Free-energy functional method, interface solutions

Abstract We review a new theoretical approach to the kinetics of surfactant adsorption at fluid-fluid interfaces. It yields a more complete description of the kinetics both in the aqueous solution and at the interface, deriving all equations from a free-energy functional. It also provides a general method to calculate dynamic surface tensions. For non-ionic surfactants, the results coincide with previous models. Non-ionic surfactants are shown to usually undergo diffusion-limited adsorption, in agreement with the experiments. Strong electrostatic interactions in salt-free ionic surfactant solutions are found to... 

The minimization of this functional presents a problem which for many component mixtures can be quite timeconsuming if the truly optimal form of the interface and free energy is to be found. One may use an iterative method of solution much like the famous scheme used to solve for the Hartree-Fock wave function in electronic structure calculations [4]. An alternative, much to be preferred when sufficiently accurate, is to use a simple parametrized form for the particle densities through the interface and then determine the optimal values of these parameters. The simplest possible scheme is, of course, to take the profile to be a step function. 

The main, currently used, surface complexation models (SCMs) are the constant capacitance, the diffuse double layer (DDL) or two layer, the triple layer, the four layer and the CD-MUSIC models. These models differ mainly in their descriptions of the electrical double layer at the oxide/solution interface and, in particular, in the locations of the various adsorbing species. As a result, the electrostatic equations which are used to relate surface potential to surface charge, i. e. the way the free energy of adsorption is divided into its chemical and electrostatic components, are different for each model. A further difference is the method by which the weakly bound (non specifically adsorbing see below) ions are treated. The CD-MUSIC model differs from all the others in that it attempts to take into account the nature and arrangement of the surface functional groups of the adsorbent. These models, which are fully described in a number of reviews (Westall and Hohl, 1980 Westall, 1986, 1987 James and Parks, 1982 Sparks, 1986 Schindler and Stumm, 1987 Davis and Kent, 1990 Hiemstra and Van Riemsdijk, 1996 Venema et al., 1996) are summarised here. 

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