Dubinin-Radushkevich equation characteristic curve

A proper comparison of the N2 and CO2 adsorption experiments as well as the differences between samples is conducted by using the characteristic curves plots [9,10]. The characteristic curves have been calculated by applying the Dubinin-Radushkevich equation [24-25] (eq. 1) to the different adsorption isotherms. 

The best utility of the Dubinin-Radushkevich equation lies in the fact that the temperature dependence of such equation is manifested in the adsorption potential A, defined as in eq. (3.2-30), that is if one plots adsorption data of different temperatures as the logarithm of the amount adsorbed versus the square of adsorption potential, all the data should lie on the same curve, which is known as the characteristic curve. The slope of such curve is the inverse of the square of the characteristic energy E = PEq. 

Dubinin (i960) assumed a distribution of the Gaussian type for the characteristic curve and derived the following, which is called Dubinin-Radushkevich equation. 

The most popular equations used to describe the shape of a characteristic curve or a correlation curve are the two-parameter Dubinin-Radushkevich (DR) equation... 

Characteristic Curve Equation. The first analytical equation of the characteristic curve was proposed by Dubinin and Radushkevich (2) as ... 

In 1947 Dubinin and Radushkevich put forward an equation for the characteristic curve in terms of the fractional filling, W/W0, of the micropore volume, W0. This relation is usually expressed in the form... 

Various attempts were made by Dubinin and his co-workers to apply the fractional volume filling principle and thereby obtain a characteristic curve for the correlation of a series of physisorption isotherms on a zeolite (Dubinin, 1975). As was noted in Chapter 4, the original Dubinin-Radushkevich (DR) equation (i.e. Equation (4.39)) was found to be inadequate and in its place the more general Dubinin-Astakhov (DA) equation was applied (i.e. Equation (4.45)). 

Dubinin, M.M. and Radushkevich, L.V., Equation of the characteristic curve of activated charcoal. Proc. Akad. Sci. USSR 55 (1947) 331. 

Since N2 adsorption is done at 77 K and CO2 at 273 or 298 K, the experiments cannot be directly compared, which introduces strong concerns about the similarities and differences among both adsorptives. Thus, a better way to compare the two experiments is to plot the characteristic curves [33—35, 37], These characteristic curves, obtained applying the Dubinin-Radushkevich (DR) equation [47] to the adsorption isotherms, are the plot of the logarithm of the volume of liquid adsorbed versus the square of the adsorption potential corrected for the affinity coefficient ((3) of the adsorptive ((/l//3) = (RTln(/o//)/[3), T being the temperature, / the fugacity, and/ the saturation fugacity). 

On the basis of volume-filling mechanism and thermodynamic considerations, Dubinin and Radushkevich [19] found empirically that the characteristic curves obtained using the Potential Theory for adsorption on many microporous carbons could be linearized using the Dubinin-Radushkevich (DR) equation. 

Dubinin and his co-workers [156-158] as well as Radushkevich [159] found that the characteristic adsorption curve is related to the porous structure of the adsorbent. Radushkevich [159] proved theoretically the equations of the characteristic adsorption curves for the two extreme types of adsorbents with narrow and wide pores. Based on this Dubinin proposed the expression known in literature as the Dubinin-Radushkevich (DR) isotherm equation [136]. 

Dubinin, M.M. Radushkevich, L. V (1947) The equation of the characteristic curve of the activated charcoal. Proceedings of the USSR Academy of Sciences USSR Physicochimica Section, 55, 331-337. 

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See also in sourсe #XX -- [ , ]

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