Density functional theory for a model colloid–polymer mixture: bulk fluidphases

Abstract

We describe a density functional theory for mixtures of hard sphere (HS) colloids andideal polymers, the Asakura–Oosawa model. The geometry-based fundamentalmeasures approach which is used to construct the functional ensures the correctbehaviour in the limit of low density of both species and in the zero-dimensionallimit of a cavity which can contain at most one HS. Dimensional crossover isdiscussed in detail. Emphasis is placed on the properties of homogeneous (bulk)fluid phases. We show that the present functional yields the same free energy and,therefore, the same fluid–fluid demixing transition as that given by a differentapproach, namely the free-volume theory. The pair direct correlation functionscij(2)(r)of the bulk mixture are given analytically. We investigate the partial structure factorsSij(k)and the asymptotic decay, r → ∞, of the total pair correlationfunctions hij(r)obtained from the Ornstein–Zernike route. The locus in the phase diagram of the crossoverfrom monotonic to oscillatory decay of correlations is calculated for several size ratiosq = Rp/Rc, whereRp is the radius of thepolymer sphere and Rcthat of the colloid. We determine the (mean-field) behaviour of the partialstructure factors on approaching the fluid–fluid critical (consolute) point.