Legendre-Fenchel transforms capture layering transitions in porous media

Galteland, Olav; Bering, Eivind; Kristiansen, Kim; Bedeaux, Dick; Kjelstrup, Signe

doi:10.1039/d1na00846c

Cited by 6 publications

(3 citation statements)

References 23 publications

(47 reference statements)

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“…refs. 23 – 30 , not intending to be an exhaustive bibliography of this vast domain), and provide also an excellent ground for testing nanothermodynamics and for incubating new concepts and new ideas for nanoscale thermodynamics 8 – 10 , 19 , 31 . We consider a fluid confined in a slit pore with a fluctuating width, .…”

Section: Resultsmentioning

confidence: 99%

Nanoscale thermodynamics needs the concept of a disjoining chemical potential

Dong

2023

Nat Commun

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Disjoining pressure was discovered by Derjaguin in 1930’s, which describes the difference between the pressure of a strongly confined fluid and the corresponding one in a bulk phase. It has been revealed recently that the disjoining pressure is at the origin of distinct differential and integral surface tensions for strongly confined fluids. Here we show how the twin concept, disjoining chemical potential, arises in a reminiscent way although it comes out eighty years later. This twin concept advances our understanding of nanoscale thermodynamics. Ensemble-dependence (or environment-dependence) is one hallmark of thermodynamics of small systems. We show that integral surface tension is ensemble-dependent while differential surface tension is not. Moreover, two generalized Gibbs-Duhem equations involving integral surface tensions are derived, as well as two additional adsorption equations relating surface tensions to adsorption-induced strains. All the results obtained in this work further evidence that an approach alternative of Hill’s nanothermodynamics is possible, by extending Gibbs surface thermodynamics instead of resorting to Hill’s replica trick. Moreover, we find a compression-expansion hysteresis without any underlying phase transition.

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Section: Resultsmentioning

confidence: 99%

Nanoscale thermodynamics needs the concept of a disjoining chemical potential

Dong

2023

Nat Commun

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“…We have previously proposed thermodynamic definitions for the pressure of heterogeneous media, applying Hill's idea of thermodynamics for small systems [13,14,[22][23][24]]. Hill's definitions have so far only been tested under simple conditions [22,23,25,26].…”

Section: Introductionmentioning

confidence: 99%

Defining the pressures of a fluid in a nanoporous, heterogeneous medium

et al. 2022

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We describe the thermodynamic state of a single-phase fluid confined to a porous medium with Hill’s thermodynamics of small systems, also known as nanothermodynamics. This way of defining small system thermodynamics, with a separate set of control variables, may be useful for the study of transport in non-deformable porous media, where presently no consensus exists on pressure computations. For a confined fluid, we observe that there are two pressures, the integral and the differential pressures. We use molecular simulations to investigate and confirm the nanothermodynamic relations for a representative elementary volume (REV). For a model system of a single-phase fluid in a face-centered cubic lattice of solid spheres of varying porosity, we calculate the fluid density, fluid-solid surface tension, replica energy, integral pressure, entropy, and internal energy.

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“…T. L. Hill was the pioneer who tried to extend thermodynamics for small systems 2,3 . His approach, named now as nanothermodynamics [4][5][6] , is attracting much renewed interest [7][8][9][10][11][12][13][14] (see the monograph of Bedeaux, Kjelstrup and Schnell 7 for a recent review). Is it necessary to resort to Hill's nanothermodynamics to study the dimensional cross-over problem described above?…”

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confidence: 99%

Thermodynamics, statistical mechanics and the vanishing pore width limit of confined fluids

2023

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Temperature, particle number and volume are the independent variables of the Helmholtz free energy for a bulk fluid. For a fluid confined in a slit pore between two walls, they are usually complemented by the surface area. However, an alternative choice is possible with the volume replaced by the pore width. Although the formulations with such two sets of independent variables are different, we show they are equivalent and present their relations. Corresponding general statistical-mechanics results are also presented. When the pore width becomes very small, the system behaves rather like a two-dimensional (2D) fluid and one can wonder if thermodynamics still holds. We find it remains valid even in the limit of vanishing pore width and show how to treat the divergences in the normal pressure and the chemical potential so that the corresponding 2D results can be obtained. Thus, we show that the Gibbs surface thermodynamics is perfectly capable of describing small systems.

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Legendre-Fenchel transforms capture layering transitions in porous media

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...

Cited by 6 publications

References 23 publications

Nanoscale thermodynamics needs the concept of a disjoining chemical potential

Nanoscale thermodynamics needs the concept of a disjoining chemical potential

Defining the pressures of a fluid in a nanoporous, heterogeneous medium

Thermodynamics, statistical mechanics and the vanishing pore width limit of confined fluids

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