Legendre-Fenchel transforms capture layering transitions in porous media

TL;DR

This paper explores how Legendre-Fenchel transforms can effectively describe layering transitions in nanoconfined fluids within porous media, especially when traditional transforms fail due to non-convex energy functions.

Contribution

It demonstrates the application of Legendre-Fenchel transforms to capture layering transitions and non-convex energy landscapes in nanoconfined fluids, extending thermodynamic analysis methods.

Findings

Helmholtz energy becomes non-convex near close-packed structures.

Legendre-Fenchel transform enables conversion between Helmholtz and Gibbs energies in non-convex cases.

The transform aligns with Maxwell construction principles.

Abstract

We have investigated the state of a nanoconfined fluid in a slit pore in the canonical and isobaric ensembles. The systems were simulated with molecular dynamics simulations. The fluid has a transition to a close-packed structure when the height of the slit approaches the particle diameter. The Helmholtz energy is a non-convex function of the slit height if the number of particles does not exceed that of one monolayer. As a consequence, the Legendre transform cannot be applied to obtain the Gibbs energy. The Gibbs energy of a non-deformable slit pore can be transformed into the Helmholtz energy of a deformable slit pore using the Legendre-Fenchel transform. The Legendre-Fenchel transform corresponds to the Maxwell construction of equal areas.