Polanyi adsorption potential concept

In the second picture, an interfacial layer or region persists over several molecular diameters due to a more slowly decaying interaction potential with the solid (note Section X-7C). This situation would then be more like the physical adsorption of vapors (see Chapter XVII), which become multilayer near the saturation vapor pressure (e.g.. Fig. X-15). Adsorption from solution, from this point of view, corresponds to a partition between bulk and interfacial phases here the Polanyi potential concept may be used (see Sections X-7C, XI-1 A, and XVII-7). 

The Dubinin-Radushkevieh (DR) equation is usually applied to describe the physical adsorption of organic vapors on microporous adsorbents. It is based on the micropore volume-filling theory and the Polanyi concept of adsorption potential. The DR equation can be expressed as... 

The concept of a pore potential is generally accepted in gas adsorption theory to account for capillary condensation at pressures well below the expected values. Gregg and Sing ° described the intensification of the attractive forces acting on adsorbate molecules by overlapping fields from the pore wall. Adamson has pointed out that evidence exists for changes induced in liquids by capillary walls over distances in the order of a micron. The Polanyi potential theory postulates that molecules can fall into the potential field at the surface of a solid, a phenomenon which would be greatly enhanced in a narrow pore. 

In the Dubiiiin-Radushkevitch (DR) equation [115], an adsorption model derived from a concept of Dubinin [20] based on Polanyi potential theory, the fluid volume V adsorbed in micropores at pressure P is represented empirically as... 

This model for mixed adsorption (Grant and Manes 1966) is based upon the idea of equipotential energies among the components of the adsorbed mixture and is thus related to the Polanyi potential theory discussed in Section 3.3.5. As previously recorded, Dubinin and Radushkevich (1947) postulated a direct relation between the affinity coefficient Pi of a component i and the molar volume Vmt of the saturated pure liquid. The equipotential energy concept for two components is thus (eiiPi) = (ey/ft). Hence, by use of equation (3.18) for each component... 

Equation (7.24) is of fundamental importance in surface sdence. It rdates interfadal forces with the adsorption of a vapor to a solid surface. The concept goes back to Michael Polanyi and it is known as the potential theory of adsorption [802]. The basic idea is that vapor molecules close to a surface feel a potential-similar to the gravitation field of the earth. The potential isothermally compresses the gas dose to the surface. Once the pressure becomes higher than the equilibrium vapor pressure, it condenses and forms a liquid film. 

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