Two-dimensional symmetry breaking of fluid density distribution in closed nanoslits

Stable and metastable fluid density distributions (FDDs) in a closed nanoslit between two identical parallel solid walls have been identified on the basis of a nonlocal canonical ensemble density functional theory. Similar to Monte Carlo simulations, periodicity of the FDD in one of the lateral (parallel to the walls surfaces) directions, denoted as the x direction, was assumed. In the other lateral direction, y direction, the FDD was considered uniform. It was found that depending on the average fluid density in the slit, both uniform as well as nonuniform FDDs in the x direction can occur. The uniform FDDs are either symmetric or asymmetric about the middle plane between walls; the latter FDD being the consequence of a symmetry breaking across the slit. The nonuniform FDDs in the x direction occur either in the form of a bump on a thin liquid film covering the walls or as a liquid bridge between those walls and provide symmetry breaking in the x direction. For small and large average densities, the stable state is uniform in the x direction and is symmetric about the middle plane between walls. In the intermediate range of the average density and depending on the length L(x) of the FDD period, the stable state can be represented either by a FDD, which is uniform in the x direction and asymmetric about the middle of the slit (small values of L(x)), or by a bump- and bridgelike FDD for intermediate and large values of L(x), respectively. These results are in agreement with the Monte Carlo simulations performed earlier by other authors. Because the free energy of the stable state decreases monotonically with increasing L(x), one can conclude that the real period is very large (infinite) and that for the values of the parameters employed, a single bridge of finite length over the entire slit is generated.