Dynamics and Phase Transitions in Confined Geometries

Physical phenomena are often very sensitive to surfaces and boundary conditions. This thesis focuses on the experimental and theoretical aspects of phase transitions in two dimensions and its coupling to other degrees of freedom (such as the third dimension or other occuring phase transitions). First, we study the out-of-plane buckling of a two-dimensionally confined colloidal crystal. When the potential confining colloids in two dimensions is relaxed, we find that the buckling transitions can be described by various statistical mechanical models of phase transitions. The effects of surfactants on the dynamics of an air-water interface are also studied, both experimentally and theoretically. In particular, we study the propagation of surface capillary waves in the presence of surface active agents which change the mechanical properties of the interface. Experimentally, the effects of a Langmuir monolayer of pentadecanoic acid (PDA) on capillary wave propagation is studied. The attenuation of these waves is drastically enhanced in the presence of particular surface densities of PDA. These results, along with recent optical characterization of surfactant monolayers, motivates the study of wave propagation and scattering near surfaces nonuniformly covered. The calculated wave scattering due to a heterogeneous surface morphology demonstrates the possibility of inter -surface mode conversion as well as Mie resonances at a single scatterer. These possible effects suggest methods of detection and are related to the experimental results. Finally, in light of recent numerical simulations, we model the coupling of a two-dimensional isostructural phase transition with the dislocation mediated theory of two-dimensional melting. The coupling manifests itself as an interaction between an Ising order parameter describing a first order isostructural transition near its critical point and a vector coulomb gas representing the dislocation field of a melting two-dimensional crystal. We find, in agreement with numerical results, an instability to a hexatic phase induced by the Ising-characterized phase separation.