Entropy in self-assembly

Colloidal systems show beautiful examples of how entropy can lead to self-assembly of ordered structures, challenging our perception of disorder. In fact, dispersion of hard colloidal particles, systems in which by default entropy is the only thermodynamic driving force, displays both translational and orientational order on increasing density. Entropy is also a fundamental concept for describing effective interactions between colloidal particles. In several cases, entropy maximization generates strong attractive forces, capable of inducing condensation and sometimes crystallization. These entropic forces can even be exploited to drive colloids in specific locations or to orient them in the build-up of supracolloidal aggregates. Depletion interactions and combinatorial contributions are two important manifestations of these forces. Entropy also plays a leading role in systems exploring the bottom of their potential energy surface. In patchy colloids, particles interacting with highly anisotropic and localized potentials, ground-state structures are often degenerate in energy, leaving entropy to decide the thermodynamically stable polymorph. A striking result is the possibility of generating colloidal ``liquids'' thermodynamically more stable than colloidal ``crystals'' even at vanishing temperature.