Phase behaviour and structure of model colloid-polymer mixtures

We study the phase behaviour and structure of model colloid-polymer mixture s. By integrating out the degrees of freedom of the non-adsorbing ideal pol ymer coils, we derive a formal expression for the effective one-component H amiltonian of the colloids. Using the two-body (Asakura-Oosawa pair potenti al) approximation to this effective Hamiltonian in computer simulations, we determine the phase behaviour for size ratios q = sigma(p)/sigma(c), = 0.1 , 0.4, 0.6, and 0.8, where sigma(c) and sigma(p) denote the diameters of th e colloids and the polymer coils, respectively. For large q; we find both a fluid-solid and a stable fluid-fluid transition. However, the latter becom es metastable with respect to a broad fluid-solid transition for q less tha n or equal to 0.4. For q = 0.1 there is a metastable isostructural solid-so lid transition which is likely to become stable for smaller values of q. We compare the phase diagrams obtained from simulation with those of perturba tion theory using the same effective one-component Hamiltonian and with the results of the free-volume approach. Although both theories capture the ma in features of the topologies of the phase diagrams, neither provides an ac curate description of the simulation results. Using simulation and the Perc us-Yevick approximation we determine the radial distribution function g(r) and the structure factor S(k) of the effective one-component system along t he fluid-solid and fluid-fluid phase boundaries. At state-points on the flu id-solid boundary corresponding to high colloid packing fractions (packing fractions equal to or larger than that at the triple point), the value of S (k) at its first maximum is close to the value 2.85 given by the Hansen-Ver let freezing criterion. However, at lower colloid packing fractions freezin g occurs when the maximum value is much lower than 2.85. Close to the criti cal point of the fluid-fluid transition we find Omstein-Zernike behaviour a nd at very dilute colloid concentrations S(k) exhibits pronounced small-ang le scattering which reflects the growth of clusters of the colloids. We com pare the phase behaviour of this model with that found in studies of additi ve binary hard-sphere mixtures.