J. Phys. Chem. 1996, 100, 10331-10336
10331
Ultramicropore Characterization of Microporous Carbons by Low-Temperature Helium Adsorption N. Setoyama and K. Kaneko* Department of Chemistry, Faculty of Science, Chiba UniVersity, 1-33 Yayoi, Inage, Chiba 263, Japan
F. Rodriguez-Reinoso Departamento de Quimica Inorganica, UniVersidad de Alicante, Apartado 99, 03080 Alicante, Spain ReceiVed: February 15, 1996; In Final Form: April 16, 1996X
The adsorption isotherms of helium at 4.2 K were determined to elucidate the presence of ultramicropores in microporous solids such as activated carbons with different extents of activation. These isotherms were compared with the adsorption isotherms of nitrogen at 77 K. The micropore volumes determined from the Rs analysis of helium adsorption agreed well with those of nitrogen adsorption except for the most highly activated carbon. Carbons with low-to-medium burnoff had no ultramicropores (pore width < 0.7 nm), but the presence of this porosity (inaccessible to nitrogen) was shown in the carbon with the highest burnoff. The Dubinin-Radushkevich (DR) and pore size distribution (PSD) analysis also supported this finding.
Introduction The characterization methods of the micropore structure of activated carbon have been widely used because these materials having a high adsorption capacity are very important materials for industrial applications. However, the detailed structure of micropores is not sufficiently elucidated. Activated carbons are noncrystalline solids, and consequently, their structure cannot be determined by X-ray diffraction analysis. Physical adsorption of gases has been commonly used for the characterization of the microstructure of activated carbon. Several molecules have been used as molecular probes, the most common ones being nitrogen, argon, carbon dioxide, and organic molecules.1-3 The selection of the molecular probe is a key problem for the micropore characterization by physical adsorption because the results obtained are influenced by probe properties such as molecular size, shape, and polarity as well as by chemical properties. Nitrogen adsorption at 77 K has noticeably contributed to the characterization of microporous solids, although nitrogen adsorption at 77 K has a serious diffusion problem for the ultramicropore system. In the case of a zeolite whose micropore structure is determined by X-ray diffraction,4 the micropore volume determined from nitrogen adsorption is usually greater than the micropore volume deduced from the X-ray method5 due to the specific interaction between the quadrupole moment and the gradient of the electrostatic field on the cation of the zeolite lattice. On the other hand, the quadrupolar interaction of a nitrogen molecule with the “graphitic” crystallite basal plane determines the commensurate structure of the nitrogen adsorbed on the graphite.6 Such a strong interaction of the nitrogen molecule with the graphitic basal plane of the entrance of the ultramicropore (pore width < 0.7 nm) on the activated carbons gives rise to a serious blocking effect which interferes with the smooth diffusion of a nitrogen molecule at 77 K. Then, the nitrogen adsorption method is not necessarily fit for evaluation of the ultramicroporosity of activated carbons. Furthermore, the orientational structure of the nitrogen molecule of a nonspherical shape should be taken into account in the narrow micropores. However, the nitrogen adsorbed in X
Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(96)00467-4 CCC: $12.00
micropores usually has been assumed to be like a bulk liquid state. A molecular adsorption method for the micropore structure determination is necessary for the exact density of the adsorbed layer in the micropore, although the liquid density of the adsorbate has been widely used.7 Recently, Iiyama et al.8,9 have shown that water molecules adsorbed in carbon micropores have a more ordered structure than liquid and even CCl4 molecules in the micropores have a long-range order measured by X-ray diffraction analysis as compared with the liquid state. Magnetic susceptibility measurements showed the presence of clusters of oxygen molecules in carbon micropores.10,11 The Grand Canonical Monte Calro simulation by Auket et al.12 showed that the density of nitrogen restricted in a graphitic slitshaped pore depends on the pore width and it is greater than the liquid density (0.808 g/cm3 at 77 K) by 15% (0.93 g/cm3) in a pore system of width < 1.5 nm. Although the problem of the density of adsorbed molecules in micropores is not limited to nitrogen adsorption, the evaluation of the ultramicroporosity of noncrystalline solids such as activated carbons by adsorption of nitrogen has a serious problem. A new method for pore characterization using a smaller, inert, and spherical molecule should be developed. The helium molecule is the most hopeful probe for the evaluation of the ultramicroporosity, and consequently, we have carried out the characterization of the microporosity13-16 of activated carbon fibers (ACFs) with helium adsorption at 4.2 K, showing significant differences in the microporosity deduced from helium and nitrogen adsorption due to the presence of ultramicropores. The combined micropore analysis of smallangle X-ray scattering and nitrogen adsorption also showed the presence of ultramicropores in these fibers.17 In the present work we have applied the low-temperature adsorption of helium to activated carbons exhibiting some molecular sieving effects. Experimental Section The series D of activated carbons was prepared from olive stones by carbonization (nitrogen flow, 1173 K, 2 h) of the acidwashed precursor followed by activation (1098 K, different residence times) under a flow of carbon dioxide.18 The extent of activation is given by the burnoff reached in each case, and such burnoff is included in the nomenclature of the samples. © 1996 American Chemical Society
10332 J. Phys. Chem., Vol. 100, No. 24, 1996
Setoyama et al.
Figure 1. Adsorption isotherms of helium at 4.2 K (A; solid symbols) and nitrogen at 77 K (B; open symbols) on D-19 (circles), D-34 (squares), D-52 (triangles), and D-80 (diamonds).
For example, carbon D-19 corresponds to a weight loss of the char of 19% upon activation. The adsorption isotherms of helium at 4.2 K and nitrogen at 77 K were determined with a McBain-type gravimetric system described in previous works.13-16 The samples were outgassed at 573 K for 5 h prior to the adsorption measurements. The equilibrium for helium adsorption was reached within about 5 min for all experimental points. It took more than 90 min to determine the experimental points for the initial introduction of nitrogen gas. The rest of the points on nitrogen adsorption were determined in less than 30 min. Results and Discussion Helium and Nitrogen Adsorption Isotherms. The adsorption isotherms of helium at 4.2 K and nitrogen at 77 K are shown in Figure 1. The amount adsorbed is expressed by volume of liquid adsorbed (W) to compare both sets of isotherms. The density of helium adsorbed on the “graphitic” pore surface was taken as 0.202 g/cm3. Although the density of helium adsorbed in the slit-shaped micropore is not perfectly established, we have used the above density value on reasonable grounds.19-21 The bulk liquid density of 0.808 g/cm3 was used for nitrogen adsorption at 77 K. The amount adsorbed for both adsorptives increases with burnoff over the whole range of relative pressures, the uptake for helium at low relative pressures being always larger than that for nitrogen in all carbons. All isotherms are of type I,22 suggesting that the carbons mainly have uniform micropores. However, the plateau is more parallel to the pressure axis in the case of helium adsorption, while the plateau for nitrogen exhibits a small slope. The nitrogen isotherm for D-80 shows a remarkable uptake at relative pressures in the range 0.010.3, which is ascribed to the presence of large micropores.23 This adsorption occurs by a “cooperative pore filling” mechanism which corresponds to the filling process by molecules in the monolayer-coated micropore walls.7 The helium adsorption isotherm for D-80 has no gradual uptake in the range 0.01-0.3 of relative pressure because an adsorbed molecule even in the second layer interacts strongly with the “graphitic” surface at 4.2 K.19 Consequently, even the second-layer adsorption occurs at rather low relative pressures, producing a sharp initial uptake for D-80, as shown in Figure 1. As the low-pressure region of the adsorption isotherms is very important, it is preferable to express the pressure axis of the isotherm in a logarithmic scale, as shown in Figure 2. While the large adsorption of helium begins even below P/P0 ) 10-6, a considerable adsorption of nitrogen is observed only at about
Figure 2. Adsorption isotherms of helium and nitrogen in the wide pressure range. Symbols and markers are same as in Figure 1.
P/P0 ) 10-4. The marked adsorption of helium at the very low relative pressure is caused by the accelerated bilayer adsorption discussed above. The relatively limited increase in helium adsorption after the initial rapid uptake is due to the dominant cooperative pore filling of the residual space between the second adsorbed layer on the walls of slightly larger micropores. The density of adsorbed helium above the third layer resembles that of the liquid state, as deduced from neutron diffraction experiments by Carneiro et al.20 Accordingly, the cooperative filling of helium should occur in large micropores whose pore width is greater than the thickness of four helium layers. The adsorption of helium at the 0.01-0.3 relative pressure range stems from the cooperative filling process, but the absolute amount is relatively small even for D-80 and can be almost neglected for other samples. As the bilayer formation of adsorbed helium on each pore wall of the slit-shaped pore almost finishes at a very low relative pressure, the micropore space of D-80 is already occupied with four helium layers and the residual space is too small to produce a clear cooperative filling, as observed in the nitrogen adsorption. There is a slight decrease of helium uptake at the highest relative pressures (P/P0 > 0.8, Figure 1A), which is caused by the incomplete buoyancy correction. As the density of bulk helium gas at 4.2 K is very large (11.61 mg/cm3), a small error in the carbon density produces an negligible error. The density values for carbons, as determined by helium picnometry were: D-19 ) 2.14, D-34 ) 2.15, D-52 ) 2.17, and D-80 ) 2.20 g/cm3 and should be used for a more exact calculation. Although some uncertainty is always expected upon measuring the helium density of microporous carbons, these values follow the right sequence expected after increasing activation of a lignocellulosic char.24 Even in this case the possible error in the buoyancy correction is completely negligible for relative pressures below 0.1, and only the adsorption data below this relative pressure are used for the evaluation of the ultramicroporosity. Hence, the observed helium adsorption isotherms are helpful for this purpose. A careful comparison of the helium isotherm with that of nitrogen should provide important information on the ultramicroporosity. Rs Analysis. Since the morphological comparison of the helium and nitrogen adsorption isotherms does not provide clear
Ultramicropore Characterization of Microporous Carbons
J. Phys. Chem., Vol. 100, No. 24, 1996 10333 TABLE 1: Micropore Parameters from rs Analysis He adsorption 0.7 < Rs < 1.0
D-19 D-34 D-52 D-80
Figure 3. Standard adsorption isotherms of helium at 4.2 K (solid symbols) and nitrogen at 77 K (open symbols) on nonporous carbon black.
Figure 4. Rs plots of helium and nitrogen adsorption isotherms for series D samples. Symbols and markers are same as in Figure 1. Solid lines were obtained from least-squares fitting with the region of 0.7 < Rs < 1.0 for helium adsorption and 0.7 < Rs < 1.5 for nitrogen adsorption.
information, the comparison plot analysis with Rs plots is requisite. This analysis needs a standard isotherm for both helium and nitrogen on a nonporous material having a chemical nature similar to those of the test samples. We selected a nonporous carbon black (Mitsubishi #32) as an appropriate standard. Figure 3 shows the standard adsorption isotherm for helium at 4.2 K and nitrogen at 77 K.23 The standard adsorption isotherm for nitrogen is of type II,22 while that of helium has a sharp uptake at the low relative pressure region, which can be ascribed to the accelerated bilayer adsorption. The BET surface area from nitrogen adsorption was 69.2 m2/g, whereas the surface area from helium adsorption was 64 m2/g, as deduced from the Steele equation,19 using 0.089 nm2 as the crosssectional area of a helium atom.20 Both values of surface area determined from helium and nitrogen adsorption show a good agreement. The Rs plots for helium and nitrogen adsorption isotherms are given in Figure 4. The micropore volume (W0), total surface area (aS), and external surface area (aEXT) including mesoporous surface area can be determined from the Rs plots for helium and nitrogen adsorption isotherms. The Rs analysis for nitrogen is already established, and it provides the following information. All Rs plots for nitrogen show a downward bending at Rs ) 0.7, and the sample with lower burnoff (D-19) shows a more significant swing (filling swing) below Rs ) 0.5, which stems from the strong adsorption field due to the overlapped moleculesurface potential.23 As a marked filling swing suggests a narrow micropore system, carbons with low-to-medium burnoff have
N2 adsorption 0.7 < Rs < 1.5
1.5 < Rs < 2.5
W 0, cm3 g-1
aEXT, m2 g-1
W0, cm3 g-1
aEXT, m2 g-1
W0, cm3 g-1
aEXT, m2 g-1
0.29 0.38 0.45 0.75
46 71 86 45
0.28 0.38 0.46 0.70
53 81 95 65
0.31 0.43 0.52 0.73
20 24 31 24
a small micropore width (probably less than 0.9 nm). However, the Rs plot for D-80 exhibits a slight condensation swing, indicating the presence of wider micropores. The Rs plots for nitrogen bend downward above Rs ) 1.5, as for other activated carbons.1,2 As the error of the buoyancy correction is negligibly small in the nitrogen adsorption, the bending at high values of Rs is clearly associated with the presence of mesopores. The mesopore size can be estimated from the modified Kelvin equation.25 The estimated mesopore size corresponding to Rs ) 1.5 is 9.2 nm. Therefore, this bending corresponds to the complete filling of small mesopores (pore width smaller than 9.2 nm). As the carbons with low-to-medium burnoff have relatively narrow micropores, the contribution of mesoporosity is explicitly observed in the clear bending at the high region of Rs. Although carbon D-80 has mesopores, the obscure bending suggests the small contribution of mesopores. The whole Rs region is limited to the 0.5-1.5 range in the case of helium adsorption (see Figure 3), but the Rs plots for helium are rather similar to those of nitrogen, exhibiting a downward bending at Rs ) 0.7. One has to exclude the Rs data above Rs ) 1.1 as a consequence of the possible erroneous buoyancy correction at high relative pressures as mentioned above. We chose the Rs region of helium up to Rs ) 1.1, where the buoyancy correction is not important. The Rs region used in this analysis corresponds to the multilayer adsorption region, as shown in Figure 3, and thereby, the information obtained from the Rs plot in the limited range is important. The W0 and aEXT values from the Rs analysis are shown in Table 1. The Rs plots for nitrogen were analyzed for two regions corresponding to 0.7 < Rs < 1.5 and 1.5 < Rs < 2.5 in order to get a detailed information on the pore structure. As the bending at Rs ) 1.5 comes from the presence of small mesopores, the difference in W0 values for the two regions corresponds to the pore volume of small mesopores (width < 9.2 nm). The contribution of small mesoporosity is about 10% of the total pore volume, which cannot be neglected. It is concluded that the Rs plot for the region of 0.7 < Rs < 1.5 provides pore parameters of W0 and aEXT without the contribution of mesopores. A good agreement is observed for the helium and nitrogen adsorption, except for carbon D-80. This agreement indicates the absence of ultramicropores (to which the nitrogen molecule is inaccessible) in D-19, D-34, and D-52. The W0 value deduced from helium adsorption in D-80 is greater than that obtained from nitrogen adsorption, suggesting the presence of ultramicropores. Although the Rs plot for helium is less reliable in the high region of Rs, the values of aEXT from both helium and nitrogen are consistent with each other. DR Analysis. The Dubinin Radushkevich (DR) equation can describe the adsorption process in micropores.26 The Weibull distribution of the Polanyi’s adsorption potential (A) is presumed in a general Dubinin-Astakhov description, from which the DR equation is obtained as the special case for the microporous activated carbons. This DR equation is expressed as follows:
W ) W0 exp (-(A/βE0)2)
(1)
10334 J. Phys. Chem., Vol. 100, No. 24, 1996
Setoyama et al. TABLE 2: DR Parameters He adsorption D-19 D-34 D-52 D-80
Figure 5. DR plots of helium and nitrogen adsorption isotherms for series D samples. Symbols and markers are same as in Figure 1.
where
A ) -∆G ) RT ln(P0/P)
(2)
Here, W0 is the micropore volume and E0 is the characteristic adsorption energy corresponding to the micropore structure. β is an affinity coefficient, which is a shifting factor of the characteristic curve for several adsorptives with reference to β ) 1.0 for benzene. The β for nitrogen is 0.33,27 and the β for helium was taken as 0.04 after a previous study.15 The authors also calculated the β value using the Kadlec approach,28,29 given by
β)
(
)
R R0/χ0 + Rs/χs R0 Rg/χg + Rs/χs
(3)
where R and χ denote the polarizability and diamagnetic susceptibility, respectively. The subscripts of “0”, “g”, and “s” express the reference adsorptive (benzene), the test adsorptive (helium), and the adsorbent, respectively. The Rs and χs values of graphite were used as those of the series D. The calculated β value was 0.03, which was slightly smaller than the experimental one (0.04) used in this work. The analysis of the DR plots can provide the values of W0 and βE0 from both the helium and nitrogen isotherms. To get the correct information on the micropore structures, the adsorption in micropores was separated from the experimental adsorption isotherms with subtracting the adsorption on mesoporous and/or external surface by use of Rs analysis.30 The net adsorption in the micropores is expressed as
WMIC ) WTOT- WEXT ) WTOT- aEXTθSTN
(4)
where WMIC is the net adsorption in micropores, WEXT is the amount adsorbed on the mesoporous and external surface, WTOT is the adsorbed amount determined experimentally, and θSTN is the amount adsorbed per unit of surface area on the standard adsorbent used, which is given by
θSTN ) WSTN/aSTN
(5)
where aSTN and WSTN are the surface area and the adsorbed amount for the standard adsorbent, respectively. As aEXT can be determined from the Rs plot, as shown in Table 1, WMIC can be determined at the whole range of P/P0. The DR plots for helium and nitrogen adsorption are shown in Figure 5. Here, the amount adsorbed only by micropores (WMIC) was used for construction of the DR plots. It is observed that the plots for the three samples with lower burnoff (D-19,
N2 adsorption
W0, cm3 g-1
E0, kJ mol-1
W0, cm3 g-1
E0, kJ mol-1
0.29 0.39 0.47 0.61
29.0 23.3 19.6 21.9
0.28 0.38 0.47 0.60
29.0 23.8 20.7 18.9
D-34, and D-52) are linear over a wide range of relative pressures for both adsorptives. Both the W0 (obtained for the net adsorption isotherms in micropores) and E0 values are listed in Table 2. The comparison of the DR plots for helium and nitrogen gives the information on the ultramicroporosity. The good agreement of the DR plots for helium and nitrogen in the case of carbon D-34 and D-52 indicates that the microporosity of these two carbons does not depend on the size of the molecular probe. This agreement is not limited to helium and nitrogen, since it was previously observed for some hydrocarbon molecules.1 Consequently, the values of W0 and E0 obtained from the adsorption of helium and nitrogen for sample D-34 and D-52 almost coincide with each other. Furthermore, there is a good agreement in the W0 values obtained from the DR and Rs analysis for these two samples, suggesting an effective elimination of the adsorption on the mesoporous and/or external surface (WEXT in eq 4). Hence the regions of 0.7 < Rs < 1.5 for nitrogen and 0.7 < Rs < 1.0 for helium give correct information on the micropore structures. The DR plot for helium on carbon D-19 is situated on that for nitrogen, but it is almost parallel to that for nitrogen. Hence both gases give the same value of E0, which is the largest value of all carbons of the series. Therefore, carbon D-19 has the narrowest microporosity according to the Dubinin-Stoeckli equation as shown later (eq 8). However, the agreement of E0 for helium and nitrogen in D-19 is not consistent with the differences of amount adsorbed between both gases, as shown in Figure 5. If the size dependence of probe molecules was not present, the both DR plots should be unity like the results for D-34 and D-52, leading to a coincidence of E0 and W0 values. In this case, a part of the nitrogen molecules adsorbed on narrow micropores in D-19 will exhibit a less packed state compared to the liquid one because a nitrogen molecule has an elliptical shape and is larger than a helium atom. Nitrogen molecules cannot have a dense packing structure especially in ultramicropores having a pore width below 0.7 nm. Therefore, the helium adsorption uptake expressed as the logarithm of volume adsorbed will be slightly greater than the nitrogen one in the DR plot for D-19, suggesting the presence of a little amount of ultramicropores. Only carbon D-80 shows a clear disagreement of the DR plots for helium and nitrogen. That is, the slope for the helium plot is smaller than that for nitrogen. Hence the E0 value deduced from helium will be larger than that from nitrogen, thus indicating the presence of narrower micropores (ultramicropores), to which nitrogen molecules are not accessible. However, it is difficult to believe that this high burnoff may produce wedge-shaped and cage-shaped micropores of the type depicted in Figure 6. This quite narrow microporosity in carbon D-80 was detected previously when comparing the adsorption of nitrogen, carbon dioxide, and hydrocarbons in the series of carbons.1 As shown in Figure 5, there is a remarkable deviation from linearity in the DR plots for helium and nitrogen in the region of (A/β)2 < 50 and the extrapolated value of W0 does not coincide with the W0 value obtained from the Rs analysis. The
Ultramicropore Characterization of Microporous Carbons
J. Phys. Chem., Vol. 100, No. 24, 1996 10335
Figure 6. Schematic models of ultramicropore structures: A, wedgeshaped pore; B, cage-type ultramicropore. Shaded sections are the ultramicropore which only helium molecules are effectively accessible to.
deviation, caused by adsorption in large micropores, shows that the fraction of larger micropores is greater in carbon D-80, thus leading to a serious disagreement in the values of W0 deduced from the DR and Rs analysis. Micropore Size Distribution. The adsorption at an equilibrium pressure P in a microporous system having an adsorption site energy distribution F(q) can be described by the generalized adsorption isotherm (GAI)
W ) ∫L(P,q) F(q) dq
(6)
where L(P,q) is the local adsorption isotherm for adsorption at a given energy site q. Several expressions have been proposed for GAI.31-34 Dubinin29 and Stoeckli33 used the DR equation (in this case, q ) E0) as L(P,q) and the Gaussian distribution as F(q). The well-known Dubinin-Stoeckli equation is obtained by integration of the GAI for whole q values:
W)
W0 2x1 + 2mδ2A2
[
exp -
mχ02A2
]
1 + 2mδ2A2
[ ( 1 + erf
× χ0
δx2x1 + 2mδ2A2
)]
(7)
where δ is the dispersion of the pore size distribution (PSD) and χ0 is the mean half-width of the PSD and related to E0. The E0 and χ0 are empirically related as
χ0E0) k
(8)
where k is a constant (10 kJ nm mol-1).29 The shape of the PSD is given by the Gaussian distribution
[
]
(χ0 - χ)2 W0 dW exp ) dχ δx2π 2δ2
(9)
The three parameters of the PSD (W0, δ, and χ0) are obtained by numerical fitting of the adsorption isotherm given by eq 7. The helium and nitrogen PSDs for four carbons are given in Figure 7. The peaks of the PSD shift to a greater pore width with the progress of carbon burnoff, indicating that the microporosity widening takes place upon activation. The helium
Figure 7. Micropore size distributions (PSDs) of series D samples. PSDs of bold line were obtained from helium adsorption, and PSDs of narrow line were obtained from nitrogen adsorption.
PSD is almost coincident with the nitrogen PSD except for carbon D-80. The helium PSD for D-80 shifts to a smaller micropore width compared with that of the nitrogen PSD. On the other hand, the PSD for D-80 is more broad than for other carbons. Recent molecular simulation studies with this type of activated carbons showed a bimodal PSD,35,36 which was divided to small and large micropores. The PSD obtained in this work will have a meaning of averaged information for the bimodal PSD, since the PSD is described as a single-peaked one. The fraction of the larger micropores is negligibly small, hence the PSD for the carbons except D-80 shows a narrow dispersion. The smaller side shift of the helium PSD for D-80 indicates that the fraction of smaller micropores from helium adsorption will be larger than that of nitrogen in D-80. The difference of W0 between helium and nitrogen from Rs analysis agrees with this fact, showing the presence of ultramicropores deduced from the DR plot. Acknowledgment. This work was supported by the Grantin-Aid for the fundamental scientific research from the Ministry of Education and Science, Japanese Government. References and Notes (1) Rodriguez-Reinozo, F.; Garrido, J.; Martin-Martinez, J. M.; MolinaSabio, M.; Torregrosa, R. Carbon 1989, 27, 23. (2) Rodriguez-Reinozo, F.; Linares-Solano, A. In Chemistry and Physics of Carbon; Thrower, P. A., Ed.; Marcel Dekker: New York, 1989; Vol. 21, p 1. (3) Selles-Perez, M. J.; Martin-Martinez, J. M. Carbon 1992, 30, 41. (4) Breck, D. W. J. Chem. Educ. 1964, 48, 678. (5) Breck, D. W.; Grose, R. W. AdV. Chem. Ser. 1973, 121, 319. (6) Steele, W. A.; Vernov, A. V.; Tildesley, D. J. Carbon 1987, 25, 7. (7) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982; Chapter 4. (8) Iiyama, T.; Nishikawa, K.; Otowa, T.; Kaneko, K. J. Phys. Chem. 1995, 99, 10075. (9) Iiyama, T.; Nishikawa, K.; Otowa, T.; Suzuki, T.; Kaneko, K. In Fundamentals of Adsorption; LeVan, M. D., et al., Eds.; in press. (10) Kanoh, H.; Kaneko, K. J. Phys. Chem. 1995, 99, 5746. (11) Kanoh, H.; Kaneko, K. Chem. Phys. Lett. 1995, 237, 329. (12) Aukett, P. N.; Quirke, N.; Riddiford, S.; Tennison, S. R. Carbon 1992, 30, 913.
10336 J. Phys. Chem., Vol. 100, No. 24, 1996 (13) Kuwabara, H.; Suzuki, T.; Kaneko, K. J. Chem. Soc., Faraday Trans. 1991, 87, 1915. (14) Kaneko, K.; Setoyama, N.; Suzuki, T.; Kuwabara, H. In Fundamentals of Adsorption; Suzuki, M., Ed.; Kodansya: Tokyo, 1993; p 315. (15) Setoyama, N.; Ruike, M.; Kasu, T.; Suzuki, T.; Kaneko, K. Langmuir 1993, 9, 2612. (16) Kaneko, K.; Setoyama, N.; Suzuki, T. In Characterization of Porous Solids III; Rouquerol, J., et al., Eds.; Elsevier: Amsterdam, 1994; p 593. (17) Ruike, M.; Kasu, T.; Setoyama, N.; Suzuki, T,; Kaneko, K. J. Phys. Chem. 1994, 98, 9594. (18) Rodriguez-Reinoso, F.; Martin-Martinez, J. M.; Molina-Sabio, M.; Torregrosa, R.; Garrido-Segovia, J. J. Colloid Interface Sci. 1985, 106, 315. (19) Steele, W. A. J. Chem. Phys. 1956, 25, 819. (20) Carneiro, K.; Passell, L.; Thomlinson, W.; Taub, H. Phys. ReV. B 1981, 24, 1170. (21) Setoyama, N.; Kaneko, K. Adsorption 1995, 1, 165. (22) Sing, K. S. W.; Evertt, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603. (23) Kaneko, K.; Ishii, C.; Ruike, M.; Kuwabara, H. Carbon 1992, 30, 1075. (24) Garrido, J. Ph.D. Thesis, University of Alicante, Spain, 1984. (25) Dollimore, D.; Heal, G. R. J. Colloid Interface Sci. 1970, 33, 508.
Setoyama et al. (26) Dubinin, M. M. Chem. ReV. 1960, 60, 235. (27) Dubinin, M. M. In Chemistry and Physics of Carbon; Walker, P. L., Jr., Ed.; Marcel Dekker: New York, 1966; Vol. 2, p 51. (28) Kadlec, O. In Characterization of Porous Solids; Gregg, S. J., Sing, K. S. W., Stoeckli, H. F., Eds.; Society of Chemical Industry: London, 1979; p 13. (29) Dubinin, M. M.; Polyakov, N. S.; Kataeva, L. I. Carbon 1991, 29, 481. (30) Jaroniec, M.; Choma, J. In Chemistry and Physics of Carbon; Thrower, P. A., Ed.; Marcel Dekker: New York, 1989; Vol. 22, pp 197. (31) Sircar, S. Carbon 1987, 25, 39. (32) Wojsz, R.; Rozwadowski, M. Carbon 1986, 24, 225. (33) Stoeckli, H. F. J. Colloid Interface Sci. 1977, 59, 184. (34) Dubinin, M. M.; Stoeckli, H. F. J. Colloid Interface Sci. 1980, 75, 34. (35) Lastoskie, C.; Gubbins, K. E.; Quirke, N. J. Phys. Chem. 1993, 97, 4786. (36) Molina-Sabio, M.; Rodriguez-Reinozo, F.; Valladares, D.; Zgrablich, G. In Characterization of Porous Solids III; Rouquerol, J., et al., Eds.; Elsevier: Amsterdam, 1994; pp 573.
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