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J. Phys. Chem. 1996, 100, 7580-7585
High-Resolution Adsorption Isotherms of Microporous Solids Gamini Amarasekera and M. J. Scarlett Centre for Applied Colloid and BioColloid Science, Swinburne UniVersity of Technology, P.O. Box 218, Hawthorn 3122, Australia
D. E. Mainwaring* Department of Applied Chemistry, Royal Melbourne Institute of Technology, P.O. Box 2476V, Melbourne 3001, Australia ReceiVed: August 17, 1995; In Final Form: NoVember 30, 1995X
High-resolution static adsorption of nitrogen and argon at 77 K was determined on six microporous carbons and two synthetic zeolites. The adsorption behavior at very low relative pressures such as 10-6 was examined in close detail. An S-shaped feature was observed in the low-pressure region of most of the nitrogen and argon isotherms on microporous carbons. A novel mechanism for the physical processes involved in the filling of micropores designated as monolayer-induced micropore filling is proposed to account for this behavior. Examination of the low-pressure region of these high-resolution adsorption isotherms also revealed that the ultramicropores are filled in the region of 10-5 relative pressure.
Introduction Micropore-filling mechanisms are one of the areas of increasing theoretical and experimental interest in the study of molecule-surface interactions. In particular, molecular simulation researchers are now focusing on the initial processes of pore filling at low relative pressures.1-3 Seaton et al. incorporated pore connectivity and metastable vapor/liquid phases in simulation studies to explore sorption hysteresis.4 Mechanisms involved in the initial pore filling of carbons have been explored experimentally by Kaneko and co-workers.5 Physisorption of gases in micropores of diameters of less than 2 nm6 leads to filling of the micropore volume,7 with the narrowest micropores filling first. As the pressure increases and more gas molecules adsorb, the larger micropores progressively fill. On the other hand, physisorption of gases in mesopores with diameters between 2 and 50 nm6 at relative pressures below the onset of capillary condensation results in the adsorption of successive layers of molecules on the surface7 as the pressure increases. Two differing mechanisms are currently believed to contribute to volume filling of micropores.7 “Primary” micropore filling is the predominant mechanism in the smaller micropores where dimensions are comparable to the diameters of gas molecules. It results from overlap of the potential fields from the neighboring walls of the pore which significantly enhances the gassolid interaction energy above that for the corresponding plane surface.8 However, calculations on the adsorption of noble gases on carbon9 show that the magnitude of the enhancement of the gassolid interaction energy decreases sharply as the pore width increases, but in a manner dependent on the pore shape. For example, for slit-shaped pores, the enhancement is a maximum when pore widths approximately equal one molecular diameter but becomes almost negligible at twice the molecular diameter. Hence as the micropore width increases, the contribution of primary micropore filling becomes relatively less important. Micropore filling by “cooperative” effects has been proposed as the major filling mechanism for larger micropores.7,10,11 This X
Abstract published in AdVance ACS Abstracts, April 1, 1996.
S0022-3654(95)02414-2 CCC: $12.00
is a secondary process whereby adsorbing gas molecules associate with other molecules previously adsorbed, rather than complete a monolayer by interaction with the walls of the pore. The dimensions of these larger micropores approach the lower limit of the mesopore range, and presumably the nature of the adsorbate/adsorbate interactions involved in cooperative effects must be at least superficially similar to those responsible for multilayer adsorption in mesopores as indicated by the differential heat being only slightly higher.10,12 However, the process occurring in larger micropores is quite distinct from that in mesopores in that it involves volume filling rather than layer by layer coverage of the surface. Micropores are often subdivided into different classes on the basis of the predominant filling mechanism. The most accepted subdivision is into ultramicropores (0.3-0.7 nm),7 which fill mainly by potential field overlap and are able to accommodate between one and two layers of adsorbed molecules, and supermicropores (∼0.7-1.8 nm),7 where filling is dominated by cooperative effects and which can accommodate up to approximately five layers of adsorbed molecules. It has been generally accepted13,14 that filling of ultramicropores occurs up to relative pressure ∼10-2 and that supermicropores fill at higher relative pressures between ∼10-2 and 10-1. The actual size ranges given for the ultramicropore and supermicropore regions can only be a very approximate guide, as they depend on the gas used and on the pore geometry.13 Furthermore, the effective diameter of the gas molecule in the adsorbed state, and hence its ratio to the pore width, is affected by the nature of its interaction with the atoms of the micropore wall.12 Kaneko and co-workers14 have recently proposed that micropore filling be considered as a three- rather than a two-stage process. This proposal was based on their observation of small steps in the nitrogen isotherms of several microporous carbons between relative pressure 10-2 and 10-3. They suggested that a distinct monolayer forms on the walls of supermicropores before cooperative filling begins and that completion of the monolayer is accompanied by a phase change to a disordered solid state,15 similar to that observed at much higher relative pressures for adsorption of nitrogen on graphite and graphitized carbons.16 © 1996 American Chemical Society
High-Resolution Adsorption Isotherms Additional measurements of gas adsorption at very low pressures are needed to help clarify these mechanisms of volume filling of micropores at the molecular level. Although gas adsorption has been extensively used to characterize microporous materials, most published isotherms17 contain comparatively few data points below relative pressure 10-2 and even fewer below 10-4. We have determined highly detailed adsorption isotherms for nitrogen and argon gas at 77 K on six microporous carbons and two synthetic zeolites. Isotherms were measured over the relative pressure range 10-6-1. Each isotherm contains approximately 100 data points, including, in most cases, a minimum of 40 points in the region below 10-4 relative pressure. The carbons are derived from a range of precursor materials, both natural and synthetic, yielding a range of micro-, meso-, and macropores18 as well as varying amounts of inorganic constituents and oxygen-containing surface functional groups.11,19,20 Such carbons have a micrographitic structure with slit-shaped micropores,9,21 which contain most of the pore volume and result in type I adsorption isotherms.18 The zeolites, on the other hand, have well-established crystalline structures. They are entirely microporous with uniform-sized micropores,22 showing type I adsorption behavior. Here, some high-resolution adsorption isotherms of these carbons and zeolites are presented. A new model for the physical processes involved in the filling of micropores, designated as “monolayer-induced micropore filling (MIMF)” is also proposed, to account for the unusual features observed in the low-pressure region of most of the carbon isotherms. Experimental Section Samples. Measurements were performed on the following microporous solids: the carbonaceous adsorbents Ambersorb XEN 575 (derived from a sulfonated styrene/divinylbenzene copolymer, Rohm and Haas), PICA G 210 AS (from coconut shells), CCV RC III (from brown coal), Row 0.8 supra and RZN1 (from peat, Norit NV), molecular sieve carbon Carbosphere 60/80 (Alltech), and the synthetic zeolites molecular sieve type 5A and molecular sieve type 13X. Adsorption Isotherms. Outgassing and determination of adsorption isotherms were carried out using a modified Micromeretics ASAP 2000 automated surface area analyzer, which included an enhanced gas analysis manifold and a lower pressure transducer. Each sample was outgassed at 623 K under vacuum for a minimum of 20 h to a final pressure of 267 mPa. The sample tube was then back-filled with helium gas, transferred from the degassing to the analysis manifold, re-evacuated using the turbomolecular pump to a final pressure below 1.33 mPa, and brought to liquid nitrogen temperature. Prior to each isotherm determination, the system was tested for leaks by isolating the sample tube and analysis manifold from the pumping system and monitoring the rate of vacuum loss. In addition, the system dead space was measured using helium gas. To increase the accuracy of the volume-adsorbed calculations, the system dead volume with the sample was measured with helium, at both room temperature and at analysis bath temperature, and then converted to standard temperature. The dead volume at 273 K varied between 15 and 18 cm3. The saturation vapour pressure, p0 of the analysis gas (nitrogen or argon) was measured at 77 K. The p0 measurements were repeated at least every 2 h during the course of isotherm determination beyond relative pressure 10-2. All gases used were of better than 99.99% purity.
J. Phys. Chem., Vol. 100, No. 18, 1996 7581 During isotherm determination, each dose of gas was allowed to completely equilibrate. This was verified by monitoring the pressure at 45 s intervals. Equilibrium was considered to be achieved if the pressure change over 11 previous intervals was less than 0.01% of the average pressure. The pressure change and average pressure were calculated using the Savitzky-Golay convolution method for polynomial functions.23 Pressure monitoring and testing continued until the equilibrium condition was satisfied. Below relative pressure 10-2, a 3 cm3 dose was used. The time required for equilibration was typically 10-25 minutes per point at very low relative pressures around 10-6, although in a few instances times as long as 2 hours per point were necessary. Equilibration times gradually increased to 2-3 hours per point close to relative pressure 10-2. Above relative pressure 10-2, the added dose was varied to give preset regularly-spaced relative pressure points. Reliability of Adsorption Measurements at Low Pressure. All sample outgassing and isotherm determinations were carried out using the procedure described above. Low system pressures, below 1 Torr (133 Pa), were measured using a “Baratron 1 Torr” transducer which had a sensitivity of 6.67 mPa and long term stability of better than 0.12%. The transducer was found to have minimal fluctuation and/or drift in tests with very low doses of gas (as small as 1 cm3) which were well within the incremental pressure increase (0.003 Pa) resulting from these dose volumes and with long equilibration times (up to 8-10 hours per point) on a variety of different types of microporous solids. The temperature of the sample and saturation pressure tubes was kept constant by means of isothermal jackets which maintained a constant level of liquid nitrogen around the tubes. Monitoring showed that the Dewars contain sufficient liquid nitrogen for about 60 h of operation, during which time measurements were completed. Notably, the low-pressure readings were taken within the first 48 h. In calculating the volume of gas adsorbed from the measured pressure, thermal transpiration corrections were applied for the temperature gradient in the manifold using Weber’s coefficients taking into consideration the inside diameter of the sample tube and the hard sphere diameter of the gas molecule. The manifold temperature was measured to an accuracy of 0.02 °C. Results and Discussion When plotted over the entire relative pressure range from 10-6 to 1, all isotherms have the type I shape expected for microporous solids. This is as shown for the nitrogen isotherms of the zeolite 13X and the carbon Ambersorb XEN 575 in Figure 1a,b. However, the low-pressure region of the Ambersorb isotherm shows a pronounced S-shaped feature. This can be seen even more clearly when the low-pressure region of the isotherm is plotted on the expanded scale given in Figure 1c. Most of the carbon isotherms studied here show a similar S-shaped feature in the relative pressure region of 10-5, the only exceptions being the nitrogen isotherms for RNZ1 and Carbosphere 60/80. The low-pressure regions of the nitrogen and argon isotherms are compared in Figure 2a,b for Row 0.8 supra, where both isotherms exhibit the S-shaped feature, and in Figure 3a,b for RNZ1, where the S-shaped feature is absent from the nitrogen isotherm. In contrast to carbon, no S-shaped feature is observed in the isotherms of zeolites 13X and 5A, which have a similar overall shape to those reported in the literature.22 At the start of an isotherm with a S-feature, e.g., see Figure 1c, the measured equilibrium pressure first increases in the usual fashion as successive doses of gas are added up to the first inflection point X. Beyond the first inflection point, the
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Figure 2. Low-pressure region of (a) the nitrogen isotherm at 77 K for Row 0.8 Supra and (b) the argon isotherm at 77 K for Row 0.8 Supra.
Figure 1. Nitrogen isotherm at 77 K for (a) zeolite 13X and (b) Ambersorb XEN 575. (c) Low-pressure region of the nitrogen isotherm at 77 K for Ambersorb XEN 575.
equilibrium pressure begins to decrease rather than increase as gas is added, until the second inflection point Y is reached, where in some cases the pressure is below that at the start of the isotherm (i.e., after the addition of the first dose). As further gas is added beyond point Y, the pressure again starts to increase, and the remainder of the isotherm has the conventional shape. The coordinates of the inflection points X and Y for the various carbons studied are listed in Table 1. For example, for the isotherm shown in Figure 1b,c the respective pressures were initial vacuum prior to the first dose, 1.33 mPa; after the first dose, 258 mPa; point X, 301.9 mPa; point Y, 227.4 mPa. This type of adsorption behavior observed here has not been reported previously, the observation of which is facilitated by automated instrumentation capable of attaining the large number of stable points at the very low equilibrium pressures necessary for accurate study of the micropore region. Notably, it is not present in all carbon isotherms although identical sample pretreatment and measurement conditions were used, and it was not present in the zeolite isotherms. Thus, by carrying out the adsorption experiment under and with equilibrium constrained to conditions of constant volume and total gas content, parts of the V(T,p) isotherm, which are according to statistical theory
Figure 3. Low-pressure region of (a) the nitrogen isotherm at 77 K for RNZ1 and (b) the argon isotherm at 77 K for RNZ1.
unstable or metastable, are observed during the microscope filling processes. Futhermore, the S-shaped feature in the Ambersorb XEN 575 nitrogen isotherm was demonstrated to be present in repeat runs on samples of different mass. These are shown in Figure 4 (a and b). The S-shaped feature remains for a 10-fold increase in equilibration time (minimum 3 h) for each pressure point (curve d) and with the usual equilibration time but using a reduced dose of 1 cm3 to generate considerably more data points (curve
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J. Phys. Chem., Vol. 100, No. 18, 1996 7583
TABLE 1: Coordinates of the S-shaped Feature in the Carbon Isotherms carbon
X 106 × p/p0 V (cm3/g)
Y 106 × p/p0 V (cm3/g)
N2 Ambersorb XEN 575a Ambersorb XEN 575b Ambersorb XEN 575c Ambersorb XEN 575d Row 0.8 supra RZN1e Pica G 210 AS CCV RC III Carbosphere 60/80e
2.9 1.2 2.5 5.0 3.6
9 9 4 3 15
2.2 0.8 1.6 0.6 3.0
47 40 52 49 40
4.0 2.2
25 12
3.8 1.7
46 40
Ambersorb XEN 575 Row 0.8 supra RZN1 Pica G 210 AS CCV RC III Carbosphere 60/80
15.8 10.3 9.4 6.9 5.2 4.4
19 12 12 12 9 6
13.1 6.9 7.5 5.6 3.6 3.2
62 47 28 40 31 25
Ar
c
a-d Repeat runs on samples of different mass: a and b same conditions; 1 cm3 dose; d3 h equilibration time. e No S-shaped feature observed.
Figure 4. Repeats of the low-pressure region of the nitrogen isotherm at 77 K for Ambersorb XEN 575 for different sample masses: curves a and b, identical conditions; curve c, 1 cm3 dose; curve d, 3 h equilibration time. Sample mass: (a) 0.1474, (b) 0.2811, (c) 0.1381, and (d) 0.1840 g.
c). Here it can be seen that an increase in carbon sample mass (b) or a reduction in gas dose volume (c) both produce curves at lower pressures but with the same S-shaped feature. Increasing the equilibration time has little influence on the pressure minimum with point Y remaining in the same region, whereas point X occurred at a higher relative pressure. Comparison of the initial adsorption (point X) of a and d suggests that long equilibrium times may involve adsorption-desorption processes for the N2/XEN 575 system. The processes of initial adsorption at very low pressures (approach to point X) on this sample and carbons of a more model geometry (activated carbon fibers) require detailed study to define the complex features. The role of adsorption-desorption processes in the very-low-pressure region is currently being investigated. However, the S-shaped feature occurring during the low-temperature adsorption process remains over this wide range of experimental conditions. Detailing the S-shaped feature requires the use of sufficiently small doses of gas at extremely low relative pressures, otherwise the critical region may be bypassed. Thus, for the Ambersorb XEN 575 nitrogen isotherm, this was shown by arbitrarily increasing the dose from 3 to 7 cm3, which caused the S-shaped feature to disappear and resulted in an isotherm of conventional shape.
Proper sample degassing is also most important, especially to observe point X. For example, it was found that if the Ambersorb XEN 575 sample was outgassed to a final pressure of 400 mPa rather than 267 mPa point X no longer appeared. This illustrates the importance of degassing to a particular final pressure rather than for a fixed time, as the efficiency of the pumping system may vary. The pressure drop from X to Y in these carbon isotherms corresponds to an increase in adsorption potential as adsorption proceeds. On approaching X during adsorption, even though a state of lower free energy is, in principle, available with a higher adsorption at the given pressure, there is insufficient gas present both to maintain the pressure and to fulfill the adsorption requirement, leading to an initial S-shape in the isotherm. Here, a phenomenological model involving monolayer-induced micropore filling (MIMF) is developed to account for this behavior by considering the physical processes involved in filling micropores in the lower size range of the supermicropore region and phase changes occurring at low coverages in micropores. The micropores in carbons have been frequently considered to be slit-shaped,9,21 and we have assumed this for the purposes of discussion. However, the principles of the model are equally applicable to wedge- and cylindrical-shaped pores. For wedgeshaped pores, the MIMF process will operate in those sections of a pore which have suitable width. For cylindrical pores, where the attenuation of the micropore field is much more gradual than for slit-shaped pores,9 the pore widths for operation of the MIMF process may be correspondingly larger. Figure 5 illustrates the operation of the MIMF model for a supermicropore capable of accommodating three layers of adsorbate molecules. Since the pore is slit-shaped, enhancement of the adsorption potential due to overlap of the potential fields of adjoining pore walls becomes negligible at sizes greater than two molecular diameters.9 The equilibrium pressure after the addition of each dose of gas is proportional to the number of nonadsorbed free gas molecules remaining in the system (NF). Figure 5 illustrates the pore diagrammatically in cross section. For the purpose of describing the operation of MIMF, each dose of gas is assumed to contain five gas molecules of which three adsorb on the pore walls, leaving two free. Figure 5a shows the system prior to adding dose one. All the adsorption sites on the pore walls are assumed to have the same potential.9,24 After the addition of dose one there will be three adsorbed molecules randomly positioned on the pore walls. One such arrangement is shown in Figure 5b. Beyond this stage all sites on the pore walls will no longer be equivalent. Rather, those sites adjacent to sites where molecules have already adsorbed may be expected to have a somewhat larger adsorption potential, as they are simultaneously attracted by the pore walls and the other adsorbate atom, i.e., it is likely that there will be some tendency to form small clusters of neighboring molecules on the walls,25,26 such as those shown in Figure 5c after the addition of dose two. Irrespective of whether or not clusters form, adsorption on the walls of three out of the five molecules of dose three can complete a partial monolayer on each pore wall up to level B-B′ as shown in Figure 5d. We propose that a phase transition to a disordered solid then occurs. Kaneko and co-workers14,15 suggested a similar type of phase transition on completion of the monolayer. The solid surface of the pore with its adsorbed partial monolayer to level B-B′ can be considered as a single solid-like phase.8 The gap between the partial monolayers so produced acts as an ultramicropore of the smallest size and so fills spontaneously due the enhanced adsorption potential. This leads to the adsorption of an additional three molecules,
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Figure 6. Low-pressure region of the nitrogen isotherm at 77 K for PICA G 210 AS.
Figure 5. MIMF process: NA ) number of molecules adsorbed on the pore wall; NF ) number of free (nonadsorbed) molecules in the gas phase; NEA ) number of molecules adsorbed in the middle of the pore space as the result of enhanced potential.
comprising the two remaining molecules from dose three and one additional free molecule from an earlier dose as shown in Figure 5e, causing the equilibrium pressure to decrease. Thus 5e rather than 5d represents the equilibrium point after dose three. Figure 5f,g shows the completion of partial monolayer up to level C-C′ and spontaneous filling of the gap after addition of dose four. Progressive monolayer completion followed by spontaneous filling continues in a similar manner with the addition of each dose of gas until the pore is completely filled as in Figure 5h. The number of free unadsorbed gas molecules NF first increases after doses one and two, and hence the experimental equilibrium pressure increases. This corresponds to the initial section of the isotherm up to the first inflection point X. With the beginning of partial monolayer completion and spontaneous filling after dose three, the number of free gas molecules and hence the measured pressure begin to decrease until the pore is completely filled at or near the second inflection point Y, after which the pressure again increases. Even with this simple phenomenological model, there are many possible arrangements of the adsorbed molecules other
than those shown in Figure 5. Although these different arrangements lead to slightly different values of NF after equilibration of each dose, they nevertheless produce the same general pattern of pressure increase, decrease, and then increase again, which is characteristic of the S-shaped feature. The MIMF process can only take place in those micropores where the gap between the partial monolayers does not exceed two molecular diameters, i.e., for micropores with widths three or four times the molecular diameter. The lower limit corresponds to the boundary of the ultramicropore region. Any ultramicropores present fill by potential overlap, before the MIMF process begins to fill the smallest supermicropores. Since the S-shaped feature appears in our isotherms close to a relative pressure of 10-5, ultramicropores must complete filling in this pressure region, well below the values suggested by other authors for filling of ultra- and supermicropores.7,14 The presence of an initial near vertical section in the isotherm before the measured pressure starts to decrease (prior to X) indicates the presence of ultramicropores. The nitrogen isotherm of the PICA 210 AS carbon in Figure 6 provides a good example of this. For micropores wider than four molecular diameters, filling occurs by cooperative effects, as suggested by Sing.7 No S-shaped feature is observed in the nitrogen or argon isotherms of zeolites 5A or 13X. These solids do not have micropores in the appropriate size range for the MIMF process to occur. These zeolites have uniform pores in the ultramicropore size range with free apertures of 0.42 and 0.74 nm respectively,22 equivalent to one and two molecular diameters. Importantly, the almost vertical initial section of the nitrogen isotherm for zeolite 13X was at a relative pressure near to 5 × 10-6 as shown in Figure 1a, which corresponds to the filling of these ultramicropores. Specific interactions27-29 may further enhance the adsorption potential in those micropores in which the MIMF process operates. Contributions to the adsorbate/adsorbent and adsorbate/ adsorbate interactions26 will vary for different solid/gas combinations due to differences in surface functional groups18,20 and metal ion content in the solid26 and dipole and/or quadrupole moment of the gas.7 Specific interactions would be expected to be more important for nitrogen than for argon as a result of its much larger quadrupole moment,7 which would lead to both stronger adsorbate/adsorbent and adsorbate/adsorbate interactions. Where the carbon concerned possesses polar oxygencontaining surface functional groups and/or metal cations, specific interactions with the nitrogen quadrupole moment would be expected to significantly increase the strength of the adsorption potential for nitrogen over that for argon. Comparison of the nitrogen and argon isotherms of the carbons RZN1 (Figure 3,b) and Carbosphere 60/80 (not shown) provides evidence for the much larger adsorption potential for
High-Resolution Adsorption Isotherms nitrogen than for argon. For both carbons the argon isotherms show a pronounced S-shaped feature without a preceding near vertical section, demonstrating that, whereas these two carbons have pores in the required size range for the MIMF process, they do not have ultramicropores. In contrast the nitrogen isotherms have the conventional shape for ultramicroporous solids with an initial steep section, indicating enhancement of the adsorption potential, and no S-shaped feature. This enhancement cannot be due to overlap of the potentials of adjacent pore walls since argon showed ultramicropores to be absent but may instead be due to strong specific infractions for these particular nitrogen/carbon systems. The magnitude of such enhancement, however, is less defined, in contrast to the enhancement due to the pore walls which has been the subject of detailed study.9,24,30 The stronger specific interactions for nitrogen than argon may mask the effect of the MIMF process causing the S-shaped feature which is present in all the argon isotherms studied to become less pronounced in the corresponding nitrogen isotherms, as in the PICA 210 AS carbon, or even to disappear, as in the case of the RZN 1 and Carbosphere 60/80 carbons. A wide variety of empirical methods, such as the DubininRudeshkevich and Dubinin-Astakhov equations, t and Rs plots, and the Micropore method, are commonly used to analyze experimental adsorption isotherms in the micropore region.5,7 None of these methods are generally applicable to all gassolid systems over the entire micropore range of relative pressures, since they are not based on a complete physical description of the mechanism of micropore filling. The MIMF model helps to provide a better understanding of the processes of volume filling of micropores at the molecular level, a prerequisite for the development of improved equations for analysis of the micropore region of isotherms. Furthermore, since any such equations must be extensively evaluated by experiment and since ultramicropores have been found to fill at ∼10-5 relative pressure, many more detailed measurements will be needed in the very-low-pressure region. References and Notes (1) Paterson, B. K.; Gubbins, K. E. Mol. Phys. 1987, 62, 215. (2) Tan, Z.; Van Swol, F.; Gubbins, K. E. Mol. Phys. 1987, 62, 1213.
J. Phys. Chem., Vol. 100, No. 18, 1996 7585 (3) Nicholson, D. Characterization of porus solids II; RodriguezReinoso, F., et al., Eds.; Elsevier: Amsterdam, 1991; p 11. (4) Liu, H.; Zhang, L.; Seaton, N. A. Langmuir 1993, 9, 2576. (5) Kaneko, K. J. Membr. Sci. 1994, 96, 59. (6) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603. (7) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982. (8) Dubinin, M. M. Progress in Surface and Membrane Science; Danielli, J. F., Rosenberg, M. D., Cadenhead, D. A., Eds.; Academic Press: London, 1975; Vol. 9, p 1. (9) Everett, D. H.; Powl, J. C. J. Chem. Soc., Faraday Trans. 1 1976, 72, 619. (10) Atkinson, D.; McLeod, A. I.; Sing, K. S. W. J. Chem. Phys. 1984, 81, 791. (11) Marsh, H. Carbon 1987, 25, 49. (12) Everett, D. H. Characterization of porous solids; Unger, K. K., et al., Eds.; Elsevier: Amsterdam, 1988; p 1. (13) Carrott, P. J. M.; Sing, K. S. W. Characterization of porous solids; Unger, K. K., et al., Eds.; Elsevier: Amsterdam, 1988; p 77. (14) Kakei, K.; Ozeki, S.; Suzuki, T.; Kaneko, K. J. Chem. Soc., Faraday Trans. 1990, 86, 371. (15) Kaneko, K.; Suzuki, T.; Kakei, K. Langmuir 1989, 5, 879. (16) See, for example: Rouquerol, J.; Partyka, S.; Rouquerol, F. J. Chem. Soc., Faraday Trans. 1 1977, 73, 306. Piper, J.; Morrison, J. A.; Peters, C.; Ozaki, Y. J. Chem. Soc., Faraday Trans. 1 1983, 79, 2863. (17) See, for example: Lamond, T. G.; Marsh, H. Carbon 1964, 1, 281. Rodriguez-Reinoso, F.; Lopez-Gonzalez, J. De D.; Berenguer, C. Carbon 1982, 20, 513. Ali, S.; McEnaney, B. J. Colloid Interface Sci. 1985, 107, 355. Rodriguez-Reinoso, F.; Martin-Martinez, J. M.; Molina-Sabio, M.; Torregrosa, R.; Garrido-Segovia, J. J. Colloid Interface Sci. 1985, 106, 315. (18) Dubinin, M. M. Chemistry and Physics of Carbon; Walker, P. L., Jr., Ed.; Marcel Dekker: New York, 1966; pp 51-120. (19) Dietz, V. R.; Carpenter, F. G.; Arnold, R. G. Carbon 1964, 1, 245. (20) Matsumura, Y.; Yamabe, K.; Takahashi, H. Carbon 1985, 23, 263. (21) Dubinin, M. M. Carbon 1988, 26, 97. (22) Breck, D. W. Zeolite Molecular SieVes; John Wiley and Sons: New York, 1975. (23) Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627. (24) Floess, J. K.; VanLishout, Y. Am. Chem. Soc., DiV. Fuel Chem. 1991, 36 (3), 898. (25) Aristov, B. G.; Bosacek, V.; Kiselev, A. V. Trans. Faraday Soc. 1967, 63, 2057. (26) Barrer, R. M. Zeolites and Clay Minerals as Sorbents and Molecular SieVes; Academic Press: London, 1978. (27) Vernov, A. V.; Steele, W. A. Langmuir 1986, 2, 219. (28) Zhang, Q. M.; Kim, H. K.; Chan, M. H. W. Phys. ReV. 1986, B33, 413. (29) Hanzawa, Y.; Suzuki, T.; Kaneko, K. Langmuir 1994, 10, 2857. (30) Stoeckli, F. HelV. Chim. Acta 1974, 57, 2195.
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