(109e) Expansion and Contraction of Mesoporous Adsorbents: Macroscopic Approach and Density Functional Theory
In the course of gas adsorption-desorption cycles the volume of porous adsorbents non-monotonically changes. This phenomenon, called adsorption-induced deformation, has been known for decades , however, the theory is still lacking. The theory of adsorption-induced deformation was presented recently for different microporous materials: zeolites  and carbons . Experiments show [1,4] that adsorption-induced deformation of mesoporous materials is qualitatively different from the microporous ones. We exploit thermodynamic approach (suggested in [2,3] for micropores) to couple adsorption stress with the grand potential of the pore with adsorbed fluid. We use two different methods to obtain the grand potential as a function of adsorbate pressure. The first one is Derjaguin ? Broekhoff - de Boer (DBdB) macroscopic theory [5,6], which describes the interactions of the adsorbed phase with the substrate in terms of disjoining pressure. This method allows us to derive analytical expressions for the dependence of the adsorption stress on the adsorbate pressure, and demonstrates semi-quantitative agreement with experimental data [1,4]. However, because of its macroscopic nature, DBdB theory works worse for mesopores smaller 8 nm. We also use quenched solid density functional theory (QSDFT)  to calculate the grand potential and describe adsorption deformation. Since QSDFT does not exploit macroscopic values (surface tensions, disjoining pressure, etc.), its predictions have no lower limit on the pore size. We also show on example of nitrogen and argon adsorption on porous silica, that for pore size ~8 nm and larger the predictions of QSDFT and DBdB theories fairly coincide. It should be noticed that comparison of our results with experimental strain isotherms can serve as an indirect method for measuring the solid-liquid surface tension, which is not readily available. This comparison also provides an estimate of the bulk modulus of saturated and partially saturated porous bodies.
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