Page 26 - Adsorbents fundamentals and applications

EFFECTS OF ADSORBATE PROPERTIES ON ADSORPTION 11

energy between the adsorbate molecule and all atoms on the surface. The task is
then to add the interactions, pairwise, with all atoms on the surface, by integration.
It can be shown (Barrer, 1978; Ross and Olivier, 1964) that the isosteric heat
of adsorption ( H) at low coverage is related to the sorbate–sorbent interaction
potential (φ) by
H = φ − RT + F(T ) (2.10)

where F(T ) arises due to the vibrational and translational energies of the adsor-
bate molecule, and for monatomic classical oscillators, F(T ) = 3RT/2 (Barrer,
1978). For ambient temperature, H ≈ φ.

2.3. EFFECTS OF ADSORBATE PROPERTIES ON ADSORPTION:
POLARIZABILITY (α), DIPOLE MOMENT (µ), AND QUADRUPOLE
MOMENT (Q)

For a given sorbent, the sorbate–sorbent interaction potential depends on the
properties of the sorbate. Among the five different types of interactions, the
nonspecific interactions, φ D and φ R , are nonelectrostatic. The most important
property that determines these interactions (and also φ Ind ) is the polarizability, α.
On a surface without charges, such as graphite, φ Ind = 0. The value of α generally
increases with the molecular weight because more electrons are available for
polarization. From the expressions for φ D , φ R ,and φ Ind ,itis seenthatthese
energies are nearly proportional to α. The dispersion energy also increases with
the magnetic susceptibility, χ, but not as strongly as α.
Table 2.1 summarizes interaction energies for a number of sorbate–sorbent
pairs. Here, groupings are made for the theoretical nonelectrostatic
) energies.
(φ D + φ R + φ Ind ) and the electrostatic (φ Fµ + φ ˙ FQ
The nonelectrostatic energies depend directly on the polarizability of the sor-
bate molecule; χ makes a contribution to the dispersion energy, and χ also
increases with molecular weight.
Two types of sorbents are included in Table 2.1, one without electric charges
on the surface (graphitized carbon) and one with charges (three zeolites). On
carbon, dispersion energy dominates. On zeolites, the permanent dipole and
quadrupole can make significant contributions toward, and indeed can dominate,
the total energy. N 2 has a moderately strong quadrupole but no permanent dipole,
accounts for about 1/3 of the
hence φ Fµ = 0. From Table 2.1, it is seen that ˙ FQ
+
energies on chabazite and Na-Mordenite. Na-X zeolite contains more Na ions
because its Si/Al ratio is lower than the other two zeolites. Consequently φ ˙ FQ
contributes about 1/2 of the interaction energies for N 2 on Na-X. The other sor-
bate molecules included in Table 2.1 both have strong dipoles and quadrupoles
(except H 2 O, which has a strong dipole only). For adsorption of these molecules
) interactions clearly dominate.
on zeolites, the (φ Fµ + φ ˙ FQ
A comparison of N 2 and O 2 holds particular interest for the application of air
separation. Both molecules are nonpolar and have very similar polarizabilities and
magnetic susceptibilities. However, their quadrupole moments differ by nearly