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Gibbs Ensemble Monte Carlo Simulation of Fluids in Confinement: Relation between the Differential and Integral Pressures

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Open AccessArticle

Two-Phase Equilibrium Conditions in Nanopores

1
PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
2
Engineering Thermodynamics, Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands
3
Department of Materials Science and Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Nanomaterials 2020, 10(4), 608; https://doi.org/10.3390/nano10040608
Received: 25 February 2020 / Revised: 20 March 2020 / Accepted: 21 March 2020 / Published: 26 March 2020
(This article belongs to the Special Issue Nanoscale Thermodynamics)
It is known that thermodynamic properties of a system change upon confinement. To know how, is important for modelling of porous media. We propose to use Hill’s systematic thermodynamic analysis of confined systems to describe two-phase equilibrium in a nanopore. The integral pressure, as defined by the compression energy of a small volume, is then central. We show that the integral pressure is constant along a slit pore with a liquid and vapor in equilibrium, when Young and Young–Laplace’s laws apply. The integral pressure of a bulk fluid in a slit pore at mechanical equilibrium can be understood as the average tangential pressure inside the pore. The pressure at mechanical equilibrium, now named differential pressure, is the average of the trace of the mechanical pressure tensor divided by three as before. Using molecular dynamics simulations, we computed the integral and differential pressures, p ^ and p, respectively, analysing the data with a growing-core methodology. The value of the bulk pressure was confirmed by Gibbs ensemble Monte Carlo simulations. The pressure difference times the volume, V, is the subdivision potential of Hill, ( p - p ^ ) V = ϵ . The combined simulation results confirm that the integral pressure is constant along the pore, and that ϵ / V scales with the inverse pore width. This scaling law will be useful for prediction of thermodynamic properties of confined systems in more complicated geometries.
Keywords: pressure; confinement; equilibrium; thermodynamic; small-system; hills-thermodynamics; pore; nanopore; interface pressure; confinement; equilibrium; thermodynamic; small-system; hills-thermodynamics; pore; nanopore; interface
MDPI and ACS Style

Rauter, M.T.; Galteland, O.; Erdős, M.; Moultos, O.A.; Vlugt, T.J.H.; Schnell, S.K.; Bedeaux, D.; Kjelstrup, S. Two-Phase Equilibrium Conditions in Nanopores. Nanomaterials 2020, 10, 608.

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