Micropore Analysis

Abstract

As discussed in chapter 4, the state and thermodynamic stability of pure fluids in mesopores depends on the interplay between the strength of fluid-wall and fluid-fluid interactions on the one hand, and the effects of confined pore space on the other hand. The most prominent phenomenon observed in mesopores is pore condensation, which represents a first-order phase transition from a gas-like state to a liquid-like state of the pore fluid occurring at a pressure P less than the corresponding saturation pressure Po of the bulk fluid, i.e., pore condensation occurs at a chemical potential /lless than the value /lo at gas-liquid coexistence of the bulk fluid. The relative pressure where this condensation occurs depends on the pore diameter. The relationship between the pore size and the relative pressure where capillary condensation occurs can be described by the classical Kelvin equation. However, in the classical Kelvin equation the shift from bulk coexistence (/lo-/l), is expressed in terms of macroscopic quantities, whereas a more comprehensive understanding of the underlying physics was achieved only recently by applying microscopic approaches based on the Density Functional Theory (OFT), and computer simulation studies (Monte Carlo and Molecular Dynamics). We have discussed these different approaches from a more theoretical point of view in chapter 4. Here, we will discuss their significance for the pore size analysis of mesoporous materials. 8.2 METHODS BASED ON THE KELVIN EQUATION Adsorption studies leading to measurements of pore size and pore size distributions generally make use of the Kelvin equation [1], which was discussed in chapter 4. The Kelvin equation relates the equilibrium vapor pressure of a curved surface, such as that of a liquid in a capillary or pore (P), to the equilibrium pressure of the same liquid on a planar surface (Po). For a cylindrical pore the Kelvin equation is given by-2yV InP/R =-o rRT (cf 4.58) where r is the surface tension of the liquid, V is the molar volume of the condensed liquid contained in a narrow pore of radius r, R is the gas S. Lowell et al., Characterization of Porous Solids and Powders: Surface Area, Pore Size and Density