Effective interactions in soft condensed matter physics

In this work, we present a review of recently achieved progress in the fiel d of soft condensed matter physics, and in particular on the study of the s tatic properties of solutions or suspensions of colloidal particles. The la tter are macromolecular entities with typical sizes ranging from 1 nm to 1 mum and their suspension typically contain, in addition to the solvent, sma ller components such as salt ions or free polymer chains. The theoretical t ool introduced is the effective Hamiltonian which formally results by a can onical trace over the smaller degrees of freedom for a fixed, "frozen" conf iguration of the large ones. After presenting the formal definitions of thi s effective Hamiltonian, we proceed with the applications to some common so ft matter systems having a variable softness and ranging from free polymer chains to hard colloidal particles. We begin from the extreme case of nondi verging effective interactions between ultrasoft polymer chains and derive an exact criterion to determine the topology of the phase diagrams of such systems. We use star polymers with a variable arm number f as a hybrid syst em in order to interpolate between these two extremes. By deriving an effec tive interaction between stars we can monitor the change in the phase behav ior of a system as the steepness of the repulsion between its constituent p articles increases. We also review recent results on the nature and the eff ects of short-range attractions on the phase diagrams of spherical, nonover lapping colloidal particles. (C) 2001 Elsevier Science B.V. All rights rese rved.