Legendre-Fenchel transforms capture layering transitions in porous media

O Galteland and E Bering and K Kristiansen and D Bedeaux and S Kjelstrup, NANOSCALE ADVANCES, 4, 2660-2670 (2022).

DOI: 10.1039/d1na00846c

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.

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