Legendre-Fenchel transforms capture layering transitions in porous media.

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.

A Legendre-Fenchel Transform for Molecular Stretching Energies.

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.

Entropy Production beyond the Thermodynamic Limit from Single-Molecule Stretching Simulations.

Single-molecular systems are a test bed to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. Isometric and isotensional single-molecule stretching experiments and their theoretical interpretations have shown the lack of a thermodynamic limit at those scales and the nonequivalence between their corresponding statistical ensembles. This disparity between thermodynamic results obtained in both experimental protocols can also be observed in entropy production, as previous theoretical results have shown. In this work, we present results from molecular dynamics simulations of stretching of a typical polymer, polyethylene-oxide, where this framework is applied to obtain friction coefficients associated with stretching at the two different statistical ensembles for two different system sizes, from which the entropy production follows. In the smallest system, they are different up to a factor of 2, and for the bigger system, the difference is smaller, as predicted. In this way, we provide numerical evidence that a thermodynamic description is still meaningful for the case of single-molecule stretching.

Stretching and breaking of PEO nanofibres. A classical force field and ab initio simulation study.

The burgeoning development of nanotechnology is allowing us to construct more and more nano-scale systems in the real world that used to only exist in computer simulations. Among them, nanofibres made of only a few aligned polymeric chains in particular might soon have important roles in nanofabrications as well as in nanomedicine. In this work, we present a broad exploration by computer simulations of elastic and inelastic properties of polyethylene-oxide (PEO) nanofibres under load. We cover the full range from unloaded fibres up to their breaking point, focusing on all features that arise from chain-chain interactions and collective behaviour of the chains. We employ both molecular dynamics (MD) simulations and density functional theory (DF). The classical force field is represented by a minimal reactive force field model, allowing for the breaking of covalent bonds. Density functional (DF) computations provide a benchmark to gauge and validate the empirical force field approach, and offer an intriguing view of the bundle chemical evolution after breaking. Force-field based MD is employed for the systematic investigation of bundles of up to 24 chains, and for a single bundle of 100 chains. Low-temperature results for bundles under moderate loading provide a size-dependent sequence of cross-sections, structures, cohesive energies and elastic properties. A remarkably high Young's modulus on the order of 100 GPa was estimated with DF and MD, explained by the semi-crystalline state of the fibres giving mechanical properties comparable to those of carbon nanotubes and of graphene. Breaking is investigated by simulations with constant strain rate or constant stress. The bundle breaks whenever the potential energy is raised above its metastability range, but also below that limit due to creep activated by thermal fluctuations. A Kramer's-type approximation for the rate of chain breaking is proposed and compared to simulation data.