Page 52 - Partition & Adsorption of Organic Contaminants in Environmental Systems

BET MULTILAYER ADSORPTION THEORY 43

In other words, the b constant in Eq. (4.3), which is related to the molar heat
of adsorption, varies with the range of P in many of these systems. By con-
trast, the nonlinearity in the original Langmuir derivation is attributed to the
degree of site saturation (i.e., to an entropic effect) rather than to an energetic
factor. Thus, unless the observed nonlinearity is proven to be truly entropic
in nature, the isotherm is more appropriately referred to as a Langmuir-type
isotherm, or simply a type I isotherm.

4.3 FREUNDLICH EQUATION

The Freundlich equation was developed mainly to allow for an empirical
account of the variation in adsorption heat with concentration of an adsorbate
(vapor or solute) on an energetically heterogeneous surface. It has the general
form

Q = K f C n (4.5)

where Q is the amount adsorbed per unit mass of the solid (adsorbent); C is
the vapor or solute concentration at equilibrium; K f is the Freundlich constant,
equal to the adsorption capacity at C = 1; and n is an exponent related to the
intrinsic heat of vapor or solute adsorption. The n value is in principle less
than 1, because the adsorption isotherm is commonly concave to the C axis,
and varies with the extent of adsorption (i.e., with Q). Depending on the
adsorbent, the constancy of n may apply to a narrow or wide range of C.It
can be determined from the slope of the plot of log Q versus log C over a spe-
cific range.
Unlike the Langmuir model, the Freundlich equation does not approach
(arithmetic) linearity at low C, nor does it approach a limiting (fixed) adsorp-
tion capacity as C reaches saturation. These features are opposed to the
general adsorption characteristics. Basically, the Freundlich equation with its
adjustable parameters offers a simple mathematical tool rather than a phys-
ical model to account for the energetic heterogeneity of adsorption at differ-
ent regions of the isotherm. Interpretation of the temperature effect on
adsorption by Freundlich equation is generally difficult. This is because the
vapor or solute concentration (C) can be increased by increasing the temper-
ature while the adsorbed mass (Q) usually decreases with increasing temper-
ature. For many applications, however, the Freundlich equation is quite
mathematically convenient.

4.4 BET MULTILAYER ADSORPTION THEORY

The Brunauer–Emmett–Teller (BET) theory (Brunauer et al., 1938) was for-
mulated to deal with submonolayer-to-multilayer vapor adsorption on a solid.