Adsorption on porous solids — hysteresis

Until now we have mainly treated adsorption onto non-porous surfaces. In reality, most industrial and many natural materials are porous Textiles, paper, bricks, sand, porous rocks, food products, zeolites etc. We start our discussion with a classification of pores according to their size, which is recommended by IUPAC  

This classification is certainly not perfect because the filling of pores is also determined by their shape (cylinders, slits, cones, irregular) and pores may be separate or connected. 

To characterize the size of pores, the hydraulic radius ah was introduced. The hydraulic radius is the ratio of void volume and void area. For a long cylindrical pore of length l and radius r (r -C /) the hydraulic radius is for instance 

Above a certain critical temperature no multilayers should adsorb. Hence, even porous solids should behave like flat surfaces, if no pores of molecular size are present. Capillary condensation plays a role only below the critical temperature. 

Adsorption to porous materials is often characterized by hysteresis in the adsorption behavior. Such a hysteresis is observed when, after the adsorption process, a desorption experiment is done in which the pressure is progressively reduced from its maximum value and the desorption isotherm is measured. During the desorption process, the liquid phase vaporizes from the pores. The desorption isotherm does not precisely track the adsorption isotherm, but lies above it. Moreover isotherms often flatten out with high P/Po values, because filling up of pores decreases the available surface area. 

As a general rule, adsorbates above their critical temperatures do not give multilayer type isotherms. In such a situation, a porous absorbent behaves like any other, unless the pores are of molecular size, and at this point the distinction between adsorption and absorption dims. Below the critical temperature, multilayer formation is possible and capillary condensation can occur. These two aspects of the behavior of porous solids are discussed briefly in this section. Some lUPAC (International Union of Pure and Applied Chemistry) recommendations for the characterization of porous solids are given in Ref. 178. 

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