Page 36 - Adsorbents fundamentals and applications

EQUILIBRIUM ISOTHERMS AND DIFFUSION 21

where
RT
C = (3.10)
βE 0
where E 0 is the characteristic energy of adsorption of a standard vapor (usually
benzene). A theoretical basis has been given for the D–R equation (Chen and
Yang, 1994), by a simple statistical mechanical derivation assuming a mean field
that is related to the characteristic energy and some simplifying manipulations.
This mean field was later related to the pore dimension and other properties
(Chen and Yang, 1996; Hutson and Yang, 1997).
The exponent “2” in the D–R equation can be replaced by n, which is called
the Dubinin–Astakhov equation (or D–A equation). The value of n empirically
ranges from below 1 to about 14 (Kapoor and Yang, 1988; Kapoor et al., 1989a).
The parameter n can be related to heterogeneity (Jaroniec and Madey, 1988;
Rudzinski and Everett, 1992). The theoretical basis given by Chen and Yang
(1994) is also valid for the D–A equation.
The potential theory isotherm can be extended to adsorption of mixed gases,
as done by Bering et al. (1963 and 1965), and reviewed in Yang (1987). The
model by Grant and Manes (1966) has been discussed in detail by Yang (1987).
A simple and explicit model has been proposed by Doong and Yang (1988),
which is given below. Doong and Yang (1988) extended the D–R equation to
mixed-gas adsorption in a simple way by using the concept of maximum available
pore volume without any additional equations such as the Lewis relationship (see
Yang, 1987). For binary mixtures:

2

P 01
V 1 = (V 01 − V 2 ) exp − C 1 ln (3.11)
P 1
2

P 02
V 2 = (V 02 − V 1 ) exp − C 2 ln (3.12)
P 2
In Eq. 3.11, V 01 is the limiting pore volume for component 1 and V 2 is the
actual adsorbed amount for component 2. All parameters that characterize the
gas-sorbent system for the single gases remain unchanged for the mixture. The
two equations can be solved easily. This model can be readily extended to mul-
ticomponent mixtures. This model has been applied favorably for fitting experi-
mental data (Doong and Yang, 1988). It has been used recently for the adsorption
of mixtures of CO 2 /H 2 O on NaX zeolite and γ -alumina (Rege and Yang, 2001a),
and it compared favorably against the ideal adsorbed solution theory. The D–A
equation can be extended in the same manner as the D–R equation, by retaining
the individual exponent (n i ) for each component (Takahashi et al., 2001).
Wood (2002) has recently made an extensive comparison of different models
for predicting mixture adsorption from single-component D–R isotherms. The
data of a total of 93 binary mixtures of organic vapors on activated carbon were
compared. Despite the simplicity of the model (Eqs. 3.11 and 3.12), predictions
were among the best.