A three dimensional integral equation approach for fluids under confinement: Argon in zeolites

Abstract

In this work, we explore the ability of an inhomogeneous integral equation approach to provide a full three dimensional description of simple fluids under conditions of confinement in porous media. Explicitly, we will consider the case of argon adsorbed into silicalite-1, silicalite-2, and an all-silica analogue of faujasite, with a porous structure composed of linear (and zig-zag in the case of silicalite-1) channels of 5-8 Å diameter. The equation is based on the three dimensional Ornstein-Zernike approximation proposed by Beglov and Roux [J. Chem. Phys. 103, 360 (1995)] in combination with the use of an approximate fluid-fluid direct correlation function furnished by the replica Ornstein-Zernike equation with a hypernetted chain closure. Comparison with the results of grand canonical Monte Carlo/molecular dynamics simulations evidences that the theory provides an accurate description for the three dimensional density distribution of the adsorbed fluid, both at the level of density profiles and bidimensional density maps across representative sections of the porous material. In the case of very tight confinement (silicalite-1 and silicalite-2), solutions at low temperatures could not be found due to convergence difficulties, but for faujasite, which presents substantially larger channels, temperatures as low as 77 K are accessible to the integral equation. The overall results indicate that the theoretical approximation can be an excellent tool to characterize the microscopic adsorption behavior of porous materials. C 2015 AIP Publishing LLC. [http://dx

Evidence of a Structural Change in Pure-Silica MEL upon the Adsorption of Argon

“…Coincidentally, an integral equation approach predicts integrated profiles as the one found here for the y-axis, with three peaks at the intersections, although with different relative intensity. 33 This indicates that atoms are located at energetically favored positions.…”

“…The structure of the adsorbed fluid was characterized by evaluating the Ar−Ar and Ar−O average pair distribution functions, as well as one-, two-, and three-dimensional density distribution maps. 33 More details of the simulations can be found in the Supporting Information.…”

Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms

“…The integral equations theory is a significant theory for discussing thermodynamics of multiple spectrum of materials such as soft materials and simple fluids. For instance, Zhou et al (2004) applied the integral equations theory for finding the depletion potential for the colloidal particle, Aguirre-Manzo and González-Mozuelos (2021) discuss the charged colloids with high charges with the salt in suspensions using the theory of the integral equations, Pérez-Molina et al (2021) used the chaotic data with the theory of the integral equations for the estimation of the virial coefficients of the equation of state, Kalyuzhnyi et al (2021) applied the theory of the integral equations with the numerical analysis techniques for the study of the mixtures of colloids, Hashimoto et al (2019) use the theory of the integral equations with the atomic force microscope data for the determination of the number density distribution of colloidal particles on a substrate, Filippov et al (2019) used the theory of the integral equations for the dusty plasma mixtures, Munaò and Saija (2019) studied the hertzian spheres in case of the low temperatures using the theory of the integral equations in addition to the Monte-Carlo simulation, Herrera (2018) found some structural and thermodynamic properties of fluids described by hard sphere and Yukawa potential using the theory of the integral equations, Arauz-Lara showed some application of the integral equations theory to the colloidal fluids, Pizio et al (2011) discussed a model for the simple fluids using the second order of the integral equations theory, Lukšič et al (2011) applied the integral equations theory for the mixtures of the electrolytes and non-charged hard spheres for purpose of the determination of the structural properties and thermodynamics of these mixtures, Fukudome et al (2014) showed a new formula for the direct correlation function for the hard sphere fluids, Wu et al (2014) calculated the static structure factor for the charged spheres using the integral equations theory, Lomba et al (2015) used the three dimensional integral equations approximation for discussing of fluids with confinement and applied in the case of the argon in zeolites, Miyata and Miyazaki (2016) discussed the one component fluids interacting via Lennard-Jones interaction for the study of the temperature derivative of the radial distribution function using the integral equations theory, Melnyk et al (2016) found the structure factor of the fluids of the hard core type interacting via short range Yukawa potential using the integral equations theory and the simulation methods, Al-Raeei (2022a) derived a state equation for London interaction. Also, Al-Raeei (2021) applied the theory for the study of some soft materials, Zhou (2010) discussed the fluids with the honeycomb interaction with the integral equations theory.…”

Connect the Thermodynamics of Bulk and Confined Fluids: Confinement-Adsorption Scaling

“…Such selectivity is extensively exploited in various chemical processes, for example, catalytic cracking in oil industry . Nowadays, it is widely recognized that the properties of fluids confined in porous media can be dramatically different from those of the bulk ones. − Understanding the behavior of confined fluids is important not only from a fundamental point of view but also for conceiving innovative industrial processes.…”

“…A large literature exists on the study of confined fluids by theoretical and simulation methods − ,− (references given here are just for illustration but far from being exhaustive). Models with simple pore geometry (e.g., slit or cylinder) are widely studied.…”