10.1098/rsta.2000.0809 Interactions and phase transitions of colloidal dispersions in bulk and at interfaces ByH.L¨ owen,E.Allahyarov,J.Dzubiella,C.vonFerber, A.Jusufi,C.N.LikosandM.Heni Institut f¨ ur Theoretische Physik II, Heinrich-Heine-Universit¨ atD¨ usseldorf, D-40225 D¨ usseldorf, Germany Recent progress in the theory and computer simulation of effective interactions and phase transitions of colloidal dispersions is reviewed. Particular emphasis is put on the role of the discrete solvent in determining the effective interaction between charged colloids, bulk fluid–fluid phase separation of star-polymer–colloid mixtures, and on interfacial freezing transitions of sterically stabilized colloids on patterned substrates. Keywords: effective interaction; charged colloids; star polymers; phase separation; surface freezing 1. Introduction Colloidal dispersions represent excellent model systems with a clear separation of length-scales between microscopic degrees of freedom (such as solvent particles, counter- and salt-ions, monomers of grafted polymer chains, etc.) and the mesocopi- cally sized colloidal particles. Typically, one is only interested in colloidal properties such as, for example, structural correlations or phase transitions of the colloidal par- ticles. In this case, only thermodynamic averages with respect to the microscopic degrees of freedom are needed, resulting in effective interactions between the col- loids. In this paper, we apply this concept to different situations of colloidal science, highlighting recent progress in the theory and computer simulation of effective inter- actions between charged colloidal suspensions, as well as mechanisms of fluid–fluid phase separation in mixtures of colloids and polymers. Finally, we also address inter- facial freezing transitions induced by a periodic substrate pattern. The paper is organized as follows. The role of a molecular solvent on the effective interactions is emphasized in § 2. The effective interactions in star-polymer–colloid mixtures and their impact on fluid–fluid phase separation are briefly sketched in § 3. Finally, we describe recent results on surface freezing of neutral colloidal particles on topographically structured templates in § 4, and conclude in § 5. 2. Influence of a granular solvent on the effective interaction between charged colloids (a ) General remarks: modelling on different levels Basically, the theoretical model for the description of charged colloidal particles can be done on five different levels (for a recent review, see Hansen & L¨owen (2000)). Phil. Trans. R. Soc. Lond. A (2001) 359, 909–920 909 c  2001 The Royal Society