Population Inversion, Selective Adsorption, and Demixing of Lennard-Jones Fluids in Nanospherical Pores

Abstract

The density functional theory has been employed to investigate the population inversion, selective adsorption, and demixing of confined mixture fluids in a spherical nanocavity. In the case of hard sphere fluids for which only the entropy effect has the dominant role, the selective adsorption process strongly depends on size ratio, population of the adsorbed component, and pore size. The effects of such parameters as interaction strength, size ratio, and thermodynamic state on population inversion and selective adsorption have been investigated for L-J mixture fluids. The results for L-J asymmetric binary mixture fluids indicate that the mole fraction of large species (molecules with bigger radii) inside the cavity becomes greater with increasing size ratio or with decreasing temperature than does that for the other component despite its lower population in the bulk fluid (i.e., the so-called population inversion phenomenon). Our results indicate that the inversion population density decreases with size ratio, and the mole fraction of the component with the bigger radius in the pore increases with temperature. Thus, by selecting a small spherical cavity under special conditions, it will be possible to give rise to the selective separation of component 2 in spite of its lower concentration in the bulk asymmetric L-J mixture. Finally, we have investigated the phase separation, demixing phenomenon, of an asymmetric L-J mixture inside a spherical cavity. Also we investigated the cases for which the layered demixing phenomenon occurs in the asymmetric L-J fluid in a nanospherical pore as a result of the difference between the entropy and energy effects.

The Effects of Inserting a Tiny Sphere in the Center of a Nanospherical Pore on the Structure, Adsorption, and Capillary Condensation of a Confined Fluid (A DFT Study)

“…The integral limits for weighted densities in MFMT for studying the problem of fluids around a spherical particle have been reported in refs 22 and 24. It should be noted, however, that these integral limits do not apply for fluids around a spherical particle when the radius of the particle is less than σ/ 2. As already mentioned in our previous work, 12 the calculation of the integral of weighted densities is impossible in a direct way for the case of an SP for r 1 < σ/2, where r 1 stands for each point inside the pore. In all previous studies, the weighted densities for these cases were, therefore, solved by convolutions that can be conveniently handled by means of Fourier techniques.…”

“…It should be noted, however, that these integral limits do not apply for fluids around a spherical particle when the radius of the particle is less than σ/2. As already mentioned in our previous work, the calculation of the integral of weighted densities is impossible in a direct way for the case of an SP for r 1 < σ/2, where r 1 stands for each point inside the pore. In all previous studies, the weighted densities for these cases were, therefore, solved by convolutions that can be conveniently handled by means of Fourier techniques. − That is why, not only for the bispherical pore but also for the bicylindrical one, previous studies , calculated the profile of density and the properties of the fluid for cases in which R s > 0.5σ, where R s represents the radius of either the inner sphere or the inner cylinder.…”

“…cut cut (12) where σ is the moleculal diameter and r cut is the cutoff distance which has been assumed to be r cut = 4σ. In this work, we set a hard sphere diameter as a Lennard-Jones diameter, σ.…”

“…Over the past few years, the thermodynamic properties of small systems have been the subject of many theoretical and experimental studies in both physics and chemistry. − It is well-known that the molecular structures and thermodynamic properties of fluids are drastically different from each other in different geometries when the size of the system is in the nanometer scale. Recently, the properties of fluids confined in different nanopores have created a great interest among scientists. − …”

Spatial modulation of the composition of a binary liquid near a repulsive wall

“…Classical density functional theory (DFT) [28] has been used [29,30] in the past to study the density profiles of binary mixtures near walls that have different interactions with the two components of the mixture. We are not aware of any theoretical analysis of the spatial dependence of the composition of a binary liquid near a repulsive wall that has the same interaction with the two components of the mixture.…”