Attraction between like - charged colloidal particles induced by a surface : a density - functional analysis

We show that the first non-linear correction to the linearised PoissonBoltzman n (or DLVO) theory of effective pair interactions between chargestabilised, co lloidal particles near a charged wall leads to an attractive component of entro pic origin. The position and depth of the potential compare favourably with rec ent experimental measurements 82.70.Dd;64.10th;83.20Di Typeset using REVTEX 1 Recent direct measurements confirm the overall validity of the classic Derjagui n-LandauVerwey-Overbeek (DLVO) effective pair potential between charge-stabili zed colloidal particles in the bulk of an aqueous dispersion [1], but give convincing evidence for an attractive component to the interaction when two co lloidal particles are confined in a slit [2,3] or close to a planar wall cite4. In this letter we use a density functional analysis [5] to show t hat such an attraction can be due to non-linear corrections to linearised Poiss on-Boltzmann (PB) theory which forms the basis of the DLVO potential. Mesoscopic colloidal particles carrying ionizable radicals on their surface build up electric double -layers of microscopic co and counterions when dispersed in water. The effective forces between these “dressed” particles or polyions derive from a sum of direct and induced interactions. The direct interactions include excluded volume and Coulomb repulsions between the bare surface charges, and van der Waals attractions; the latter are generally quite negligible, except at very high salt concentrations corresponding to the strong screening regime [6]. The indirect interactions are induced by the locally inhomogeneous distribution of microions, which screen the bare Coulomb repulsion; these induced interactions are identified with the free energy of the microions in the ”external” field due to any given configuration of polyions, and hence have electrostatic and entropic contributions. In practice the free energy of the microions, which depends parametrically on the positions {Ri} of the N polyions (assumed here to be spherical) is calculated within density functional theory (DFT) by minimising an appropiate free energy functional F with respect to the local densities ρα(r) of the co and counterions. To be specific, consider polyions of radius R, carrying a total positive charge Ze (Z > 0), and monovalent coions (local density, ρ+(r)) and counterions (ρ−(r)). Z must be regarded as an effective charge much smaller than the bare structual charge. The “renormalized” charge accounts for the shortcomings of linearised PB theory (as used later in this paper) at very short distances from the polyion surfaces [7]. Correlations between microions will be neglected, which amounts to working within the framework of mean-field, or Poisson-Boltzmann theory. The solvent(water) is merely treated as a continium of dielectric constant ǫ (“primitive” model). Under these conditions the free 2 energy functional reduces to the sum of ideal and electrostatic contributions: F [ρ+, ρ−] = Fid[ρ+, ρ−] + Fel[ρ+, ρ−] (1) Fid[ρ+, ρ−] = ∑