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Simulation study on the relationship between a high resolution αs-plot and the pore size distribution for activated carbon
Carbon Vol. 36, No. 10, pp. 1459–1467, 1998 © 1998 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0008-6223/98 $—see front matter
PII: S0008-6223(98)00138-9
SIMULATION STUDY ON THE RELATIONSHIP BETWEEN A HIGH RESOLUTION a -PLOT AND THE PORE SIZE S DISTRIBUTION FOR ACTIVATED CARBON N S, T S and K K* Department of Chemistry, Faculty of Science, Chiba University, 1–3 Yayoi, Inage, Chiba 263, Japan (Received 5 August 1996; accepted in revised form 5 February 1998) Abstract—The effects of the micropore structure of activated carbons on the high resolution a -plot for s nitrogen adsorption isotherms were examined with the grand canonical Monte Carlo simulation. Adsorption isotherms of nitrogen were simulated in graphitic slit pores at 77 K as a function of the slit width (w). As no pore effect was observed below P/P =0.6 for w=3.5 nm, a -plots for the simulated 0 s adsorption isotherms were constructed using the standard isotherm simulated for w=3.5 nm. The simulated a -plots had filling and cooperative swings which were experimentally shown in the previous s works, and the shape of the simulated a -plot varied with the micropore structure. As the subtracting s pore effect (SPE) method for the specific surface area (SSA) determination using the a -plot was proposed s in the previous experimental works, the theoretical ground for the SPE method was discussed. The best evaluation method of SSA using the a -plot was shown, almost agreeing with the SPE method. This s simulation study showed clearly that the SPE method is available for pore systems of w≥0.7 nm, whereas even the SPE method underestimates the SSA of the pores of w≤0.6 nm. The observed swings of the a -plot were simulated using the different micropore size distribution. The bimodal micropore size s distribution lead to both of filling and cooperative swings, while a single pore size distribution <0.9 nm gave only the filling swing. Thus, four representative types of the a -plot for activated carbons were s proposed and it was shown how to understand the micropore size distribution through the a -plot. s © 1998 Elsevier Science Ltd. All rights reserved. Key Words—A. Activated carbon, C. adsorption, D. surface areas, D. porosity.
This paper discusses the concept of the surface area and the meaning of the superhigh surface area for microporous solids. For these questions, the concept of superhigh surface area and the subtracting pore effect method (SPE method ) were proposed to determine the SSA for microporous carbon from experimental data [2,3]. The SPE method uses the a -analysis, which is the comparison plot proposed s by Gregg and Sing [4]. In general, the a -plot has s been applied to determine the micropore volume (W ) and the SSA of mesoporous and external sur0 faces (a ). Kaneko et al. improved the resolution EXT of the a -plot at a low a -region using the high s s resolution nitrogen adsorption isotherm, as shown in Fig. 1. Figure 1 shows the high resolution nitrogen adsorption isotherms of different kinds of activated carbons. Recently, the high resolution nitrogen adsorption isotherm whose relative pressure ranges from P/P =10−6 to 1 has been of great interest. Sing 0 and co-workers studied the high resolution nitrogen adsorption isotherms for some activated carbons which have different micropore structures [5]. They suggested that the adsorption process on the different pore sizes could be classified by three types from the high resolution a -analysis. On the other hand, it has s been indicated that such a class can be effectively investigated by the SPE method with high resolution a -plots for activated carbons, as shown in Fig. 2. s The dotted line in the plots gives W and a , which 0 EXT
1. INTRODUCTION
Molecular adsorption measurements have been widely used for the characterization of surface structures of solid materials. One of the major methods is nitrogen adsorption at 77 K. In the case of porous materials such as activated carbons, IUPAC has recommended that the pore volume can be correctly determined but the surface area is an ill-defined quantity [1]. However, the quantity of the surface area of activated carbon is quite convenient regardless of the fundamental arguments. Routine Brunauer– Emmett–Teller (BET ) analysis has been widely used to determine the specific surface area (SSA) of activated carbons. The BET analysis is very easy and it is possible to compare the BET surface area values for various activated carbons irrespective of the IUPAC recommendation. An intense demand for a new activated carbon with a large surface area has demanded a more accurate assessment of the surface area instead of the BET method. The carbon scientists believed that the upper limit of the surface area of activated carbon is 2630 m2 g−1 which originates from the single infinite graphene sheet structure, whereas activated carbons with a superhigh surface area >2630 m2 g−1 were developed. *Corresponding author. Fax: 81 3 90 788; e-mail: [email protected] 1459
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Fig. 1. High resolution nitrogen adsorption isotherms at 77 K on pitch-based ACFs A10 ($) and A30 (&), and activated mesocarbon microbeads (#).
Fig. 2. Typical shapes of nitrogen a -plots for activated cars bons. FS and CS are denoted as filling swing and cooperative swing, respectively.
are obtained from the intercept and slope of the line, respectively. The slope is directly proportional to the SSA of the standard adsorption isotherm, which is used for construction of the a -plot. This concept s was extended to determine the SSA of micropore walls for activated carbons in addition to W and 0 a . The slope of the line passing through the origin, EXT which is shown as the broken line in Fig. 2, was assigned to the total SSA as the sum of microporous SSA (a ) and a , irrespective of any uncertainty. MIC EXT The deviations from the broken line below a =1 s were termed as filling swing (FS ) and condensation swing (CS) in the preceding work [2]. Both upward deviations come from enhanced surface–molecule interactions as a function of the pore size, and thereby each swing should be ascribed to the different enhanced surface–molecule interaction: the FS suggests empirically the presence of micropores whose width is <1.0 nm [3]. The a -plot for a low burn-off s activated carbon having a remarkable molecular sieve (MS ) effect shows only this FS at a <0.5 corresponds ing to relative pressure below P/P <0.01. This FS 0 should be associated with the "primary micropore filling" proposed by Gregg and Sing [4]. In these pores, the interaction between the graphitic surface and a molecule is noticeably enhanced due to overlapping of the potentials from the opposite pore walls [6 ], to provide a marked upward deviation at the low a -region. s On the other hand, the CS was attributed to the presence of relatively larger micropores, assumed to be w>1.0 nm. It is presumed that the adsorption in the vacant space between the monolayer adsorbed pore-walls is accelerated compared with the multilayer adsorption on the flat surface. The upward deviation of CS in the a -plot can occur at the s a -region where the monolayer on the pore-walls s almost finishes. This process is similar to capillary condensation in a mesoporous system, and thereby is designated as condensation swing. However, this CS is associated with "cooperative adsorption" proposed by Gregg and Sing [4]; the cooperative swing (CS ) is more preferable in order to distinguish it from the capillary condensation. In this article, CS denotes cooperative swing. The CS is frequently observed at a >0.7 for superhigh SSA carbons and s the presence of CS leads to a serious overestimation of SSA by routine BET analysis. The pore effect should be removed from the SSA determination procedure. Slope determination with the SPE-method is typically reliable in the case of highly activated carbons showing CS and a clear linear region around a =0.5. The a -plot of the superhigh surface area s s carbon has no FS below a =0.5; it is expected that s the slope of the linear line passing through the origin below a =0.5 provides a correct SSA. Although the s SPE method can give a reasonable SSA of various activated carbons with the relevance to their adsorption properties for different gases, it has no clear theoretical basis.
High resolution a -plot and the pore size distribution S
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Therefore it is necessary to study the high resolution a -plot with the molecular simulation techs nique. The molecular simulation can provide the relationship between the morphology of the a -plot s and the pore size distribution. Molecular simulation studies on adsorption have been developed in recent years to give important theoretical aspects for fluid in the narrow pores [7–10]. It can reasonably describe the adsorption phenomena using the fundamental interaction quantities for the ideal micropore of different morphologies. In particular, grand canonical Monte Carlo (GCMC ) simulation gives a reliable description on the fluid behavior in narrow pores. Also the GCMC simulation can evaluate the pore size distribution (PSD) [7,11]. The generalized adsorption isotherm for a pore system having the PSD is given by eqn (1) [12].
P
W( p)= F( p, w)r(w) dw
(1)
Here, W(p) is the amount of adsorption determined experimentally. F( p, w) is the local adsorption isotherm at the pore width of w. The simple adsorption equation such as the Langmuir and Dubinin– Radushkevith equations can be used for the description of the local adsorption. r(w) is the PSD function for determining the PSD shape. As the PSD from the molecular simulation is reliable for a real activated carbon, a GCMC study can lead to defining the complete theoretical relationship between the a -plot and PSD. It gives a theoretical basis on the s high resolution a -plot for porosity evaluation. s
2. ADSORPTION SIMULATION IN A GRAPHITE SLIT MICROPORE
A graphitic slit pore is assumed as a model for micropores in activated carbon. The schematic pore model is shown in Fig. 3. A pair of semi-infinite graphite slabs comprised the slit pore wall. The geometry of the unit cell is defined as HL2 where H is an interplane distance between the pore walls and L2 is the cross-sectional area on a single side of the pore-wall. L2 is fixed to have a constant value (36 nm2). H should be transformed to the effective pore size (w) obtained from the adsorption measurement [13,14]. In this study, H is associated with w using the simplest approximation; w=H−0.34(in nm)
(2)
where 0.34 nm is the interlayer spacing of graphite. Although a nitrogen molecule is not spherical the one-center Lennard–Jones (LJ ) potential was used; the LJ parameters are s =0.375 nm and ff e /k =95.2 K. The interaction of a molecule with a ff B single graphite surface (U(z)) is described by Steele’s
Fig. 3. The schematic model of graphite slit pore used on the simulation.
10-4-3 potential [15]. U(z)=
G AB AB
2pres2D 0.4
s 10 z
−
s 4 z
−
s4 [3D(0.61D+z)3]
H (3)
Here, z is the distance between a molecule and the surface of a single graphite slab. r=114 nm−3 is the density of graphite, D=0.335 nm is the interlayer spacing of graphitic layer. The LJ parameters for the surface–molecule interaction are s =0.34 nm and sf e /k =28.3 K. The entire potential (U (z)) of a molesf B t cule in the graphite slit is given by U (z)=U(z)+U(H−z) (4) t The periodic boundary conditions are introduced for the calculation of total intermolecular interaction energy in the unit cell by a common way [16 ]. Adsorption simulation was carried out by GCMC simulation with applying Metropolis sampling to justify the configuration of fluid particles inside the unit cell [16 ]. The amount of particles and configurations are randomly changed to generate a new configuration, and total interaction energy (intermolecular and surface–molecule) for new configuration is compared to that for old the configuration at given chemical potentials. If such configuration is energetically accepted by the Metropolis sampling, the accepted one plays a role of an old configuration for the next step. If that is rejected, the configuration is still used for a further trial. Each trial step (creation of a molecule, erasure of a molecule and movement of a molecule) was counted as one step even in the case of the trial rejections, and the calculation of 3×106 times was carried out to obtain an equilibrium condition.
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3.1 Simulated adsorption isotherms Figure 4(a and b) shows the simulated nitrogen adsorption isotherms at 77 K for different pore width systems. Two adsorption jumps which appear below and above P/P =2×10−3 were observed. These 0 adsorption jumps were already published in previous simulation studies [11,17]. In this work, the jumps below and above P/P =2×10−3 are designated as 0 the monolayer jump and filling jump, respectively. Because a snapshot analysis of the monolayer population in the pore at each point of the simulated isotherm explicitly indicates that the micropore walls are almost perfectly covered after the monolayer jump and the residual pore space after the monolayer completion is fully occupied by molecules after the filling jump. The isotherms for pores of w=0.4 and 0.5 nm have the monolayer jump below P/P =10−6, 0 which is not shown here. Experimentally, it is quite difficult to measure the reliable adsorption data below P/P =10−6, and thereby we these simulation 0 isotherms are not considered for experimental com-
parison. In the case of pore width of 0.6–0.9 nm, only the monolayer jump is observed. The position of the monolayer jump shifts to a higher P/P value 0 with the increase of w. However, the monolayer jump becomes gradual and it appears at almost similar P/P above w>1.2 nm, as shown in Fig. 4(b). This 0 is because the overlapping effect of the molecule–surface interaction in such pores can be neglected. Consequently, the monolayer adsorption on the porewalls can be regarded as that on the flat surface for the pore system of w≥1.2 nm. The explicit filling jump is observed for pores of w>1.1 nm. As the residual space on the pores of w≤0.9 nm is too narrow to accept another filling layer, there is no filling jump for pores of w≤0.9 nm. On the contrary, the extremely sharp filling jump appears for pores of w≥1.4 nm. This filling is quite close to capillary condensation, as often indicated in earlier simulation works, although this filling does not need meniscus formation. The Kelvin equation describing the capillary condensation predicts the continuous relation of the filling pressure (P /P ) with f 0 w, but there should be a critical change in the pore width range of 1.0–1.3 nm. The minimum of P /P f 0 is given at a pore width of w=1.1 nm, which corresponds to the three layer thickness of the adsorbed nitrogen layer. Hence the filling process is not the capillary condensation.
3.2 Construction of a simulated a -plot s
Fig. 4. The simulated adsorption isotherms of nitrogen at 77 K: (a) isotherms for 0.4≤w≤1.1 nm; (b) isotherms for 1.2≤w≤2.5 nm. All isotherms are changed from small w to large w, as the increase of the amounts of molecules at P/P =1 from the bottom to the top in each figure. 0
If the adsorption isotherm on nonporous materials such as carbon black is determined as a reference, the a -plot can be experimentally constructed for s activated carbons [2,18,19]. In this study, various adsorption isotherms were simulated for an ideal graphite slit-pore of different widths. Hence if the standard adsorption isotherm is simulated for the flat graphite surface, the a -plot can be constructed s easily and directly. It is difficult, however, to simulate the adsorption isotherm on the flat graphitic surface. The enhancement of the molecule–surface interaction can be neglected for the graphitic slit pore of w≥1.3 nm, as shown in Fig. 4(b). Hence the adsorption isotherm for a graphite mesopore can be used as the standard isotherm if the capillary condensation on it is removed. Figure 5 shows the simulated adsorption isotherm of the pore of w=3.5 nm which corresponds to the thickness of the ten adsorbed nitrogen layers at least. The snapshots for the adsorption isotherm indicate no anomalous pore effect below P/P =0.6. The adsorption proceeds by the 0 multilayer adsorption mechanism on each pore wall. Furthermore, the a -value above P/P =0.6 is not as s 0 important for the a -analysis to the micropore system. s Consequently, the simulated adsorption isotherm is acceptable for standard isotherms. Initially the a -value is determined from the stans dard adsorption isotherm using the following defini-
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Fig. 6. The a -plots constructed from the simulated adsorps tion isotherms: (a) isotherms for 0.4≤w≤1.1 nm; (b) isotherms for 1.2≤w≤25 nm. The definition of each plot is same as for Fig. 4.
Fig. 5. The simulated adsorption isotherm for w=3.5 nm as a standard isotherm. The snapshots correspond to the assigned points ($) in the isotherm.
tion [4]. W (5) a= s W 0.4 Here W is the amount adsorbed on the pore of 0.4 w=3.5 nm at P/P =0.4. Thus all of the a -values are 0 s automatically obtained using the standard isotherm at the corresponding P/P . a -values up to 1.2 are 0 s used because the standard isotherm has limited applicability below P/P =0.6. 0 All a -plots for simulated adsorption isotherms for s slit pores of 0.4–2.5 nm are shown in Fig. 6(a and b). The a -plot for the standard adsorption isotherm s becomes linear in the whole a -range but the s a -range is restricted below 1.2. Here all pores of s different widths have the same surface area; only w was changed in the unit pore for simulation, as shown in Fig. 3. Accordingly, the upward deviations
from the linear plot suggest the presence of the enhanced interaction potential caused by the surface– molecule interaction and/or intermolecular one. All upward deviations are observed below and/or above a =0.5, which just correspond to the FS and CS, s respectively, as mentioned in Section 1. There is a definite node at a =0.5 except for a -plots for s s w≤0.6 nm. The pore system of w≤0.9 nm has a significant FS and the a -plots of w=1.0 and 1.1 nm have the slight s FS and clear CS. This fact supports strongly the fact that FS is ascribed to the enhanced surface–molecule interaction, and both the deviating a -value and the s deviated area depends on the slit width. The noticeable CS is observed for pores of w≥1.0 nm and the deviating a -value shifts to a s higher value with an increase in w, as shown in Fig. 6(b). This deviation corresponds to the filling jump, which is observed at P/P >10−3 in Fig. 4. 0 The a -plot for pores of w≥1.4 nm deviates almost s perpendicularly, while it has no FS. As the pores of w=1.2 and 1.3 nm have slight FS, the boundary of CS and FS is situated at a =0.5. The a -value shows s
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Fig. 7. The relationship between w and the a -value where s the filling jump occurred.
ing the jump of CS is plotted against w, as shown in Fig. 7. A greater micropore width gives a greater a -value for w≥1.4 nm. Consequently, the definite s observation of the CS jump should lead to the pore width using the relation of Fig. 7.
3.3 The specific surface area determination with a -plot s
The SPE method was proposed to determine a correct SSA for the microporous solids. This simulation study can provide a theoretical basis for the SPE
method. As all simulated adsorption isotherms were obtained for the same unit cell with a constant SSA of 72 nm2, all a -plots must give an identical SSA s regardless of the different filling state. The a -plot s corresponding to the flat surface of SSA=72 nm2 is shown by the solid line. Hence it is necessary to find a reasonable slope for all plots which coincides with the solid line. For the pores having w≥1.2 nm, the simulated a -plot has an almost linear region below a =0.5, s s which agrees with the solid line from the isotherm of w=3.5 nm. Then the SSA for those pore systems can be correctly determined from the slope of the line passing both the point of a =0.5 and the origin. s Although the a -plots for pores of 0.7≤w≤1.1 nm s do not have such a linear region below a =0.5, all s plots gather at the same point of a =0.5, which is s not on the solid line at a =0.5. This is because s adsorption at a =0.5 almost corresponds to the s completion of the monolayer on each pore wall. The monolayer completion is still enhanced due to the strong molecule–surface interaction; the gathering point is deviated from the solid line. The calculation of SSA should be corrected if the slope for these a -plots is obtained from the amount adsorbed at s a =0.5, as shown as the broken line in Fig. 6(a). The s SSA obtained from the broken line is overestimated by ca 15% from the correct SSA by the solid line.
Fig. 8. PSD model of each type of activated carbons. (a) MS, (b) R, (c) B and (d) SAC types.
High resolution a -plot and the pore size distribution S
Hence, 0.85 of the slope at a =0.5 provides the s correct SSA. The a -plots for pores of w≤0.6 nm also do not s have a linear region. Furthermore, each plot crosses to the solid line at a =0.3 where the adsorbed layer s cannot form the compact monolayer. It can be easily presumed that the cross-sectional area of an adsorbed molecule on the pores of w≤0.6 nm should be greater than that of w≤0.7 nm, because the most suitable packing state of the adsorbed monolayer must be obtained for the pores from w≥0.7 nm. However, an accurate SSA can be formally obtained from the a -plots for pores of 0.4 and 0.5 nm if a slope is s selected from the adsorbed amount at a =0.3 for s the a -plot having a rectangular FS. Unfortunately, s the shape of the plot for w=0.6 nm is close to that for w=0.7–0.9 nm and therefore it is quite difficult to distinguish them so as to determine a correct SSA experimentally.
3.4 Pore size distribution and a -plot s
As real activated carbons have the PSD, the relationship between PSD and a -plot should be elucis dated. The adsorption isotherm including PSD information is given by, W( p)=∑ F( p, w ) f (w ) i i
(6)
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where F( p, w ) is the local adsorption isotherm at a i whole range of relative pressure on the pore width of w , and f(w ) is a PSD constant to determine a i i portion of F( p, w ) for W( p). Sum of each f(w ) was i i determined to satisfy the following condition. ∑ F(w )=1 (7) i Thus the SSA of the isotherm given by eqns (6) and (7) is obtained as 72 nm2. The following section will discuss the relationship between a -plot and typical PSDs which are expected s to be often observed in real activated carbons. 3.4.1 Molecular sieve type. The MS carbon is presumed to have narrow micropores <0.7 nm and a sharp PSD. Then the MS type distribution is assumed with values ranging from 0.5 to 0.7 nm, as shown in Fig. 8(a). The corresponding a -plot is s shown in Fig. 9(a). The a -plot has a rectangular rise s of the FS at a ≤0.5. Although the SSA of this type s by the BET analysis is underestimated due to an imperfect monolayer packing as mentioned already, there is no simple way to determine the correct SSA even using the a -plot. However, there is a clear step s in the a -plot at a =0.4 where the solid line crosses. s s Then probably it is possible to determine the SSA from the slope of the line connecting the origin and the edge of the step [20–22].
Fig. 9. Calculated a -plots corresponding to the PSD in Fig. 8. Definition of each plot is same as Fig. 8. s
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3.4.2 Representative (R) type. Activated carbon fibers (ACFs) with a medium burn-off whose SSA does not exceed ca 1500 m2 g−1 [23] are presumed to have this PSD type, as shown in Fig. 8(b). This type is a representative of activated carbon. The a -plot (Fig. 9(b)) has a clear FS, but the swing s is not as steep as the MS type. This a -plot has a s linear region at 0.52000 m2 g−1 [3]. The longer activation should widen a part of micropores of ca 1 nm in width. 3.4.4 Super active carbon (SAC) type. The intense activation with the excess KOH provides a highly porous carbon of very thin minute graphitic crystallites which has a superhigh surface area. These activated carbons are often named super active carbons (SACs). Strictly speaking, the superhigh surface area should be used for the SSA of >2630 m2 g−1 which is obtained for the infinite single graphene sheet [2]. This article uses the term of superhigh surface area for SSA of >2000 m2 g−1, because the routine BET evaluation often gives an overestimated value of ca 2500 m2 g−1 for 2000 m2 g−1 of the true SSA. The SAC should have a PSD whose mean pore width ranges from 1.5 to 2.0 nm. Here the PSD is used with mean width of 2.0 nm, as shown in Fig. 8(d). The resulting a -plot is shown in Fig. 9(d ). s This has a single significant CS having a gradual rise. This a -plot is observed for SACs such as AX21, s activated mesocarbon microbeads and some ACFs [2,3,24]. This a -plot has an explicit linear region s passing through the origin below a =0.5, which s completely agrees with the solid line. Then, the SSA can be accurately determined by the SPE method, while the BET analysis uses the data of CS and gives a seriously overestimated value. 3.5 Availability of high resolution a -plot s The high resolution a -plot obtained from the
s nitrogen adsorption isotherm in the P/P range of 0
10−6–1 gives a characteristic type according to the pore width. Even if there is a PSD, the a -plots can s be classified to four basic types, which give a semiquantitive description of the pore structure. The slope of the linear region combining the origin with the definite point on the a -plot provides the correct SSA. s Hence the SPE method proposed from the experimental approach in previous work is supported by this simulation study. The morphological analysis of the high resolution a -plot is quite useful for determining s the pore structure of the activated carbons.
Acknowledgements—This work was supported by the Grant-in-Aid for the fundamental scientific research from the Ministry of Education and Science, Japanese Government. The authors also acknowledge Professor K. S. W. Sing (Bristol University, U.K.) for important suggestions and discussion on this work.
REFERENCES 1. Rouquerol, J., Avnir, D., Fairbridge, C. W., Everett, D. H., Pernicone, N., Ramsay, J. D. F., Sing, K. S. W. and Unger, K. K., Pure Appl. Chem., 1994, 66, 1739. 2. Kaneko, K., Ishii, C., Ruike, M. and Kuwabara, H., Carbon, 1992, 30, 1075. 3. Kaneko, K., Ishii, C. and Rybolt, T., Characterization of Porous Solids III, Eds. J. Rouquerol, F. RodriguezReinoso, K. S. W. Sing and K. K. Unger. Elsevier, Amsterdam, 1994, p. 583. 4. Gregg, S. J. and Sing, K. S. W., Adsorption, Surface Area and Porosity, 2nd Ed. Academic Press, New York, 1982, p. 242. 5. Kenny, M., Sing, K. S. W. and Theocharis, C., Fundamentals of Adsorption, ed. M. Suzuki. Kodansya, Tokyo, 1993, p. 323. 6. Everett, D. H. and Powl, J. C., J. Chem. Soc., Faraday Trans. I, 1976, 72, 619. 7. Seaton, N. A., Walton, J. P. R. B. and Quirke, N., Carbon, 1989, 27, 853. 8. Evans, R., Marconi, U. M. B. and Tarazona, P., J. Chem. Soc., Faraday Trans. 2, 1986, 82, 1763. 9. Peterson, B. K., Walton, J. P. R. B. and Gubbins, K. E., J. Chem. Soc., Faraday Trans. 2, 1986, 82, 1789. 10. Balbuena, P. B. and Gubbins, K. E., Langmuir, 1993, 9, 1801. 11. Lastoskie, C., Gubbins, K. E. and Quirke, N., Langmuir, 1993, 9, 2693. 12. Jaroniec, M. and Choma, J., Chem. Phys. Carbon, 1989, 22, 197. 13. Aukett, P. N., Quirke, N., Riddiford, S. and Tennison, S. R., Carbon, 1992, 30, 913. 14. Kaneko, K., Cracknell, R. F. and Nicholson, D., Langmuir, 1994, 10, 4606. 15. Steele, W. A., Surf. Sci., 1973, 36, 317. 16. Allen, M. P. and Tildesley, D. J., Computer Simulation of Liquids. Clarendon Press, Oxford, 1987. 17. Lastoskie, C., Gubbins, K. E. and Quirke, N., J. Phys. Chem., 1993, 97, 4786. 18. Rodriguez-Reinoso, F., Martin-Martinez, J. M., PradoBurguete, C. and McEnaney, B., J. Phys. Chem., 1987, 91, 515. 19. Carrott, P. J. M., Roberts, R. A. and Sing, K. S. W., Carbon, 1987, 25, 769.
High resolution a -plot and the pore size distribution 1467 S 20. Kakei, K., Ozeki, S., Suzuki, T. and Kaneko, K., 22. Setoyama, N., Kaneko, K. and Rodriguez-Reinoso, F., J. Chem. Soc., Faraday Trans., 1990, 86, 371. J. Phys. Chem., 1996, 100, 10331. 21. Rodriguez-Reinoso, F., Garrido, J., Martin-Martinez, 23. Setoyama, N., Ruike, M., Kasu, T., Suzuki, T. and J. M., Molina-Sabio, M. and Torregrosa, R., Carbon, Kaneko, K., Langmuir, 1993, 9, 2612. 1989, 27, 23. 24. Kaneko, K. and Ishii, C., Colloids Surf., 1992, 67, 203.
PII: S0008-6223(98)00138-9
SIMULATION STUDY ON THE RELATIONSHIP BETWEEN A HIGH RESOLUTION a -PLOT AND THE PORE SIZE S DISTRIBUTION FOR ACTIVATED CARBON N S, T S and K K* Department of Chemistry, Faculty of Science, Chiba University, 1–3 Yayoi, Inage, Chiba 263, Japan (Received 5 August 1996; accepted in revised form 5 February 1998) Abstract—The effects of the micropore structure of activated carbons on the high resolution a -plot for s nitrogen adsorption isotherms were examined with the grand canonical Monte Carlo simulation. Adsorption isotherms of nitrogen were simulated in graphitic slit pores at 77 K as a function of the slit width (w). As no pore effect was observed below P/P =0.6 for w=3.5 nm, a -plots for the simulated 0 s adsorption isotherms were constructed using the standard isotherm simulated for w=3.5 nm. The simulated a -plots had filling and cooperative swings which were experimentally shown in the previous s works, and the shape of the simulated a -plot varied with the micropore structure. As the subtracting s pore effect (SPE) method for the specific surface area (SSA) determination using the a -plot was proposed s in the previous experimental works, the theoretical ground for the SPE method was discussed. The best evaluation method of SSA using the a -plot was shown, almost agreeing with the SPE method. This s simulation study showed clearly that the SPE method is available for pore systems of w≥0.7 nm, whereas even the SPE method underestimates the SSA of the pores of w≤0.6 nm. The observed swings of the a -plot were simulated using the different micropore size distribution. The bimodal micropore size s distribution lead to both of filling and cooperative swings, while a single pore size distribution <0.9 nm gave only the filling swing. Thus, four representative types of the a -plot for activated carbons were s proposed and it was shown how to understand the micropore size distribution through the a -plot. s © 1998 Elsevier Science Ltd. All rights reserved. Key Words—A. Activated carbon, C. adsorption, D. surface areas, D. porosity.
This paper discusses the concept of the surface area and the meaning of the superhigh surface area for microporous solids. For these questions, the concept of superhigh surface area and the subtracting pore effect method (SPE method ) were proposed to determine the SSA for microporous carbon from experimental data [2,3]. The SPE method uses the a -analysis, which is the comparison plot proposed s by Gregg and Sing [4]. In general, the a -plot has s been applied to determine the micropore volume (W ) and the SSA of mesoporous and external sur0 faces (a ). Kaneko et al. improved the resolution EXT of the a -plot at a low a -region using the high s s resolution nitrogen adsorption isotherm, as shown in Fig. 1. Figure 1 shows the high resolution nitrogen adsorption isotherms of different kinds of activated carbons. Recently, the high resolution nitrogen adsorption isotherm whose relative pressure ranges from P/P =10−6 to 1 has been of great interest. Sing 0 and co-workers studied the high resolution nitrogen adsorption isotherms for some activated carbons which have different micropore structures [5]. They suggested that the adsorption process on the different pore sizes could be classified by three types from the high resolution a -analysis. On the other hand, it has s been indicated that such a class can be effectively investigated by the SPE method with high resolution a -plots for activated carbons, as shown in Fig. 2. s The dotted line in the plots gives W and a , which 0 EXT
1. INTRODUCTION
Molecular adsorption measurements have been widely used for the characterization of surface structures of solid materials. One of the major methods is nitrogen adsorption at 77 K. In the case of porous materials such as activated carbons, IUPAC has recommended that the pore volume can be correctly determined but the surface area is an ill-defined quantity [1]. However, the quantity of the surface area of activated carbon is quite convenient regardless of the fundamental arguments. Routine Brunauer– Emmett–Teller (BET ) analysis has been widely used to determine the specific surface area (SSA) of activated carbons. The BET analysis is very easy and it is possible to compare the BET surface area values for various activated carbons irrespective of the IUPAC recommendation. An intense demand for a new activated carbon with a large surface area has demanded a more accurate assessment of the surface area instead of the BET method. The carbon scientists believed that the upper limit of the surface area of activated carbon is 2630 m2 g−1 which originates from the single infinite graphene sheet structure, whereas activated carbons with a superhigh surface area >2630 m2 g−1 were developed. *Corresponding author. Fax: 81 3 90 788; e-mail: [email protected] 1459
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Fig. 1. High resolution nitrogen adsorption isotherms at 77 K on pitch-based ACFs A10 ($) and A30 (&), and activated mesocarbon microbeads (#).
Fig. 2. Typical shapes of nitrogen a -plots for activated cars bons. FS and CS are denoted as filling swing and cooperative swing, respectively.
are obtained from the intercept and slope of the line, respectively. The slope is directly proportional to the SSA of the standard adsorption isotherm, which is used for construction of the a -plot. This concept s was extended to determine the SSA of micropore walls for activated carbons in addition to W and 0 a . The slope of the line passing through the origin, EXT which is shown as the broken line in Fig. 2, was assigned to the total SSA as the sum of microporous SSA (a ) and a , irrespective of any uncertainty. MIC EXT The deviations from the broken line below a =1 s were termed as filling swing (FS ) and condensation swing (CS) in the preceding work [2]. Both upward deviations come from enhanced surface–molecule interactions as a function of the pore size, and thereby each swing should be ascribed to the different enhanced surface–molecule interaction: the FS suggests empirically the presence of micropores whose width is <1.0 nm [3]. The a -plot for a low burn-off s activated carbon having a remarkable molecular sieve (MS ) effect shows only this FS at a <0.5 corresponds ing to relative pressure below P/P <0.01. This FS 0 should be associated with the "primary micropore filling" proposed by Gregg and Sing [4]. In these pores, the interaction between the graphitic surface and a molecule is noticeably enhanced due to overlapping of the potentials from the opposite pore walls [6 ], to provide a marked upward deviation at the low a -region. s On the other hand, the CS was attributed to the presence of relatively larger micropores, assumed to be w>1.0 nm. It is presumed that the adsorption in the vacant space between the monolayer adsorbed pore-walls is accelerated compared with the multilayer adsorption on the flat surface. The upward deviation of CS in the a -plot can occur at the s a -region where the monolayer on the pore-walls s almost finishes. This process is similar to capillary condensation in a mesoporous system, and thereby is designated as condensation swing. However, this CS is associated with "cooperative adsorption" proposed by Gregg and Sing [4]; the cooperative swing (CS ) is more preferable in order to distinguish it from the capillary condensation. In this article, CS denotes cooperative swing. The CS is frequently observed at a >0.7 for superhigh SSA carbons and s the presence of CS leads to a serious overestimation of SSA by routine BET analysis. The pore effect should be removed from the SSA determination procedure. Slope determination with the SPE-method is typically reliable in the case of highly activated carbons showing CS and a clear linear region around a =0.5. The a -plot of the superhigh surface area s s carbon has no FS below a =0.5; it is expected that s the slope of the linear line passing through the origin below a =0.5 provides a correct SSA. Although the s SPE method can give a reasonable SSA of various activated carbons with the relevance to their adsorption properties for different gases, it has no clear theoretical basis.
High resolution a -plot and the pore size distribution S
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Therefore it is necessary to study the high resolution a -plot with the molecular simulation techs nique. The molecular simulation can provide the relationship between the morphology of the a -plot s and the pore size distribution. Molecular simulation studies on adsorption have been developed in recent years to give important theoretical aspects for fluid in the narrow pores [7–10]. It can reasonably describe the adsorption phenomena using the fundamental interaction quantities for the ideal micropore of different morphologies. In particular, grand canonical Monte Carlo (GCMC ) simulation gives a reliable description on the fluid behavior in narrow pores. Also the GCMC simulation can evaluate the pore size distribution (PSD) [7,11]. The generalized adsorption isotherm for a pore system having the PSD is given by eqn (1) [12].
P
W( p)= F( p, w)r(w) dw
(1)
Here, W(p) is the amount of adsorption determined experimentally. F( p, w) is the local adsorption isotherm at the pore width of w. The simple adsorption equation such as the Langmuir and Dubinin– Radushkevith equations can be used for the description of the local adsorption. r(w) is the PSD function for determining the PSD shape. As the PSD from the molecular simulation is reliable for a real activated carbon, a GCMC study can lead to defining the complete theoretical relationship between the a -plot and PSD. It gives a theoretical basis on the s high resolution a -plot for porosity evaluation. s
2. ADSORPTION SIMULATION IN A GRAPHITE SLIT MICROPORE
A graphitic slit pore is assumed as a model for micropores in activated carbon. The schematic pore model is shown in Fig. 3. A pair of semi-infinite graphite slabs comprised the slit pore wall. The geometry of the unit cell is defined as HL2 where H is an interplane distance between the pore walls and L2 is the cross-sectional area on a single side of the pore-wall. L2 is fixed to have a constant value (36 nm2). H should be transformed to the effective pore size (w) obtained from the adsorption measurement [13,14]. In this study, H is associated with w using the simplest approximation; w=H−0.34(in nm)
(2)
where 0.34 nm is the interlayer spacing of graphite. Although a nitrogen molecule is not spherical the one-center Lennard–Jones (LJ ) potential was used; the LJ parameters are s =0.375 nm and ff e /k =95.2 K. The interaction of a molecule with a ff B single graphite surface (U(z)) is described by Steele’s
Fig. 3. The schematic model of graphite slit pore used on the simulation.
10-4-3 potential [15]. U(z)=
G AB AB
2pres2D 0.4
s 10 z
−
s 4 z
−
s4 [3D(0.61D+z)3]
H (3)
Here, z is the distance between a molecule and the surface of a single graphite slab. r=114 nm−3 is the density of graphite, D=0.335 nm is the interlayer spacing of graphitic layer. The LJ parameters for the surface–molecule interaction are s =0.34 nm and sf e /k =28.3 K. The entire potential (U (z)) of a molesf B t cule in the graphite slit is given by U (z)=U(z)+U(H−z) (4) t The periodic boundary conditions are introduced for the calculation of total intermolecular interaction energy in the unit cell by a common way [16 ]. Adsorption simulation was carried out by GCMC simulation with applying Metropolis sampling to justify the configuration of fluid particles inside the unit cell [16 ]. The amount of particles and configurations are randomly changed to generate a new configuration, and total interaction energy (intermolecular and surface–molecule) for new configuration is compared to that for old the configuration at given chemical potentials. If such configuration is energetically accepted by the Metropolis sampling, the accepted one plays a role of an old configuration for the next step. If that is rejected, the configuration is still used for a further trial. Each trial step (creation of a molecule, erasure of a molecule and movement of a molecule) was counted as one step even in the case of the trial rejections, and the calculation of 3×106 times was carried out to obtain an equilibrium condition.
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3.1 Simulated adsorption isotherms Figure 4(a and b) shows the simulated nitrogen adsorption isotherms at 77 K for different pore width systems. Two adsorption jumps which appear below and above P/P =2×10−3 were observed. These 0 adsorption jumps were already published in previous simulation studies [11,17]. In this work, the jumps below and above P/P =2×10−3 are designated as 0 the monolayer jump and filling jump, respectively. Because a snapshot analysis of the monolayer population in the pore at each point of the simulated isotherm explicitly indicates that the micropore walls are almost perfectly covered after the monolayer jump and the residual pore space after the monolayer completion is fully occupied by molecules after the filling jump. The isotherms for pores of w=0.4 and 0.5 nm have the monolayer jump below P/P =10−6, 0 which is not shown here. Experimentally, it is quite difficult to measure the reliable adsorption data below P/P =10−6, and thereby we these simulation 0 isotherms are not considered for experimental com-
parison. In the case of pore width of 0.6–0.9 nm, only the monolayer jump is observed. The position of the monolayer jump shifts to a higher P/P value 0 with the increase of w. However, the monolayer jump becomes gradual and it appears at almost similar P/P above w>1.2 nm, as shown in Fig. 4(b). This 0 is because the overlapping effect of the molecule–surface interaction in such pores can be neglected. Consequently, the monolayer adsorption on the porewalls can be regarded as that on the flat surface for the pore system of w≥1.2 nm. The explicit filling jump is observed for pores of w>1.1 nm. As the residual space on the pores of w≤0.9 nm is too narrow to accept another filling layer, there is no filling jump for pores of w≤0.9 nm. On the contrary, the extremely sharp filling jump appears for pores of w≥1.4 nm. This filling is quite close to capillary condensation, as often indicated in earlier simulation works, although this filling does not need meniscus formation. The Kelvin equation describing the capillary condensation predicts the continuous relation of the filling pressure (P /P ) with f 0 w, but there should be a critical change in the pore width range of 1.0–1.3 nm. The minimum of P /P f 0 is given at a pore width of w=1.1 nm, which corresponds to the three layer thickness of the adsorbed nitrogen layer. Hence the filling process is not the capillary condensation.
3.2 Construction of a simulated a -plot s
Fig. 4. The simulated adsorption isotherms of nitrogen at 77 K: (a) isotherms for 0.4≤w≤1.1 nm; (b) isotherms for 1.2≤w≤2.5 nm. All isotherms are changed from small w to large w, as the increase of the amounts of molecules at P/P =1 from the bottom to the top in each figure. 0
If the adsorption isotherm on nonporous materials such as carbon black is determined as a reference, the a -plot can be experimentally constructed for s activated carbons [2,18,19]. In this study, various adsorption isotherms were simulated for an ideal graphite slit-pore of different widths. Hence if the standard adsorption isotherm is simulated for the flat graphite surface, the a -plot can be constructed s easily and directly. It is difficult, however, to simulate the adsorption isotherm on the flat graphitic surface. The enhancement of the molecule–surface interaction can be neglected for the graphitic slit pore of w≥1.3 nm, as shown in Fig. 4(b). Hence the adsorption isotherm for a graphite mesopore can be used as the standard isotherm if the capillary condensation on it is removed. Figure 5 shows the simulated adsorption isotherm of the pore of w=3.5 nm which corresponds to the thickness of the ten adsorbed nitrogen layers at least. The snapshots for the adsorption isotherm indicate no anomalous pore effect below P/P =0.6. The adsorption proceeds by the 0 multilayer adsorption mechanism on each pore wall. Furthermore, the a -value above P/P =0.6 is not as s 0 important for the a -analysis to the micropore system. s Consequently, the simulated adsorption isotherm is acceptable for standard isotherms. Initially the a -value is determined from the stans dard adsorption isotherm using the following defini-
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Fig. 6. The a -plots constructed from the simulated adsorps tion isotherms: (a) isotherms for 0.4≤w≤1.1 nm; (b) isotherms for 1.2≤w≤25 nm. The definition of each plot is same as for Fig. 4.
Fig. 5. The simulated adsorption isotherm for w=3.5 nm as a standard isotherm. The snapshots correspond to the assigned points ($) in the isotherm.
tion [4]. W (5) a= s W 0.4 Here W is the amount adsorbed on the pore of 0.4 w=3.5 nm at P/P =0.4. Thus all of the a -values are 0 s automatically obtained using the standard isotherm at the corresponding P/P . a -values up to 1.2 are 0 s used because the standard isotherm has limited applicability below P/P =0.6. 0 All a -plots for simulated adsorption isotherms for s slit pores of 0.4–2.5 nm are shown in Fig. 6(a and b). The a -plot for the standard adsorption isotherm s becomes linear in the whole a -range but the s a -range is restricted below 1.2. Here all pores of s different widths have the same surface area; only w was changed in the unit pore for simulation, as shown in Fig. 3. Accordingly, the upward deviations
from the linear plot suggest the presence of the enhanced interaction potential caused by the surface– molecule interaction and/or intermolecular one. All upward deviations are observed below and/or above a =0.5, which just correspond to the FS and CS, s respectively, as mentioned in Section 1. There is a definite node at a =0.5 except for a -plots for s s w≤0.6 nm. The pore system of w≤0.9 nm has a significant FS and the a -plots of w=1.0 and 1.1 nm have the slight s FS and clear CS. This fact supports strongly the fact that FS is ascribed to the enhanced surface–molecule interaction, and both the deviating a -value and the s deviated area depends on the slit width. The noticeable CS is observed for pores of w≥1.0 nm and the deviating a -value shifts to a s higher value with an increase in w, as shown in Fig. 6(b). This deviation corresponds to the filling jump, which is observed at P/P >10−3 in Fig. 4. 0 The a -plot for pores of w≥1.4 nm deviates almost s perpendicularly, while it has no FS. As the pores of w=1.2 and 1.3 nm have slight FS, the boundary of CS and FS is situated at a =0.5. The a -value shows s
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Fig. 7. The relationship between w and the a -value where s the filling jump occurred.
ing the jump of CS is plotted against w, as shown in Fig. 7. A greater micropore width gives a greater a -value for w≥1.4 nm. Consequently, the definite s observation of the CS jump should lead to the pore width using the relation of Fig. 7.
3.3 The specific surface area determination with a -plot s
The SPE method was proposed to determine a correct SSA for the microporous solids. This simulation study can provide a theoretical basis for the SPE
method. As all simulated adsorption isotherms were obtained for the same unit cell with a constant SSA of 72 nm2, all a -plots must give an identical SSA s regardless of the different filling state. The a -plot s corresponding to the flat surface of SSA=72 nm2 is shown by the solid line. Hence it is necessary to find a reasonable slope for all plots which coincides with the solid line. For the pores having w≥1.2 nm, the simulated a -plot has an almost linear region below a =0.5, s s which agrees with the solid line from the isotherm of w=3.5 nm. Then the SSA for those pore systems can be correctly determined from the slope of the line passing both the point of a =0.5 and the origin. s Although the a -plots for pores of 0.7≤w≤1.1 nm s do not have such a linear region below a =0.5, all s plots gather at the same point of a =0.5, which is s not on the solid line at a =0.5. This is because s adsorption at a =0.5 almost corresponds to the s completion of the monolayer on each pore wall. The monolayer completion is still enhanced due to the strong molecule–surface interaction; the gathering point is deviated from the solid line. The calculation of SSA should be corrected if the slope for these a -plots is obtained from the amount adsorbed at s a =0.5, as shown as the broken line in Fig. 6(a). The s SSA obtained from the broken line is overestimated by ca 15% from the correct SSA by the solid line.
Fig. 8. PSD model of each type of activated carbons. (a) MS, (b) R, (c) B and (d) SAC types.
High resolution a -plot and the pore size distribution S
Hence, 0.85 of the slope at a =0.5 provides the s correct SSA. The a -plots for pores of w≤0.6 nm also do not s have a linear region. Furthermore, each plot crosses to the solid line at a =0.3 where the adsorbed layer s cannot form the compact monolayer. It can be easily presumed that the cross-sectional area of an adsorbed molecule on the pores of w≤0.6 nm should be greater than that of w≤0.7 nm, because the most suitable packing state of the adsorbed monolayer must be obtained for the pores from w≥0.7 nm. However, an accurate SSA can be formally obtained from the a -plots for pores of 0.4 and 0.5 nm if a slope is s selected from the adsorbed amount at a =0.3 for s the a -plot having a rectangular FS. Unfortunately, s the shape of the plot for w=0.6 nm is close to that for w=0.7–0.9 nm and therefore it is quite difficult to distinguish them so as to determine a correct SSA experimentally.
3.4 Pore size distribution and a -plot s
As real activated carbons have the PSD, the relationship between PSD and a -plot should be elucis dated. The adsorption isotherm including PSD information is given by, W( p)=∑ F( p, w ) f (w ) i i
(6)
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where F( p, w ) is the local adsorption isotherm at a i whole range of relative pressure on the pore width of w , and f(w ) is a PSD constant to determine a i i portion of F( p, w ) for W( p). Sum of each f(w ) was i i determined to satisfy the following condition. ∑ F(w )=1 (7) i Thus the SSA of the isotherm given by eqns (6) and (7) is obtained as 72 nm2. The following section will discuss the relationship between a -plot and typical PSDs which are expected s to be often observed in real activated carbons. 3.4.1 Molecular sieve type. The MS carbon is presumed to have narrow micropores <0.7 nm and a sharp PSD. Then the MS type distribution is assumed with values ranging from 0.5 to 0.7 nm, as shown in Fig. 8(a). The corresponding a -plot is s shown in Fig. 9(a). The a -plot has a rectangular rise s of the FS at a ≤0.5. Although the SSA of this type s by the BET analysis is underestimated due to an imperfect monolayer packing as mentioned already, there is no simple way to determine the correct SSA even using the a -plot. However, there is a clear step s in the a -plot at a =0.4 where the solid line crosses. s s Then probably it is possible to determine the SSA from the slope of the line connecting the origin and the edge of the step [20–22].
Fig. 9. Calculated a -plots corresponding to the PSD in Fig. 8. Definition of each plot is same as Fig. 8. s
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3.4.2 Representative (R) type. Activated carbon fibers (ACFs) with a medium burn-off whose SSA does not exceed ca 1500 m2 g−1 [23] are presumed to have this PSD type, as shown in Fig. 8(b). This type is a representative of activated carbon. The a -plot (Fig. 9(b)) has a clear FS, but the swing s is not as steep as the MS type. This a -plot has a s linear region at 0.52000 m2 g−1 [3]. The longer activation should widen a part of micropores of ca 1 nm in width. 3.4.4 Super active carbon (SAC) type. The intense activation with the excess KOH provides a highly porous carbon of very thin minute graphitic crystallites which has a superhigh surface area. These activated carbons are often named super active carbons (SACs). Strictly speaking, the superhigh surface area should be used for the SSA of >2630 m2 g−1 which is obtained for the infinite single graphene sheet [2]. This article uses the term of superhigh surface area for SSA of >2000 m2 g−1, because the routine BET evaluation often gives an overestimated value of ca 2500 m2 g−1 for 2000 m2 g−1 of the true SSA. The SAC should have a PSD whose mean pore width ranges from 1.5 to 2.0 nm. Here the PSD is used with mean width of 2.0 nm, as shown in Fig. 8(d). The resulting a -plot is shown in Fig. 9(d ). s This has a single significant CS having a gradual rise. This a -plot is observed for SACs such as AX21, s activated mesocarbon microbeads and some ACFs [2,3,24]. This a -plot has an explicit linear region s passing through the origin below a =0.5, which s completely agrees with the solid line. Then, the SSA can be accurately determined by the SPE method, while the BET analysis uses the data of CS and gives a seriously overestimated value. 3.5 Availability of high resolution a -plot s The high resolution a -plot obtained from the
s nitrogen adsorption isotherm in the P/P range of 0
10−6–1 gives a characteristic type according to the pore width. Even if there is a PSD, the a -plots can s be classified to four basic types, which give a semiquantitive description of the pore structure. The slope of the linear region combining the origin with the definite point on the a -plot provides the correct SSA. s Hence the SPE method proposed from the experimental approach in previous work is supported by this simulation study. The morphological analysis of the high resolution a -plot is quite useful for determining s the pore structure of the activated carbons.
Acknowledgements—This work was supported by the Grant-in-Aid for the fundamental scientific research from the Ministry of Education and Science, Japanese Government. The authors also acknowledge Professor K. S. W. Sing (Bristol University, U.K.) for important suggestions and discussion on this work.
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High resolution a -plot and the pore size distribution 1467 S 20. Kakei, K., Ozeki, S., Suzuki, T. and Kaneko, K., 22. Setoyama, N., Kaneko, K. and Rodriguez-Reinoso, F., J. Chem. Soc., Faraday Trans., 1990, 86, 371. J. Phys. Chem., 1996, 100, 10331. 21. Rodriguez-Reinoso, F., Garrido, J., Martin-Martinez, 23. Setoyama, N., Ruike, M., Kasu, T., Suzuki, T. and J. M., Molina-Sabio, M. and Torregrosa, R., Carbon, Kaneko, K., Langmuir, 1993, 9, 2612. 1989, 27, 23. 24. Kaneko, K. and Ishii, C., Colloids Surf., 1992, 67, 203.