Page 45 - Adsorption Technology & Design, Elsevier (1998)

42 Fundamentals of adsorption equilibria

3.3.3 The Freundlich isotherm
There is abundant evidence to show that, for many systems, the heat of
adsorption decreases in magnitude with increasing extent of adsorption. If
the decline in heat of adsorption is logarithmic, it implies that adsorption
sites are distributed exponentially with respect to an adsorption energy
which differs between groups of adsorption sites. This is precisely the
assumption made by Zeldowitch as early as 1935 in his derivation of a now
classic isotherm reflecting the variation in heat of adsorption with coverage.
The equation obtained by Zeldowitch is synonymous with the well-known
Freundlich isotherm, previously considered to be an empirical isotherm.
Although the derivation of the isotherm by Laidler (1954) will not be
recapitulated here, the theory leads to

RgT
In0 - ~ In p + constant (3.12)
Q0

for small values of 0. Qo is a constant Contained in a term exp(Q/Qo) which
Zeldowitch introduced to account for the way in which the energy of
adsorption sites was distributed. Equation (3.12) may be recast into the
familiar Freundlich isotherm
0 = kp TM (3.13)

valid for n > 1. Unlike the Langmuir isotherm it does not indicate an
adsorption limit when coverage is sufficient to fill a monolayer (0 = 1).
The isotherm may be regarded as a convenient representation of the Lang-
muir equation at intermediate coverages (0 < 0 < 1). Application of the
Freundlich equation to the adsorption of organic chemicals onto carbons is
common and the hybrid Langmuir-Freundlich theory has proved useful in
correlating data for the adsorption of gas mixtures.

3.3.4 The Brunauer-Emmett-TeUer (BET) equation
Except for type I (Langmuir) isotherms, all the other types referred to in
Section 3.2 imply that the extent of adsorption does not reach a limit
corresponding to completion of a monolayer. The formation of multilayers,
however, is implicit in the theory proposed by Brunauer, Emmett and Teller
(1938) who, in agreement with Langmuir, argued that the rate of condensa-
tion (adsorption) onto the bare surface equals the rate of evaporation from
the first layer of adsorbate. If 0 denotes the fraction of surface which is bare
and Zm 01 the number of first layer sites occupied (in which Zm is the number
of molecules necessary to complete a monolayer and 01 is the corresponding