Physical Adsorption in Micropores:  A Condensation Approximation Approach

Abstract

An approach to adsorption in micropores is developed on the basis of the condensation approximation method. In the case of micropores with half-width less than 0.8 nm, a volume filling of the single micropore and a two-dimensional (2D) condensation on its walls occur at the same critical pressure, pc. From this point of view, the statistical mechanical theories of adsorption on homogeneous surfaces considering lateral interactions may be taken to be a starting point to the description of physical adsorption in micropores. The increased well depth, *, in micropores causes the 2D condensation on their surface to occur at a smaller pc compared with a nonporous surface. As a consequence, the overall adsorption isotherm is determined by the distribution of micropore walls over adsorption energies resulting from a random distribution of micropore widths, d. Proceeding from a model of heterogeneity and the normal distribution of micropore widths, the log-normal distributions of micropore volumes over * and pc are obtained, and an occupied adsorption volume as a function of outer pressures is found. This approach has been successfully applied to seven benzene adsorption isotherms on four species of active carbons. It provides a correct description of equilibrium data in a wide temperature range, leads to reasonable distribution function of * and d, and gives values of an average micropore size that are close to the experimental one.S0743-7463(97)01211-0 CCC: $15.00

Interpreting Pore Dimensions in Gas Shales Using a Combination of SEM Imaging, Small-Angle Neutron Scattering, and Low-Pressure Gas Adsorption

“…After degassing, the sample was loaded for adsorption with the desirable P / P 0 ranging from 0.001 to 0.950 for both adsorption and desorption. At −196 °C, adsorbate N 2 upon contact with the solid binds on the grain boundary because of condensation approximation . The amount of gas adsorbed is a function of relative pressure ( P / P 0 ), where P is the absolute equilibrium pressure and P 0 is the condensation pressure of nitrogen, measured by the volumetric method. − The adsorbed gas volume depends on the surface geometry and the local energies associated with that specific surface. ,, Shale adsorption isotherm using low-pressure N 2 adsorption falls in the type IV isotherm (as N 2 adsorption can only access the mesopores) and H3 hysteresis pattern of the IUPAC classification of sorption isotherms. ,,− In mesopores of shales, multilayer and capillary condensation is due to fluid–wall and fluid–fluid attractive interactions and gas condensation to a liquidlike phase at pressure ( P ) less than the saturation pressure ( P 0 ) of the bulk liquid.…”

Contribution of a Repulsive Potential in a Micropore Volume Filling. A Surface of Micropore Walls

“…Gregg and Sing − suggested that a monolayer formation on the pore walls significantly enhances the adsorption affinity in the pore core (the volume of the pore remaining after the adsorbed layers are formed on micropore walls) and, thus, that a complete pore filling occurs. It was shown that this suggestion is valid in the case of narrow micropores for which the ratio of adsorption affinity in the pore core to that in the first layer R is greater than 1 . Keeping in mind this phenomenon and models of the adsorption behavior with lateral interactions, an adsorption process in an individual micropore can be describe as follows. , As the pressure is increased from zero, adsorption begins to occur on the pore walls.…”

“…It was shown that this suggestion is valid in the case of narrow micropores for which the ratio of adsorption affinity in the pore core to that in the first layer R is greater than 1 . Keeping in mind this phenomenon and models of the adsorption behavior with lateral interactions, an adsorption process in an individual micropore can be describe as follows. , As the pressure is increased from zero, adsorption begins to occur on the pore walls. When a micropore surface coverage, θ , comes to the critical value at the critical condensation pressure p c , surface condensation is initiated.…”

“…An excess of adsorption energy in micropores with respect to an open graphite surface, Δ ε = ( ε * − ε * 0 ), is given as Proceeding from this equation, the following approximate relation between ε * and d / r 0 was introduced where k is the energy parameter, which may be taken to be 4. Equation 5 is valid for d / r 0 > 1 …”

Steric effects on molecular adsorption at columnar surfaces. A model for the adsorption of pyridine on gold electrodes

“…Recently, Monte Carlo simulations of a simple adsorption model have been made to determine the influence of the diameter and depth of pores present in an ideal columnar-structured (cs) 2D surface (profile) [9]. In this model 2D-condensation at pore walls has been prevented [10]. It was found that the apparent adsorption energy decreases as the pore diameter is decreased and the pore depth is increased.…”