Dissertation Phase Behaviour of Colloidal Systems

Depending on the pair interactions of the constitutive system particles, colloidal dispersions display a rich phase behaviour. An important class of colloidal systems is characterised by pair potentials that contain a hard core in addition to versatile potential tails. This class of systems are investigated in the present thesis, focussing on two different aspects. The first one is represented by the critical behaviour of long–range interaction systems, to which we apply the self–consistent Ornstein–Zernike approximation, a liquid state theory known to remain reliable in the critical region. We modify this theory in order to make it applicable to systems exhibiting Coulomb interactions in addition to other potential tails, and are able to calculate effective critical exponents with unprecedented accuracy. With the help of this technique we find a cross–over between mean–field and SCOZA critical behaviour of charged Yukawa, charged Kac, and Kac–Yukawa systems. Furthermore we verify a new relation for the ascertainment of the critical exponent γ, a relation which relies on the perturbation on the interaction of a reference system with a Kac–potential. The second focus is laid on the search for solid equilibrium structures of hard core systems, for which we employ a search strategy based on a genetic algorithm. To ensure the convergence of the algorithm for hard core particles we introduce theMinimum Distance Parametrisation of crystal lattices. Additionally, we develop an efficient search strategy to detect all equilibrium structures of the square–shoulder model (SSM) at zero temperature, which can be extended to systems with certain continuous potential tails via metric scaling. In this way, we are able to distinguish, e.g., a new centred tetragonal phase for the hard core Yukawa model. The astonishingly large variety of the identified equilibrium structures for the SSM consist of cluster, columnar, lamellar, and compact phases, appearing in this sequence when increasing the pressure. The succession, as well as the thermodynamic properties of the respective structures, are predicted by the so called continuum theory. This theory relies on averaging the particle densities and energies and is applied to all four structural archetypes in the SSM.