BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 73

in the monolayerformed on a given surface is known, the surface area can be
evaluated by using thefollowing formulae:

S =w aN

(5)

BET m A

where N A is the Avogadro number. The derivation of the BET equation involves
the following major assumptions: the surface is flat, all adsorption sites exhibit
the same adsorption energy; there are no lateral interactions between adsorbed
molecules; the adsorption energy for all molecules except those in the first layer is
equal to the liquefaction energy; and an infinite number of layers can be formed.
In the case of adsorption on active carbons, some of these assumptions are often
not valid. In particular, surfaces are geometrically and energetically heteroge-
neous, there are lateral interactions between adsorbed molecules, and interactions
of adsorbed molecules vary with the distance from the surface. Therefore, one
should not expect the monolayer capacity evaluated by the BET method to be
particularly accurate. In addition, the available values of cross sectional area, even
in the case of the most commonly used adsorbates, are somewhat uncertain and
may actually vary from one type of the surface to another [1, 2].
Moreover, the determination of the specific surface area based on the molecu-
lar size and monolayer capacity should be treated with some caution, because the
ability of molecules to effectively cover the surface depends on the molecular
size and surface roughness. Since adsorbed molecules cannot satisfactory probe
the surface on the scale smaller than their size, the surface area determined using
larger molecules might be smaller than that obtained from adsorption data for
smaller molecules. Despite all these problems and limitations, the BET method is
currently a standard way for evaluation of the specific surface area of solids. For
several reasons, nitrogen (at 77 K) is generally considered to be the most suitable
adsorbate for surface area evaluation and it is usually assumed that the nitrogen
monolayer is close packed. For many years nitrogen adsorption data at 77 K have
been used to characterize the porous structures of a variety of materials and refer-
ence nitrogen adsorption isotherms for different nanoporous carbons have been
reported. However, it is possible to characterize nanoporous carbons by using
other adsorbates, some of whichmay be more convenient to use and provide a
better insight into the porous structures. Consequently, reference adsorption data
on carbons have been published for argon and n-butane, benzene, neo pentane
and methanol. In particular, argon deserves much attention, because it was found
to be convenient for the characterization of microporous and mesoporous. The
intercept on the adsorption axis evaluated by the back extrapolation of the -plot-
provides the micropore adsorption capacity :