Page 125 - Adsorption by Powders and Porous Solids

110 ADSORPTION BY POWDERS AND POROUS SO~D~

Langmuir equation contains the two disposable constants, n, and b, which cannoth
evaluated by any independent method.
It is now generally accepted that there is no sound reason why isotherms on micra.
porous solids should conform any more closely to the classical Langmuir mechanism
than isotherms on non-porous or mesoporous adsorbents. Indeed, a considerable
amount of the evidence now available gives strong support to the view that the limit.
ing uptake is controlled rather by the accessible micropore volume than by the inter,
nal surface area (Gregg and Sing, 1982).
In the context of gas separation (see Yang, 1987) or for some other purposes, it
may be expedient to apply an equation of the Langmuir form; but we consider it
advisable to treat this as empirical relation. Thus, we may write

where the parameters n, and b are to be regarded as empirical constants within stated
ranges of p and T.
We have concluded that the limiting uptake at the plateau of a Type I isotherm is
not directly related to the surface area. However, it is now appropriate to return
briefly to the initial stage of physisorption by microporous solids and consider the
question: does monolayer adsorption ever precede micropore filling ?
Some time ago Brunauer (1970) argued that monolayer adsorption of nitrogen and
other small molecules does occur on the walls of micropores wider than about
0.7 nm. Although as we have seen, Brunauer's original theory is now questionable,
some recent evidence does support his view that monolayer adsorption can take place
on the walls of the wider micropores before secondary micropore filling occurs.
These aspects are discussed in later chapters.

4.4.4. The Dubinin-Stoeckli theory

Dubinin was the pioneer of the concept of micropore filling. His approach was based
on the early potential theory of Polanyi, in which the physisorption isotherm data
were expressed in the form of a temperature-invariant 'characteristic curve'.
In 1947 Dubinin and Radushkevich put forward an equation for the characteristic
curve in terms of the fractional filling, W/W,, of the micropore volume, W,. This rela-
tion is usually expressed in the form
W/W, = exp [ - (A/EI2I (4.39)
where A, the Polanyi 'adsorption potential', is an adsorption affinity,
A = -RT In (p/pO) (4.40)
and E is a characteristic energy for the given system.
The isotherm equation is obtained by combining Equations (4.39) and (4.40). With
the introduction of a scaling factor, j3, it becomes
~1% exp{ - [RT In (pO/p)l BE,)^ I (4.41)
=
where Eo is a 'characteristic energy'.