The modified fundamental measure theory (MFMT) has been employed to investigate the effects of inserting a tiny sphere in the center of a nanospherical pore on the structure, adsorption, and capillary condensation of fluids confined in it. In the first part of this Article, we have solved the weighted density integrals for all pores with spherical symmetries, including spherical and bispherical pores. In the second part, we show that the structure, amount of adsorption, and position of the fluid's capillary condensation change drastically when even a very thin sphere, R(s) = 0.01σ, is inserted into the center of a spherical pore (SP). In fact, the existence of a forbidden region around the inner sphere for the case of bispherical pores, even when R(s) = 0.01σ, causes a remarkable shift in both the amount of adsorption and the bulk density at which the capillary condensation occurs. Moreover, the insertion causes a sudden increase in the value of the contact density of the liquid, or the liquid in equilibrium with its vapor, at the wall of the outer sphere compared to that for an SP. In other words, the insertion of a tiny sphere in an SP causes the liquid droplet, which is formed in the center of the SP, to sprinkle throughout the whole nanopore. Also, we have demonstrated that the critical temperature and densities decrease with decreasing radius of the inner sphere.

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.

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