Page 265 - Adsorbents fundamentals and applications

250 CARBON NANOTUBES, PILLARED CLAYS, AND POLYMERIC RESINS

et al., 1992), and H 2 -D 2 -HD on NaA zeolite at 120-77 K (Stephanie-Victoire
et al., 1998). The separation factors for these systems were all small (near or
below 2).
The use of carbon nanotubes for isotope separations has been proposed recently
by Scholl, Johnson and co-workers (Wang et al., 1999; Challa et al., 2001), based
on “quantum sieving.” Quantum sieving was first discussed by Beenakker et al.,
(1995) to describe the molecular transport in a pore that is only slightly larger
than the molecule. In their description, a hard-sphere molecule with a hard-core
diameter σ is adsorbed in a cylindrical pore with a pore diameter d.When d-σ
is comparable with the de Broglie wavelength λ (λ = h/mv,where h is Planck’s
constant, m is mass, and v is the radial velocity), the transverse motion energy
levels are quantized. For He at room temperature, λ ≈ 0.1 nm. Hence, separation
can be achieved by using differences in the quantum levels of the heavier and
lighter molecules that are confined in the pore. From their hard-sphere theory,
high selectivities were predicted for He isotopes at low temperatures and pressures
in pores about 4 ˚ A in diameter. Wang et al. (1999) employed path-integral Monte
Carlo simulations with accurate potential models for studying isotope separations
in SWNT bundles.
Wang et al. (1999) treated a low-pressure binary mixture in equilibrium with
an adsorbed phase in the narrow pore. Because of the low density of adsorbate
in the pore, the molecules undergo unhindered axial translational motion, and the
transverse (radial) degrees of freedom are in their ground state and quantized.
The chemical potential of the adsorbate molecule or atom can be expressed
in terms of the ground-state energy (E) of its transverse wave function. By
equating the chemical potentials of the adsorbate molecule and that in the gas
phase, the selectivity can be calculated. The selectivity of component 1 over
2is S = (x 1 /x 2 )/(y 1 /y 2 ),where x i (y i ) are the pore (gas) mole fractions. The
selectivity approaching zero pressure (S 0 ) is given by:

m 2 E 1 − E 2
S 0 = exp − (9.2)
m 1 kT
where m is the molecular mass. This equation applies only when the ground
state is populated. When the excited states (l) are also populated, Challa et al.
(2001) obtained:
 l 
exp(−E /kT )
1
m 2  l 
S 0 =   (9.3)
l
m 1  exp(−E /kT ) 
2
l
The selectivities calculated from these two equations for T 2 /H 2 at 20 K were
essentially the same (Wang et al., 1999; Challa et al., 2001). That calculated from
Eq. 9.3 are shown in Figure 9.12. The results from the path integral MC calcula-
tions are also shown, and were nearly the same as that from the simple equations.