Random Pinning Models: Phase Transitions in Aqueous Solutions of Colloidal Particles

Self-assembly of colloidal particles may occur, for example, both under the action of external fields and due to the presence of pinning centers in a real experimental system. Of particular interest is the formation of condensed phases from an aqueous solution of colloidal particles on a substrate in an external rotating magnetic field. Substrate defects (for example, the substrate roughness) are of great importance in an experiment. These defects can act as pinning centers, to which colloidal particles are strongly attracted; this may lead to a change in the melting scenario. Changing the field rotation angle, one can obtain different colloidal structures. At small rotation angles, the system behaves like a two-dimensional system with a purely repulsive soft-disk potential, whereas at large angles it is similar to a generalized Lennard-Jones (LJ) system with an (nm)-potential. When the field rotates in the plane of the system, its phase diagram qualitatively resembles that of a classical model system with a LJ pair potential. The results of the computer simulation of a two-dimensional system with a LJ potential in the presence of Gauss pinning are discussed in the context of its influence on the phase diagram and melting scenario. It is shown that random pinning with a Gauss potential leads to an increase in the hexatic phase range; formation of dense clusters near pinning centers, which reduce the average effective density of the system; and a change in the melting scenario.