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

Abstract

We have described for the first time the thermodynamic state of a highly confined single-phase and single-component fluid in a slit pore using Hill’s thermodynamics of small systems. Hill’s theory has been named nanothermodynamics. We started by constructing an ensemble of slit pores for controlled temperature, volume, surface area, and chemical potential. We have presented the integral and differential properties according to Hill, and used them to define the disjoining pressure on the new basis. We identified all thermodynamic pressures by their mechanical counterparts in a consistent manner, and have given evidence that the identification holds true using molecular simulations. We computed the entropy and energy densities, and found in agreement with the literature, that the structures at the wall are of an energetic, not entropic nature. We have shown that the subdivision potential is unequal to zero for small wall surface areas. We have showed how Hill’s method can be used to find new Maxwell relations of a confined fluid, in addition to a scaling relation, which applies when the walls are far enough apart. By this expansion of nanothermodynamics, we have set the stage for further developments of the thermodynamics of confined fluids, a field that is central in nanotechnology.

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

“…This equation has been called the Hill-Gibbs equation [17,23]. The temperature, fluid pressure, and solid pressures, chemical potentials, and surface tension are defined from the variables involved as…”

“…The replica energy [27,28] expresses in a simpler way, the energy required to add one more small system to the ensemble of systems under the conditions controlled. The combination of terms can define the integral pressure minus the integral solid chemical potential times number of solid particles [23],…”

“…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 [25,22,23,26]. They have not been studied for a variety of shapes and pore sizes.…”

Special Issue on Nanoscale Thermodynamics

“…The next three papers [3][4][5] concern the pressure of confined fluids and their description in equilibrium. Rauter et al show [3] that the integral pressure is constant across phase boundaries and that this finding is equivalent to assuming validity of Young's and Young-Laplace's law.…”

“…In agreement with this, Máté Erdős et al [4] document the interrelation of the differential and the integral pressure. Galteland et al [5] show how the disjoining pressure can be understood using Hill's theory, and present Maxwell relations for small systems.…”