10498
J. Phys. Chem. B 2000, 104, 10498-10501
Self-Diffusivities of N2, CH4, and Kr On 4A Zeolite Pellets by Isotope Exchange Technique D. V. Cao, R. J. Mohr, M. B. Rao, and S. Sircar* Air Products and Chemicals, Inc., Allentown, PennsylVania 18195-1501 ReceiVed: March 30, 2000; In Final Form: September 6, 2000
The isotope exchange technique (IET) was used to measure equilibria and kinetics for adsorption of pure N2, CH4, and Kr on a 4A zeolite sample. The intracrystalline self-diffusivities for these gases were measured under truly isothermal conditions. The self-diffusivities of Kr and CH4 were smaller than that of N2 by 2 and 1 order of magnitudes, respectively. The self-diffusivity of N2 was independent of its surface coverage but the self-diffusivities of CH4 and Kr increased with increasing coverages in the high-pressure region. This effect was much more pronounced for Kr. The activation energies for self-diffusion of the gases increased in the order Kr > CH4 > N2 while the isosteric heats of adsorption of these gases in the Henry’s law region were very close. The activation energies were larger than the corresponding isosteric heats of adsorption for each gas.
Introduction The isotope exchange technique (IET) can be used to simultaneously measure pure or multicomponent gas adsorption equilibria and kinetics (self-diffusion) without disturbing the adsorbed phase.1,2 The method consists of (a) equilibrating an adsorbent of known mass with a pure gas or a multicomponent gas mixture, (b) changing the isotope concentrations of the components in the gas phase at the start of the experiment (time t ) 0) while maintaining the total gas-phase mole fraction of component i of the mixture (yi), the total gas-phase pressure (P), and the system temperature (T) constant, and (c) monitoring the changes in the isotope concentrations of component i as a function of time until a new isotopic equilibrium state is reached. The adsorbed phase remains equilibrated with the gas phase at the chosen values of P, T, and yi during the entire isotope exchange process. Thus, this technology measures self-diffusivities for ad(de)sorption of gases.3 The equilibrium Gibbsian surface excesses of component i (nmi ) at P, T, and yi also remain constant during the process and no heat is generated or consumed. Thus, the IET provides complete control over the initial and final equilibrium adsorption states on the adsorbent and absolute system isothermality prevails during the process. These advantages cannot be realized by most other conventional methods for measurement of adsorption equilibria and kinetics.4 It can be shown that the equilibrium Gibbsian surface excess of component i at P, T, and yi can be estimated by1
nmi (P,T,yi) ) (VFyi)
[
]
/∞ y// ij - yij /o y/∞ ij - yij
(1)
where V is the total specific helium void volume of the closed adsorption system of IET experiment. The molar density of the // gas phase at P and T is given by F. The variables y/ο ij , yij and /∞ yij are, respectively, the gas-phase mole fractions of the jth isotope of component i at the initial equilibrium state, at the start of the exchange process after the gas-phase isotope concentrations are changed, and at the final equilibrium state. The fractional isotope uptake (f/ij) of the jth isotope of component i at time t during the exchange process is given by1
f/ij(t)
)
[
/m n/m ij (t) - nij (o)
][
/m n/m ij (∞) - nij (o)
)
]
/ y// ij - yij(t) /∞ y// ij - yij
(2)
/m /m where n/m ij (t), nij (o), and nij (∞) are, respectively, the Gibbsian surface excess of the jth isotope of component i at time t, at the initial equilibrium state, and at the final equilibrium state. The gas-phase mole fraction of the jth isotope of component i at time t is given by y/ij(t). Equation 1 shows that the pure or multicomponent gas equilibrium adsorption characteristics can be mapped as functions of P, T, and yi by carrying out the IET experiments at different values of these variables. Equation 2 shows that the diffusivity or mass transfer coefficient for self-diffusion of component i from the gas phase (pure or multicomponent) to the adsorbent (or vice versa) at any given P, T, and yi (or nmi and T) can be estimated by fitting the fractional uptake data with an isothermal transport model. A key characteristic of the IET process is that1
n/m ij (e) y/ij(t)
)
nmi yi
(3)
where n/m ij (e) is the equilibrium Gibbsian surface excess of the jth isotope of component i at P, T, and y/ij(t). For the chemical potential driving force model of mass transport, which reduces to the conventional isothermal Fickian diffusion model (FDM) under the constraint of eq 3, one can show that1,5
f/ij(t)
)1-
tan qn )
∞
6R(1 + R) exp[-D/ijqn2t/a2]
n)1
9 + 9R + qn2R2
∑
3qn 3 + Rqn2
R)
[
/o y/∞ ij - yij
/∞ y// ij - yij
(4)
]
(5)
where D/ij is the self-diffusivity of the jth isotope of component i at P, T, and yi (or nmi and T). Equations 4 and 5 apply only for isothermal ad(de)sorption in spherical adsorbent particles (crystal
10.1021/jp0012101 CCC: $19.00 © 2000 American Chemical Society Published on Web 10/21/2000
Self-Diffusivities of N2, CH4, and Kr
J. Phys. Chem. B, Vol. 104, No. 45, 2000 10499
TABLE 1: Physical Properties of Adsorbates gas N2 CH4 Kr
kinetic liquid molar polarizability quadrupole moment mol wt diama (Å) volb (cm3/mol) (cm3 x 1025) (esu cm × 1013) 28.0 16.0 84.0
3.68 3.82 3.49
31.6 37.7 32.3
17.6 26.0 24.8
1.52 0 0
a Leonard-Jones parameters from viscosity data. b At normal boiling point.
or pellet) of radius a in a constant volume adsorption experiment.5 It is common to assume that the self-diffusivities of different isotopes of component i (trace or bulk) are equal [D/ij ) D/i ] so that a single self-diffusivity (D/i ) as a function of P, T, and yi characterizes the transport of component i. The IET has been used to measure adsorption equilibria and kinetics for pure N2 and N2-O2 binary mixtures on a carbon molecular sieve,1 and those for pure N2 and CH4 and their binary mixtures on 4A zeolite.2 The present work reports new data on pure Kr adsorption equilibria and kinetics on 4A zeolite measured by IET as well as some additional data (pressures above 4 atm) for adsorption of pure N2 and CH4 on the same adsorbent. A comparative analysis of the kinetic data for N2, CH4, and Kr on the zeolite reveals several interesting and surprising behaviors.
Figure 1. Pure gas adsorption isotherms of N2, CH4, and Kr on 4A zeolite at 283 K (solid lines represent smooth curves through the data points).
Adsorbent and Adsorbates The adsorbent used in this study was a commercial sample (UOP) of pelletized 4A zeolite in the bead form (a ) 1.015 mm). The average size of the 4A zeolite crystals was 1.95 µm (effective diameter). Helium pycnometry and mercury porosimetry measurements showed that the total pore volume within the zeolite beads was 0.4 cm3/g and the average binder pore diameter was 178 Å. The adsorbent was regenerated by heating under vacuum (10-6 Torr) at 400 °C for 12 h before the adsorption measurements were conducted. Table 1 shows the relevant physical properties of the adsorbates (N2, CH4, and Kr). The molecular weights of these gases differ significantly but their liquid molar volumes, polarizabilities, and kinetic diameters are very similar. N2 has a weak quadrupole moment while CH4 and Kr are nonpolar. The kinetic diameters reported in Table 1 are Leonard-Jones parameters computed from viscosity data.6 These values (absolute and relative) often differ from source to source. However, all three molecules have comparable diameters and they are smaller than the free apertures (4.2 Å) of 4A (NaA) zeolite crystal cages.7 Pure Gas Adsorption Equilibria and Kinetics We measured the equilibrium isotherms and kinetics for adsorption of pure N2, CH4, and Kr on the 4A zeolite beads in the pressure range of 0-6 atm using the IET protocol. The measurements were carried out at least at two different temperatures for each gas. The low-pressure adsorption isotherm data for N2 and CH4 were consistent with that measured previously.2 A detailed description of the experimental apparatus and the method is given elsewhere.1,2 Figure 1 shows the adsorption isotherms at 283 K. All isotherms are Type I by the Brunauer classification8 as expected for adsorption of gases on microporous solids. CH4 is more strongly adsorbed than Kr and N2 presumably because of its larger polarizability. Kr and N2 exhibit similar adsorption capacities in the low-pressure region. However, Kr adsorption capacity is larger than that for N2 in the high-pressure region. Figure 2 replots the data of Figure 1 in the low-pressure region
Figure 2. Pure gas adsorption isotherms of N2, CH4, and Kr on 4A zeolite and 283 K in the low-pressure Henry’s law region.
as ln nmi against ln P. It shows that all three gases exhibit a prolonged Henry’s law region (0 < P < 0.8 atm) at 283 K where the isotherms are linear (nmi ) KiP). The Henry’s law constant for component i is given by Ki. Consequently, the slopes of the plots of Figure 2 are unity. Figure 3 shows three typical fractional uptake curves for adsorption of pure N2, CH4, and Kr on the 4A zeolite beads measured by IET at 283 K. The initial and final fractional adsorbate loadings (θi ) nmi /mi) for these runs were 0.13, 0.41, and 0.18, respectively, for N2, CH4, and Kr. The corresponding equilibrium gas-phase pressures were respectively, 1.05, 1.33, and 1.14 atm. The saturation adsorbate loadings (mi) for these adsorbates were obtained by fitting the adsorption isotherms with the multisite Langmuir model of Honig and Nitta.2,9,10 These variables are given in Table 2. The plot shows that the relative rates of self-diffusion of these gases into the zeolite are in the order N2 > CH4 > Kr. These uptake curves can be quantitatively described by the Fickian Diffusion Model (eqs 4 and 5) as shown by the solid lines in Figure 3. The estimated time constants (D/i /a2) for these runs are given in the figure. It may be seen that the self-diffusivity of CH4 is 1 order of
10500 J. Phys. Chem. B, Vol. 104, No. 45, 2000
Cao et al.
Figure 3. Fractional uptakes for isothermal adsorption of N2, CH4, and Kr by the 4A zeolite at 283 K.
Figure 4. Self-diffusivities of N2, CH4, and Kr on the 4A zeolite at 283 K as functions of fractional surface coverages.
TABLE 2: Kinetic and Equilibrium Properties for Adsorption of Pure Gases on 4A Zeolite
The figure shows that the self-diffusivity of N2 is practically constant over a large range of θi values (0 < θi < 0.8). The self-diffusivities of CH4 and Kr, on the other hand, are independent of surface coverage in the low-pressure region and then they increase with increasing θi. This effect is much more pronounced for Kr than CH4. No clear explanation for these behaviors can be given at this time.
gas
saturation adsorption capacity (mi) (mmol/g)
N2 CH4 Kr
2.05 2.42 2.61
a
data of Figure 3a fractional surface 1012D/i coverage (θi) (cm2/s) 0.13 0.41 0.18
42.30 3.73 0.14
1012D/i o at θi ) 0a (cm2/s) 42.78 3.61 0.134
Isosteric Heats and Activation Energies
T ) 283 K.
magnitude smaller than that of N2 and the self-diffusivity of Kr is 2 orders of magnitude smaller than that of N2. The adsorbing isotope molecules travel from the bulk gasphase outside the zeolite pellets into the zeolite crystals through the mesopores (average diameter of 178 Å) of the binder material. The desorbing isotope molecules follow the reverse path. The flow through the binder pores is controlled by Knudsen diffusion. The Knudsen diffusivity (DK, cm2/s) of a gas of molecular weight (M) at temperature (T, K) through a mesopore of diameter (d, Å) is given by11
DK ) 4.85 × 10-5d(T/M)0.5
(6)
We estimated the time constants (DK/a2) for Knudsen diffusion of N2, CH4, and Kr through the mesopores of the zeolite sample at 283 K to be 2.66, 3.52, and 1.54 s-1, respectively. The pellet radius (a ) 1.015 mm) was used as the characteristic distance of diffusion for these calculations. These time constants are three to 5 orders of magnitude larger than the corresponding adsorption time constants measured by IET (Figure 3). Thus, the mesopores of the zeolite binder offer negligible resistance for transport of these gases compared to that imposed by the zeolite crystal (pore mouth resistance and/or intracrystalline diffusion). Consequently, the characteristic distance of diffusion for calculating the self-diffusivity of N2, CH4, and Kr into 4A zeolite crystal from the data measured by IET should be the crystal size (a ) 0.975 µm). Table 2 reports these diffusivities at 283 K. Figure 4 shows the self-diffusivities of N2, CH4, and Kr on the 4A zeolite beads as functions of fractional adsorbate loadings (θi) at 283 K. The ordinate of Figure 4 represents the ratio of self-diffusivity of a gas (D/i ) at any given value of θi to the self-diffusivity of that gas (D/o i ) at the limit of zero surface coverage (θi f 0). These limiting values are given in Table 2.
We calculated the pure gas isosteric heats of adsorption (qoi ) in the Henry’s law region for N2, CH4, and Kr on the 4A zeolite by measuring the Henry’s law constants (Ki) at different temperatures and using the following thermodynamic equation:2
qoi d ln Ki )- 2 dT RT
(7)
We also calculated the pure gas activation energies (Eoi ) for self-diffusion of N2, CH4, and Kr at zero coverage on the 4A zeolite by measuring D/o i at different temperatures and using the equation:2
Eoi d ln D/o i )+ 2 dT RT
(8)
Table 3 summarizes these data. It may be seen that all three gases have very similar isosteric heats of adsorption in the Henry’s law region. The isosteric heat for N2 is slightly larger presumably due to its permanent quadrupole. The activation energies for self-diffusion of these gases at zero coverage, which are larger than the corresponding isosteric heats of adsorption, vary substantially. They increase in the order Kr > CH4 > N2. In other words, the activation energies increased as the selfdiffusivities of the gases on the zeolite decreased. This result is surprising in view of very similar molecular properties of these adsorbates (Table 1), and no simple explanation could be given. In particular, it is not at all clear why the self-diffusivities of these gases are so different when their physical properties (Table 1) and isosteric heats of adsorption (Table 3) are so similar. It appears that self-diffusion for these adsorbates in 4A zeolite framework is controlled by the relative size of the gas molecule and the zeolite pore aperture (gas to solid or cavity to cavity). Thus, the kinetic diameters reported in Table 1 are not reliable
Self-Diffusivities of N2, CH4, and Kr
J. Phys. Chem. B, Vol. 104, No. 45, 2000 10501
TABLE 3: Temperature Dependence of Henry’s Law Constants and Limiting Self-Diffusivities of Gases 1012D/i ° (cm2/s)
Ki [(mmol/g)/atm] gas
253 K
273 K
283 K
N2 CH4 Kr
1.47 2.30
0.69 1.27
0.52 0.96 0.42
a
333 K
253 K
273 K
283 K
14.26 0.95
31.37 2.47
42.78 3.61 0.13
0.16
333 K
qoi a (kcal/mol)
Eoi a (kcal/mol)
1.05
4.70 4.20 4.30
5.24 6.37 7.72
At the limit of zero surface coverage.
to estimate self-diffusivities when the relative sizes between the molecules and the pore apertures are close. Comparative Literature Data Freude12 measured intracrystalline self-diffusivity of CH4 in 4A zeolite crystals at 300 K using a nuclear magnetic relaxation /o method. A DCH value of 0.50 × 10-11 cm2/s was obtained on 4 crystals of 1.23 µm diameter at the limit of zero surface /o coverage. We estimated a DCH value of 0.69 × 10-11 cm2/s 4 using eq 8 and the data of Table 3. This agreement is indeed remarkable and it suggests that the measured CH4 self-diffusivity by IET is for intracrystalline diffusion (cavity to cavity). Haq and Ruthven13 measured intracrystalline transport diffusivities of N2 and CH4 on 4A zeolite pellets at 298-363 K and estimated the activation energies to be 4.46 and 4.54 kcal/mol, respectively. The corresponding isosteric heats of adsorption were 4.53 and 4.70 kcal/mol. Summary The isothermal isotope exchange technique (IET) was used to measure pure gas equilibrium isotherms and kinetics for adsorption of N2, CH4, and Kr on a commercial sample of 4A zeolite beads. The CH4 was more strongly adsorbed than N2 and Kr by the zeolite. The N2 and Kr adsorption capacities on the zeolite were very similar in the low-pressure region, while the Kr capacity was larger than N2 in the high-pressure region. The isosteric heats of adsorption for all three gases in the Henry’s law region were very close. The isothermal Fickian diffusion model quantitatively described the uptakes of these gases by the zeolite. Intracrystalline diffusion was the primary resistance for gas transport. The selfdiffusivity of CH4 was 1 order of magnitude smaller than that for N2. The self-diffusivity of Kr was 2 orders of magnitude
smaller than that for N2. The self-diffusivity of N2 did not change with its surface coverage. The self-diffusivities of CH4 and Kr were independent of their surface coverages in the low-pressure region and then they increased with increasing surface coverage. This effect was more pronounced for Kr. The activation energies for self-diffusion of these gases were very different. They increased in the order Kr > CH4 > N2. The activation energies for all gases were larger than the corresponding isosteric heats of adsorption. Some of these results are very surprising and no simple explanation could be given. Acknowledgment. The authors are grateful to J. Shabrach and B. Messersmith for carrying out some of the IET experiments. References and Notes (1) Rynders, R. M.; Rao, M. B.; Sircar, S. AIChE J. 1997, 43, 2456. (2) Mohr, R. J.; Vorkapic, D.; Rao, M. B.; Sircar, S. Adsorption 1999, 5, 145. (3) Ka¨rger, J.; Ruthven, D. M. Diffusions in Zeolites; Wiley-Interscience: New York 1992. (4) Sircar, S. Ind. Eng. Chem. Res. 1999, 38, 3670. (5) Crank, J. Mathematics of Diffusion; Oxford University Press: London 1956. (6) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Theory of Gases and Liquids; Wiley: New York 1954. (7) Breck, D. W. Zeolite Molecular SieVes; R. E. Krieger Publishing: Malabar, FL 1984. (8) Young, D. M.; Crowell, A. D. Physical Adsorption of Gases; Butterworth: London 1962. (9) Honig, J. M. Adsorption Theory from the Viewpoint of OrderDisorder Theory; Gas Solid Interface; Flood, E. A., Ed.; Marcel Dekker: New York, 1966. (10) Nitta, T.; Shigetomi, T.; Kuro-oka, M.; Katayama, T. J. Chem. Eng. Jpn. 1984, 17, 39. (11) Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press, Cambridge, MA, 1970. (12) Freude, D. Zeolites 1986, 6, 12. (13) Haq, N.; Ruthven, D. M. J. Colloid Interface Sci. 1986, 112, 154.
