Surface tension of chemically complex aqueous droplets is significant to atmospheric aerosol particle dynamics and fate. Isotherm-based predictive surface tension models are available which consider one layer of solute molecules sorbed at the liquidvapor interface. However, the concentration depth profile (CDP) of solute molecules near the surface is continuous, making the single monolayer assumption inappropriate. Here, this work extends the isotherm framework by dividing the surface region into multiple layers to capture the continuity of the spatial distribution of solute molecules for binary solutions. Partition functions are established based on the displacement of water molecules by solute molecules. The number of displaced water molecules and energy of solute molecules at the surface and in the bulk are key model parameters relating surface tension and solute activity. Number densities of surface molecules from molecular dynamic (MD) simulations available in the literature are applied to determine model parameters. Finally, the model is extended to predict surface tension for mixture solutions, considering both independent and dependent adsorptions of different solute species to the liquidvapor interface. The proposed model works well for both electrolyte and nonelectrolyte solutions and their mixtures from pure solvent to pure solute.
Bibliographical noteFunding Information:
This material is based upon work supported by the National Science Foundation under NSF CAREER Grant no. 1554936. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF). The authors would also like to thank Dr. Wieslaw Suszynski at the Coating Process Fundamentals Lab in the Department of Chemical Engineering and Materials Science at the University of Minnesota. Besides, many thanks to Prof. Hallie Chelmo from the University of North Dakota for the discussion about the molecule adsorption mechanism and to Dr. Mária Lbadaoui-Darvas from EPFL in Switzerland for the help with organic solute molecule distribution at the surface.
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