Fluids in Extreme Confinement - Franosch, Thomas; Lang, Simon; Schilling, Rolf (Physical Review Letters, 2012)
For extremely confined fluids with a two-dimensional density n in slit geometry of an accessible width L, we prove that in the limit Li̊ghtarrow0, the lateral and transversal degrees of freedom decouple, and the latter become ideal-gas-like. For a small wall separation, the transverse degrees of freedom can be integrated out and renormalize the interaction potential. We identify nL2 as the hidden smallness parameter of the confinement problem and evaluate the effective two-body potential analytically, which allows calculating the leading correction to the free energy exactly. Explicitly, we map a fluid of hard spheres in extreme confinement onto a 2D fluid of disks with an effective hard-core diameter and a soft boundary layer. Two-dimensional phase transitions are robust and the transition point experiences a shift O(nL2).
EAM Import::2019-03-14

Mode-coupling theory of the glass transition for confined fluids - Lang, Simon; Schilling, Rolf; Krakoviack, Vincent; Franosch, Thomas (Physical Review E, 2012)
We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.
EAM Import::2019-03-12