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)

Abstract

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.

Modeling the Electric Double Layer at the Liposome Vesicle via Classical Density Functional Theory: Solution of Poisson’s Equations for Curved Membranes

“…Moreover, due to the confinement effect, the concentration of cations in contact with the inner wall is higher than that of the outer wall for all concentrations. As we had reported in our previous research, the accumulation of molecules at the concave wall (inner wall) is higher compared to the convex wall (outer wall) due to the entropy effect, even the concave and convex walls have the same size. Note that in our case study, the inner membrane wall is concave with a size of 3σ, while the radius of the convex membrane wall is equal to 9σ.…”

“…Given the importance of vesicles as the best drug nanocarriers, this work has been dedicated to the investigation of the EDL structure at a liposome vesicle membrane as a curved membrane via MFMT incorporated with RPM. Referring to our previous research studies, the curvature drastically impacts the amount of net ion charges inside the spherical cavity and therefore the EDL capacitance. , Also, the curvature effects on ion selectivity leads to excess adsorption . Due to the importance of the curvature on the ionic distribution into the cavity of the liposome vesicle, this study investigates the structure of EDL inside and outside of the curved membrane.…”

“…The weight functions, w i (α) ( r 1 ), have been previously described in the spherical coordinate system F c ex [ ρ i false( r false) ] = 1 2 ∬ ∑ i , j z i z j ρ i ( r i ) ρ j ( r j ) ε | r i − r j | normald r i nobreak0em0.1em⁡ normald r j where the expression “ z i ” and “ z j ” refer to the ion’s valences and | r i – r j | is related to the ion distance.…”

“…The weight functions, w i (α) (r 1 ), have been previously described in the spherical coordinate system. 53 F c ex [ρ i (r)] may be written as…”

“…Referring to our previous research studies, the curvature drastically impacts the amount of net ion charges inside the spherical cavity and therefore the EDL capacitance. 52,53 Also, the curvature effects on ion selectivity leads to excess adsorption. 30 Due to the importance of the curvature on the ionic distribution into the cavity of the liposome vesicle, this study investigates the structure of EDL inside and outside of the curved membrane.…”