Fluids in Extreme Confinement

TL;DR

This paper analytically studies fluids in extreme slit confinement, showing how degrees of freedom decouple and deriving an effective 2D model with corrections, revealing robust phase transitions with shifted transition points.

Contribution

It provides an exact analytical mapping of confined hard-sphere fluids to effective 2D systems, including correction terms for free energy and phase transition shifts.

Findings

Degrees of freedom decouple as slit width approaches zero

Effective 2D interaction potential derived analytically

Phase transition points shift by order of nL^2

Abstract

For extremely confined fluids with two-dimensional density $n$ in slit geometry of accessible width $L$, we prove that in the limit $L\to 0$ the lateral and transversal degrees of freedom decouple, and the latter become ideal-gas-like. For small wall separation the transverse degrees of freedom can be integrated out and renormalize the interaction potential. We identify $n L^2 $ as 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 ${\cal O}(n L^2)$.