Polanyi potential theory

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. 

Peculiarities of Adsorption in Microporous Carbons (the Polanyi Potential Theory Dubinin and Related)... 

Fig. 3.3. Equipotential contours according to the Polanyi potential theory.

In Eq. (31), Pq is the saturation pressure and Pc is the pore condensation pressure. The assumed exponential dependence of the condensation pressure on the adsorption free energy change is similar in basis to the Polanyi potential theory [101] and the Frenkel-Halsey-Hill (FHH) theory [102-104]. In the HK method, the mean free energy change due to adsorption is calculated... 

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... 

Hobson and co-workers (1963, 1967, 1969, 1974) and Eamshaw and Hobson (1968) analysed the data of argon on Coming glass in terms of the Polanyi potential theory. They proposed an equation relating the amount adsorbed in equivalent liquid volume (V) to the adsorption potential... 

Based on the Polanyi potential theory, different approaches to describe the adsorption behavior of a purely microporous material (isotherm type I, Figure 21.25) have been undertaken by Dubinin and Stockli in collaboration with different other scientists. The simplest relationship that can be considered the base for all other variants is the Dubinin-Radushkevich equation [58] ... 

The experimental verification of the Polanyi potential theory can be carried out by calculating the characteristic curve from one experimental isotherm and in determining from the characteristic curve the adsorption isotherms at any other temperature. It is essential that the basic isotherm used for obtaining the characteristic adsorption curve should cover the whole range of values and followed with great accuracy. 

The Polanyi potential theory successfully represents the temperature dependence of adsorption. It is also the only theory that gives quantitative description of physical adsorption on strongly heterogeneous surfaces, such as those of active carbons and oxide gels. However, the significance of the theory had been limited for a long time because it did not provide an analytical expression for the adsorption isotherm. This problem was solved by Dubinin and coworkers. ... 

Urano et al. combined the generalizations of the Polanyi potential theory and the Freundlich isotherm equation to derive a relationship that these workers claimed could successfully predict the adsorption isotherms for several organic compounds from aqueous solutions on active carbons. Their adsorption equation is represented as... 

Having calculated the curve characteristic for a given temperature it is possible to determine adsorption isotherms at other temperatures. The Polanyi potential theory does not give a definite equation of adsorption isotherm which, to some extent, replaces the characteristic adsorption equation. 

The DR isotherm remained known to a relatively small group of researchers until Hobson called attention to its applicability to non porous surfaces. In a letter to the Journal of Chemical Physics, Hobson, not without wonder, observed that the appearance of the Dubinin-Radushkevich equation in the present context (submonolayer adsorption of nitrogen on Pyrex) is surprising for two reasons. First, it is a particular equation within the Polanyi potential theory, which is a theory of condensation and might not be expected to apply to physical adsorption at very low coverage. Second, most of the adsorbents to which the Dubinin-Radushkevich equation have been applied have been porous, whereas our conclusion suggests that Pyrex is non-porous for nitrogen. Thus, unless and until a basic derivation for this equation is provided, it can only be considered as a useful empirical relation . 

Rosene and Manes studied the effect of pH on the total adsorption from aqueous solutions of sodium benzoate + benzoic acid by activated charcoal. They interpreted their data in terms of the Polanyi potential theory applied to bisolute adsorption (see later p. 117), in which the concentrations of neutral benzoic acid and benzoate anions depend on the pH of the solution (activity coefficient corrections were ignored). They confirmed that, at constant total equilibrium concentration, the adsorption dropped from a relatively high plateau for pH <2 down to a small adsorption at pH >10. The analysis of results is somewhat more complex than with essentially non-electrolyte adsorption, and in this case there were additional effects involving chemisorption of benzoate ion by residual ash in the carbon which had, therefore, to be eliminated. Even with ash-extracted carbon there was evidence of some residual chemisorption. The theoretical analysis correlated satisfactorily with the experimental data on the basis that at pH >10 sodium benzoate is not physically adsorbed and that the effect of pH is completely accounted for by its effect on the concentration of free acid. In addition the theory explains successfully the increase in pH (called by the authors hydrolytic adsorption ) when solutions of sodium benzoate are treated with neutral carbon. However, no account is taken in this paper of the effect of pH on the surface charge of the carbon. 

An alternative approach to multisolute adsorption is by application of the Polanyi potential theory. Its use for binary solute systems was outlined in reference 3 (pp. 111-114) Rosene and Manes have now extended consideration to ternary solute systems. The same principles apply as in the binary solute case the driving force for adsorption per unit volume is... 

A further complication arises from shifts in chemical equilibria between the adsorbing components, and this is particularly marked in the case of organic acids and their salts, where the effect of pH must be taken into account (see earlier p. 109). Other accounts of the application of the Polanyi potential theory are given by Rosene " and Ozcan." ... 

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... 

Microporous materials exhibit type 1 isotherms since the size of the pores restricts adsorption into a few layers. The Held strength within the pores is so great that it is difficult to determine whether the adsorbate packs as a liquid or in a more condensed form. Polanyi [51] assumed that above the critical temperature the adsorbate can adsorb only as a vapor whose density increases as it approaches the surface around the critical temperature the vapor near the surface starts to liquefy, and substantially below the critical temperature the adsorbate completely liquefies. Under this final condition, the adsorbed volume of liquid (v) can be determined from the adsorption isotherm. Polanyi potential theory states that the adsorption potential for adsorbate in the liquid state is given by the isothermal work required (e) to compress the vapor from its equilibrium pressure (P) to its saturated vapor pressure... 

This equation is based on the Polanyi potential theory for the determination of micropore volume [53,54]. In this theory it is postulated that the force of attraction at any point in the adsorbed film is given by the adsorption potential (e), defined as the work done by... 

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