Page 35 - Adsorbents fundamentals and applications

20 SORBENT SELECTION: CRITERIA

As in the extended Langmuir equation for mixtures, the hybrid Lang-
muir–Freundlich equation (Eq. 3.3) can also be extended to an n-component
mixture (Yon and Turnock, 1971):

q mi B i P i 1/n i
q i = (3.5)
n
1/n j
1 + B j P j
j=1
This equation is referred to as loading ratio correlation (LRC), and has been
very useful for practical design and process simulation.

3.1.2. Potential Theory Isotherms for Single and Mixed Gases
The isotherms derived from the potential theory have found utility in interpreting
adsorption by capillary condensation, or pore filling. Thus they are especially use-
ful for adsorption on microporous materials such as activated carbon. However,
because the characteristic curve, to be described later, is assumed to be indepen-
dent of temperature, which applies to adsorption by the temperature-independent
dispersion forces, the resulting isotherms are applicable only to relatively nonpo-
lar surfaces. The theory, nonetheless, is general in that it encompasses multilayer
adsorption on energetically nonuniform surfaces.
The potential theory is empirical. It assumes, by Polanyi in 1914 (Yang, 1987),
that the cumulated volume of the adsorbed space, V , is a function of the poten-
tial, ε:

P 0
P 0
ε = F = vdP = RT ln (3.6)
P P
where F is the free energy change upon adsorption and P 0 is the saturated
vapor pressure. The volume in the adsorbed space is

(3.7)
V = nV m
where n = number of moles adsorbed per unit mass of sorbent and V m = molar
volume of adsorbate.
Dubinin (1960) assumed the following empirical form for the adsorbed
amount:
2
ε
V = V 0 exp −k (3.8)
β 2
where V 0 is the limiting volume of the adsorbed space, which equals microp-
ore volume, and β is the affinity coefficient characterizing the polarizability of
the adsorbate. Eq. 3.8 is referred to as the Dubinin–Radushkevich (or D–R)
equation. The D–R equation can be recast into:

2

P 0
V = V 0 exp − C ln (3.9)
P