Colloids and surfaces a: physicochemical and engineering aspects

Colloids and Surfaces A: Physicochemical and Engineering Aspects 167 (2000) 31 – 46 www.elsevier.nl/locate/colsurfa

Modeling self-assembly of surfactants at solid/liquid interfaces. I. Hydrophobic surfaces
Robert A. Johnson, R. Nagarajan *
161 Fenske Laboratory, Department of Chemical Engineering, The Pennsyl6ania State Uni6ersity, Uni6ersity Park, PA 16802 -4400, USA

Abstract A theory ofsurfactant self-assembly on isotropic hydrophobic surfaces is presented by extending the well established treatment of self-assembly in solution. The free-energy model for the formation of surface aggregates includes an additional term (beyond those used for bulk aggregates) to account for the replacement of the solid surface-water contact by the solid surface-aggregate core contact. Thisfree-energy contribution is characterized by a single parameter, the displacement tension k. Illustrative calculations of the critical aggregation concentration (CAC), aggregate shape and size are presented for anionic, zwitterionic, and nonionic surfactants. For all types of surfactants, the CAC is much lower than the bulk CMC. Regardless of the value of k, surface aggregates of ionic surfactant arealways smaller than the bulk-phase analogs. Conversely, surface aggregates of zwitterionic and nonionic surfactants can be either smaller or larger than those in solution, depending on the interplay between headgroup repulsion and aggregate core-solid surface attraction. A rich variety of aggregate morphologies including hemispheres, hemicylinders, finite disks, and continuous monolayers are predicteddepending upon the surfactant and the solid surface. More interestingly, increasing the chemical potential of the surfactant (by increasing the total surfactant concentration) can induce the morphological transformation of surface aggregates to less energetically favorable structures. Thus the same surfactant on a given solid surface can self-assemble into various shapes depending upon the totalsurfactant concentration. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Self assembly; Surfactants; Solid/liquid interfaces

1. Introduction The adsorption of surfactants from solutions onto solid surfaces has been investigated over the years because of the numerous practical applications where solid-liquid contact occurs [1]. Both
* Corresponding author: Tel.: + 1-814-863-1973;fax: +1814-865-7846. E-mail address: rxn@psu.edu (R. Nagarajan)

hydrophobic surfaces and hydrophilic surfaces carrying charges have been examined. It has been postulated that adsorbed surfactants will self-assemble at the solid/liquid interface in a manner analogous to bulk-phase micellization [2,3]. This is to be distinguished from the situation where micelles already formed in the bulksolution adsorb at the solid surface. The self-assembly at the solid/liquid interface is perturbed from the corresponding bulk-phase micellization due to compet-

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R.A. Johnson, R. Nagarajan / Colloids and Surfaces A: Physicochem. Eng. Aspects 167 (2000) 31–46ing surfactant-surface and solvent-surface interactions. This perturbation makes possible the formation of surface aggregates that can differ significantly in size and microstructure from those formed in the bulk. Numerous studies, both theoretical and experimental, have been made concerning the adsorption behavior of surfactants. In general, the amount of surfactant adsorbed is measured orpredicted as a function of the properties of the surfactant solution. On the theoretical side, the main approach has employed thermodynamic considerations to derive analytical representations of surfactant adsorption and two-dimensional condensation at solid surfaces [4 – 10]. In these studies, the microstructure of the adsorbed surfactant was taken to be lamellar. Of particular note is the recent work...