Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions

Abstract

We investigate the dependence of the stickiness parameters $t_{ij}=1/(12\tau _{ij})$ -- where the $\tau_{ij}$ are the conventional Baxter parameters -- on the solute diameters $\sigma_{i}$ and $\sigma_{j}$ in multicomponent sticky hard sphere (SHS) models for fluid mixtures of mesoscopic neutral particles. A variety of simple but realistic interaction potentials, utilized in the literature to model \textit{short-ranged attractions} present in real solutions of colloids or reverse micelles, is reviewed. We consider: i) van der Waals attractions, ii) hard-sphere-depletion forces, iii) polymer-coated colloids, iv) solvation effects (in particular hydrophobic bonding and attractions between reverse micelles of water-in-oil microemulsions). We map each of these potentials onto an equivalent SHS model, by requiring the equality of the second virial coefficients. The main finding is that, for most of the potentials considered, the size-dependence of $t_{ij}(T,\sigma_{i},\sigma _{j})$ can be approximated by essentially the same expression, i.e. a simple polynomial in the variable $\sigma_{i}\sigma_{j}/\sigma_{ij}^{2}$, with coefficients depending on the temperature $T$, or -- for depletion interactions -- on the packing fraction $\eta_{0}$ of the depletant particles.