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Surfactants exist in atmospheric aerosols mixed with inorganic salts and can significantly influence the formation of cloud droplets due to bulk–surface partitioning and surface tension depression. To model these processes, we need continuous parametrizations of the concentration dependent properties of aqueous surfactant–salt solutions for the full composition range from pure water to pure surfactant or salt. We have developed density functions based on the pseudo-separation method and Young's mixing rule for apparent partial molal volumes for solutions that mimic atmospheric droplets of marine environments. The developed framework requires only model parameters from binary water–salt and water–surfactant systems and includes the effect of salinity on micellization with composition-dependent functions for the critical micelle concentration (CMC). We evaluate different models and data available in the literature to find the most suitable representations of the apparent partial molal volume of sodium chloride (NaCl) in aqueous solutions and the CMC of selected atmospheric and model surfactants in pure water and aqueous NaCl solutions. We compare model results to experimental density data, available in the literature and obtained from additional measurements, for aqueous solutions containing one of the ionic surfactants sodium octanoate, sodium decanoate, sodium dodecanoate or sodium dodecylsulfate mixed with NaCl in different relative ratios. Our model follows the experimental trends of increasing densities with increasing surfactant concentrations or increasing surfactant–salt mixing ratios both, below and above the CMC, capturing the effect of the inorganic salt on the surfactant micellization. [ABSTRACT FROM AUTHOR]

We introduce the CMC based Ionic Surfactant Activity model (CISA) to calculate activity coefficients in ternary aqueous solutions of an ionic surfactant and an inorganic salt. The surfactant can be either anionic or cationic and in the present development, the surfactant and inorganic salts share a common counterion. CISA incorporates micellization into the Pitzer–Debye–Hückel (PDH) framework for activities of mixed electrolyte solutions. To reduce computing requirements, a parametrization of the critical micelle concentration (CMC) is used to estimate the degree of micellization instead of explicit equilibrium calculations. For both binary and ternary systems, CISA only requires binary experimentally-based parameters to describe water–ion interactions and temperature–composition dependency of the CMC. The CISA model is intended in particular for atmospheric applications, where higher-order solution interaction parameters are typically not constrained by experiments and the description must be reliable across a wide range of compositions. We evaluate the model against experimental activity data for binary aqueous solutions of ionic surfactants sodium octanoate and sodium decanoate, as common components of atmospheric aerosols, and sodium dodecylsulfate, the most commonly used model compound for atmospheric surfactants. Capabilities of the CISA model to describe ternary systems are tested for the water–sodium decanoate–sodium chloride system, a common surrogate for marine background cloud condensation nuclei and to our knowledge the only atmospherically relevant system for which ternary activity data is available. For these systems, CISA is able to provide continuous predictions of activity coefficients both below and above CMC and in all cases gives an improved description of the water activity above the CMC, compared to the alternative model of Burchfield and Wolley [J. Phys. Chem., 88(10), 2149–2155 (1984)]. The water activity is a key parameter governing the formation and equilibrium growth of cloud droplets. The CISA model can be extended from the current form to include the effect of other inorganic salts with the existing database of binary PDH parameters and using appropriate mixing rules to account for ion specificity in the micellization process. [ABSTRACT FROM AUTHOR]