Fluid phase separation inside a static periodic field: an effectively two-dimensional critical phenomenon

When a fluid with a bulk liquid-vapor critical point is placed inside a static external field with spatial periodic oscillations in one direction, a new phase arises. This new phase-the so-called "zebra" phase-is characterized by an average density roughly between that of the liquid and vapor phases. The presence of the zebra phase gives rise to two new phase transitions: one from the vapor to the zebra phase, and one from the zebra to the liquid phase. At appropriate values of the temperature and chemical potential, the latter two transitions become critical. This phenomenon is called laser-induced condensation I. O. Go?tze, J. M. Brader, M. Schmidt, and H. Lo?wen, Mol. Phys. 101, 1651 (2003)]. The purpose of this paper is to elucidate the nature of the critical points, using density functional theory and computer simulation of a colloid-polymer mixture. The main finding is that critical correlations develop in two-dimensional sheets perpendicular to the field direction, but not in the direction along the field: the critical correlations are thus effectively two-dimensional. Hence, static periodic fields provide a means to confine a fluid to effectively two dimensions. Away from criticality, the vapor-zebra and liquid-zebra transitions become first-order, but the associated surface tensions are extremely small. The consequences of the extremely small surface tensions on the nature of the two-phase coexistence regions are analyzed in detail.