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arXiv · 2111.15253

Legendre-Fenchel transforms capture layering transitions in porous media

Olav Galteland·Eivind Bering·Kim Kristiansen·Dick Bedeaux·Signe Kjelstrup
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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.

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Olav Galteland, Eivind Bering, Kim Kristiansen, Dick Bedeaux, Signe Kjelstrup. 2021-11-30. Legendre-Fenchel transforms capture layering transitions in porous media. https://arxiv.org/abs/2111.15253

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