Two-Phase Equilibrium Conditions in Nanopores

Abstract

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.

Finite-size effects of diffusion coefficients computed from molecular dynamics: a review of what we have learned so far

“…It has been shown that the physical properties of liquids in confinement such as the pressure, density, viscosity and diffusivity can spatially vary (i.e. evidence of localised phenomena) [151][152][153][154][155][156][157][158][159][160][161]. These local effects typically subside within a couple of molecular diameters away from the walls [162][163][164][165].…”

Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore

“…It is The subdivision potential is defined here as the increase in the total internal energy as the number of slit pores increases while keeping , and constant. This definition is different from the definition in a previous article by us [ 23 ], where only the entropy, volume and number of particles were kept constant and not the surface area. This led to a different expression for the subdivision potential.…”

“…The approach following Gibbs is most popular [ 15 , 16 , 17 , 18 , 19 ]. However, the method of Hill may offer an attractive alternative [ 20 , 21 , 22 , 23 , 24 , 25 ], partly because it may provide an independent check on Gibbs procedure, but also because general geometric scaling relations are obtainable from Hill’s method. We will see that this is also the case in the present study.…”

When Thermodynamic Properties of Adsorbed Films Depend on Size: Fundamental Theory and Case Study

“…This function, which can be viewed as a correction from macroscopic thermodynamics, has been called the subdivision potential, because the process of subdividing the ensemble into a larger number of smaller systems, while keeping , , and constant, requires the energy . It has recently been shown to contain interesting size-scaling laws [ 15 , 19 , 20 ]. The replica energy, the subdivision potential and the scaling laws are particular for the variables that control the ensemble.…”