Microscopic theory of solvent mediated long range forces : influence of wetting

PACS. 61.20Gy – Theory and models of liquid structure. PACS. 82.70Dd – Colloids. Abstract. – We show that a general density functional approach for calculating the force between two big particles immersed in a solvent of smaller ones can describe systems that exhibit fluid-fluid phase separation: the theory captures effects of strong adsorption (wetting) and of critical fluctuations in the solvent. We illustrate the approach for the Gaussian core model, a simple model of a polymer mixture in solution and find extremely attractive, long ranged solvent mediated potentials between the big particles for state points lying close to the binodal, on the side where the solvent is poor in the species which is favoured by the big particles. Determining the effective force between two (big) particles immersed in a solvent constitutes a canonical problem in condensed matter science. From the statistical mechanics viewpoint one should integrate out the relevant degrees of freedom of the solvent particles in order to obtain the the effective pair potential [1]. In the case of colloidal systems, where the colloidal component is very much larger than the particles constituting the solvent, the description of the complex, multi-component system in terms of an effective colloid-colloid potential forms a cornerstone of the subject. Well-known examples are the DLVO potential for charge stabilized systems and the hard-sphere potential for sterically stabilized systems [2]. The effective potential between colloids exhibits new features if particles of intermediate size, such as non-adsorbing polymer or small colloids, are added to the solvent. When two big colloids (b) are sufficiently close that the intermediate sized particles are depleted from the region between the big colloids the effective bb potential, V ef f bb (r), can exhibit entropically driven attraction. Within the Asakura-Oosawa (AO) model [3], where the colloids are hard spheres and the polymer is treated as ideal (inter-penetrating and non-interacting) the resulting depletion potential is purely attractive and its finite range is equal to the 'diameter' of the polymer coil. For mixtures of hard-sphere like colloids the effective potential between the bigger colloids exhibits both attraction and repulsion; short ranged correlations arising from the packing of the smaller colloids gives rise to an exponentially damped, oscillatory effective potential whose decay length is simply the bulk correlation length [4], in keeping with the c EDP Sciences