Reference Data for Argon Adsorption on Graphitized and

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J. Phys. Chem. B 2001, 105, 12516-12523

Reference Data for Argon Adsorption on Graphitized and Nongraphitized Carbon Blacks Leon Gardner, Michal Kruk, and Mietek Jaroniec* Department of Chemistry, Kent State UniVersity, Kent, Ohio 44242 ReceiVed: May 8, 2001; In Final Form: October 15, 2001

Standard argon adsorption data at 77 and 87 K are presented for two proposed reference carbons, one nongraphitized and the other graphitized. Surface properties of the reference carbons are analyzed on the basis of low-pressure adsorption data. The usefulness of the reference adsorption isotherms reported in this work was illustrated for the Rs plot analysis of surface properties of graphitized carbons, as well as for the determination of the external surface area and micropore volume of activated carbons. The information derived from the analysis of argon adsorption data at both 87 and 77 K was in a good agreement with earlier results obtained from nitrogen adsorption isotherms at 77 K.

Introduction For many years, nitrogen adsorption data at 77 K have been used to characterize the porous structures of a wide variety of materials,1 and reference nitrogen adsorption isotherms for different carbons have been published.2-6 However, it is possible to characterize porous carbons by using other adsorptives, some of which may perhaps be more convenient to use and may allow one to gain better insight into the porous structures. Consequently, reference adsorption data on carbons have been published for argon and n-butane,7 benzene,8 neopentane,9 and methanol.10 In particular, argon deserves much attention, because it was found to be convenient in the characterization of microporous11-14 and mesoporous15,16 adsorbents, such as activated carbons, zeolites, silicas, and ordered mesoporous materials. Because of the fact that argon gas is in a monoatomic state, it is attractive from the point of view of theoretical and computer simulation studies of adsorption in porous media.14,15,17-19 In addition, the monolayer formation for argon at 87 K on the carbon surfaces takes place at higher pressures than that for nitrogen at 77 K (as can be seen for instance from ref 19), and consequently, argon at 87 K may be a better adsorptive to use in instruments that cannot measure very low relative pressures. Moreover, as discussed elsewhere,20 argon adsorption isotherms at 87 K appear to be better equilibrated at very low relative pressures than those for nitrogen at 77 K, when reasonable equilibration times are used during measurements on the best adsorption analyzers currently commercially available. Also, the BET surface areas calculated from nitrogen data are often inaccurate, especially for microporous carbons,21 and it is worthwhile to explore whether the application of other gases, such as argon, in the BET analysis may provide the means of improvement. Experimental adsorption data can be analyzed in a wide variety of ways to attempt a comprehensive characterization of porous structures and surface properties of porous solids. Such characterization includes the analysis of adsorption potential distributions (APDs),6,22,23 adsorption energy distributions,22 and the comparative plot analysis, such as the Rs plot method.1,24 Pore size analysis can be carried out using the BJH method * To whom correspondence should be addressed. E-mail: Jaroniec@ columbo.kent.edu. Phone: (330) 672 3790. Fax: (330) 672 3816.

and its later modifications,25,26 the Horvath-Kawazoe method27 and the Dubinin-Stoeckli method,28 as well as methods based on local adsorption isotherms generated using the density functional theory (DFT)13-15,29 or computer simulations.14 Many of these methods use reference adsorption data directly, as it is the case in the Rs plot and BJH method, or require such data at the stage of development of models and determination of parameters, as it is needed in DFT and computer simulations of adsorption in real systems. To facilitate both the characterization of porous solids using adsorption methods and the theoretical/computational studies of gas adsorption, reference adsorption data are reported herein for a nongraphitized carbon black (BP 280) and a graphitized carbon black (Carbopack F) for argon adsorption at 77 and 87 K. The usefulness of these reference data in the Rs plot analysis of the surface and structural properties of carbons is briefly discussed. Materials and Methods Materials. The nongraphitized Black Pearls (BP) carbon black labeled BP 280 was supplied by Cabot Corporation Special Blacks Division (Billerica, MA). Its nitrogen adsorption isotherm has been reported in a tabular form elsewhere,5 and nitrogen adsorption properties have been discussed.5,30-32 The graphitized carbon blacks labeled Carbopacks F and Y were supplied by Supelco (Bellefonte, PA). Their nitrogen adsorption isotherms have been reported in ref 6 (including data for Carbopack F in tabular form), and nitrogen adsorption properties have been discussed therein. An activated carbon labeled G (after the notation used in ref 23) is a synthetic activated carbon on a ceramic support prepared at Corning Research Center in Corning, New York,33 and its synthesis, structure, and nitrogen adsorption properties have been reported elsewhere.23,33 The amount adsorbed for this carbon is expressed per unit mass of carbon, rather than per mass of carbon and ceramic support. Experimental. Argon adsorption measurements were carried out at 87 and 77 K using an ASAP 2010 static volumetric adsorption analyzer from Micromeritics (Norcross, GA). This automatic instrument is equipped with 1000, 10, and 1 Torr pressure transducers and was used to accurately measure argon adsorption data in a relative pressure range of 10-6-10-7 to 0.99. High purity (99.999%) argon was used. The saturation vapor pressure (corresponding in cases of measurements at 77

10.1021/jp011745+ CCC: $20.00 © 2001 American Chemical Society Published on Web 11/28/2001

Reference Data for Argon Adsorption

Figure 1. Adsorption isotherms for Carbopack F at 87 and 77 K, drawn in linear scale.

and 87 K to vapor-solid and vapor-liquid equilibria, respectively) was measured periodically during the adsorption measurements. Prior to the measurements, all samples were outgassed under vacuum at 473 K for 2 h. Calculation Methods. The BET specific surface area was evaluated on the basis of argon data in the relative pressure range from 0.06 to 0.2 using the argon cross-sectional area of 0.138 nm2.26 The micropore volume and the external surface area were calculated using the Rs plot method.1 The APD22 was calculated as follows. The adsorption potential A is defined as the negative of the change in the Gibbs free energy of adsorption:22 A ) -∆G ) RT ln(p0/p), where R is the universal gas constant, T is the absolute temperature, p0 is the saturation vapor pressure, and p is the equilibrium vapor pressure. Then APD is calculated by numerical differentiation of the adsorption isotherm: X(A) ) -dV(A)/dA, where V(A) is the amount adsorbed expressed in cm3 of liquid adsorbate per gram. Results and Discussion Adsorption-desorption isotherms for Carbopack F at 87 and 77 K are shown in Figure 1, drawn in linear scale. Both isotherms show steps typical for low-temperature argon adsorption on a graphitized carbon black,34 with the steps at 77 K being more pronounced than those at 87 K. This temperature behavior is consistent with the previous studies.35-37 The isotherms are almost completely reversible, suggesting that Carbopack F is macroporous. Using the relative pressure range from 0.06 to 0.2 and the argon atom cross-sectional area of 0.138 nm2, the BET specific surface areas of 5.88 and 6.01 m2 g-1 were obtained from data at 77 and 87 K, respectively. So, the assessed argon BET specific surface area was quite independent of temperature. It is important to note here that these specific surface areas are in good agreement with the results of an accurate specific surface area assessment that can be made on the basis of nitrogen adsorption data at 77 K in the following way. It is known that nitrogen at low temperatures is capable of forming monolayers commensurate with the underlying graphite structure.38-41 For such a monolayer arrangement of molecules, the area occupied by a nitrogen molecule can be calculated with high accuracy from the known distance between carbon atoms in the graphite planes.40 Using the distance provided in ref 39, the cross-sectional area of the nitrogen molecule in the commensurate monolayer can be evaluated as 0.1571 nm2 (which is consistent with the estimate that can be made on the basis of data reported in ref 42 but slightly different from the value of 0.1575 nm2 provided in ref 40). As discussed

J. Phys. Chem. B, Vol. 105, No. 50, 2001 12517 in ref 40, during nitrogen adsorption at 77 K on a highly graphitized carbon, the commensurate monolayer is attained after completion of the step at a relative pressure of about 0.01. This step corresponds to the transition from 2-D fluid phase to 2-D solid (commensurate) phase.40 For Carbopack F, this transition appears to be completed at a relative pressure of about 0.007 (see data reported in ref 6), and the corresponding amount adsorbed is 1.3589 cm3 STP g-1. Using the aforementioned cross-sectional area for the nitrogen molecule in the commensurate monolayer, the specific surface area of 6.16 m2 g-1 is obtained. Taking into account possible errors in the measurement of nitrogen adsorption data and an uncertainty in the identification of the point of completion of the phase transition, one can expect that the specific surface area of Carbopack F is within about 2% or less from this value, i.e., in the range of 6.16 ( 0.12 m2 g-1. This accurate assessment of the specific surface area actually coincides with the nitrogen BET specific surface area using the commonly employed cross-sectional area of 0.162 nm2, as already noted elsewhere.40 In particular, the BET specific surface area of 6.15 m2 g-1 was obtained in the relative pressure range from 0.04 to 0.2 and reported in ref 6 as 6.2 m2 g-1 as a result of rounding to two significant digits. It is clear that the argon BET specific surface area is close to the aforementioned accurate specific area assessment, which was based on nitrogen adsorption data and the knowledge of the nitrogen monolayer structure. Furthermore, the agreement can be improved by adjusting the argon cross-sectional area used, as will be discussed later. It should be noted here that the independent determination of the argon cross-sectional area similar to that described above for nitrogen is unfortunately rather difficult because argon forms monolayers that are not in registry with the graphite surface.40,43 However, one can use nitrogen data to assess the cross-sectional area of argon at 77 K in the incommensurate solid phase, as proposed by Rouquerol et al.40 Namely, the step corresponding to transition from 2-D fluid to 2-D solid phase on Carbopack F is completed at a relative pressure of about 0.05, which corresponds to the amount adsorbed of 1.8165 cm3 STP g-1. This amount adsorbed divided by the molar volume of gas at STP, and subsequently multiplied by the Avogadro constant and the cross-sectional area of argon in a 2-D incommensurate solid phase, provides the specific surface area of Carbopack F, which should be equal to the aforementioned accurate specific surface area determined from nitrogen adsorption data. After solving for the cross-sectional area of argon in the 2-D solid phase, the value of 0.1262 nm2 is obtained, which is very close to the value of 0.125 nm2 determined by Rouquerol et al.40 Unfortunately, this crosssectional area value is expected to be useful in the specific surface area calculations essentially only for highly graphitized carbons, because many other carbonaceous adsorbents, such as nongraphitized carbon blacks and activated carbons, are not expected to exhibit the monolayer packing that would correspond to 2-D solid phase because of their surface heterogeneity. An attempt to find an argon cross-sectional area value more useful in characterization of carbonaceous materials will be described hereafter. Adsorption-desorption isotherms for BP 280 at 87 and 77 K are shown in Figure 2, drawn in a linear scale. The isotherm at 87 K is intermediate in shape between types II and IV of the BDDT classification,1 whereas the isotherm at 77 K is of type II. These isotherms reflect monolayer-multilayer formation on the surface of large mesopores and macropores, which is followed to some extent by capillary condensation in the case of adsorption at 87 K. Using the cross-sectional area of 0.138

12518 J. Phys. Chem. B, Vol. 105, No. 50, 2001

Figure 2. Adsorption isotherms for BP 280 at 87 and 77 K, drawn in linear scale.

Figure 3. Adsorption isotherms for Carbopack F at 87 and 77 K, drawn in logarithmic scale.

nm2 for the argon atom on the surface and the relative pressure range from 0.06 to 0.2, the BET specific surface areas of 36.6 and 35.9 m2 g-1 have been evaluated from data at 77 and 87 K, respectively. Thus, the specific surface area estimation from argon data was fairly independent of temperature. However, it was appreciably lower than the nitrogen BET specific surface area of 40.2 m2 g-1 calculated from data at 77 K.5 The calculations in ref 5 were made in the relative pressure range from 0.06 to 0.25 which is different than that used for BET analysis of argon data, but the use of the same range, i.e., 0.060.2, would lead to the same result. Therefore, it seems that the nitrogen and argon BET specific surface areas become less consistent as surface heterogeneity increases and the degree of graphitization decreases. Adsorption-desorption isotherms for Carbopack F are shown in Figure 3, drawn in a logarithmic scale to better show the adsorption behavior at low pressures. These curves show steps corresponding to the formation of the first adsorbed layer at relative pressures between 5 × 10-4 and 5 × 10-3, similarly to the data for Sterling FT-G(2700) graphitized carbon black reported in ref 19. As reported previously, Carbopack F has a relatively high degree of graphite crystallinity and, hence, a high degree of surface homogeneity.6 The the monolayer step is more pronounced at 77 K than at 87 K, as expected from previous studies.35-37 At 77 K, one can also observe a step that is associated with the transition from a two-dimensional incommensurate fluid state to a two-dimensional incommensurate solid state40 at a relative pressure of about 0.04. Adsorption-desorption isotherms for BP 280 are shown again in Figure 4, drawn in a logarithmic scale to better show the

Gardner et al.

Figure 4. Adsorption isotherms for BP 280 at 87 and 77 K, drawn in logarithmic scale.

Figure 5. Adsorption potential distributions (APDs) for Carbopack F and BP 280 at 87 and 77 K.

adsorption behavior at low pressures. In contrast to the iostherms for Carbopack F, the curves are both smooth, which can be explained as an effect of the strong surface heterogeneity of the sample.6,30-32 Also, the monolayer step is once again more pronounced at the lower temperature. APDs for Carbopack F and BP 280 at 87 and 77 K are shown in Figure 5. APDs for BP 280 at both temperatures have a single, broad peak of about the same width and located at about the same position (about 4 kJ mol-1). This peak is associated with monolayer formation on the surface. This assignment is consistent with a previous study of nitrogen adsorption at 77 K.6 The broadness of the peak provides further evidence that the BP 280 has significant surface heterogeneity, as discussed elsewhere in the case of nitrogen adsorption at 77 K.6 The APD for Carbopack F at 77 K shows evidence of six peaks located at about 4.54, 2.05, 0.64, 0.24, 0.10, and 0.03 kJ mol-1 (see Figures 5 and 6). The APD for Carbopack F at 87 K has only three peaks among those observed at 77 K, which are located at about 4.70, 0.72, and 0.25 kJ mol-1. The peak at about 4.5 kJ mol-1 can be attributed to the monolayer formation, the peak at 2.05 kJ mol-1 can be attributed to the two-dimensional fluidsolid-phase transition, the peak at about 0.7 kJ mol-1 can be attributed to the second layer formation, the peak at about 0.25 kJ mol-1 can be attributed to the third layer formation, the peak at 0.1 kJ mol-1 can be attributed to the forth layer formation, and the peak at 0.03 kJ mol-1 can be attributed to the fifth layer formation. Clearly, the 2-D fluid-solid-phase transition does not persist to the temperature of 87 K. Moreover, the formation of the forth and fifth layers becomes less distinct at higher

Reference Data for Argon Adsorption

Figure 6. Part of Figure 5 for lower values of the adsorption potential, expanded to better show the multilayer formation on Carbopack F.

temperature (i.e., 87 K), in agreement with earlier studies.35-37 The broadening of phase transitions as temperature is increased is also reflected in the fact that the peaks on the APD curves are in general lower and broader at higher temperature. In the case of carbons, it is often possible to identify a minimum on APD that would reflect the monolayer completion, as noted elsewhere.44,45 The corresponding monolayer capacity was proposed to be suitable for calculation of the specific surface area for microporous carbons (although for some microporous carbons, such a minimum on APD is not observed) as well as for carbon blacks from nitrogen adsorption data at 77 K.23 This idea can also be applied for the carbons under study. In the case of Carbopack F at 87 K and BP280 at both temperatures, there is a unique minimum at about 2 kJ mol-1 between the peaks corresponding to the first layer formation and either the second layer formation peak (in the case of Carbopack F) or a broad feature attributable to the multilayer formation (in the case of BP 280). In the case of Carbopack F at 77 K, there are two minima between these peaks, one before and another one after the peak corresponding to the 2-D fluid-solid-phase transition. Our interest will be devoted here only to the first of the aforementioned minima, i.e., to the one corresponding to the 2-D disordered fluid phase, because it is the only phase among these two that is expected to exist for carbons with heterogeneous surfaces, including nongraphitized carbon blacks and activated carbons. Moreover, the cross-sectional area corresponding to the 2-D solid phase has already been determined above. Using the specific surface area of 6.16 m2 g-1 evaluated above on the basis of nitrogen adsorption data at 77 K, one can attempt to determine the argon cross-sectional area corresponding to these minima. The amount adsorbed at the minimum for argon at 77 K is 1.629 cm3 STP g-1 (the minimum is located at the adsorption potential value of 2.79 kJ mol-1, which corresponds to a relative pressure of 0.0126), which allows one to evaluate the cross-sectional area of 0.141 nm2 for the 2-D fluid phase at 77 K. It is assumed that the minimum actually corresponds to completion of the 2-D fluid phase monolayer. The amount adsorbed at the minimum for argon at 87 K is 1.622 cm3 STP g-1 (the minimum is located at the adsorption potential value of 2.61 kJ mol-1, which corresponds to a relative pressure of 0.0276), which allows one to evaluate the cross-sectional area of 0.141 nm2 for the 2-D fluid phase at 87 K. For these calculations, the data from single adsorption runs were used, although the data from repeated runs were found to provide essentially the same values of cross-sectional areas. It is notable that the same cross-sectional area for the 2-D fluid phase was determined from argon data at 77 and 87 K, although

J. Phys. Chem. B, Vol. 105, No. 50, 2001 12519 the relative pressures at which these monolayers are completed are somewhat different. The value of 0.141 nm-1 is close to the 0.138 nm-1 value assessed from the density of bulk liquid argon.26 It is quite remarkable that the use of the value determined here in the BET analysis would allow one to obtain the argon BET specific surface areas of 6.01 and 6.14 m2 g-1, which are in very good agreement with the accurate specific surface area of 6.16 m2 g-1 evaluated from nitrogen adsorption data. This agreement further demonstrates that the use of a proper cross-sectional area value may lead to a significant improvement of the accuracy of the BET analysis. However, this cross-sectional area value itself may not reflect the actual arrangement of atoms or molecules on the surface in the pressure range used for the BET analysis (as is the case for argon at 77 K on Carbopack F) or even may not be directly related to the packing at any pressure close to the monolayer completion (as appears to be the case for nitrogen at 77 K on Carbopack F). In these cases, the correctness of the BET specific surface area, if observed, must result from the compensation of errors rather than from the strict validity of the BET model. So, the crosssectional areas most suitable for the BET analysis can be considered as effective values leading to correct surface area assessments, rather than the actual cross-sectional area values in the monolayer. In the case of BP 280, the minima on APDs are much less distinct than in the case of Carbopack F. Nonetheless, a minimum corresponding to the monolayer completion can be located. In the case of argon adsorption at 77 K, this minimum is located at 2.22 kJ mol-1 (i.e., at a relative pressure of 0.027), and the corresponding amount adsorbed was 8.97 cm3 STP g-1. Using the cross-sectional area of 0.138 nm2 for the argon atom, the specific surface area of 33.2 m2 g-1 is obtained. In the case of argon at 87 K, this minimum is located at 2.44 kJ mol-1 (i.e., at a relative pressure of 0.035), and the corresponding amount adsorbed was 8.36 cm3 STP g-1, which allows one to evaluate the specific surface area of 31.0 m2 g-1. Not only are these specific surface areas inconsistent with one another but also they are much lower than the argon and nitrogen BET specific surface areas provided above. However, these estimates are quite consistent with the specific surface area assessed from the minimum on APD for nitrogen adsorption data. The relative pressures of the monolayer completion determined from argon APDs for BP 280 are also reasonable in comparison to those determined for Carbopack F in the way discussed above. So, it is expected that the specific surface areas determined from APDs for BP 280 reflect the actual specific area better than the BET specific surface areas. Because the minimum is somewhat more pronounced at 77 K, it is expected that the corresponding surface area assessment (33.2 m2 g-1) or its further refinement using the cross-sectional area of 0.141 nm2 determined from the examination of data for Carbopack F, which gives 33.9 m2 g-1, is the best estimate of the specific surface area for BP 280 among the assessments considered. It should be noted that this assessment is much lower than the nitrogen BET specific surface area calculated from data in the relative pressure range from 0.06 to 0.25.5 However, it needs to be kept in mind that the nitrogen BET method provides overestimated specific surface areas for silicas, which are adsorbents of strongly heterogeneous surfaces,46,47 and therefore, a significant overestimation of the specific surface area using the BET method is not unlikely for nongraphitized carbons with heterogeneous surfaces. Figure 7 shows the Rs plot for Carbopack Y graphitized carbon black using Carbopack F as the reference solid, both at 77 and 87 K. The plot is almost linear over a wide range of Rs

12520 J. Phys. Chem. B, Vol. 105, No. 50, 2001

Figure 7. Rs plots for Carbopack Y and BP 280 using Carbopack F as the reference solid, at 77 and 87 K. The Rs plots for BP280 were offset vertically by 20 cm3 STP g-1 for clarity.

Gardner et al.

Figure 9. Rs plots for activated carbon G using BP 280 as the reference solid, at 77 and 87 K.

Figure 10. Rs plots for activated carbon G using Carbopack F as the reference solid, at 77 and 87 K. Figure 8. Argon adsorption isotherm for activated carbon G, at 77 and 87 K.

values at both temperatures, showing that adsorption properties of Carbopacks F and Y are very similar. Slight deviations from linearity can be attributed to a higher surface heterogeneity related to a lower degree of graphitization of Carbopack Y.6 Figure 8 shows the Rs plot for BP 280 using Carbopack F as the reference solid, both at 77 and 87 K. These curves have no extensive linear regions, illustrating that the two solids compared are quite dissimilar. This Rs plot for BP280 exhibits some oscillations as it increases. In particular, it is initially quite steep, then the slope decreases, and this pattern of behavior repeats itself for larger Rs values. Similar behavior, although much less pronounced, is observed for Carbopack Y. Because the adsorption properties of Carbopack F and BP 280 indicate that the former has a much more homogeneous surface, the shape of the Rs plot for Carbopack Y is indicative of its higher surface heterogeneity, when compared to that of Carbopack F. Therefore, the former can be used as a reference adsorbent to study graphitized carbons, allowing one to estimate the degree of their structural perfection. The oscillatory nature of the Rs plots discussed above can be related to the sharpness of steps corresponding to the layering transitions on the carbon surface. It was demonstrated in a theoretical study that when an adsorbent with a homogeneous surface is used as a reference, the comparative plot for an adsorbent with a heterogeneous surface of the same average adsorption energy exhibits an initial steep rise, then levels off to some extent and finally exhibits a steep increase once again close to the monolayer completion.48 It should be noted that the theoretical study was restricted only

to monolayer adsorption. The behavior described above arises from the fact that the heterogeneous adsorbent exhibits a higher population of adsorption sites of both lower and higher adsorption energy, whereas the homogeneous adsorbent exhibits a higher population of adsorption sites of moderate adsorption energy. Consequently, the heterogeneous adsorbent adsorbs more strongly at lower pressures (lower Rs values) at the sites of higher energy giving rise to an initial steep part of the plot. Then, the sites of the moderate energy become occupied, and because they are more populated for the homogeneous adsorbent, its amount adsorbed increases more steeply than that for the heterogeneous adsorbent, leading to a more leveled part of the Rs plot. As the pressure (or alternatively, Rs) is further increased, the adsorption sites of the lowest energy become occupied, and because they are more populated for the heterogeneous adsorbent, the increase in the amount adsorbed for it is relatively larger than that for the homogeneous one, leading to another steep region in the Rs plot. This simple consideration can be extended for multilayers, taking into consideration that the formation of consecutive layers on adsorption sites of lower energy takes place at higher pressures than that on higher energy sites. So, the Rs plot for the multilayer adsorption is a superposition of behaviors for the consecutive layers, leading to a kind of oscillatory behavior observed in Figure 7. It could be expected that an ideal reference solid for an activated carbon would be a nonmicroporous material of activated carbon surface structure. A claim has already been made that such a solid can be produced by heat treatment of an activated carbon,2 but this claim was questionable, because the high-temperature necessary to close the micropores could lead

Reference Data for Argon Adsorption

J. Phys. Chem. B, Vol. 105, No. 50, 2001 12521

TABLE 1: Argon Standard Reduced Adsorption Data for Cabot BP 280 at 77 K (Amounts Adsorbed Were Divided by the Amount Adsorbed at a Relative Pressure of 0.4, i.e., 15.65 cm3 STP g-1) p/p0 9.66 × 1.10 × 10-5 1.78 × 10-5 2.75 × 10-5 3.94 × 10-5 5.34 × 10-5 6.91 × 10-5 8.66 × 10-5 1.06 × 10-4 1.27 × 10-4 1.49 × 10-4 1.73 × 10-4 1.98 × 10-4 2.25 × 10-4 2.53 × 10-4 2.83 × 10-4 3.13 × 10-4 3.45 × 10-4 3.79 × 10-4 4.14 × 10-4 4.50 × 10-4 4.88 × 10-4 5.27 × 10-4 5.66 × 10-4 6.58 × 10-4 7.50 × 10-4 8.51 × 10-4 9.60 × 10-4 1.08 × 10-3 1.21 × 10-3 1.35 × 10-3 1.50 × 10-3 1.67 × 10-3 1.86 × 10-3 2.07 × 10-3 2.30 × 10-3 2.56 × 10-3 10-6

Rs 6.54 × 0.0131 0.0196 0.0262 0.0327 0.0393 0.0458 0.0524 0.0589 0.0654 0.0720 0.0785 0.0851 0.0916 0.0981 0.105 0.111 0.118 0.124 0.131 0.137 0.144 0.150 0.157 0.170 0.183 0.196 0.209 0.222 0.235 0.248 0.261 0.274 0.287 0.300 0.313 0.326

p/p0 10-3

2.85 × 3.18 × 10-3 3.55 × 10-3 3.97 × 10-3 4.46 × 10-3 5.01 × 10-3 5.65 × 10-3 6.38 × 10-3 7.22 × 10-3 8.21 × 10-3 9.34 × 10-3 0.0106 0.0109 0.0121 0.0148 0.0168 0.0190 0.0243 0.0301 0.0338 0.0390 0.0446 0.0500 0.0604 0.0701 0.0802 0.0902 0.100 0.119 0.141 0.162 0.182 0.202 0.222 0.243 0.263 0.283 10-3

Rs 0.339 0.352 0.365 0.378 0.391 0.403 0.416 0.429 0.441 0.454 0.466 0.478 0.481 0.490 0.508 0.519 0.530 0.550 0.568 0.578 0.590 0.601 0.611 0.627 0.641 0.653 0.665 0.676 0.695 0.716 0.736 0.755 0.774 0.794 0.814 0.835 0.857

p/p0 0.303 0.323 0.343 0.361 0.380 0.400 0.420 0.440 0.460 0.480 0.500 0.520 0.540 0.560 0.580 0.600 0.620 0.640 0.660 0.680 0.700 0.720 0.739 0.760 0.780 0.801 0.820 0.841 0.861 0.882 0.901 0.921 0.940 0.958 0.972 0.981 0.995

Rs 0.879 0.903 0.927 0.949 0.974 1.00 1.03 1.05 1.08 1.11 1.13 1.16 1.18 1.21 1.24 1.27 1.29 1.32 1.35 1.38 1.41 1.44 1.48 1.52 1.55 1.60 1.64 1.69 1.74 1.80 1.86 1.94 2.01 2.10 2.17 2.22 2.27

to partial graphitization of the material.3 Despite the fact that the activated carbon used belonged to nongraphitizable carbons (carbons that cannot be transformed into highly graphitized form upon the heat treatment), as pointed out in the reply to the criticism put forward in ref 3,21 the heat treatment used was likely to result in major structural changes. No proof of complete elimination of micropores was also provided, although it is clear that if some micropores persisted after the heat treatment, their content had to be small. So, our view is consistent with that of Carrott et al.3 that it is justified to use a reference adsorbent for activated carbons that is not derived from an activated carbon but has different origin. Herein, we propose to use the nongraphitized carbon black BP 280 as a reference adsorbent in the comparative plot analysis on the basis of argon data. The suitability of BP 280 as a reference adsorbent has already been demonstrated in the case of nitrogen adsorption at 77 K.23,31 As suggested be Carrott et al.,3 a graphitized carbon (such as Carbopack F discussed herein) is not good as a reference adsorbent for activated carbons, although its usefulness as a reference adsorbent in studies of partially or fully graphitized carbons is clear on the basis of the discussion presented above. To illustrate the problems of the choice of the reference adsorbent for activated carbons, the results of comparative plot analysis are shown herein for carbon G (its argon adsorption isotherms20 at 77 and 87 K are shown in Figure 8). It is seen that the form of the Rs plot is dependent on the choice of the reference solid, as already demonstrated in the case of nitrogen adsorption data at 77 K.31 The Rs plots for carbon G with BP

TABLE 2: Argon Standard Reduced Adsorption Data for Carbopack F Graphitized Carbon Black at 77 K (Amounts Adsorbed Were Divided by the Amount Adsorbed at a Relative Pressure of 0.4, i.e., 3.173 cm3 STP g-1) p/p0 10-5

5.85 × 1.16 × 10-4 1.70 × 10-4 2.19 × 10-4 2.63 × 10-4 3.04 × 10-4 3.41 × 10-4 3.75 × 10-4 4.23 × 10-4 4.66 × 10-4 5.04 × 10-4 5.39 × 10-4 5.70 × 10-4 5.98 × 10-4 6.30 × 10-4 6.54 × 10-4 6.77 × 10-4 6.98 × 10-4 7.19 × 10-4 7.39 × 10-4 7.58 × 10-4 7.77 × 10-4 7.96 × 10-4 8.14 × 10-4 8.33 × 10-4 8.52 × 10-4 8.72 × 10-4 8.92 × 10-4 9.12 × 10-4 9.34 × 10-4 9.56 × 10-4 9.81 × 10-4 1.01 × 10-3 1.04 × 10-3 1.07 × 10-3 1.10 × 10-3 1.14 × 10-3 1.18 × 10-3 1.23 × 10-3 1.29 × 10-3 1.35 × 10-3 1.42 × 10-3 1.51 × 10-3 1.62 × 10-3

Rs 6.08 × 0.0122 0.0184 0.0245 0.0307 0.0368 0.0430 0.0492 0.0590 0.0688 0.0787 0.0885 0.0984 0.108 0.118 0.128 0.138 0.148 0.158 0.168 0.177 0.187 0.197 0.207 0.217 0.227 0.237 0.247 0.257 0.267 0.276 0.286 0.296 0.306 0.316 0.326 0.336 0.345 0.355 0.365 0.375 0.384 0.394 0.404

p/p0 10-3

10-3

1.75 × 1.91 × 10-3 2.11 × 10-3 2.37 × 10-3 2.69 × 10-3 3.11 × 10-3 3.65 × 10-3 4.32 × 10-3 5.16 × 10-3 6.19 × 10-3 7.57 × 10-3 9.22 × 10-3 0.0111 0.0123 0.0126 0.0151 0.0178 0.0202 0.0215 0.0228 0.0241 0.0247 0.0254 0.0259 0.0276 0.0283 0.0301 0.0309 0.0328 0.0336 0.0354 0.0361 0.0377 0.0384 0.0403 0.0428 0.0454 0.0503 0.0601 0.0708 0.0809 0.0910 0.101 0.111

Rs

p/p0

Rs

p/p0

Rs

0.413 0.423 0.432 0.441 0.450 0.459 0.467 0.475 0.482 0.489 0.496 0.503 0.508 0.511 0.512 0.517 0.522 0.526 0.528 0.530 0.532 0.533 0.534 0.535 0.537 0.538 0.541 0.542 0.546 0.547 0.550 0.551 0.554 0.556 0.559 0.563 0.567 0.572 0.579 0.585 0.589 0.594 0.598 0.602

0.121 0.131 0.141 0.151 0.161 0.171 0.181 0.191 0.201 0.211 0.221 0.231 0.241 0.251 0.260 0.270 0.280 0.289 0.299 0.308 0.318 0.327 0.336 0.349 0.360 0.371 0.381 0.390 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510 0.520 0.530 0.540 0.550

0.605 0.609 0.613 0.617 0.621 0.625 0.629 0.634 0.639 0.644 0.649 0.655 0.661 0.667 0.674 0.682 0.690 0.700 0.711 0.724 0.738 0.755 0.776 0.812 0.852 0.895 0.936 0.970 1.00 1.03 1.05 1.07 1.09 1.10 1.12 1.13 1.14 1.15 1.17 1.18 1.19 1.20 1.21 1.22

0.560 0.570 0.579 0.590 0.599 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710 0.720 0.728 0.741 0.750 0.760 0.770 0.780 0.790 0.800 0.810 0.819 0.829 0.839 0.848 0.854 0.859 0.865 0.872 0.900 0.930 0.937 0.947 0.956 0.970 0.978 0.985 0.991

1.24 1.25 1.26 1.28 1.30 1.32 1.34 1.36 1.39 1.42 1.44 1.47 1.50 1.53 1.55 1.58 1.60 1.62 1.64 1.67 1.69 1.71 1.73 1.75 1.77 1.79 1.82 1.85 1.88 1.92 1.96 2.02 2.11 2.18 2.34 2.52 2.59 2.72 2.93 3.21 3.39 3.67 3.94

280 as a reference have a pronounced filling swing49,50 (for Rs below 0.5; see Figure 9) and a clear condensation swing49,50 (for Rs between 0.5 and 0.8). The Rs plots with Carbopack F as a reference exhibit very pronounced filling and condensation swings (for Rs below 0.5 and between 0.5 and 0.7, respectively, see Figure 10) and, in addition, a small step at Rs close to 1. For a properly chosen reference adsorbent, the latter feature would be attributable to the condensation of argon in mesopores,16 but no evidence for this phenomenon can be found on the adsorption isotherm for carbon G. Likewise, the indication of filling and condensation swings can be found on the Rs plots for BP 280 with Carbopack F as a reference (Figure 7), although it is known6,30-32 that BP 280 is nonmicroporous and consequently the observed swings are clearly not related to microporosity. Therefore, the use of highly graphitized carbons as reference adsorbents for the analysis activated carbons and nongraphitized carbons may be misleading and should be avoided in most cases. On the other hand, nongraphitized carbon blacks, such as BP 280, are suitable as reference adsorbents for comparative analysis of activated carbons and nongraphitized carbons. To this end, it is interesting to note that a recent computer simulation study allowed for the construction of Rs plots for micropores using simulated data for a reference material

12522 J. Phys. Chem. B, Vol. 105, No. 50, 2001

Gardner et al.

TABLE 3: Argon Standard Reduced Adsorption Data for Cabot BP280 at 87 K (Amounts Adsorbed Were Divided by the Amount Adsorbed at a Relative Pressure of 0.4, i.e., 15.60 cm3 STP g-1) p/p0 6.38 × 1.83 × 10-5 3.53 × 10-5 5.67 × 10-5 8.16 × 10-5 1.10 × 10-4 1.41 × 10-4 1.77 × 10-4 2.14 × 10-4 2.53 × 10-4 2.95 × 10-4 3.39 × 10-4 3.85 × 10-4 4.34 × 10-4 4.85 × 10-4 5.38 × 10-4 5.93 × 10-4 6.50 × 10-4 7.10 × 10-4 7.72 × 10-4 8.36 × 10-4 9.03 × 10-4 9.72 × 10-4 1.04 × 10-3 1.12 × 10-3 1.20 × 10-3 1.28 × 10-3 1.36 × 10-3 1.45 × 10-3 1.54 × 10-3 1.63 × 10-3 1.73 × 10-3 1.83 × 10-3 1.93 × 10-3 2.04 × 10-3 2.15 × 10-3 2.27 × 10-3 2.39 × 10-3 2.51 × 10-3 2.65 × 10-3 2.78 × 10-3 2.92 × 10-3 3.07 × 10-3 3.22 × 10-3 3.38 × 10-3 10-6

Rs 6.56 × 0.0131 0.0196 0.0262 0.0327 0.0391 0.0456 0.0521 0.0585 0.0650 0.0714 0.0778 0.0843 0.0907 0.0971 0.103 0.110 0.116 0.123 0.129 0.135 0.142 0.148 0.154 0.160 0.167 0.173 0.179 0.186 0.192 0.198 0.204 0.211 0.217 0.223 0.229 0.235 0.241 0.247 0.254 0.260 0.266 0.272 0.278 0.284

p/p0 10-3

3.55 × 3.73 × 10-3 3.91 × 10-3 4.10 × 10-3 4.30 × 10-3 4.51 × 10-3 4.73 × 10-3 4.96 × 10-3 5.20 × 10-3 5.45 × 10-3 5.73 × 10-3 6.02 × 10-3 6.32 × 10-3 6.64 × 10-3 7.02 × 10-3 7.36 × 10-3 7.73 × 10-3 8.10 × 10-3 8.49 × 10-3 8.91 × 10-3 9.32 × 10-3 9.78 × 10-3 0.0102 0.0111 0.0126 0.0151 0.0175 0.0200 0.0252 0.0299 0.0349 0.0400 0.0451 0.0501 0.0581 0.0701 0.0801 0.0900 0.100 0.119 0.140 0.160 0.180 0.200 0.220 10-3

Rs 0.290 0.296 0.301 0.307 0.313 0.319 0.325 0.330 0.336 0.342 0.348 0.354 0.359 0.365 0.371 0.377 0.383 0.388 0.393 0.399 0.404 0.410 0.415 0.424 0.437 0.455 0.470 0.483 0.505 0.522 0.536 0.549 0.560 0.570 0.584 0.603 0.618 0.630 0.643 0.665 0.687 0.709 0.730 0.751 0.773

p/p0 0.240 0.261 0.281 0.301 0.321 0.341 0.361 0.381 0.401 0.421 0.441 0.461 0.480 0.500 0.520 0.541 0.561 0.581 0.601 0.621 0.641 0.660 0.680 0.700 0.720 0.740 0.760 0.782 0.799 0.820 0.840 0.860 0.879 0.898 0.910 0.919 0.927 0.935 0.947 0.953 0.963 0.972 0.982 0.987

TABLE 4: Argon Standard Reduced Adsorption Data for Carbopack F Graphitized Carbon Black at 87 K (Amounts Adsorbed Were Divided by the Amount Adsorbed at a Relative Pressure of 0.4, i.e., 3.108 cm3 STP g-1)

Rs

p/p0

0.79 0.818 0.842 0.867 0.892 0.919 0.945 0.972 1.00 1.03 1.06 1.09 1.11 1.14 1.17 1.20 1.23 1.27 1.30 1.34 1.37 1.41 1.45 1.49 1.54 1.59 1.65 1.72 1.78 1.87 1.96 2.07 2.21 2.39 2.52 2.65 2.80 2.97 3.29 3.50 3.97 4.68 6.22 7.73

1.28 × 2.49 × 10-4 3.54 × 10-4 4.50 × 10-4 5.38 × 10-4 6.20 × 10-4 6.95 × 10-4 7.65 × 10-4 8.30 × 10-4 8.91 × 10-4 9.49 × 10-4 1.00 × 10-3 1.06 × 10-3 1.11 × 10-3 1.16 × 10-3 1.20 × 10-3 1.25 × 10-3 1.30 × 10-3 1.34 × 10-3 1.39 × 10-3 1.43 × 10-3 1.48 × 10-3 1.52 × 10-3 1.57 × 10-3 1.62 × 10-3 1.67 × 10-3 1.72 × 10-3 1.77 × 10-3 1.83 × 10-3 1.89 × 10-3 1.96 × 10-3 2.03 × 10-3 2.10 × 10-3 2.18 × 10-3 2.27 × 10-3 2.36 × 10-3 2.47 × 10-3 2.58 × 10-3 2.71 × 10-3 2.86 × 10-3

with exactly the same surface properties as those for the micropores assumed in simulations.50 The Rs plots generated therein more closely matched the Rs plots for the activated carbon calculated herein using BP 280 as a reference. The Rs plots shown in Figure 10 allowed for the determination of the structural parameters of carbon G. The micropore volume and external surface area derived from argon data at 77 K were 0.76 cm3 g-1 and 30 m2 g-1, respectively, whereas those derived from data at 87 K were 0.77 cm3 g-1 and 30 m2 g-1, respectively. These results are consistent with one another and with those from nitrogen adsorption data at 77 K23 (0.80 cm3 g-1 and 20 m2 g-1, respectively). It should be noted that the pore volumes and external surface areas were rounded herein to 0.01 cm3 g-1 and 10 m2 g-1, respectively, to reflect the reproducibility of these data, estimated on the basis of previous nitrogen adsorption studies. Argon adsorption isotherm data for the two reference solids at 87 and 77 K are provided in Tables 1-4. In each case, these measurements were carefully repeated twice, and the agreement between runs in each case was excellent. Table 1 shows the standard reduced argon adsorption data for BP 280 at 77 K. A

10-4

Rs 9.17 × 0.0184 0.0274 0.0364 0.0456 0.0548 0.0641 0.0735 0.0829 0.0924 0.102 0.111 0.121 0.131 0.140 0.150 0.160 0.169 0.179 0.188 0.198 0.208 0.217 0.227 0.237 0.246 0.256 0.265 0.275 0.284 0.294 0.303 0.312 0.322 0.331 0.340 0.349 0.358 0.366 0.375

10-3

p/p0

Rs

p/p0

Rs

3.02 × 3.19 × 10-3 3.39 × 10-3 3.62 × 10-3 3.86 × 10-3 4.13 × 10-3 4.44 × 10-3 4.81 × 10-3 5.23 × 10-3 5.69 × 10-3 6.20 × 10-3 6.75 × 10-3 7.55 × 10-3 8.13 × 10-3 8.75 × 10-3 9.40 × 10-3 0.0100 0.0113 0.0125 0.0150 0.0175 0.0202 0.0250 0.0301 0.0351 0.0401 0.0452 0.0501 0.0573 0.0695 0.0793 0.0890 0.0987 0.117 0.137 0.156 0.176 0.195 0.215 0.235

0.383 0.391 0.399 0.406 0.414 0.420 0.427 0.434 0.441 0.447 0.452 0.458 0.465 0.469 0.473 0.477 0.480 0.486 0.491 0.498 0.505 0.511 0.518 0.525 0.531 0.536 0.541 0.545 0.551 0.560 0.567 0.573 0.580 0.591 0.602 0.616 0.633 0.649 0.671 0.694

0.256 0.276 0.297 0.317 0.337 0.360 0.381 0.400 0.420 0.440 0.460 0.480 0.500 0.520 0.540 0.560 0.580 0.600 0.620 0.640 0.660 0.680 0.700 0.720 0.740 0.760 0.780 0.800 0.819 0.840 0.860 0.879 0.899 0.919 0.940 0.954 0.964 0.975 0.984 0.988

0.719 0.746 0.778 0.817 0.861 0.914 0.959 1.00 1.04 1.07 1.10 1.13 1.15 1.18 1.21 1.23 1.26 1.30 1.34 1.38 1.44 1.50 1.57 1.65 1.72 1.78 1.84 1.91 1.98 2.07 2.17 2.30 2.45 2.63 2.90 3.27 3.63 4.22 5.09 5.9

10-3

total of 111 data points were measured, covering a relative pressure range of 9.66 × 10-6-0.995. Reduced adsorption amounts were obtained by dividing the actual adsorbed amounts by the amount adsorbed at a relative pressure of 0.4, which for this sample was 15.65 cm3 STP g-1. Figure 11 shows reduced adsorption isotherms that compare these data with the data published by Selles-Perez and Martin-Martinez.7 The results in Table 1 are in excellent agreement up to a relative pressure

Figure 11. Reduced isotherms for argon adsorption at 77 K from this study (for BP 280) and from ref 7.

Reference Data for Argon Adsorption of 0.56, with the reduced adsorption differing by not more than 2-3% (except for the lowest relative pressure reported in ref 7, i.e., 0.005, at which the difference is about 4%). The results begin to diverge after this, with the differences growing with increasing relative pressure, until the difference is 11% at a relative pressure of 0.96. The reference solid used in ref 7 was an activated carbon heated at high temperatures (2000 K), and the differences in reduced adsorption may reflect differences in the surface, and perhaps even in pore structure properties of these reference solids. The uncertainty about surface and structural properties of the reference adsorbent proposed in ref 7 has already been discussed herein. Table 2 shows the standard reduced argon adsorption data for Carbopack F at 77 K. In this case, 175 data points were measured in the relative pressure range of 5.85 × 10-5-0.991. The amount adsorbed at a relative pressure of 0.4 was 3.173 cm3 STP g-1. Table 3 shows the standard reduced argon adsorption data for BP 280 at 87 K. In this case, 134 sample points were measured in the relative pressure range of 6.38 × 10-6-0.987. The amount adsorbed at the relative pressure of 0.4 was 15.60 cm3 STP g-1. Table 4 shows the standard reduced argon adsorption data for Carbopack F at 87 K. In this case, 120 data points were collected in the relative pressure range of 1.28 × 10-4-0.988. The amount adsorbed at the relative pressure of 0.4 was 3.108 cm3 STP g-1. Conclusions Two carbons, the nongraphitized BP 280, and the graphitized Carbopack F, were shown to be suitable as reference adsorbents for argon adsorption studies on nongraphitized carbons, such as activated carbons and graphitized carbons, respectively, both at 87 and 77 K. The reference data were used to construct the Rs plots and calculate the external surface area and micropore volume of a sample activated carbon. From the Rs plots, it was determined that BP 280 is a more suitable reference solid for argon adsorption studies on microporous carbons. The values of the external surface area and micropore volume obtained from these Rs plots showed a good agreement with the results from an earlier study using nitrogen at 77 K. Acknowledgment. The Cabot Corporation Special Black Division, Dr. W. R. Betz from Supelco, Inc., and Dr. K. P. Gadkaree from Corning, Inc., are gratefully acknowledged for providing the carbon samples. References and Notes (1) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982. (2) Rodriguez-Reinoso, F.; Martin-Martinez, J. M.; Prado-Burguette, C.; McEnaney, B. J. Phys. Chem. 1987, 91, 515. (3) Carrott, P. J. M.; Roberts, R. A.; Sing, K. S. W. Carbon 1987, 25, 769. (4) Selles-Perez, M. J.; Martin-Martinez, J. M. J. Chem. Soc., Faraday Trans. 1991, 87, 1237. (5) Kruk, M.; Jaroniec, M.; Gadkaree, K. P. J. Colloid Interface Sci. 1997, 192, 250.

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