BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 88

microporous solids with moderate structural heterogeneity, the use of the isotherm
equations obtained by generalization of DA equation with n = 3 [the JC Eq. (53)
with n = 3] is substantiated better than the use of those generated by DA equation
with n = 2. It is noteworthy that some authors postulated that DA equation can
be used to describe adsorption in uniform micropores several years before this
postulate found some experimental justification. The distribution function F( z ) to-
gether with the quantities and are used to characterize the structural heterogeneity
of microporous solids. Energetic heterogeneity of a microporous solid generated
by the overlapping of adsorption forces from the opposite micropore walls can be
described by the adsorption potential distribution in micropores . This distribution
associated with Eq. (53) is given by:

v

−− 1

n

n

�� A (54)

( ) ( )

− n

n − 1

XAv = br A 1 + -

€‚

mi

b ƒ„

-

The adsorption potential distribution in micropores X mi (A) given by Eq. (54) can
be characterized by the following quantities. Although description of micropo-
rous structures of nanoporous carbons is a difficult and still not fully solved task,
comparative studies of various adsorption models can facilitate elaboration of
methods for characterization of microporous solids. It was shown that the gamma
distribution function F( z ) gives a good description of structural heterogeneity for
many microporous carbonaceous materials. For microporous active carbons with
small structural heterogeneity the JC equation gives a good description of adsorp-
tion in micropores, while the JC equation can be used for adsorption on micropo-
rous active carbons with strong structural heterogeneity [1, 2, 19].

1.2.2.9 DUBININ-RADUSHKEVICH (DR) EQUATION
The Dubinin-Radushkevich (DR) equation, proposed in 1947, undoubtedly oc-
cupies a central position in the theory of physical adsorption of gases and vapors
on microporous solids. The amount adsorbed in micropores a mi is:

=−

(55)

a aa

mi me

where a is the sum of the amount adsorbed in micropores a mi and in mesopores a me .
According to the DR equation a mi is a simple exponential function of the square
of the adsorption potential A:

2

�� A

(56)

aa =

0 exp

− B

-

€‚

mi mi

ƒ„

-

Here B is the temperature-independent structural parameter associated with the
micropore sizes, andbis the similarity coefficient, which reflects the adsorbate