DOI: 10.1021/la900867k 12177 Langmuir 2009, 25(20), 12177–12184 Published on Web 09/15/2009 pubs.acs.org/Langmuir © 2009 American Chemical Society Nonequilibrium Phase Transformations at the Air-Liquid Interface Christoffer A ˚ berg,* ,† Emma Sparr, † Karen J. Edler, ‡ and Ha˚kan Wennerstr€ om † † Physical Chemistry, Lund University, SE-221 00 Lund, Sweden, and ‡ Chemistry Department, University of Bath, Bath BA2 7AY, U.K. Received March 11, 2009. Revised Manuscript Received July 12, 2009 A theoretical model is presented for the formation of an ordered phase close to the air-liquid interface of an open binary aqueous solution. The chemical potential of water in the liquid phase is, in general, not equal to the chemical potential of water in the ambient atmosphere. There are therefore nonequilibrium conditions close to the air-liquid interface. There is also a gradient in the chemical potential of water, which could lead to the formation of a new interfacial phase. The formation of an interfacial phase is analyzed in terms of the equilibrium phase behavior corresponding to the local water chemical potential. The possibility of forming an interfacial phase is strongly dependent on the ambient conditions, bulk composition, and diffusive transport properties of the phases in question. Explicit calculations are presented for the formation of a lamellar liquid-crystalline phase close to the air-liquid interface of an isotropic surfactant solution with parameters chosen from the sodium bis(2-ethylhexyl)sulfosuccinate (AOT)/water system. We consider the relevance of the model to neutron reflectivity studies of the interface between air and surfactant/ water systems, as well as to surfactant/polymer/water systems. 1. Introduction When a liquid sample is exposed to ambient air, there are typically nonequilibrium conditions at the interface. Volatile compounds in the liquid tend to evaporate into the air, while nitrogen, oxygen, and carbon dioxide in the air can dissolve in the liquid phase. The driving force for such events is a gradient in the chemical potential of the different components. Such transport processes can give rise to local thermodynamic properties in the interfacial part of the liquid that differ from bulk values. One example of this is the slight dip in temperature that occurs at the interface between (pure) water and air with a relative humidity (RH) below 100%. 1 For aqueous solutions and water/solvent mixtures, the selective evaporation of water in general gives rise to local changes in concentration, which can have important prac- tical consequences. 2 For the case in which the bulk system is close to a phase separation, the interfacial gradients in concentration and thus in chemical potential can result in the local formation of new phases. In this work, we explore this possibility for binary systems of water and an amphiphile. Spontaneous film formation at the air-liquid interface of mixtures of a cationic surfactant with polyethylenimine (PEI) has previously been reported by one of us. 3-6 The films can be made highly ordered and macroscopically (micrometer) thick. A similar film can also be seen in solutions with a mixture of cationic and anionic surfactants and a water-soluble polymer. 7,8 In this case, the resulting film is sufficiently robust to be removed from the air- liquid interface, even without the help of a cross-linking agent. From these studies, we emphasize in particular the observation that film formation is prevented by increasing the relative humidity in the container. This supports the view, central to the current work, that the formation of the film is due to a difference in water chemical potential between the ambient atmosphere and the bulk solution. In other words, the system is not at equilibrium, and the relevant situation is instead the steady state that forms after an initial induction period. However, we assume that locally at each position there is equilibrium, so that the part of the solution closest to the air-liquid interface will be in local equilibrium with the atmos- phere. Dry ambient conditions therefore correspond to a consider- ably lower chemical potential of the water close to the interface than in the bulk solution. From this point of view, it is not surprising that the more ordered phases, which form at low water chemical potentials in surfactant systems, can be found close to the air-liquid interface. In essence, a thin layer of the condensed phase can potentially span the full equilibrium phase diagram, from the bulk solution composition to the composition that represents equilibrium with the ambient air. We note that an analogous situation is found in the so-called penetration scan method of monitoring phase equilibria in binary water/amphiphile systems, 9 as well as studies of surfactant dissolution in water. 10-12 A related problem is the dynamic behavior of an oil phase in contact with an aqueous surfactant solution. Miller and co-workers have conducted exten- sive studies of this problem and have noted the common appearance of an intermediate phase close to the original oil -water interface. 13 The paper is organized as follows. In the next section, we outline a general theoretical model for the description of the *Corresponding author. Tel: þ353 1 716 2447. Fax: þ353 1 716 2415. E-mail: christoffer.aberg@gmail.com. (1) Cammenga, H. K.; Schreiber, D.; Rudolph, B. E. J. Colloid Interface Sci. 1983, 92, 181–188. (2) Kabalnov, A.; Wennerstr€ om, H. Manuscript in preparation. (3) O’Driscoll, B. M. D.; Fernandez-Martin, C.; Wilson, R. D.; Knott, J.; Roser, S. J.; Edler, K. J. 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