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

Colloids display intriguing transitions between gas, liquid, solid and liquid crystalline phases. Such phase transitions are ubiquitous in nature and have been studied for decades. However, the predictions of phase diagrams are not always realized; systems often become undercooled, supersaturated, or trapped in gel-like states. In many cases the end products strongly depend on the starting position in the phase diagram and discrepancies between predictions and actual observations are due to the intricacies of the dynamics of phase transitions. Colloid science aims to understand the underlying mechanisms of these transitions. Important advances have been made, for example, with new imaging techniques that allow direct observation of individual colloidal particles undergoing phase transitions, revealing some of the secrets of the complex pathways involved.F igure 1 illustrates three types of phase diagram. The ®rst (Fig. 1a) is a simple system of hard spheres. Introducing attractions results in three-phase equilibria, as in atomic systems such as argon (Fig. 1b). With shorter-range attractions the gas±liquid (or¯uid±¯uid) equilibrium becomes metastable (Fig. 1c). This is often observed in protein systems. One might assume equilibrium diagrams show the complete picture, with perhaps the initial distance from the phase boundary (indicative of the distance to equilibrium) controlling the speed with which the equilibrium phases are attained; however, this is the exception rather than the rule.Hard-sphere colloids suspended in a solvent provide an excellent illustration of the dif®culties involved in understanding the equilibrium states and the mechanisms by which systems evolve. Entropy considerations predict that these systems will form crystals if the volume fraction is increased. Above the`freezing' volume fraction, f f 0:494, it is entropically favourable if some spheres are in a crystal, but above the`melting' volume fraction, f m 0:545, all spheres should be in a crystal (Fig. 1a). However this is not always the situation found experimentally, either because the conditions the theory assumes (low polydispersity, for example) are not satis®ed, or the dynamics of the system have dictated a different structure (note that we cannot say that this structure is the equilibrium structureÐif entropy favours crystal formation then a crystal will form eventually, however the system may remain in the less-favoured state for a signi®cant amount of time). This crystallization process is often interpreted within the familiar framework of nucleation and growth. There has been renewed interest in this mechanism recently, both with simulations 1 and experimentally 2,3 : by monitoring the individual particles undergoing the transition it is possible to evaluate and improve the model.The classical theory predicts that the free energy cost, DG, of forming a nucleus of radius r is:where g is the surface free energy, r is the density of the bulk liquid, and Dm is the chemical potential difference between the bulk solid and bulk liquid...

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We studied the free fluid-fluid interface in a phase-separated colloid-polymer dispersion with laser scanning confocal microscopy and directly observed thermally induced capillary waves at the interface in real space. Experimental results for static and dynamic correlation functions validate the capillary wave model down to almost the particle level. The ultralow interfacial tension, the capillary length, and the capillary time are found to be in agreement with independent measurements. Furthermore, we show that capillary waves induce the spontaneous breakup of thin liquid films and thus are of key importance in the process of droplet coalescence.

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.