4190
Langmuir 1996, 12, 4190-4196
Gas Adsorption on Zeolites at High Pressure J. Vermesse, D. Vidal, and P. Malbrunot* Laboratoire d’Inge´ nierie des Mate´ riaux et des Hautes PressionssC.N.R.S., Universite´ de Paris-Nord, 93430 Villetaneuse, France Received April 10, 1995. In Final Form: May 28, 1996X High-pressure adsorption of helium, neon, argon, nitrogen, krypton, and methane on zeolites 3A, 4A, 5A, and 13X was measured at room temperature up to 500 MPa. The corresponding isotherms are qualitatively comparable to those previously obtained with the same gases adsorbed on activated carbon. They are analyzed and compared to those calculated on the basis of the Ruthven thermodynamic model of adsorption on zeolites. The respective importance of the contributions of solid-gas and gas-gas interactions and the exact role of pores were established. Attractive forces involve the isotherm maximum whereas repulsive forces are predominant at high pressure and involve a slight reincrease of adsorption. As concerns the well-calibrated pores of zeolites, in addition to their molecular sieving effect, they contribute mainly to increasing the specific area.
Introduction Zeolites play an important role in industrial gas separation processes, which are based on adsorption at high pressure, i.e., the well-known pressure swing adsorption (PSA) processes.1-6 The size of their pore diameters, about 0.3, 0.4, 0.5, and 1 nm, is the reason why they are referred to as molecular sieves. Nevertheless, in gas separation processes, the competitive adsorption of each component is related to solid-gas interactions. The aim of the present experimental study was to investigate the respective roles of molecular sieving and molecular interactions in gas adsorption at high pressure. Adsorptions at high pressure of gases of different molecular diameters and interactions on zeolites with different pore sizes and cations were experimentally determined. Present measurements of gas adsorption on commercial zeolites at room temperature over a large pressure range constitute significant basic data to verify the validity of theoretical models of adsorption. Such temperature and pressure conditions are of particular interest in industrial engineering processes for which these models are currently used. Adsorption of helium, neon, argon, krypton, nitrogen, and methane on zeolites 3A, 4A, 5A, and 13X, at 25 °C and up to 500 MPa, was measured by the dielectric method,7 previously used to determine gas adsorption at high pressure on activated carbon.8 Experimentation The dead space volume of the adsorption cell is one of the basic parameters of adsorption measurements using the volumetric method we employed, especially at high pressure. It is deduced from volume Vs of the adsorbent sample (its skeleton volume) and more precisely from the volume of the adsorbent inaccessible to gas molecules.9 The volume Vs is measured by helium gas * Author to whom all correspondence should be addressed: e-mail,
[email protected]. X Abstract published in Advance ACS Abstracts, July 15, 1996. (1) Yang, R. T. Gas Separation by Adsorption Processes: Butterworths: Boston, MA, 1987. (2) Jasra, R. V.; Bath, S. G. T. Sep. Sci. Technol. 1988, 23, 945. (3) Jasra, R. V.; Choudary, N. V.; Bath, S. G. T. Sep. Sci. Technol. 1991, 26, 885. (4) Sircar, S.; Hanley, B. F. Sep. Sci. Technol. 1993, 28, 2553. (5) Chou, C. T.; Huang, W. C. Ind. Eng. Chem. Res. 1994, 33, 1250. (6) Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure Swing Adsorption; VCH Publishers: New York, 1994. (7) Vidal, D.; Malbrunot, P.; Guengant, L.; Vermesse, J.; Bose, T. K.; Chahine, R. Rev. Sci. Instrum. 1990, 61, 1314. (8) Malbrunot, P.; Vidal, D.; Vermesse, J.; Chahine, R.; Bose, T. K. Langmuir 1992, 8, 577.
S0743-7463(95)00283-6 CCC: $12.00
Figure 1. Schematic diagram of the measurement method of adsorption at high pressure: 1, high-pressure vessel containing the capacitance; 2, high-pressure vessel containing the glass sample cell. displacement at high temperature in order to avoid errors due to the weak adsorption of helium at room temperature.9,10 In our method,7 gas density at high pressure is obtained from in situ dielectric constant measurements. Two pressure vessels of volumes V1 and V2, contain respectively a capacitance cell and a glass sample cell filled with the adsorbent (Figure 1). The two pressure vessels are placed inside a thermostatic bath which maintains a constant temperature of 25 ( 0.05 °C. In the first step, vessel 1 is kept under pressure; when the thermodynamic equilibrium of gas is reached, its density F0 is obtained from a capacitance measurement. The gas is then expanded into vessel 2, a new equilibrium takes place, and the corresponding density F is deduced from a second capacitance measurement. The excess amount of adsorption δNa is
δNa ) (F0 - F)V1 - F(V2 - Vs)
(1)
Before each set of measurements, the adsorbent is outgassed under vacuum for at less 24 h at 400 °C. Afterward, it is kept (9) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouque´rol, J.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603. (10) Malbrunot, P.; Vidal, D.; Vermesse, J.; Bose, T. K.; Chahine, R. Submitted for publication in Langmuir.
© 1996 American Chemical Society
Gas Adsorption on Zeolites at High Pressure
Langmuir, Vol. 12, No. 17, 1996 4191
Table 1. Helium Density, Gs, Nominal Aperture Size, and Specific BET surface, Ssp, of the Different Studied Zeolites
zeolite
nominal aperture size (nm)
Fs (g cm-3)
3A 4A 5A 13X
0.3 0.4 0.5 1.0
2.32 2.33 2.47 2.41
ssp (BET) (m2 g-1) 400 400 600
Table 2. As a Function of Pressure, P, and Molar Density, 1/V; Experimental Adsorption ma of Gases on Zeolite 13X at 25 °C P (MPa)
1/V (mol/cm3)
10.8 18.0 28.3 64.7 87.2 2.5 5.0 7.5 10.0 12.5 15.0 17.5 23.1
ma (mmol/g)
P (MPa)
1/V (mol/cm3)
ma (mmol/g)
0.004 281 5 0.006 855 3 0.010 243 0.019 870 0.024 535
(a) Neon 0.308 112.5 0.464 208.5 0.567 314.8 0.667 398.7 0.662 490.8
0.028 965 0.040 819 0.049 458 0.054 555 0.059 096
0.686 0.495 0.405 0.44 0.544
0.001 023 0.002 074 0.003 145 0.004 228 0.005 314 0.006 393 0.007 452 0.009 492 6
(b) Argon 1.498 54.3 2.122 78.3 2.4 108.9 2.51 206.3 2.53 324.3 2.51 421.4 2.45 512.4 2.383
0.018 289 0.021 972 0.025 093 0.030 660 0.0345 575 0.036 867 0.038 604
1.451 1.109 0.885 0.601 0.504 0.482 0.546
2.5 5.0 7.5 10.0 10.4 15.0 24.6
0.001 062 7 0.002 245 8 0.003 563 3 0.005 016 7 0.004 672 5 0.007 421 5 0.012 728
(c) Krypton 2.74 52.1 3.049 76.9 3.048 108.1 2.920 211.1 2.795 331.2 2.4 427.5 1.697
0.019 119 0.021 686 0.023 763 0.027 651 0.030 345 0.031 926
0.895 0.665 0.553 0.4 0.379 0.415
6.6 12.2 22.7 55.8 79.9
0.002 505 8 0.004 744 3 0.008 506 8 0.015 775 0.018 79
(d) Nitrogen 2.945 110.5 3.016 206.2 2.666 327.3 1.391 424.5 0.813 521.8
0.0212 79 0.025 999 0.029 549 0.031 636 0.033 360
0.813 0.753 0.982 1.114 1.305
2.5 5.0 8.9 14.5 23.0 50.6
0.001 055 0.002 202 0.003 843 5 0.006 708 3 0.010 750 0.016 925
(e) Methane 2.84 75.0 3.10 107.6 3.09 204.0 2.695 325.7 2.106 424.1 1.245 521.3
0.019 558 0.021 691 0.025 387 0.028 133 0.029 739 0.031 039
0.969 0.809 0.685 0.704 0.726 0.83
in a sealed glass capsule at a residual pressure of less than 10-3 Pa, and this capsule is introduced into vessel 2. During the expanding operation, a pressure of about 0.6 MPa is sufficient to break the thin glass diaphragm at the top of the capsule. The maximum absolute error of our method is 0.3 mg g-1 (mainly due to cumulative errors on successive weighings). The reproducibility of several independent determinations of adsorption was, in all cases, on the order of this absolute error, and in most cases was lower. The relative error is not highly significant because adsorption is the quantity of excess obtained by the difference between two measured quantities and thus depends on the adsorption value itself. In the present case, it varies from 4% (low and high pressures) to less than 1% (vicinity of the maximum of adsorption). The zeolites studied were “Siliporite” type zeolites manufactured by CECA-FRANCE (ELF-ATOCHEM group), the characteristic parameters of which are summarized in Table 1.
Results and Discussion Results are presented in Tables 2-5. For each zeolite and the different gases, as a function of pressure P (and corresponding molar gas density F ) 1/V), the excess
Table 3. As a Function of Presure, P, and Molar Density, 1/V; Experimental Adsorption, ma, of Gases on Zeolite 5A at 25 °C P (MPa)
1/V (mol/cm3)
13.2 20.0 26.4 62.6 86.5
ma (mmol/g)
P (MPa)
1/V (mol/cm3)
ma (mmol/g)
0.004 976 3 0.007 386 3 0.009 486 6 0.019 245 0.024 237
(a) Neon 0.456 114.8 0.442 214.9 0.468 322.1 0.724 404.5 0.918 491.7
0.029 182 0.041 303 0.049 833 0.054 762 0.059 035
1.01 0.934 0.868 1.075 1.275
8.4 13.1 26.2 59.8 83.3
0.003 271 9 0.005 313 0 0.010 732 0.019 243 0.022 544
(b) Argon 2.46 113.0 2.566 213.0 2.344 332.3 1.67 429.1 1.47 523.5
0.025 402 0.030 941 0.034 794 9.037 033 0.038 803
1.356 1.16 1.09 1.085 1.13
10.0 14.7 24.3 51.5 77.5
0.004 808 1 0.007 643 4 0.012 931 0.019 173 0.021 809
(c) Krypton 2.778 108.5 2.444 215.1 1.845 333.3 1.152 420.6 0.964 501.1
0.023 838 0.027 807 0.030 425 0.031 867 0.032 986
0.876 0.76 0.717 0.697 0.723
9.6 20.3 32.7 62.8 83.0
0.003 793 2 0.007 773 2 0.011 392 0.016 800 0.019 048
(d) Nitrogen 2.575 114.8 2.392 214.6 2.011 327.1 1.298 408.1 1.107 492.7
0.021 564 0.026 276 0.029 521 0.031 289 0.032 853
0.941 1.068 1.4 1.564 1.694
8.4 16.2 24.3 50.4 77.3
0.003 853 7 0.007 808 7 0.011 410 0.017 092 0.019 787
(e) Methane 2.91 109.3 2.493 210.6 2.053 329.7 1.397 424.6 1.147 533.3
0.021 848 0.025 618 0.028 256 0.029 802 0.031 238
0.9905 0.745 0.642 0.61 0.635
Table 4. As a Function of Pressure, P, and Molar Density 1/V: Experimental Adsorption, ma, of Gases on Zeolite 4A at 25 °C P (MPa)
1/V (mol/cm3)
13.7 21.0 27.4 63.8 88.5
0.005 124 8 0.007 681 3 0.009 760 8 0.019 470 0.024 596
(a) Neon 0.365 117.3 0.320 218.5 0.304 327.1 0.635 410.8 0.728 501.8
0.029 554 0.041 627 0.050 157 0.055 097 0.059 483
0.84 0.781 0.569 0.768 0.925
7.0 15.6 24.8 55.5 80.3
0.002 902 9 0.006 570 3 0.010 357 0.018 606 0.022 288
(b) Argon 1.86 110.3 1.856 206.4 1.56 325.1 0.791 424.0 0.527 536.0
0.025 182 0.030 717 0.034 644 0.036 967 0.039 067
0.388 0.253 0.165 0.107 0.128
11.0
0.005 381 0
(c) Krypton 0.52 15.0
0.007 947 3 0.162
10.0 20.3 32.5 62.5 82.5
0.004 043 9 0.007 882 5 0.011 399 0.016 804 0.019 031
(d) Nitrogen 2.24 113.9 1.958 214.8 1.552 328.3 0.784 410.6 0.648 495.4
0.021 550 0.026 319 0.029 580 0.031 368 0.032 930
0.511 0.85 1.20 1.373 1.489
9.2 17.6 25.6
0.004 109 0.008 557 8 0.011 842
(e) Methane 1.556 52.1 0.968 78.2 0.775 112.4
0.017 324 0.019 890 0.021 997
0.14 0.205 5.7 × 10-3
ma P (mmol/g) (MPa)
1/V (mol/cm3)
ma (mmol/g)
adsorption ma ) δNa/ms, where ms is the adsorbent mass, is tabulated. In the case of helium, these values are reported in Table 3 of ref 10. It must be mentioned that adsorption values on zeolite 3A are negative, except for helium and neon. This is also partially the case for the 4A zeolite with krypton and methane at the highest pressures. Because they have no physical meaning, these negative adsorption values do not appear in the tables.
4192 Langmuir, Vol. 12, No. 17, 1996
Vermesse et al.
Figure 2. Experimental adsorption of helium on zeolites: O, 13X zeolite; 4, 5A zeolite; - - -, 4A zeolite; ;, 3A zeolite.
Figure 3. Experimental adsorption of neon on zeolites: O, 13X zeolite; 4, 5A zeolite; - - -, 4A zeolite; ;, 3A zeolite.
Table 5. As a Function of Pressure P and Molar Density 1/V: Experimental Adsorption ma of Neon on Zeolite 3A at 25 °C P (MPa)
1/V (mol/cm3)
ma (mmol/g)
P (MPa)
1/V (mol/cm3)
ma (mmol/g)
12.6 20.0 25.9 62.5 86.4
0.004 737 7 0.007 343 0 0.009 322 0 0.019 149 0.024 185
0.213 0.209 0.233 0.71 0.856
113.9 212.2 317.6 399.7 492.8
0.028 982 0.041 009 0.049 495 0.054 469 0.059 052
0.973 0.891 0.783 0.841 0.938
On the basis of results and conclusions of our last study on adsorbent density,10 it appears that these negative adsorptions result from the fact that volume Vs of adsorbent measured with helium is unadapted in the present case. This is due to the size of gas molecules which do not easily penetrate, or cannot penetrate at all, into zeolite pores. Thus, volume Vs measured with helium is too small, with the consequence being negative values for δNa (see eq 1). Under such conditions, negative values of adsorption can be considered as a test of gas penetration into the zeolite. Corrected adsorbent densities (in fact lower values) would lead to elimination of negative adsorption. At present, it is not possible to obtain a perfect evaluation of these corrections. Nevertheless, we have undertaken experimental work in order to obtain the Vs values of adsorbents measured with each adsorbed gas, a situation in which the present problem of negative adsorption would be cancelled out. Isotherms of adsorption of each gas on the several zeolites represented in Figures 2-7 illustrate our experimental data in the form of the adsorption variation as a function of gas density. The similarity of present isotherms with those previously obtained on activated carbon8 is noteworthy: at low and moderate densities, the adsorption increases to a maximum, whereas beyond them it decreases, reaches a shallow minimum, and increases again at the highest densities. It can be shown that the shape of adsorption isotherms is independent of the nature of the adsorbent and the complexity of its microporous structure. Adsorption would appear to be more strongly influenced by a universal mechanism such as van der Waals type intermolecular forces, both between gas atoms and between gas and solid atoms. Other important remarks are as follows: (i) Only helium isotherm curves continuously increase with density (Figure 2). On the contrary, other gas isotherms reach a maximum, and at the higher densities, a decrease is followed by a second increase, which is
Figure 4. Experimental adsorption of argon on zeolites: O, 13X zeolite; 4, 5A zeolite; - - -, 4A zeolite.
Figure 5. Experimental adsorption of krypton on zeolites: O, 13X zeolite; 4, 5A zeolite; - - -, 4A zeolite.
especially pronounced for neon and nitrogen (Figures 3 and 6). Such an increase in adsorption at high density has been previously observed by Michels et al.,11 but only in the case of nitrogen on alumina. These authors explained this by a possible reorientation of nitrogen molecules at high density in a position perpendicular to the adsorbent surface. (11) Michels, A. M. J. F.; Menon, P. G.; Ten Seldam, C. A. Recl. Trav. Chim. Pays-Bas 1961, 80, 483.
Gas Adsorption on Zeolites at High Pressure
Langmuir, Vol. 12, No. 17, 1996 4193
Figure 6. Experimental adsorption of nitrogen on zeolites: O, 13X zeolite; 4, 5A zeolite; - - -, 4A zeolite.
Figure 7. Experimental adsorption of methane on zeolites: O, 13X zeolite; 4, 5A zeolite; - - -, 4A zeolite. Table 6. Molecular Parameters of the Different Studied Gases (symbols explained in text) Lennard-Jones interaction parameters helium neon argon krypton nitrogen methane
σ (nm)
/k (K)
T*
C6/C6(He) (C6 ) 4σ6)
dBH
0.2556 0.2756 0.3405 0.3685 0.3698 0.3817
10.22 33.74 119.8 164.41 95.05 148.2
29.17 8.84 2.49 1.81 3.14 2.01
1 5.2 65.5 145 85.3 161
0.85 0.88 0.95 0.96 0.94 0.96
(ii) As regards pore diameters of 5A and 13X zeolites, all present gases are able to penetrate them (see aperture size of zeolites in Table 1 and molecular diameter of gases σ in Table 6. The difference in the amount adsorbed is undoubtedly due to the difference in attraction of their respective cations: the stronger attraction of calcium in the 5A zeolite entails greater adsorption than on the 13X zeolite, the sodium cation of which has a weaker attraction effect. For the 5A zeolite, the maximum of the isotherms is increasingly pronounced with He, Ne, Ar, N2, Kr, and CH4, respectively, corresponding to an increase in the attractive interaction coefficient C6 ) 4σ6 (cf. Table 6). This behavior was previously established in the case of activated carbon;8,10 it confirms that the characteristic maximum of the adsorption isotherm is related to the attractive part of the intermolecular force between gas molecules as proven by Monte Carlo simulation of the adsorption of argon on a graphite-like surface.12 On zeolite 13X, similar behavior can be seen for atomic gases and
gases with spherical molecules. Nitrogen, which is a nonspherical molecule, is somewhat more strongly adsorbed than krypton, probably due to its more complex interaction potential as well as to the ability of its oblong molecules to pile up more easily than spherical ones. (iii) For the 4A zeolite, only Ne and Ar isotherms (Figure 3 and 4) are comparable to those obtained on zeolites 5A and 13X. For Kr and CH4, they are truncated at high pressure (Figures 5 and 7) since atoms or molecules have increasing difficulty in penetrating pores of 0.38 nm diameter, as previously mentioned. Nitrogen whose mean diameter (0.37 nm) is comparable to that of zeolite pores, exhibits noticeable adsorption (Figure 6). Once again, a possible explanation lies in the orientation of its nonspherical molecules, in that they present their narrowest diameter to the windows of zeolite cages and thus can penetrate inside these cages. (iv) The molecular sieve effect of the 3A zeolite with a pore diameter of 0.3 nm is clearly illustrated: all atoms and molecules with a diameter wider than 0.3 nm are excluded; only neon and helium atoms are adsorbed; and their respective isotherms exhibit the usual shape (Figures 2 and 3). (v) In all cases, gas isotherms cross the helium isotherm at high density, after which they cross themselves. Thus, at high pressure, higher adsorptions correspond to gases having higher reduced temperature; i.e., adsorption at the highest pressure is related to repulsive short range forces which predominate more and more as the gas becomes kinetic. Since no other experimental data were available in so large a pressure range, it was not possible to make a comparison with our results. However, up to 10 MPa adsorption measurements were achieved by Wakasugi et al.13 in the case of argon, nitrogen, and methane on 13X and 5A zeolites, and by Chkhaidze et al.14 in the case of methane on the 13X zeolite. Results of the former authors are systematically lower than ours but the difference, between 3 to 9%, is acceptable taking into account the respective accuracies (they claimed 5% while we previously mentioned 1 to 4%) and reproducibility between zeolite samples of different origins. Since results of the latter authors were expressed following a different definition of adsorption, they may be corrected in terms of the definition we used taking into account the pore volume of NaX zeolite reported by Dubinin et al.15 Corresponding values of adsorption are 30% higher than present results, a discrepancy which may have occurred because of the difference in zeolite samples and uncertainties in determination of the respective volumes of pores and skeleton of zeolite samples. Comparison between Experimental and Calculated Adsorption Isotherms Using a Statistical Thermodynamic Approach Taking into account the regularity of the zeolite pore structure, Ruthven and his co-workers developed a statistical thermodynamics approach of the adsorption of gases.16 The zeolite is considered as an ensemble of independent cages of volume Vc. Interactions between (12) Vermesse, J.; Levesque, D. J. Chem. Phys. 1994, 101, 9063. (13) Wakasugi, Y.; Ozawa, S.; Ogino, Y. J. Colloid Interface Sci. 1981, 79, 399. (14) Chkhaidze, E. V.; Fomkin, A. A.; Serpinskii, V. V.; Tsitsishvili, G. V. Izv. Akad. Nauk SSSR, Ser. Khim. 1985, 974. (15) Dubinin, M. M.; Zhdanov, S. P.; Zhukovskaya, E. G.; Murdmaa, K. O.; Polstyanov, E. F.; Sakavov, I. E.; Shishakov, N. A. Izv. Akad. Nauk SSSR, Ser. Khim. 1964, 1573. (16) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984; Chapter 3, and references cited therein.
4194 Langmuir, Vol. 12, No. 17, 1996
Vermesse et al.
molecules in neighboring cages may be neglected. The average number of molecules per cage 〈N〉 is given by differentiating the grand partition function Ξ with respect to the activity ζ
ζ ∂Ξ Ξ ∂ζ
( )
〈N〉 )
(1 - η)3 1 ) ZHS (1 + η + η2 - η3) η, is the packing fraction of N molecules in volume Vc
η ) (π/6) (N/Vc) d3 then
and if Ξ is expressed as a function of the configurational integral ZN for N molecules in the cage
The third term is associated with the attractive vdW gas-gas interaction where is the depth well potential. If a reduced temperature T* ) kT/ is introduced
∞
Ξ)
∑ζ
N
Nb/Vc ) 4η
ZN
N)0
1 Nb 4η ) T* kT Vc
then ∞
∑
〈N〉 )
NζNZN
N)1
(2)
∞
∑ζ N)0
N
ZN
With respect to cage dimensions, it is presumed that all gas molecules in the cages 〈N〉 are influenced by surface effects and are thus considered as adsorbed. The quantity ζ is a function of density (or pressure) and temperature of the adsorbate. Its value will be computed by means of the equation of state of the gas. The quantity ZN is a function of the number of N particles in each cage. For a finite value of the volume of these cages, the number of particles to be taken into account in the summations of the above series also have a finite value Nm. For a perfect gas, the activity ζ can be identified with pressure P. The configurational integral ZN calculated as a function of N is ZN ) 1 when N ) 0 and ZN ) K when N ) 1; K is a quantity equivalent to the Henry’s constant. Thus, with the assumption Nm ) 1, and applying the perfect gas law, eq 2 becames the equation of the Langmuir isotherm:
〈N〉 ) KP/(1 + KP)
((
)) ( )
1 Nb K 1N! Vc
N
exp
ZvdW ) ZHS - (4η/T*) It is worth noting that in the ZN expression, only the attractive gas-solid potential field is uniform throughout the zeolite cage, in contrast to the attractive gas-gas potential field which is modeled by the mean-field expression of the vdW potential. To facilitate calculations, the use of reduced units must be extended. Reducing parameters are the vdW interaction parameters gas-gas (d and ). Reduced thermodynamics quantities are (marked by an asterisk)
P* ) Pd3/; K* ) K(/d3); µ* ) µ/ The activity ζ is equal to
ζ ) P exp(δµ/kT) with δµ being the deviation of the chemical potential from the perfect gas law. Inserting reduced units
δµ/kT ) δµ*/T* and
δµ* ) ZvdW - 1 +
Other more sophisticated isotherms may be developed for different values of Nm.17 In these conditions, the curves corresponding to variations in 〈N〉 as a function of P from eq 2 have a slope parametrized by K and a plateau by Nm. Ruthven has suggested decomposing the configurational integral ZN into a three-term product, considering a van der Waals (vdW) model for the gas-solid system and for the gas-gas system
ZN )
In fact, the latter two terms corresponding to gas-gas contributions are included in the expression of the compressibility factor of the vdW gas-gas system
Nb kT Vc
The first term K is due to the vdW gas-solid interaction between N molecules of gas in the cage and the adsorbent, while the two others are associated with the vdW gasgas interaction between the same molecules. The second term represents the excluded volume effect limited to the first term of a density expansion of (1/ZHS), where ZHS is the compressibility factor of a hard sphere system. If d is the hard core of the gas-gas vdW potential, the covolume b is b ) (2π/3)d3. The hard sphere (HS) compressibility can be calculated beyond the first term of density expansion by means of the well-known equation of Carnaham et Starling18 (17) Kaminsky, R. D.; Monson, P. A. AIChE J. 1992, 38, 1979. (18) Carnahan, H. F.; Starling, K. E. J. Chem. Phys. 1969, 51, 635.
∫0η
[
]
ZvdW 1 dη η η
In the present calculation of activity, η has a value associated with density F of the adsorbate, and the value of ZvdW is a function of η. On the other hand, in the calculation of ZN, the quantity η is a function of the number N of particles in the cage, a value which increases from 0 to Nm. In order to determine 〈N〉 as a function of density η and temperature T*, ζ*(η,T*) is first calculated. Afterward, ZN is evaluated by testing several values of KH* and Nm to fit the experimental isotherm. The two vdW parameters are obtained from
d)
( ) 6Mηc NπFc
(1/3)
tc* ) kTc/
where ηc ) 0.13 and tc* ) 0.37731, and Fc and Tc are the critical density and temperature of gases. To obtain a realistic value for the maximum number of molecules per cage Nm, we considered the number of molecules which is possible to include in the most possible compact physical state: the cubic-faced centered hard sphere solid. Thus
η ) π x2/6 )
π Nm 3 d 6 Vc HS
where Vc is the volume of a cage and dHS is the diameter
Gas Adsorption on Zeolites at High Pressure
Figure 8. Comparison of adsorption isotherms of argon on 13X zeolite obtained from experiment and from statistical thermodynamic model: ;, experimental isotherm; O, original model; - - -, modified experimental isotherm (VLX ) 0.075 cm3 g-1).
of a hard sphere system given by the approximation of Barker and Henderson19 (cf. Table 6). Using the value of Vc determined by Dubinin et al.,15 we obtained, for zeolite 13X, Nm ) 43 for argon and Nm ) 144 for helium. Since the present model considers as adsorbed molecules all molecules inside zeolite cages, comparison with other experimental data requires experimental adsorption obtained using the same definition. This adsorption is the difference between the amount of gas which enters the cell containing the zeolite and the amount of gas in the dead space volume of this cell, i.e., outside the volume of zeolite and its micropores.14 Our results obtained according to eq 1 were corrected by the addition of the term FVLX, with VLX being the volume of the cages per mass unit of zeolite given by Dubinin et al.15 Experimental adsorptions were then directly expressed by the number of molecules per cage, as in the case of model data (eq 2)
〈N〉ex ) maN /M Ncm where N is the Avogadro number, M is the molecular mass, and Ncm is the number of zeolite cages per mass unit of zeolite. Figures 8 and 9 present results obtained with argon and helium on zeolite 13X. The adjustable parameters are K ) 1400 for argon and K ) 600 for helium (fitted on experiment). Except for the lower part of the density range, the discrepancy between the experiment and model is noteworthy. Experimental adsorption does not present the plateau of the model, but increases continuously at high density, an unexpected result. Moreover, the experimental number of molecules per cage is unreasonably high compared to the previously mentioned admissible maximum. This situation is due to the overestimation of the dead space by exclusion of the volume of the cage. At high gas densities, it is physically incorrect to eliminate the entire volume of cages of the free volume of molecules. In fact, considering the mean free path of molecules under these density conditions (one or more molecular diameter), the free and adsorbed molecules can coexist in a given zeolite cage. To evaluate this effect, volume VLX has been fitted to obtain, for high-pressure experimental adsorption, a plateau comparable to that obtained using the Ruthven theory. In the case of helium, no value of VLX corresponds to such a situation (Figure 9). Even for VLX ) 0, the curve (19) Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856.
Langmuir, Vol. 12, No. 17, 1996 4195
Figure 9. Comparison of adsorption isotherms of helium on 13X zeolite obtained from experiment and from a statistical thermodynamic model: ;, experimental isotherm; O, model; - - -, modified experimental isotherm (VLX ) 0).
increases monotonously with density. On the other hand, in the case of argon (Figure 8), the value VLX ) 0.075 cm3 g-1 leads to an adsorption isotherm in good agreement with that of the model. Compared to Dubinin’s value VLX ) 0.324 cm3 g-1, the preceding value of 0.075 cm3 g-1 indicates that only a small part of the volume of the zeolite cage is, in fact, occupied by adsorbed molecules; the cage volume is mainly available for free gas molecules. In fact, such a result proves that even in zeolite pores, adsorption remains a surface phenomenon. Moreover, inside the cages, near the internal surface, the existence of a density profile has been demonstrated by Monte Carlo simulation of adsorption of gas in zeolites at a pressure of 0.4 MPa.20 This density profile is comparable to that obtained in front of a graphite basal plane.21 It will probably be possible, with new adapted investigations, to localize the Gibbs surface on the internal wall of zeolite cages. Some aspects of high-pressure adsorption isotherms of gases have not been explicitly taken into account by the statistical thermodynamic model. One such aspect is the correlation between the isotherm maximum and the attractive component of gas molecule interaction forces, a correlation which has been clearly observed in present experimental results. Indeed, for the statistical thermodynamic theory, an indirect correlation exists between the height of the maximum and the attractive gas-gas interaction via adjustment of the Nm parameter. This relation, in any case, cannot describe the absence of a maximum for the helium isotherm. On the contrary, other theoretical approaches to adsorption clearly show this correlation between the nature of the intermolecular forces and the shape of adsorption isotherms. Thus, considering formal calculations of the density profile of a hard sphere fluid near a rigid wall,22 the excess surface adsorption Γ, following the standard definition, is
Γ)
∫0∞(η(z) - η) dz
with η(z) being the packing fraction of gas at a distance z from the wall. It does not present a maximum, but increases continuously with the bulk packing fraction η. Another approach is Monte Carlo simulation of adsorption (20) Razmus, D. M.; Hall, C. K. AIChE J. 1991, 37, 769. (21) Vermesse, J.; Levesque, D. Mol. Phys. 1992, 77, 837. (22) Navascue´s, G.; Tarazona, P. Mol. Phys. 1979, 37, 1077.
4196 Langmuir, Vol. 12, No. 17, 1996
of a Lennard-Jones gas on a rigid plane interface and/or a rigid interface consisting of a lattice of micropores.21 Once again since no gas-solid attractive contribution is considered, no maximum is obtained. An experimental confirmation is given by the behavior of helium (a very kinetic gas which has practically no attractive gas-solid exchange): the measured adsorption isotherms at room temperature increase continuously with density.10 We can conclude that only theories which evaluate both repulsive and attractive gas-gas contributions, as well as solid-gas attractive contributions, are able to give an excess adsorption isotherm with a maximum. This is also the case when the attractive gas-solid interaction is uniform within the volume of the zeolite cages and, of course, when it will be possible to take into account all collective molecular contributions in Monte Carlo simulation of adsorption on a zeolite-like adsorbent. At moderate densities, the attractive fraction of the molecular interactions predominates and provides an important contribution up to the minimum of the compressibility factor Z ) P/(F kT), beyond which its influence decreases. It is worth noting that, with respect to the position of the minimum of Z, the maximum of adsorption isotherms is shifted somewhat to lower densities. It is possible that this effect is due to the three-body dispersion intermolecular interaction of the Axilrod-Teller potential type, which makes a significant contribution to the bulk equilibrium properties of gas. Thus, the molecular mechanisms usually related to gas-gas or solid-gas pair potential must now be considered as resulting from two other configurations: on the one hand, three atoms of gas, and on the other, one atom of gas and two atoms of solid. The latter configuration contributes to the maximum of adsorption, especially at low density, since the strength of the solid-gas interaction is thus somewhat relatively higher than the gas-gas interaction in bulk gas. The second feature of isotherms not described by the statistical thermodynamic model is the shallow minimum of adsorption at high pressure and the slight increase which follows at the highest pressures. This behavior is entirely different from the saturated curve in a plateau shape of the original model or the continuously decreasing curve of the modified model. In fact, this discrepancy at high pressure has the same origin as that of the helium: the predominance of repulsive interactions. Conclusion Present experimental data concerning high pressure adsorption on current zeolites illustrate the well-known molecular sieve effect of 4A and especially of 3A zeolites.
Vermesse et al.
Moreover, except for helium, adsorption isotherms exhibit a maximum which becomes more and more pronounced as the gas-gas attractive coefficient C6 increases. Following this, as the pressure increases, adsorption decreases to a minimum and finally increases somewhat. Our results reinforce previous experimental data reported for activated carbon8,10 as well as simulation results of a Lennard-Jones gas adsorbed by an attractive solidgas interface.12 This behavior can be explained by the response of the gas to the application of a gas-solid attractive molecular interaction. This response is higher for strong gas-solid interactions, but appears to be stronger when the internal energy between gas molecules reaches high values as gas density increases. At moderate densities, the maximum of adsorption experimentally observed is the consequence of the attractive part of the interaction forces between gas molecules. At high density, repulsive molecular contributions are dominant and are responsible for the second adsorption increase. The difference between adsorption values at the maximum and at high density gives the level of the relative contributions of these two effects. In contrast, with a kinetic gas such as helium, the repulsive contribution is important whatever the density, and the result is a continuous increase in adsorption (Figure 2). In all cases, the porous structure of the adsorbent contributes to adsorption at the level of access of molecules having an appropriate diameter size (molecular sieve effect) and specific area, which is directly proportional to adsorbent porosity. Present results do not enable an assessment of the effect of distribution of cations in the zeolite cage. Experimental results of adsorption at high pressure can be correlated with the statistical thermodynamic approach of Ruthven if the volume of the zeolite cage permits the movement of free gas molecules. This implies an adequate dead space volume determined with helium. In the particular case of zeolites, a more detailed understanding of the adsorption phenomenon will undoubtedly be achieved by Monte Carlo simulation, which is a predictive approach taking into account the specific interaction between the gas and constitutive atoms distributed in the cage structure. It is expected to provide an answer to the previous question concerning the effect of the cation position in the zeolite cage. For these reasons, Monte Carlo simulation, which is especially well adapted to adsorption on zeolites, will be undertaken in the near future. LA950283M
