The structure of colloid-polymer mixtures

– We investigate the structure of colloid-polymer mixtures by calculating the structure factors for the Asakura-Oosawa model in the PY approximation. We discuss the role of potential range, polymer concentration and polymer-polymer interactions on the colloid-colloid structure. Our results compare reasonably well with the recent experiments of Moussäıd et al. (Moussäid A., Poon W. C. K., Pusey P. N. and Soliva M. F., Phys. Rev. Lett., 82 (1999) 225) for small wave number k, but we find that the Hansen-Verlet freezing criterion is violated when the liquid phase becomes marginal. Suspensions of sterically stabilized colloidal particles in an organic solvent containing nonadsorbing polymer have been widely studied experimentally and theoretically because of their remarkable phase behaviour. The non-adsorbing polymer coils induce an attractive depletion interaction between the colloidal particles, the range and depth of which can be easily “tuned” by varying the polymer molecular weight (and hence its radius of gyrationRg) and the polymer concentration np. This makes polymer-colloid mixtures an important experimental model system to study the role of the range of attractive interactions on phase behaviour. If Rc is the radius of a spherical colloidal particle, and ξ = Rg/Rc denotes the size ratio, it was predicted theoretically [1,2], and shown experimentally [3] and by simulations [4] that the phase diagram in the (ηc, np)-plane (where ηc = 4πncR 3 c/3 denotes the colloid packing fraction) exhibits colloid “gas”, “liquid” and “solid” phases, when ξ & 0.3, while the intermediate “liquid” phase becomes “marginal” for ξ ≈ 0.3, and disappears completely for smaller size ratios [5]. The previous theoretical work mostly focuses on calculating free energies and the resulting phase diagrams and no attempts were made to investigate the structure of the colloid-polymer mixtures, as embodied in the partial structure factors Sαβ(k) (1 ≤ α ≤ β ≤ 2), where the indices 1 and 2 refer to the colloid and polymer species, respectively). This is because the van-der-Waals–like mean-field theories in [1,2] do not readily yield structural information, and because until very recently no experimental data were available. This gap has been filled by the two-colour dynamic light-scattering measurements of Moussäıd et al. [6], which provide data for the colloid-colloid structure factor, S(k) = S11(k), over a limited range of wave numbers k, for thermodynamic states at triple-point conditions, and for three values of the size ratio ξ. In particular, they concluded that under triple-point conditions the amplitude of the first peak of the structure factor was always near 2.5, while the small-k behaviour showed () Present address: Institut für Theoretische Physik II, Universität Düsseldorf, D-40225 Düsseldorf, Germany.