Precrystallization of fluids induced by patterned substrates

It is shown that a fluid near a topographically patterned wall exhibits crystallization below the bulk freezing point (so-called precrystallization). In detail, a periodic array of fixed hard spheres is considered as a wall pattern. The actual type of the pattern corresponds to a face-centred-cubic (fcc) lattice cut along the (111), (100) or (110) orientation, a hexagonal-close-packed (hcp) solid with (110) orientation as well as a rhombic lattice distorted with respect to the triangular one. The fluid is represented by mobile hard spheres of the same diameter as the fixed wall spheres. By computer simulation we find complete wetting by a crystalline sheet proceeding via a cascade of layering transitions as the bulk freezing point is approached for the fcc (111) and hcp (110) cases, provided that the wall crystal lattice exactly matches that of the coexisting bulk crystal. On the other hand, there is incomplete wetting for the fcc (100) and (110) cases. The freezing of the first layer starts at lower bulk pressures for a lattice with a larger lattice constant as compared to that of the coexisting bulk crystal. A rhombic pattern either results in incomplete wetting by a solid sheet, which is unstable as a bulk phase, or prevents wetting completely. Using a phenomenological theory we derive scaling relations for the thickness of the crystalline layer which are confirmed by the simulation data. We furthermore show that the Lindemann rule of bulk freezing can be applied also for interfacial freezing transitions.