Potential theory of adsorption

The potential theory of adsorption first introduced in 1914 by Polanyi and later modified by Dubinin for adsorption on microporous adsorbents is still regarded as fundamentally sound and accepted as correct and better than all the other theories. This longevity of the theory is due to its essentially thermodynamic character and lack of insistence on a detailed physical picture. 

For an ideahzed, energetically homogeneous surface, aU the points equidistant from the surface will have the same potential s and wiU, therefore, form an equipo-tential plane. Thus, the broken lines in the figure represent planes connecting points of equal potential. The value of the adsorption potential s of the parallel equipotential planes decreases as their distance from the surface increases and falls to zero at the maximum distance. Each equipotential surface encloses between itself and the surface of the adsorbent a volume W. The maximum volume is enclosed between the adsorbent surface and the limiting equipotential plane at which the potential has decreased to zero. Thus, the volumes enclosed between the adsorbent and the equipotential surfaces s= s . .. are W2 W3... The quantity represents the volume of the entire adsorption space. As W increases from zero to 

FIGURE 2.24 Schematic of the surface adsorbed layer according to potential theory. Source Young, D.M. and Crowell, A.D., in Physical Adsorption of Gases, Butterworths, London, 1962, p. 198. With permission.) 

the curves =f(W) should be temperature-independent for a given gas. Since this curve characterizes the given adsorbate-adsorbent system, it is called the characteristic adsorption curve for a given adsorbent. The characteristic curve is the same for all temperatures and, hence, a unique characteristic of a given adsorbent-adsorbate system. 

As the adsorbate is compressed in the field of the adsorption potential, its density cannot be the same throughout the adsorption space but increases from the limiting equipotential surface of zero potential to the surface of the adsorbent where the adsorption potential has the highest value. Therefore, the adsorption potential is nothing but the isothermal work required to compress one mole of a vapor from its equilibrium vapor pressure (gas phase) to the vapor pressure P2 of the compressed adsorbate on the given equipotential surface. Thus, at constant temperature T, the adsorption potential, can be expressed as 

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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. 

In developing his later views on the social practice of science, Polanyi explicitly drew upon his earlier career experiences in the 1920s and 1930s. Two series of investigations at the boundaries of chemistry and physics were prominent among his examples of scientific practice and the distribution of merit within the scientific community. I turn now to these two cases the potential theory of adsorption on solid surfaces and X-ray studies of the solid state. 

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. 

Dubinin MM. The potential theory of adsorption of gases and vapors for adsorbents with energetically nonuniform surfaces. Chem. Rev., 1960 60 235-241. 

Polanyi, M., Discussion of the Potential Theory of Adsorption in Adsorption of Gases and Vapors, by Stephen Brunauer, Princeton University Press, Princeton, N. J., 1947. 

The Frenkel-Halsey-Hill (FHH) isotherm was originally developed to describe the growth of thick films and wetting phenomena on a flat surface and was later extended to studying adsorption on fractal surfaces [3, 55]. In contrast to BET theory, FHH theory applies to long-range adsorbate-absorbent interactions and its approach is closely related to the so-called potential theory of adsorption of Eucken and Polanyi (see Ref. [35]). 

The potential theory of adsorption was introduced by Polanyi in 1914. Dubinin [48,49] and Stoeckli et al. [50] improved the theory and termed it the theory of volume filling of micropores (TVFM). This theory has been widely used in correlating the effect of temperature on the adsorption isotherms of pure gases. The modern formulationof TVFM is the Dubinin-Astakhov (DA) equation, which is expressed as... 

Potential Theory of Adsorption from Dilute Solutions... 

Adsorption theory of the volume filing of micropores (TVFM theory) has been proposed by Dubinin and Radushkievich [136], but this approach has originated from the potential theory of adsorption introduced by Eucken [112] and Polanyi [113,114]. 

Experimental verification of the Polanyi theory deals with the calculation of the characteristic adsorption curve by means of an experimental isotherm and hence determination of the isotherms at different temperatures. The first practical examinations of the potential theory of adsorption carried out by Titoff [137] and Berenyi [138] showed the good agreement with experiment. 

Introduction of heterogeneity indicates insufficiency of the straightforward thermodynamic approach based on common equations of state to express the specificity of interactions between the adsorbed phase and the adsorbent. The two new physical ideas behind Eq. (45) are localization of the adsorbed molecules at different points of the surface (patches) and a possibility of dijferent energetic interaction of the molecules with the surface. These ideas have been developed in a different way in the two other thermodynamic concepts of adsorption the localized approach and the potential theory of adsorption. 

An alternative to the localized theory of adsorption is the so-called potential theory, which has been developed as a slab adsorption theory on a surface and its analog for adsorption in microporous media, the theory of volume filling in micropores (TVFM). The potential theory of adsorption, first formulated by Polanyi [91], is widely used for the description of adsorption of gases on a solid. The TVFM is applied to adsorption in activated carbons, silica gels, and other types of microporous medium. 

The described properties of the potential theory of adsorption make it preferential to the theory of localized adsorption, at least, for complex thermodynamic conditions. On the other hand, the potential theory incorporates specific physical information about the phenomenon of adsorption, which is absent in the general thermodynamic approach. A major disadvantage of the multicomponent potential theory is the computational difficulties arising in the calculation of the multicomponent segregation in the external field. This is the reason why the development of this theory has been delayed until our recent works [92-94]. The development of modem methods of computational thermodynamics [68] has made it possible to perform these calculations quite efficiently. 

Let us first verify that the complete potential theory of adsorption, without introduction of the homogeneous approximation (51) and with the same EoS for the bulk phase and for the adsorbate, is able to correlate experimental data on single-component adsorption. Figure 18 presents an example of successflil correlation of adsorption isotherms of methane and nitrogen on activated carbon at elevated pressures. Experimental data are taken from Refs. 103 (methane at 298 K) and 104 (nitrogen at 210 K). Although the estimate obtained on the basis of the... 

E. Potential Theory of Adsorption and Thermodynamics of Surface Excesses... 

An alternative approach to lAST/RAST which combines a thermodynamic treatment with a specific consideration of fluid-solid interactions is the potential theory of adsorption (Polanyi (1914)-Dubinin (1950)), especially in the form designed for multi-component mixtures pioneered by Shapiro and Stenby (1998). 

Adsorption isotherms for several of the hydrocarbons typically removed from gas streams are given in the previous section of this chapter entitled Properties of Gas Adsorption Carbons. Additional data can be obtained from the carbon manufacturers. A set of equilibrium data for the hydrocarbons and natural gas sulfur compounds on activated carbon (Pittsburgh BPL) has been presented by Grant et al. (1962,1964). These data and some additional experimental data for isobutane and carbon dioxide adsorption on Columbia NXC 8 x 10 carbon have been used by Hasz and Bairere (1964) as a basis for predicting isotherms for all of the common constituents of natural gas using the Polyani potential theory of adsorption (1914). 

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