Phase transitions in two-dimensional colloidal systems

This chapter is an introduction to phase transitions in two-dimensional (2D) systems. In contrast to three dimensions (3D), microscopic theories of melting exist in 2D. The most well known of them was developed more than 30 years ago by Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY theory). This theory predicts the unbinding of topological defects to break the symmetry in two steps at two distinct temperatures. Dissociation of dislocation pairs first melts the crystal into a still orientationally ordered (hexatic) phase and, in the second step, dissociation of free dislocations causes the system to go over to an isotropic fluid. Colloidal systems are used to verify experimentally the predictions of KTHNY theory in detail as colloids provide the possibility to visualize the change in symmetry on an "atomic" level by simple video-microscopy. Elastic moduli like Young's modulus and Frank's constant are deduced from microscopic trajectories of colloids in order to quanify the softening of the 2D ensemble in the vicinity of the phase transitions