Abstract
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.
Highlights
Surfactants, molecules containing both hydrophobic and hydrophilic parts, are important for a number of atmospheric processes (Brimblecombe and Latif 2004), including cloud formation (McFiggans et al 2006; Lin et al 2018), interfacial transport (Abbatt et al 2012) and heterogeneous chemistry (Rossignol et al 2016)
Calculated values for the mean ionic activity coefficients of NaOct, NaDec and NaDS are shown in panels a), c) and e), respectively, while the corresponding activity of water as a function of the surfactant mole fraction in their aqueous solutions is shown in panels b), d) and f)
We present the critical micelle concentration (CMC) based Ionic Surfactant Activity model (CISA) model to estimate ionic activity coefficients and water activity in aqueous surfactant solutions with or without added inorganic salt
Summary
Surfactants, molecules containing both hydrophobic and hydrophilic parts, are important for a number of atmospheric processes (Brimblecombe and Latif 2004), including cloud formation (McFiggans et al 2006; Lin et al 2018), interfacial transport (Abbatt et al 2012) and heterogeneous chemistry (Rossignol et al 2016). A different approach was taken by Kim and Frederick (1988a), who applied the Pitzer model to aqueous surfactant solutions and reported interaction parameters for C1–C8 fatty acid sodium salts (formate, propionate, butyrate, valerate, caprylate, pelargonate, caprate). These were obtained by fitting experimental data of osmotic coefficients, but disregarded micelle formation as an important source of non-idealities for especially the larger anions. We present an activity coefficient model that uses interaction parameters from binary electrolyte–water systems to predict the properties of aqueous multielectrolyte ionic surfactant solutions including micellization. The CISA model is compared with results from the model by Burchfield and Woolley (1984), which is based on the Guggenheim–Scatchard theory to describe deviation from ideal solution behaviour and numerically simpler, but requires specific model parameters for higher order solutions
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