Micropore Volume Filling. A Condensation Approximation Approach as a Foundation to the Dubinin−Astakhov Equation

Abstract

A volume filling of a single micropore and a two-dimensional (2D) condensation on its walls occur at the same critical pressure, and the local adsorption behavior may be modeled by the condensation approximation. This phenomenon underlies the approach to the micropore volume filling based on the condensation approximation (VFCA) and the Dubinin-Astakhov (DA) equation. The DA equation follows from the VFCA approach, being an approximate form to the general relationship. The physical meanings of the exponent, n, and the characteristic energy, E, with respect to the surface heterogeneity, are given. As a whole, n is determined only by the standard deviation of the micropore widths: the less the heterogeneity, the larger n, approaching to infinity for the homogeneous carbon. The characteristic energy depends on the average micropore sizes and its standard deviation. In the case of the DA equation with n ) 2 or n ) 3, standard deviations are equal to 0.4915 or 0.3493, respectively, and E depends only upon an average micropore size or upon a related adsorption potential. For the individual micropore, E determines the critical pressure of a 2D condensation. In the case of water adsorption on active carbons, the base heterogeneity due to variation in the pore widths, as perceived by water molecules, is negligible. Hence, water adsorption may be considered to be an extension of a 2D-condensation into practically homogeneous micropore volumes. It is shown that empirical relationships for calculating of average micropore sizes and an applicability of the DA equation to the adsorption on nonporous surfaces may be also explained in the framework of the VFCA approach.

Estimating the pore size distribution of activated carbons from adsorption data of different adsorbates by various methods

“…Chen and Yang showed that n is really a structural parameter of carbon [25,38]. Dobruskin [39], considering the physical meaning of the parameters of DA equation, noticed that n does not depend on the pore dimensions and it is determined only by the standard deviation of micropore sizes, hence, it characterizes the surface heterogeneity. Similar conclusion was also provided by Jagiełło and Schwarz [36], Condon [40,41] as well as other authors.…”

VOCs (acetone, toluene, and n-hexane) adsorption equilibria on mesoporous silica (MCM-41) over a wide range of supercritical carbon dioxide conditions: Experimental and theoretical approach by the Dubinin–Astakhov equation

“…Suppose that adsorption phenomenon is pore filling by liquefaction, degree of the filling (u) is given as follows [47]:…”

Adsorption of phenol from aqueous solutions on original and oxidized multiwalled carbon nanotubes

“…Use of so-called non-symmetrical function in the condensation approximation (CA) and Langmuir isotherm (as the local isotherm) results in well-known DA isotherm in the form (Crittenden et al, 1999;Dobruskin, 1998;Podkos´cielny and La´szlo´, 2007;Yang and Xing, 2010;Yang et al, 2008Yang et al, , 2016:…”