J. Phys. Chem. B 2000, 104, 4867-4872
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Sorption Behavior of 1-Butene in Perfluorocarbon Type Ion-Exchange Membranes Doped with Various Silver Salts Wei Hu,† Akihiko Tanioka,*,† Tatsuya Imase,† Susumu Kawauchi,† Hongyuan Wang,‡ and Yasunori Suma‡ Department of Organic and Polymer Materials, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro-ku, Tokyo 152-8552, Japan and AdVanced Polymer Laboratory, Japan Chemical InnoVation Institute, 22-13 Yanagibashi 2-Chome, Taito-ku, Tokyo 111-0052, Japan ReceiVed: September 14, 1999; In Final Form: March 9, 2000
The sorption mechanism of 1-butene in dry silver salt-doped perfluorosulfonate membranes and the anion effect on the σ-π complexation of Ag+/1-butene were investigated. The interaction energy, ∆E, calculated by the MP2(full)/gen 6d//HF/gen 6d molecular orbital study and the limiting heat of sorption, ∆H0, obtained from the sorption isotherm had nearly the same tendency; the affinity between the silver salts and the 1-butene molecule follow the order of AgBF4 > AgClO4 > AgNO3 > AgCF3SO3. Both the dependence of the differential heat of sorption, ∆Hs, and the half-standard entropy of sorption, ∆Ss, on the concentration of 1-butene sorbed in the membrane had a minimum, which corresponded to the value of Cm in the BET n-layer adsorption equation. 1-Butene molecules can be sorbed and form multilayers on the Ag+-sites in the membrane.
1. Introduction Membrane-based processes for olefin/paraffin separations will become economically feasible in the chemical and petrochemical industries if the membrane performance can be improved. Membranes containing Ag+ have been proved to be able to offer high selectivity for olefin/paraffin separations, since silver ions can bind olefin molecules through a σ-π complexation bond, thus facilitating the transport of olefin molecules through the membranes. Various kinds of membranes containing silver ions as a carrier have been investigated for the facilitated transport of alkenes, such as supported liquid membranes(SLMs), hydrated ion-exchange membranes, and silver salt/polymer blend membranes.1-3 However, SLMs often have stability problems because of solution loss, whereas for the hydrated Ag+exchanged membranes or hydrated silver salt/polymer blend membranes, we usually have to face the problem of maintaining the proper humidity during operation. Therefore, dry membrane processes might be more conceivable for olefin/paraffin separations because gas-solid operation is much simpler during practical use. Peinemann and Shukla reported that AgBF4/Nafion blend membranes could show a high facilitation effect for olefin gases without humidification.4 They determined that the mechanism must be an immobilized fixed carrier transport because the silver salt cannot diffuse through the dry membrane. But the details were not explicitly given. Recently, our groups have investigated the capability of dry silver salt-doped perfluorosulfonate ion-exchange membranes for olefin and paraffin separations.5-7 High ideal separation factors were obtained for alkenes/alkanes. Also, membranes doped with different kinds of silver salts exhibited differences in the permeability coefficient of 1-butene.5 From the literature results, it is likely that anions or ligands have an influence on the ability of cations to form σ-π complexes with alkenes.8-10 * To whom all correspondence should be addressed. Tel: +81-3-57342426. Fax: +81-3-5734-2876. E-mail:
[email protected]. † Tokyo Institute of Technology. ‡ Japan Chemical Innovation Institute.
Figure 1. Chemical structure of the perfluorosulfonate ion-exchange membranes (PSM).
Thus, in this study, a molecular orbital investigation was carried out for the calculation of the interaction energy, ∆E, between the 1-butene molecule and four kinds of silver salts. The sorption isotherms were also measured for 1-butene in dry perfluorosulfonate ion-exchange membranes doped with these four kinds of silver salts. On the basis of the results obtained from the sorption experiment and the MO calculation, the sorption mechanism of 1-butene in dry silver salt-doped perfluorosulfonate membranes and the anion effect on the σ-π complexation of Ag+/1-butene were investigated. This investigation might also provide the basic information for the understanding of the transport mechanism of olefin in the membrane. 2. Experiment 2.1 Membrane Preparation. Perfluorosulfonate ion-exchange membranes (PSM) with Na+ as the counterions were obtained from Asahi Chemicals. The chemical structure of the membrane is given in Figure 1. AgBF4 (98%) and AgCF3SO3 (99+ %) were purchased from Aldrich Chemical Co. Inc.; AgClO4 (90%) and AgNO3 (99.8%) were purchased from Wako Pure Chemical Industries, Ltd. All the silver salts were used without further purification. Two molar aqueous solutions of the above four kinds of silver salts were used to immerse the Na+-form PSM membranes for 48 h in order to convert them to the respective silver salt (AgX)-doped PSM membranes. The membranes were then removed from the solution. The solution on the membrane surface was carefully wiped off, and the
10.1021/jp993264k CCC: $19.00 © 2000 American Chemical Society Published on Web 04/29/2000
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membranes were vacuum-dried at 70 °C for 18 h. The membranes were kept in a desiccator after drying. The treatments cited above were performed in a dark chamber because the silver salts are photosensitive. The thickness of the membrane was 30 µm, and the equivalent weight EW () dry membrane weight/equivalent of charged group) was 950 gmol-1. 2.2 Membrane Characterization. X-ray diffraction measurements were performed on the dry AgX-doped PSM membranes. Both the wide-angle X-ray diffraction (WAXD) and the small-angle X-ray diffraction (SAXD) profiles were measured by a Rigaku Rota Flex RU200 operated at 50 kV and 180 mA and equipped with a scintillation counter. A nickel-filtered Cu KR X-ray beam(λ ) 0.15418 nm) was used as the source. The instrumental background was subtracted from the initial scanning data. The cross section of the AgX-doped PSM membranes was studied by transmission electron microscopy(TEM). 2.3 1-Butene Sorption. 1-Butene was supplied by Takachiho Chemical Industries Co., Ltd. (99% purity) and was used without further purification. Sorption mass uptake data were measured gravimetrically using a Sartorius/Nekken vacuum ultramicro balance system. The equilibrium sorption values were determined from the end points of the uptake data curves at increasing 1-butene gas pressures. Sorption isotherms were taken at 30 °C, 40 °C, 50 °C, and 60 °C for PSM membranes doped with the four kinds of silver salts.
Figure 2. WAXD profile for dry AgBF4-doped PSM membrane.
3. Molecular Orbital Study An ab initio molecular orbital study MP2(full)/gen 6d//HF/ gen 6d was undertaken for the calculation of the AgX/1-butene interaction energies. Geometry optimization was performed at the HF/gen 6d level, and MP2(full)/gen 6d with natural bond orbital (NBO) analysis was carried out to obtain energies, orbital energies, orbital occupancies, and atomic charges. The interaction energy, ∆E, can be calculated from the energy of the AgX/ 1-butene complex, EAgX/1-butene, energy of the individual 1-butene molecule, E1-butene, and energy of the individual AgX molecule, EAgX:
∆E ) EAgX/1-butene - E1-butene - EAgX
Figure 3. Small angle X-ray scan for dry AgBF4-doped PSM membrane.
(1)
The interaction energy calculated using eq 1 can be related to the sorption energy at zero amount sorbed. The calculations were performed using the Gaussian 94 program supplied by Gaussian, Inc. 4. Results and Discussion 4.1 Morphology of Dry AgX-Doped PSM Membranes. In our previous study,5 energy-dispersive X-ray spectrometry (EDS) area analysis revealed that, regardless of the kinds of doped silver salts, the concentration of doped Ag+ ions was about twice that of the charged SO3- groups in the AgX-doped PSM membranes, indicating that a large amount of anions (X-) were doped together with Ag+ ions into the membranes during the membrane immersing processes. Additionally, doped Ag+ ions were not heterogeneously distributed in the membrane, as indicated by the EDS line analysis. Figure 2 shows the WAXD profile for the dry AgBF4-doped PSM membrane. No sharp diffraction peak associated with the crystalline regions of the membrane is found. Therefore, dry AgX-doped PSM membranes used in this study are almost amorphous at their EW levels. Figure 3 gives the SAXD profile for the dry AgBF4-doped PSM membrane. Like the WAXD result, no small-angle scattering maximum arising from the long identity period of
Figure 4. Transmission electron micrograph of the cross section of AgBF4-doped PSM membrane.
the lamellar platelets is detected. The profile contains a scattering peak at a relatively large scattering angle, which was commonly assigned to the ionic-scattering maximum arising from the ion clusters.11 The apparent Bragg spacing of this reflection is about 33 Å, which can also correspond to the value found by Gierke et al. for the 1200 EW silver ion form dry Nafion polymers.12 The existence of ion clusters in the dry AgX-doped PSM membranes is also supported by a TEM study. Figure 4 shows the transmission electron micrograph of the cross section of the AgBF4-doped PSM membrane. It is seen that the metallic ion clusters separate from the fluorocarbon matrix and have diameters of several nanometers. Escoubes et al. reported that a well-defined amount of water (about 1 to 2 H2O/SO3-) was kept in the acid and neutralized
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Figure 5. Sorption isotherm of 1-butene in dry AgNO3-doped PSM membranes. Experimental data at b, 30 °C; [, 40 °C; 9, 50 °C; 2, 60 °C. Solid lines are calculated curves by the BET n-layer adsorption equation.
form of Nafion 120 after vacuum-drying (10-5 Torr) at room temperature.13 Based on the water loss curves during high temperature heating for the different Nafion polymer forms presented in their study, it is likely that the AgX-doped PSM membranes used in this study are not strictly anhydrous even after vacuum-drying at 70 °C for 18 h. A small amount of water still remained in the membranes. However, we use the phrase “dry AgX-doped PSM membranes” to distinguish our membranes from those hydrated or swollen membranes used in other studies. An image of the morphology of the dry AgX-doped PSM membranes, which is consistent with the above observations, can now be obtained. The amorphous fluorocarbon backbones form the basic framework of the membrane, whereas ion clusters are suspended from the fluorocarbon framework through the pendant side chains. The ion clusters region contains the majority of SO3- exchange groups, Ag+ counterions, anions(X-) doped together with Ag+ ions, and the residual water molecules. The ion cluster region is separated from the fluorocarbon matrix by an interfacial region of relatively large fractional void volume, consisting of the pendant side chains, some SO3- sites that have not been incorporated into clusters, and a corresponding fraction of counterions. This image of the dry AgX-doped PSM membranes is quite similar to the model presented by Yeager for the ionic diffusion in Nafion.14 4.2 Affinity between Silver Salt and 1-Butene. Figure 5 shows the representative sorption isotherm of 1-butene in the dry AgNO3-doped PSM membrane. According to the virial isotherm equation
K3p 3 ) exp 2A1c + A2c2 + ‚‚‚ c 2
(
)
(2)
a plot of log(p/c) versus c is linear at low sorbed concentrations, so that the thermodynamic equilibrium constant K3 can be derived from the extrapolation of such a plot to zero sorbed concentration. As is well-known, the virial isotherm equation was initially developed to relate the intracrystalline sorbate concentration, c, with the equilibrium pressure, p, independent of the nature of the sorption process. Here, we assume that the dry AgX-doped PSM membranes are thermodynamically inert at low 1-butene sorbed concentrations, and thus it is feasible to apply the virial isotherm equation in our system.
Figure 6. Van’t Hoff plots of the thermodynamic equilibrium constants for the sorption of 1-butene in four kinds of silver salt-doped PSM membranes.
TABLE 1: Interaction Energies of AgX/1-Butene and the Limiting Heat of Sorption of 1-Butene in Dry AgX-Doped PSM Membranes silver salts
∆E (kcal/mol)
∆H0 (kcal/mol)/ R value of van’t Hoff plot
AgBF4 AgClO4 AgNO3 AgCF3SO3
-22.75 -20.43 -20.35 -20.25
-16.7 ( 3.6/0.956 -13.8 ( 0.4/0.999 -14.0 ( 1.0/0.995 -10.7 ( 0.9/0.994
The van’t Hoff plots showing the temperature dependence of the thermodynamic equilibrium constants for the sorption of 1-butene in all four kinds of silver salts-doped PSM membranes are given in Figure 6. The interaction energies ∆E of AgX/1butene calculated by MP2(full)/gen 6d//HF/gen 6d molecular orbital study and the limiting heat of sorption of 1-butene in dry AgX-doped PSM membranes, ∆H0, obtained from the slopes of the van’t Hoff plots,
K3 ) K0 exp
( ) -∆H0 RT
(3)
are summarized in Table 1. Even though the errors of ∆H0 values are relatively large (especially for the sorption of 1-butene in dry AgBF4-doped PSM membrane), it can still be roughly seen from this table that ∆E and ∆H0 have nearly the same tendency, the affinity between the silver salts and the 1-butene molecule follow the order of AgBF4 > AgClO4 > AgNO3 > AgCF3SO3. The low affinity between AgCF3SO3 and 1-butene is unexpected according to the stability studies of olefin-silver (I) complexes in silver salt solutions or in silver salt solid-state lattices.8,9 This inconsistency can probably arise from the chemical environmental difference for complex formation in dry AgX-doped PSM membranes and in silver salt solutions or silver salt solid-state lattices. 4.3 Nature of the AgX/1-Butene Complex. The research on the affinity between silver ion and alkenes can be traced back to 1938, when Winstein and co-workers published their first paper on an alkene-silver coordination complex.15 Now, it is commonly understood that the interaction between the alkene and the silver ion can be described by a σ-type bond, resulting from the donation of π-electrons from the occupied 2p bonding orbital of the alkene system into the vacant 5s orbital of the silver ion, and a π-type bond, resulting from backdonation of d-electrons from the occupied 4d orbitals of the
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TABLE 2: Frontier Orbital Energy Levels for AgX and 1-Butene molecule
HOMO (kcal/mol)
LUMO (kcal/mol)
AgBF4 AgClO4 AgNO3 AgCF3SO3 1-butene
-334.2 -281.9 -255.1 -270.9 -223.7
-19.42 -19.91 -12.79 -16.19 118.2
TABLE 3: Changes in NAO (Natural Atomic Orbital) Electron Occupancies (∆Oc) of Ag Atoms upon Complex Formationa complex
5s
Σ4d
5s + Σ4d
AgBF4/1-butene AgClO4/1-butene AgNO3/1-butene AgCF3SO3/1-butene
0.0742 0.0909 0.1211 0.0968
-0.0288 -0.0362 -0.0558 -0.0389
0.0454 0.0547 0.0653 0.0579
a
|∆Oc(5s)| > |∆Oc(Σ4d)|.
TABLE 4: Net Charges of Ag Atoms Calculated by MP2/ gen 6d Before and After Complex Formation AgX molecule net charge complex net charge
AgBF4
AgClO4
AgNO3
AgCF3SO3
0.7784 AgBF4/ 1-butene 0.6187
0.7674 AgClO4/ 1-butene 0.6289
0.7102 AgNO3/ 1-butene 0.5766
0.7490 AgCF3SO3/ 1-butene 0.6140
silver ion into the unoccupied π*-2p antibonding orbitals of the alkene system.15-16 Table 2 shows the frontier orbital energy level for four kinds of AgX and 1-butene. From Table 2, it is seen that the energy gap between the LUMO of the silver salts and the HOMO of 1-butene, ∆(LUMOAgX/HOMO1-butene), is smaller than that between the LUMO of 1-butene and the HOMO of the silver salts, ∆(LUMO1-butene/HOMOAgX). A smaller energy gap will facilitate the electron transfer. Consequently, it will be easier for the electrons to transfer from 1-butene to the silver salts than the reverse. Table 3 also shows the changes in the natural atomic orbital (NAO) electron occupancies, ∆Oc, of Ag atoms upon complex formation. The electron occupancy of the 5s orbital of AgX always increases, whereas the total occupancy of its 4d orbitals (4dxy, 4dxz, 4dyz, 4dx2-y2, and 4dz2) always decreases. However, the net increase in the electron occupancy of the 5s orbital of AgX, |∆Oc(5s)| is higher than the net decrease in the total occupancy of its 4d orbitals, |∆Oc(Σ4d)|. This indicates that the strength of the σ-donation bond of π-electrons transferring from the occupied 2p bonding orbital of 1-butene into the vacant 5s orbital of the silver ion is stronger than that of the π-backdonation bond of d-electrons transferring from the occupied 4d orbitals of the silver ion into the unoccupied π*-2p antibonding orbitals of 1-butene. Therefore, for the σ-π complexation between AgX and 1-butene, the contribution from the σ-donation is higher than that from the π-back-donation. The net charges of Ag atoms calculated by MP2/gen 6d before and after complex formation are given in Table 4. The net charges of Ag atoms in all the silver salts decrease upon complexation as a result of a net transfer of electrons from 1-butene to Ag+. This result is also consistent with what Yang et al. found in their study on the sorption of C2H4 in Ag+-exchanged sulfonic acid resins, Ag zeolites, and Ag halides.17-19 4.4 Sorption Mechanism of 1-Butene in Dry AgX-Doped PSM Membranes. Due to the special σ-π interaction between the 1-butene and the Ag+ ion, the sorption of 1-butene molecules is expected to happen most likely on the Ag+ sites in the dry
Figure 7. Differential heats of sorption of 1-butene in dry AgNO3doped PSM membrane as a function of sorbed concentration.
Figure 8. Half-standard entropies of sorption of 1-butene in dry AgNO3-doped PSM membrane as a function of sorbed concentration.
AgX-doped PSM membranes. According to the morphology of dry AgX-doped PSM membranes, 1-butene molecules are most probably sorbed on the Ag+ sites of the ion clusters, existing at the interfacial region of the relatively large fractional void volume between the fluorocarbon framework and the ion clusters. Figure 7 and Figure 8 show the concentration dependence of the differential heats of sorption and half-standard entropies of sorption of 1-butene in dry AgNO3-doped PSM membrane, respectively. The differential heats of sorption, ∆Hs, are calculated using eq 4:
(∂ ∂Tln p) ) q
Hg - H hs RT
2
)-
∆Hs RT2
(4)
whereas the half-standard entropies of sorption, ∆Ss are calculated by eq 5:
∆Ss ) Shs - S0g )
∆Hs p - R ln 0 T p
(5)
from the sorption isotherm in Figure 5. Both curves have a minimum at the 1-butene sorbed concentration of about 0.0550.06 mg gas/mg polymer, indicating that there is a change in the sorption behavior of 1-butene around this sorbed amount. When the sorbed concentration is lower than this sorbed amount,
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TABLE 5: Coefficients of BET n-Layer Adsorption Equation for 1-Butene in Dry AgNO3-Doped PSM temperature (°C)
cm mg gas/ mg polymer
C
n
30 40 50 60
0.061 0.057 0.056 0.056
216 245 226 166
3.4 3.6 3.9 3.1
the sorption behavior of 1-butene in the dry AgNO3-doped PSM membrane is somewhat like that of simple gases or hydrocarbons sorbed into the intracrystalline cavities in zeolites. That is, the half-standard enthropies of sorption decrease monotonically with coverage due to the decrease in the configurational entropy and are independent of temperature.20-22 As the amount of 1-butene sorbed in the membrane increases, the change in the concentration dependence of ∆Hs and ∆Ss is supposed to happen when the sorbed 1-butene molecules begin to form multilayers upon the Ag+ sites. With multilayers forming, the sorbed 1-butene molecules will be loosely bound to the Ag+ sites compared with the monolayer molecules, thus causing both the differential heats of sorption and the thermal entropies to increase. Therefore, we also tried to use the BET n-layer adsorption equation
Cx[1 - (n + 1)xn + nxn+1] c ) cm (1 - x)[1 + (C - 1)x - Cxn+1]
(6)
to describe the sorption isotherm of 1-butene in the dry AgNO3doped PSM membrane. From the solid lines shown in Figure 5, it is seen that the sorption isotherm of 1-butene in the membrane can be well described by the BET n-layer adsorption equation. The coefficients of the BET n-layer adsorption equation obtained by a nonlinear least-squares data fitting are presented in Table 5. It is important to note that the sorbed concentration at which the ∆Hs-c and ∆Ss-c curves show a minimum corresponds to the value of Cm in the BET n-layer adsorption equation, which supports the above consideration that the change of the concentration dependence of ∆Hs and ∆Ss happens when the sorbed 1-butene molecules begin to form multilayers. However, we should still keep in mind that the success of the application of the BET n-layer adsorption equation here for the sorption of 1-butene in the dry AgX-doped PSM membranes must arise from a compensation of errors. For example, the BET n-layer adsorption equation is based on the assumption that the evaporation-condensation properties of the molecules in the second and higher adsorbed layers are the same as those in the liquid state.23 Apparently, this is not the case for the sorption of 1-butene in the dry AgX-doped PSM membranes, due to the fact that the net values of the differential heats of sorption are still larger than the heat of liquefaction of 1-butene, EL ) 4.816 kcal/mol, even after the multilayer sorption begins. There might be a compensation from the deformation of the fluorocarbon matrix upon 1-butene sorption so that the BET n-layer adsorption equation remains applicable. Moreover, it will be interesting to compare the sorption of 1-butene in the dry AgX-doped PSM membranes in this study with the sorption of water in similar Nafion polymers. Escoubes et al. studied the sorption of H2O in the room-temperature dried acid and neutralized forms of Nafion 120. They found that the decrease in the enthalpic energy of sorption happened at the concentration of about 4-5 H2O/SO3-, when the corresponding relative water vapor pressure was about 0.8.13 Komoroski et al. also reported in their sodium-23 nuclear magnetic resonance study of the Nafion-SO3Na polymer that at this sorbed water
concentration, a large amount of Na+ cations bound to the SO3groups would start to become free hydrated ions as a result of water molecules penetrating into the ion clusters and replacing the SO3- groups in the neighborhood of the Na+ ions.24 However, for the sorption of 1-butene in the dry AgX-doped PSM membranes in this study, 1-butene molecules might not be able to penetrate into the ion clusters due to the following considerations: the dielectric constant of 1-butene is much lower than that of H2O, at which the fraction of separated ions is expected to be exceedingly small; the size of the 1-butene molecule is significantly larger than that of H2O; only Ag+ ions have the σ-π interaction effect with 1-butene molecules, whereas both cations and anions in the ion clusters have a hydration effect with H2O; the relative vapor pressures of 1-butene under which the sorption experiments were taken are all smaller than 0.8. Thus, 1-butene molecules might only be able to be sorbed over the Ag+ sites of the ion clusters, forming multilayers at the interfacial space between the fluorocarbon framework and the ion clusters in dry AgX-doped PSM membranes. This image is quite different from the complex formation of olefin with solvated Ag+ ions in silver salt solutions and from the olefin sorption into the silver salt solid-state lattices. The unexpected low affinity between AgCF3SO3 and 1-butene mentioned above might be due to the higher steric hindrance for the complex formation caused by CF3SO3-. Furthermore, nuclear magnetic resonance study or Fourier transform infrared spectroscopy study during the 1-butene sorption process is expected to provide an additional test of the above sorption mechanism. 5. Conclusions The sorption mechanism of 1-butene in dry AgX-doped PSM membranes and the anion effect on the σ-π complexation of Ag+/1-butene were investigated. The interaction energy, ∆E, calculated by the MP2(full)/gen 6d//HF/gen 6d molecular orbital study and the limiting heat of sorption, ∆H0, obtained from the sorption isotherm had nearly the same tendency; the affinity between the silver salts and the 1-butene molecule follow the order of AgBF4 > AgClO4 > AgNO3 > AgCF3SO3. For the σ-π complexation between AgX and 1-butene, the contribution from the σ-donation is higher than that from the π backdonation. Both the dependence of the differential heats of sorption ∆Hs and half-standard entropies of sorption ∆Ss on the concentration of 1-butene sorbed in the membrane has a minimum, which can correspond to the value of Cm in the BET n-layer adsorption equation. 1-Butene molecules can be sorbed and form multilayers on the Ag+-sites in the membrane, existing at the interfacial region of the relatively large fractional void volume between the fluorocarbon matrix and the ion clusters. Acknowledgment. A part of this work has been conducted by the support of the Petroleum Energy Center (PEC) subsidized from the Ministry of International Trade and Industry. We are grateful to Mr. M. Hamada of Asahi Chemicals Co., Ltd., for providing us the samples. Notation Ai : virial coefficients c : concentration of 1-butene sorbed in the membrane, mg gas (mg polymer)-1 Cm : monolayer adsorption capacity, mg gas (mg polymer)-1 C : coefficient related to the adsorption heat of the monolayer and the heat of vaporization ∆E : interaction energy calculated by MO study, kcal mol-1
4872 J. Phys. Chem. B, Vol. 104, No. 20, 2000 ∆H0 : limiting heat of sorption, kcal mol-1 ∆Hs : differential heat of sorption, kcal mol-1 Hg : molar enthalpy of the gaseous sorbate, kcal mol-1 H h s : differential enthalpy of the sorbed molecules, kcal mol-1 K3 : thermodynamic equilibrium constant K0 : constant n : number of adsorbed layers p : equilibrium pressure, Torr q : sorbed phase concentration R : gas constant ∆Ss : half-standard entropy of sorption, cal mol-1 degree-1 S0g : molar entropy of gaseous sorbate at the standard pressure p0 () 1 atm) at temperature T, cal mol-1 degree-1 Shs : differential entropy of the sorbed molecules, cal mol-1 degree-1 T : temperature, K x : relative vapor pressure () p/p0) ∆ : energy gap, kcal mol-1 References and Notes (1) Leblanc, O. H.; Ward, W. J.; Matson, S. L.; Kimura, S. G. J. Membr. Sci. 1980, 6, 339. (2) Yamaguchi, T.; Baertsch, C.; Koval, C. A.; Noble, R. D.; Bowman, C. N. J. Membr. Sci. 1996, 117, 151. (3) Ho, W. S.; Dalrymple, D. C. J. Membr. Sci. 1994, 91, 13.
Hu et al. (4) Peinemann, K. V.; Shukla, S. K.; Schossig, M. Proc. ICOM 90; Chicago, IL, 1990, 792. (5) Adachi, K.; Hu, W.; Matsumoto, H.; Ito, K.; Tanioka, A. Polymer 1998, 39(11), 2315. (6) Hu, W.; Adachi, K.; Matsumoto, H.; Tanioka, A. J. Chem. Soc., Faraday Trans. 1998, 94(5), 665. (7) Hu, W.; Tanioka, A. J. Colloid Interface Sci. 1999, 212, 135. (8) Lewandos, G. S.; Gregston, D. K.; Nelson, f. R. J. Organomet. Chem. 1976, 118, 363. (9) Quinn, H. W.; Glew, D. N. Can. J. Chem. 1962, 40, 1103. (10) Quinn, H. W.; Can. J. Chem. 1967, 45, 1329. (11) Hashimoyo, T.; Fujimura, M.; Kawai, H. ACS Symp. Ser. 1982, 180, 217. (12) Gierke, T. D.; Munn, G. E.; Wilson, F. C. J. Polym. Sci., Part B: Polym. Phys. 1981, 19, 1687. (13) Escoubes, M.; Pineri, M. ACS Symp. Ser. 1982, 180, 9. (14) Yeager, H. L.; ACS Symp. Ser. 1982, 180, 41. (15) Winstein, S.; Lucas, H. J. J. Am. Chem. Soc. 1938, 60, 836. (16) Guo, B. C.; Castlemann, A. W. Chem. Phys. Lett. 1991, 181, 16. (17) Yang, R. T.; Kikkinides, E. S. AIChE J. 1995, 41, 509. (18) Chen, J. P.; Yang, R. T. Langmuir 1995, 11, 3450. (19) Chen, N.; Yang, R. T. Ind. Eng. Chem. Res. 1996, 35, 4020. (20) Barrer, R. M.; Davies, F. R. S.; Davies, J. A. Proc. R. Soc. London, Ser. A 1970, 320, 289. (21) Kington, G. L.; Macleod, A. C. Trans. Faraday Soc. 1959, 55, 1799. (22) Barrer, R. M.; Gibbons, R. M. Trans. Faraday Soc. 1963b, 59, 2875. (23) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309. (24) Komoroski, R. A.; Mauritz, K. A. J. Am. Chem. Soc. 1978, 7487.
