Polanyi adsorption potential

Semiernpirical Isotherm Models. Some of these models have been shown to have some thermodynamic inconsistencies and should be used with due care. They include models based on the Polanyi adsorption potential (Dubinin-Radushkevich, Dubinin-Astakhov, Radke-Prausnitz, Toth, UNI LAN. and BET). 

Fractal geometry has been used to describe the structure of porous solid and adsorption on heterogeneous solid surface [6-8]. The surface fractal dimension D was calculated from their nitrogen isotherms using both the fractal isotherm equations derived from the FHH theory. The Frenkel-Halsey-Hill (FHH) adsorption isotherm applies the Polanyi adsorption potential theory and is expressed as ... 

Weber and Van Vliet [20] briefly described the Michigan Adsorption Design and Applications Model (MADAM), which includes both equilibrium and kinetic considerations, while Manes [729] advocated the use of the Polanyi adsorption potential theory, even to account for pH effects neither of these approaches includes a description of the role of carbon surface chemistry. 

The Dubinin-Radushkevich (DR) equation was originally devised as an empirical expression of the Polanyi adsorption potential theory, and due to its simplicity it has been widely used to correlate adsorption data in many microporous sohds despite its failure in giving the correct Henry constant at extremely low pressures. This equation is based on the premise that adsorption in micropores follows a mechanism of pore filhng rather than the molecular layering and capillary condensation as proposed for mesoporous sofids. It has the form ... 

The three isotherms discussed, BET, (H-J based on Gibbs equation) and Polanyi s potential theory involve fundamentally different approaches to the problem. All have been developed for gas-solid systems and none is satisfactory in all cases. Many workers have attempted to improve these and have succeeded for particular systems. Adsorption from gas mixtures may often be represented by a modified form of the single adsorbate equation. The Langmuir equation, for example, has been applied to a mixture of n" components 11). 

Polanyi s potential theory of adsorption views the area immediately above an adsorbent s surface as containing equipotential lines which follow the contour of the surface potential. When a molecule is adsorbed it is considered trapped between the surface and the limiting equipotential plane at which the adsorption potential has fallen to zero. Figure 9.1 illustrates these equipotential planes. In the diagram, Y represents a pore and X depicts some surface impurity. 

This was a theme that Polanyi repeated in a colloquium that he organized at Berlin in the spring of 1929 and in a paper in June 1929, [26] shortly before coauthoring a paper with London in 1930, demonstrating that the adsorption potential of an adsorbent decreases with the distance from the adsorbent wall just as Polanyi had first argued in 1914. The old-fashioned potential gradient now had a firm theoretical basis in the new quantum mechanics. [27]... 

Polanyi, The potential theory of adsorption," 1013, n. 2. Polanyi noted that Arnold T. Eucken had introduced the term Ad-sorptionspotential in 1914, a few months before Polanyi s first paper on the subject. 

Polanyi, The potential theory of adsorption, 1010. The chemist Hermann F. 

A major development in understanding the adsorption of gases and vapors on microporous carbons was provided by the potential theory of adsorption by Polanyi. This theory assumes that, on the adsorbent surface, the gas molecules are compressed by attractive forces acting between the surface and the molecules, and these forces decrease with the increasing distance from the surface. The force of attraction at any given point near the surface is measured by the adsorption potential (A), which can be defined as the work done to transfer a molecule from the gas phase to a given point above the surface. 

Polanyi described the adsorption space as a series of equipotential surfaces, each one with a given adsorption potential (A) and each one enclosing a volume (W). As one moves away from the surface, the adsorption potential decreases until it goes to zero and the adsorption space increases up to a limiting value, W0 (where the potential becomes zero). On the surface, W= ) and A, = Amax. The building of the volume enclosed within the adsorption space is described by a function of the type A = flW). 

Polanyi expressed the adsorption potential (A) for a volume filling (W) as the work necessary to compress the adsorptive from its equilibrium pressure, P to the compressed adsorbate pressure, P2 ... 

The temperature invariance of the adsorption potential (fundamental postulate of Polanyi s theory) has been widely proved, especially, by the extensive work led by Dubinin [31-34],... 

Dubinin and coworkers, during the course of their extensive studies on activated carbons, have developed the so-called theory of volume filling of micropores. Based on numerous experimental data, Dubinin and collaborators have added a second postulate to the Polanyi theory, which complements it. For an identical degree of filling of the volume of adsorption space, the ratio of adsorption potentials for any two vapors is constant ... 

The Dubinin adsorption isotherm equation is a good tool for the measurement of the micropore volume. This isotherm can be deduced with the help of Dubinin s theory of volume filling, and Polanyi s adsorption potential [11,26], The Dubinin adsorption isotherm equation has the following form [11]... 

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... 

Polanyi recognized in 1914 that there was an analogy between adsorption and condensation. Through the use of free energy, he arrived at a term called the adsorption potential, for component... 

Adsorption, and chemisorption in particnlar, is closely allied to heterogeneons catalytic reactions both involve similar mass and heat transport constraints, in addition to bond formation at the solid snrface. In fact, adsorption is viewed as a precnrsor to catalytic reaction, and desorption is viewed as the step snbseqnent to the reaction itself. Adsorption of the reactant(s) and prodnct(s) must be strong enongh to deflect the original bonds, bnt not so strong as to poison the catalyst. This phenomenon has been related to the adsorption potential snggested by Polanyi (see Section 14.3.2). 

A third general approach to the correlation of adsorption equilibria for mi-croporous adsorbents was developed by Dubinin [15,16] from ideas originally suggested by Polanyi [17] and Berenyi [18,19]. The adsorbed phase within the micropores is assumed to behave as a liquid but, as a result of the force field of the adsorbent, the properties differ from those of the bulk liquid sorbate. The difference in free energy between the adsorbed fluid and the saturated liquid sorbate at the same temperature is referred to as the adsorption potential (s) which, assuming an ideal vapor phase, may be calculated from... 

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