity coefficients and water activities agree well with data available in the literature (Fig. S6 and S7).^62,63 Here, we use two descriptions of Tween20 and Triton X-100 surfactants: (1) the hydrophilic tail composed of ether and alkyl subgroups and (2) the hydrophilic tail composed of oxyethylene subgroups (Fig. S2 and Table S1), and compare the predictions of water activity to experimental measurements to determine which representation provides more accurate results for aqueous solutions containing these strong surfactants.

In Fig. 1 for Tween20 and Triton X-100, using the ether/alkyl group description as well as for OTG, AIOMFAC outputs water activities >1 at some water mass fractions, which indicates that liquid–liquid phase separation should be the stable state (which the online model does not solve for).^45,64 By determining the points of inflection of the hypothetical Gibbs energy of mixing curve of a binary system (for the single liquid phase case), which coincide with the existence of local minima on the water and organic activity curves, one can construct a good estimate of the extent of liquid–liquid phase separation,^64,65 but this onset is sensitive to group interaction parameters of the model employed. A less accurate, yet straightforward estimation of the extent of liquid–liquid phase separation (e.g., from measurements alone) can be obtained by considering the composition range over which at least one of the components exceeds a mole-fraction-based activity value of 1.0.⁶⁴ Theoretically accurate methods for determining liquid–liquid phase separation in binary and multicomponent mixtures are more involved.^66,67 These strong surfactants do undergo a pseudo-phase transition, forming micelles at the CMC. However, the local minimum in the AIOMFAC water activity predictions (water mass fractions of about 0.99, 0.98, and 0.92 for Tween20, Triton X-100, and OTG, respectively) does not always coincide with the surfactants' pseudo-phase transition at the CMC.

The AIOMFAC predictions for Tween20 and Triton X-100 using the oxyethylene group do not exhibit a signature of macroscopic liquid–liquid phase separation at any surfactant mass fraction, which is in agreement with the experimental observations. Using the oxyethylene group, there is good agreement between the model predictions and the experimental measurements for these surfactants over much of the water activity curve. Although the online version of AIOMFAC assumes a homogeneous solution and does not consider the formation of micelles or other nanostructures, when using the recommended oxyethylene group, where applicable, the model provides a good estimate of the water activity for solutions containing strong surfactants. By using the oxyethylene group, any effects of micelle formation are implicitly folded into the interaction parameters, unlike the ether-alkyl approach.

In ambient sea spray aerosol, the ratio of organics to salts can vary with formation mechanism, location, and time as well as with droplet size.^7,68,69Fig. 2 shows the water activity of Tween20 solutions containing different mass ratios of NaCl to surfactant (1 : 0, 4 : 1, 3 : 2, 2 : 3, 1 : 4, 0 : 1) while holding the water mass fraction constant at 0.75, 0.85, or 0.95. The two subgroup descriptions of Tween20 are also compared in ternary solutions containing NaCl.

Fig. 2 Water activity of aqueous solutions containing NaCl and Tween20 (a) w_water = 0.75, (b) w_water = 0.85, and (c) w_water = 0.95. The mass fraction of water is held constant while the mass ratio of surfactant to NaCl is varied. The solid line shows the predictions from the online version of AIOMFAC using oxyethylene groups in the hydrophilic tail, the dotted line shows the predictions using ether and alkyl groups in the hydrophilic tail, and the data markers show the average of three experimental measurements. Error bars indicate the instrument precision (±0.005 water activity units), which is always larger than the standard deviation between measurements.

In Fig. 2, the mass ratio of Tween20 to NaCl is increased from left to right, while the mass fraction of water is held constant in each panel. When the mass fraction of Tween20 is equal to zero, the solution is a binary NaCl–water solution, and experimental data agree with the AIOMFAC model. In panel a, showing the highest total solute concentration, there is a slight underprediction of the experimental data by both AIOMFAC subgroup descriptions as the surfactant mass fraction is increased. Under high surfactant to NaCl ratios, the oxyethylene group description is in better agreement with the experimental data than the ether/alkyl group description. In panel b, where the total solute concentration is reduced, there is good agreement with the experimental data by both subgroup descriptions of Tween20 until Tween20 becomes the only solute. As the Tween20 mass fraction reaches 0.15, the oxyethylene group representation provides more accurate predictions of the solution's water activity. In panel c, where the total solute mass fraction is 0.05, the two subgroup descriptions predict nearly identical water activities over the full range of solute ratios.

Fig. S8 and S9 show similar results for mixtures of NaCl with Triton X-100 or OTG, respectively. Due to the limited solubility of the surfactant/salt mixtures, the water mass fraction is held constant at 0.85 and 0.95 for Triton X-100 and only 0.95 for OTG. In Fig. S8a, again, the oxyethylene group shows better agreement with the experimental observations as the ratio of surfactant in the solution increases. In Fig. S8b and S9, where the water mass fraction is held constant at 0.95, similar to Fig. 2c, there good agreement between the model predictions and experimental observations over the full solute ratio range. When the solute concentrations are low both ether/alkyl and oxyethylene subgroup descriptions provide accurate predictions. Under these dilute surfactant concentrations, NaCl, which is well described by AIOMFAC, dominates the reduction of water activity, and the model is less sensitive to the selection of subgroups.

In Fig. 3, water activity measurements are shown for solutions containing a 2 : 1 mass ratio of NaCl to strong surfactant while varying the total mass ratio of solute. As both NaCl and the surfactants are non-volatile, these experiments mimic the hygroscopic growth of aerosol. In Fig. 3, a solid solute was observed in the sample in the region indicated by diagonal gray lines (hatching), and two liquid phases were observable by eye in the sample in the gray shaded region. Under some water mass fractions, three phases were observable (one solid and two liquid phases), which is indicated by the overlapping hatching and shaded regions. Water activity measurements were only collected for samples that appeared to be composed of a single macroscopic phase, although micelles were likely present in the solutions. Macroscopic liquid–liquid phase separations have previously been observed for solutions containing strong nonionic surfactants and ions.^70–72 The size of the biphasic region has been reported to depend on the salting-out capacities of the cation and anion, which are associated with its Gibbs free energy of hydration.⁷² Sodium and chloride ions have relatively low Gibbs free energy of hydration⁷³ compared to many of the ions previously used in studies of the biphasic behavior of ternary salt–nonionic-surfactant–water mixtures.^70,72 This suggests that the biphasic region would be even larger for salts that more strongly salt out organics. The corresponding model predictions carried out with the AIOMFAC online model assume, by design, a single liquid phase (even when that would be unstable). Thus, the model curves in the multi-phase composition range are only shown for information but will not represent the true equilibrium water activity.

Fig. 3 Water activity of ternary aqueous solutions containing NaCl and strong nonionic surfactants, (a) Tween20, (b) Triton X-100, and (c) OTG. The mass ratio of NaCl : surfactant is held constant at 2 : 1 for measurements (blue circles). Data markers are larger than the standard deviation between measurements and the instrument precision (±0.005 water activity units). In panels (a) and (b), the solid red line shows the AIOMFAC predictions for the mixture using the oxyethylene group, and the dotted red line shows predictions using the ether and alkyl groups. Model lines are shown in reduced opacity where they are nonpredictive due to observed macroscopic phase separations. In panels a and b, the oxyethylene group descriptions are used for the surfactant only line. The hatched region indicates where a solid phase was observed in the sample, and the shading indicates where two macroscopic liquid phases were observable by eye. Where the hatching and shaded regions overlap, three coexisting phases were observed. Note that all shown model predictions are for the assumption of a single well-mixed liquid phase.

In Fig. 3a, for Tween20, the measured water activities fall above the AIOMFAC predictions at the highest surfactant mass fractions (≤0.05 water activity units). In this mixture with twice as much NaCl by mass as surfactant, the AIOMFAC predictions using ether/alkyl groups and oxyethylene groups are nearly identical in the region where a single macroscopic phase was observed and agree well with the water activity measurements. The predicted water activities for a solution with the same water mass fraction but only NaCl or Tween20 solute are also shown. The water activity of the 2 : 1 mixture is closer to, but visually offset from the NaCl-only line, indicating that the contribution from the ions dominates the water activity in the mixture. However, contributions from the surfactant do impact the water activity as the total solute mass fraction increases. A similar trend can be observed in panel b for Triton X-100, but the solubility of the solute limits the surfactant mass fraction range to lower mass fractions. In panel c, the OTG and NaCl mixture has poor solubility, and the water activities of the solutions are dominated by the dissolved ions.

Finally, we investigate the hygroscopicity of the three nonionic surfactants. Radial growth factors were calculated for each surfactant, assuming ideal mixing of water and each surfactant (i.e., a change in droplet volume can be used to determine the change in water mass). For Tween20 and Triton X-100, we use the oxyethylene subgroup description as it better agrees with the experimental observations (Fig. 1). See the SI for further description of radial growth factor calculations. The radial growth factor curves are shown in Fig. 4. All of the surfactants show low hygroscopic growth, with radial growth factors of 1.3, 1.2, and 1.1 at 95% RH for Tween20, Triton X-100, and OTG, respectively. We also estimate the hygroscopicity parameter, κ, for each of these surfactants. For Tween20, Triton X-100, and OTG, κ is found to be 0.06, 0.03, and 0.02 at 95%, respectively. κ at 85 and 90% RH are also determined and provided in Table S2. Under these RH conditions, κ is always found to be 0.1 or lower. These values are in the range of other surface active organics (e.g., fulvic acid) as well as secondary organic aerosol generated from α- and β-pinene,⁷⁴ and can be used to approximate the hygroscopicity of strong, nonionic surfactants.

Fig. 4 Radial growth factor as a function of relative humidity for Tween20, Triton X-100, and OTG. Radial growth curves were calculated using a 50 nm radius dry particle, assuming ideal mixing.

Conclusions

Overall, the online AIOMFAC model provides good estimates of the water activity of strong nonionic surfactant solutions and their mixtures with NaCl, even though it does not consider the formation of micelles. The analogy approach used to describe the oxyethylene subgroup in the hydrophilic tail of a strong surfactant with Na⁺, Cl⁻, and organic subgroups not present in PEG, provides a significant improvement over the ether/alkyl subgroup approach. The online model has been updated to now use this analogy approach with all other inorganic ions. To further improve the predictions for strong surfactants, future work will focus on fitting AIOMFAC for the specific ion and additional organic subgroup interactions of interest (e.g., aromatic carbons, carboxyl, and improved interactions with CH_n). Further improvements may also be achieved by considering the weak temperature dependence over the atmospherically relevant temperature range.^60,75,76

This model-measurement comparison highlights the importance of selecting the appropriate subgroup description to provide the most accurate predictions of water activity. We encourage online-AIOMFAC users to utilize the oxyethylene subgroup for molecules that contain this subunit. Recently, a method to convert SMILES code descriptions of molecular structures into a set of corresponding molecular subgroups has been made available.⁷⁷ This tool will select the oxyethylene subgroup when two such subgroups are present in succession in a given molecular structure. Accurate size- and composition-dependent descriptions of water activity, in addition to surface tension, for aerosols containing strong surfactants could improve predictions of hygroscopic growth and cloud droplet activation. Future work will further explore the impacts of surfactants on water activity during hygroscopic growth, accounting for the impacts of bulk depletion on both water activity and surface tension.

The observed phase behavior of mixtures of NaCl and nonionic surfactants highlights an additional layer of complexity in understanding the impact of surfactants on aerosol hygroscopic growth and cloud droplet activation. First, liquid–liquid phase separation can alter the surface tension of the aerosol droplet.^20,29 Second, near the solubility limit of the 2 : 1 NaCl : surfactant mixtures, the mixtures became highly viscous, gel-like, and waxy. Water diffusion may be kinetically limited through such phases,⁷⁸ which could also impact the ability of aerosol droplets to undergo hygroscopic growth and cloud droplet activation. Further work is necessary to understand the complexities of phase-state in surfactant-containing aerosol and how this impacts hygroscopic growth and cloud droplet activation.

Conflicts of interest

There are no conflicts to declare.

Data availability

Data for this article, including water activity measurements, are available at https://doi.org/10.7267/6w924n102.

Supplementary Information (SI): additional figures and tables detailing subgroup descriptions of surfactants in AIOMFAC. Additional figures showing results of model testing for the analogy approach of oxyethylene groups with ions in AIOMFAC. Additional figures showing the water activity as a function of changing the solute mass ratio for Triton X-100 and OTG surfactants. Supplementary text describing bulk-to-surface partitioning in our samples and hygroscopicity calculations. Additional table showing hygroscopicity parameters at 85, 90, and 95% RH. See DOI: https://doi.org/10.1039/d5cp03917g.

Acknowledgements

AB acknowledges the National Science Foundation (NSF) for financial support through award number 2503671. AZ acknowledges funding support from the Natural Sciences and Engineering Research Council of Canada (NSERC), grant no. RGPIN-2021-02688. EKW acknowledges financial support from the Oregon State University Provost's Distinguished Graduate Fellowship. EKW acknowledges Dr Jie Zhang for help with IR spectroscopy.

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