Adsorption potential theory

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 ... 

Single-component adsorption equilibria on activated carbon of the n-alkanes Q-C4 and of the odorant tert-butyl mercaptan were measured at the operating conditions expected in a large-scale facility for adsorbed natural gas (ANG) storage. The experimental data were correlated successfully with the Adsorption Potential theory and collapsed into a single temperature-independent characteristic curve. The obtained isotherm model should prove to be very useful for predicting the adsorption capacity of an ANG storage tank and to size and optimize the operation of a carbon-based filter for ANG applications. 

The main purpose of the present work is twofold (i) to report an extensive set of singlecomponent adsorption isotherm data of the more common natural gas components on activated carbon, and (ii) to present a means of extrapolating the measured data to higher alkanes in order to be able to span the whole composition of a typical natural gas. There is experimental evidence that for the n-alkanes series this can be done using the Adsorption Potential theory, as demonstrated recently by Holland et al. on Westvaco BAX-1100 carbon, and assumed previously by us. - ... 

The Adsorption potential theory has been used extensively for correlating adsorption equilibria on porous adsorbents. It states that for a given gas-solid system the volume of the adsorbed phase, W, is a function of the adsorption potential, (fr. 

The gravimetric measurements, as well as all other conventional adsorption methods, rather than giving the total amount adsorbed, q, give just the amount in excess, q, with respect to that of bulk gas occupjdng the same volume as the adsorbed phase. However, to apply the adsorption potential theory the required variable is q and not ex- In this work, q was estimated from the measured q i value by assuming that the adsorbed-phase volume is equal to the total pore volume of the carbon, = 0.850 cm /g, determined from N2... 

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 ... 

Clarkson CR, Bustin RM, Levy JH. Application of mono/multilayer and adsorption potential theories to coal-methane adsorption isotherms at elevated temperature and pressure. Carbon 1997 35(I2) 1689-1705. 

The POLANYI-DUBININ adsorption potential theory is used to characterize the micropore network of zeolites (ref. 10). An isotherm at a given temperature T (expressed in volume adsorbed per activated zeolite mass unit, W, as a function of the relative pressure p/Pq) is treated in the DUBININ-RADUSHKEVICH model (ref. 11) (denoted D-R) in the linear form log W = f[(Tlog Po/p) ] ... 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

The models presented above have also been reviewed in Ref 18. Recently, an expression for the adsorption potential at the free water surface based on a combination of the electrostatic theory of dielectrics and classical thermodynamics has also been proposed." ... 

The potential theory postulates a unique relationship between the adsorption potential ep and the volume of adsorbed phase contained between that equipotential surface and the solid. It is convenient to express the adsorbed volume as the corresponding volume in the gas phase. 

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). 

R. K. Agarwal and J. A. Schwarz, Analysis of High-Pressure Adsorption of Gases on Activated Carbon by Potential-Theory, Carbon, 26, 873-887 (1988). 

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. 

According to the potential theory the volume V, defined by the adsorbent s surface and the equipotential plane , can contain adsorbate in three different conditions depending upon the temperature. Above the critical temperature the adsorbate can not be liquified and the gas in the adsorption volume V simply becomes more dense near the surface. At temperatures near, but less than the critical temperature, the adsorbate is viewed as a liquid near the surface and a vapor of decreasing density away from the surface. Substantially below the critical temperature... 

The potential theory asserts that the adsorption potential, when the adsorbate is in the liquid state, is given by... 

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. 

Which theory is suitable for a certain application The adsorption theory of Henry is applicable at low pressure. This, however, is natural since it can be viewed as the first term in a series of the adsorption function. A widely used adsorption isotherm equation is the BET equation. It usually fits experimental results for 0.05 < P/P0 < 0.35. For very small pressures the fit is not perfect due to the heterogeneity. For higher pressures the potential theory is more suitable at least for flat, homogeneous adsorbents. It often applies to P/Po values from 0.1 to 0.8. Practically for P/Po > 0.35 adsorption is often dominated by the porosity of the material. A more detailed description of adsorption is obtained by computer simulations [382],... 

Now let us overview the theoretical adsorption models for characterization of the pore structures according to the pore size range. For physical adsorption of the gas molecules on such microporous solids as activated carbons and zeolites, Dubinin and Radushkevich95 developed an empirical equation, which describes the volume filling process in the micropores. Their theory incorporates earlier work by Polanyi96 in regard to the adsorption potential Ad defined as... 

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. 

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