The basic structure of classical density functional theory (DFT) is reviewed from a rather general perspective. The treatment is then specialized to ionic solutions, describing the various possible extensions beyond the Poisson-Boltzmann level, that DFT offers, such as excluded volume effects, non-electrostatic interactions, connectivity (polymers) and ion correlations. The last effects are discussed rather thoroughly, with several explicit illustrations.
IntroductionInteractions between charged surfaces are important in almost all areas of colloid and surface science, including biological systems. A convenient, albeit approximate, way to model these systems is to treat the solvent implicitly as a dielectric continuum with a fixed dielectric constant and the charged species as spheres with appropriate valency. This simplified model is then often approximately solved using the PoissonBoltzmann approximation (PBA). The PBA derives from a mean-field treatment of the Coulombic forces, and is often expressed as a non-linear differential equation. Its linearized form, the Debye-Hückel theory, is valid in cases where the coupling is small. Over the years, a lot of effort has been devoted to solving the PBA in the presence of various geometrical constraints. A much more versatile formulation of the PBA is arrived at from the point of view of classical density functional theory, DFT. Here, the system free energy is expressed as a functional of the ion distributions. By using a mean-field approximation to the Coulombic energy, and ignoring short-ranged effects, one quite naturally arrives at the PBA. Advantages of a DFT formulation of these systems include: