PACS. 82.70 -Disperse systems. PACS. 64.75 -Solubility, segregation, and mixing.Abstract. -A new treatment of the phase behaviour of a colloid + nonadsorbing polymer mixture is described. The calculated phase diagrams show marked polymer partitioning between coexisting phases, an effect not considered in the usual effective-potential approaches to this problem. We also predict that under certain conditions an area of three-phase coexistence should appear in the phase diagram.Introduction. -Phase separation in colloidal suspensions, induced by the addition of nonadsorbing polymer, is a phenomenon of fundamental interest and considerable technological importance. A theoretical explanation was first advanced by Asakura and Oosawa [1], and also independently by Vrij [2], based on the exclusion of polymer from the region between two colloid particles when their surface-surface separation becomes smaller than the diameter of a free polymer coil. The resulting imbalance in osmotic pressure gives rise to an effective attractive «depletion» force between the colloid particles [3,4]. At high enough concentration of polymer this depletion force causes the suspension to separate into colloid-poor and colloid-rich phases. In the latter the particles can, depending on conditions (see below), be in either liquidlike or crystalline spatial arrangements.To predict the phase diagram of a colloid + polymer mixture, most workers to date have adopted an approach in which the depletion potential (an effective pair potential) is added to the parent interparticle potential; thermodynamic perturbation theory is then used to calculate phase stability boundaries [5,6]. Although experimental studies [6,7] show qualitative agreement with the predictions of these calculations, an important reservation

It is shown that the effect of electrostatic interactions on the liquid crystal phase transition in solutions of rodlike polyelectrolytes can be characterized by two parameters, one describing the increase of the effective diameter and the other the twisting action. The dependence of these parameters on the charge density and the salt concentration is studied both for weakly charged polyelectrolytes, for which the DebyeHucke1 approximation applies, and for highly charged polyelectrolytes, for which the full Poisson-Boltzmann equation has to be used. The isotropic-nematic phase transition cannot be described solely in terms of an effective diameter as has always been done before but one must also take the twisting effect into account. This effect, which enhances the concentrations at the transition, is particularly marked for weakly charged polyions.

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We examine the influence of attractive interactions on the phase behavior of rodlike colloids. We model the rodlike particles by spherocylinders, for which the phase diagram, in the absence of attraction, is known for arbitrary aspect ratio. We consider the case that the attraction is due to depletion forces caused by the addition of nonadsorbing polymer. The range of this attraction is determined by the size of the polymer. If the radius of gyration of the polymer is small compared to the diameter of the rods, we can model the polymer-induced attraction by a suitable generalization of the square-well model for spherical particles. However, for longer ranged attractions, pairwise additive attractions lead to phase behavior that is very different from what is found when the nonadditivity of depletion forces is taken into account. In our simulations, we find evidence for demixing transitions in the isotropic, nematic and solid phases. We compare our simulation results with predictions based on the perturbation theory of Lekkerkerker and Stroobants ͓Nuovo Cimento D 16, 949 ͑1994͔͒. A crucial input in this theory is the so-called free-volume fraction of the hard spherocylinder reference system. In the work of Lekkerkerker and Stroobants, this quantity is estimated using scaled-particle theory. We test the validity of this approach by comparing it to numerical results for the free-volume fraction. © 1997 American Institute of Physics. ͓S0021-9606͑97͒50129-2͔

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