An Improved Derivative Isotherm Summation Method To Study Surface Heterogeneity of Clay Minerals

Abstract

Due to their crystallochemical properties, clay minerals feature different types of structural surfaces which have their own adsorption energy distribution. To study that type of surface heterogeneity, the DIS (derivative isotherm summation) method has been developed by us. Now, a modified version of the DIS method is derived by using the Jagiełło-Rudziński approach and assuming that the local energy distributions are represented by the Dubinin−Asthakov distributions. Two different types of isotherms equations are used, one to describe adsorption in micropores and another one for describing adsorption on external surfaces. The derivatives of experimental adsorption isotherms with regard to ln(p/p s) are simulated by combinations of the derivatives of corresponding local adsorption isotherms. This best fit provides information on adsorption capacity of the local existing domains, on the symmetry of their energy distribution function, and on the parameters characterizing the lateral interactions in each adsorption domain. Using the new equations for the local isotherm derivatives allows now to simulate very accurately derivatives of experimental adsorption isotherms, obtained by using our high-resolution quasi-equilibrium volumetric technique. This was proven in the case for three different well characterized clay minerals: a structural microporous one (palygorskite) and two nonporous lamellar ones (kaolinites). The obtained parameters allow a description of the adsorption energy distribution of their different surfaces, their textural parameters, as well as the energy distrubution in micropores for the microporous samples. In addition to the experimental adsorption isotherms, the related experimental heats of adsorption were employed as a second independent source of information about the energetic heterogeneity of the studied clay minerals. Using the parameters determined from adsorption isotherms, the corresponding isosteric heats of adsorption were calculated and compared with experimental values. The simultaneous good fit of the experimental isotherm derivatives and of the experimental heats of adsorption was a solid check for the correctness of the determined parameters characterizing the adsorption energy distributions and the lateral interactions between the adsorbed molecules.

Towards a link between the energetic heterogeneities of the edge faces of smectites and their stability in the context of metallic corrosion

“…Using pressure sensors that work 293 14 at low pressures, this method allows the study of surface heterogeneity of solids under 294 appropriate conditions. In the case of phyllosilicates, it has been demonstrated that such 295 adsorption experiments, coupled with a careful analysis of experimental adsorption 296 isotherms, enable a derivation of a shape factor, i.e., lateral and basal surface areas (Bardot et 297 al., 1998;Cases et al, 1986Cases et al, , 2000Michot et al, 1994Sayed-Hassan et al, 2005, 298 2006, Villiéras et al, 1992, 1997a, 1997b, 2002. 299…”

“…The experimental curve can then be fitted with theoretical local 337 isotherms derived from the Langmuir (with Bragg-William-Tempkin improvement to take 338 into account lateral interaction), BET (with Hill improvement to take into account lateral 339 interactions) and Dubinin-Astakhov formalisms (Villiéras et al, 1992(Villiéras et al, , 1997a(Villiéras et al, , 1997b. 340In the present work, experimental derivatives were modeled after mathematical elimination of 341 multilayer adsorption contribution in the low energy region (right hand side of the curves) 342 16 (Villiéras et al, 1997a; Manleev et al, 2002). DIS fitting procedure was then applied to the 343 first layer free energy adsorption distribution using the Bragg-William-Tempkin model as a 344 local adsorption isotherm (Villiéras et al, 1992(Villiéras et al, , 1997a(Villiéras et al, , 1997b.…”

“…The experimental information was analyzed using the Derivative Isotherm Summation (DIS) 318 procedure designed by Villiéras et al (1992Villiéras et al ( , 1997aVilliéras et al ( , 1997b, to examine the surface energetic 319 heterogeneity of the samples. Due to the large number of experimental data points acquired 320 by the quasi-equilibrium technique, the experimental derivative of the adsorbed quantity as a 321 function of the logarithm of relative pressure could be calculated accurately.…”

“…DIS fitting procedure was then applied to the 343 first layer free energy adsorption distribution using the Bragg-William-Tempkin model as a 344 local adsorption isotherm (Villiéras et al, 1992(Villiéras et al, , 1997a(Villiéras et al, , 1997b. Each local isotherm is 345 characterized by three parameters.…”

An IGC Study of the Role of Washing Procedures on the Adsorption Properties of Activated Carbons

“…Although these parameters are of great importance, the magnitude of the adsorption energy is also of interest. Various methods have been developed for such studies such as high-resolution argon adsorption (Villiéras et al 1997), immersion calorimetry (López-Ramos et al 2000;Szymanski et al 2002) and inverse gas chromatography (IGC) (Cossarutto et al 2001;Herry et al 2001). Gas/solid chromatography has also been used for many years for studying adsorption processes and catalytic reactions.…”