Modeling of Adsorption in Finite Cylindrical Pores by Means of Density Functional Theory

Abstract

Adsorption of argon at its boiling point in finite cylindrical pores is considered by means of the non-local density functional theory (NLDFT) with a reference to MCM-41 silica. The NLDFT was adjusted to amorphous solids, which allowed us to quantitatively describe argon adsorption isotherm on nonporous reference silica in the entire bulk pressure range. In contrast to the conventional NLDFT technique, application of the model to cylindrical pores does not show any layering before the phase transition in conformity with experimental data. The finite pore is modeled as a cylindrical cavity bounded from its mouth by an infinite flat surface perpendicular to the pore axis. The adsorption of argon in pores of 4 and 5 nm diameters is analyzed in canonical and grand canonical ensembles using a two-dimensional version of NLDFT, which accounts for the radial and longitudinal fluid density distributions. The simulation results did not show any unusual features associated with accounting for the outer surface and support the conclusions obtained from the classical analysis of capillary condensation and evaporation. That is, the spontaneous condensation occurs at the vapor-like spinodal point, which is the upper limit of mechanical stability of the liquid-like film wetting the pore wall, while the evaporation occurs via a mechanism of receding of the semispherical meniscus from the pore mouth and the complete evaporation of the core occurs at the equilibrium transition pressure. Visualization of the pore filling and empting in the form of contour lines is presented.

On the Cavitation and Pore Blocking in Slit-Shaped Ink-Bottle Pores

“…However, molecular fluctuation theory, as first proposed by Hill, 38 can provide a feasible mechanism, at least in general terms. [39][40][41] The filling of pores by condensation is expected to occur when the growing adsorbate layers form bridges that increase in size until a pressure where fluid fills the vapor space. 31,42 The nucleation processes in the adsorbate fluid that precede bridging would be controlled to a large extent by the adsorbent potential energy field that tends to order the layers.…”

“…None of these advances has been able to explain comprehensively the different shapes of observed hysteresis loops and do not support a general explanation of the observations. However, molecular fluctuation theory, as first proposed by Hill, can provide a feasible mechanism, at least in general terms. − The filling of pores by condensation is expected to occur when the growing adsorbate layers form bridges that increase in size until a pressure where fluid fills the vapor space. , The nucleation processes in the adsorbate fluid that precede bridging would be controlled to a large extent by the adsorbent potential energy field that tends to order the layers. , When pressure is decreased during the desorption stage, fluctuations in the filled pore will create intermolecular spaces that increase in size as the pressure is lowered; eventually, these spaces will cluster into cavities that become unstable, and emptying occurs. Discussions of nucleation and cavitation in liquids are widespread in the scientific literature .…”

Wetting in a two-dimensional capped capillary. Part I: Wetting temperature and capillary prewetting

“…As is typical in the DF theories of fluids with vapour-and liquid-like densities, we model the solid substrate as an inert spectator phase, accounting for its presence by an additive external potential (second term in equation ( 2)). A different model for the substrate, where it, in turn, can be affected by the fluid, has been adopted by Ustinov and Do in [49] for wetting on a cylinder. The external potential due to the substrate acting on the fluid is obtained by integrating the LJ potential over the volume of the substrate.…”

“…An optimal model for the substrate potential can use ab initio results [60,61], and possibly account for the effect of the fluid on the substrate, instead of modelling it as an inert phase [49].…”

Prediction of Adsorption Isotherms and Selectivities: Comparison between Classical Density Functional Theory Based on the Perturbed-Chain Statistical Associating Fluid Theory Equation of State and Ideal Adsorbed Solution Theory

“…The most common confined system studied with DFT models is the slit-shaped pore defined by two opposing perfectly planar walls. However, also other geometries were studied comprehensively, such as cylindrical pores − and spherical cavities. , Phenomena of adsorption isotherms of ink-bottle type pores were evaluated using results obtained from DFT. The introduction of a two-dimensional external potential enabled the investigation of slit-shaped pores composed of chemically inhomogeneous walls .…”