A Legendre-Fenchel Transform for Molecular Stretching Energies

E Bering and D Bedeaux and S Kjelstrup and A de Wijn and I Latella and JM Rubi, NANOMATERIALS, 10, 2355 (2020).

DOI: 10.3390/nano10122355

Single-molecular polymers can be used to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. We have recently verified using molecular-dynamics simulations that isometric and isotensional stretching of a small polymer result in Helmholtz and Gibbs stretching energies, which are not related to a Legendre transform, as they are for sufficiently long polymers. This disparity has also been observed experimentally. Using molecular dynamics simulations of polyethylene-oxide, we document for the first time that the Helmholtz and Gibbs stretching energies can be related by a Legendre-Fenchel transform. This opens up a possibility to apply this transform to other systems which are small in Hill's sense.

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