Adsorption Behavior of Hydrocarbons on Slit-Shaped Micropores

Adsorption behavior of the hydrocarbons n-hexane, n-octane, cyclohexane, neopentane, and benzene on microporous activated carbon fibers (ACFs) was ...
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Langmuir 1997, 13, 496-501

Adsorption Behavior of Hydrocarbons on Slit-Shaped Micropores Akihiko Matsumoto,* Jian-xin Zhao, and Kazuo Tsutsumi Department of Materials Science, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441, Japan Received October 30, 1995. In Final Form: October 18, 1996X

Adsorption behavior of the hydrocarbons n-hexane, n-octane, cyclohexane, neopentane, and benzene on microporous activated carbon fibers (ACFs) was studied by use of molecular adsorption and adsorption calorimetry. The calorimetric aspects were discussed in connection with pore characteristics determined by nitrogen adsorption. The differential heats of adsorption of hydrocarbon, as well as the integral heats on ACFs of narrower pore widths, tended to become higher than those of wider pore widths, which is ascribed to micropore filling. These experimental results were also compared with the theoretical profile of the intermolecular interaction between adsorbates and adsorbents.

1. Introduction The adsorption property of molecules on porous materials depends on the character of the pores: their shapes, sizes, and chemical natures. In the case of adsorption on a micropore of less than twice the diameter of the adsorbate molecule, the enhancement of adsorption by the overlapping of interactive potential of both sides of the pore walls, called micropore filling, takes place.1a,2,3 Theoretical studies of the micropore filling were reported for the slit and cylindrical micropores, and the results were applied to experimental results to estimate porosity (pore volume, pore diameter, and surface area) of adsorbents.3-5 Activated carbon fibers (ACFs) are prepared so as to have a uniform pore width by controlled burn-off of carbon fiber.6,7 Assessment of the porosity of ACF by nitrogen adsorption suggests that certain ACFs are highly microporous with a small external area; the micropores are uniform in sizes from 0.7 to 2 nm.8 Consequently, such ACFs can adsorb a large amount of vapors in their micropores by micropore filling.9 The high-resolution electron micrographs, neutron diffraction, and small-angle neutron-scattering results revealed that the micropores of the ACFs are slit-shaped and uniform in their sizes10 and are oriented along the fiber axis.11 Therefore, the * To whom correspondence should be addressed. Telephone: +81-532-44-6811. Fax: +81-532-48-5833. E-mail: [email protected]. ac.jp. X Abstract published in Advance ACS Abstracts, January 1, 1997. (1) Sing, K. S. W. In Porosity in Carbons: Characterization and Applications; Patrick, J. W., Ed.; Edward Arnold: London, 1995; (a) Chapter 2, (b) Chapter 4. (2) Sing, K. S. W. J. Porous Mater. 1995, 2, 9. (3) Seaton, N. A.; Walton, J. P. R. B.; Quarke, N. Carbon 1989, 27, 6. (4) Jiang, S.; Zollweg, J. A.; Gubbins, K. E. J. Phys. Chem. 1994, 98, 5709. (5) Stoeckli, H. F. Helv. Chim. Acta 1974, 57, 2195. (6) Atkinson, D.; Carrott, P. J. M.; Grillet, Y.; Rouquerol, J.; Sing, K. S. W. In Proceedings of the 2nd Engineering Conference on Fundamentals of Adsorption; Liapis, A. I., Ed.; Engineering Foundation: New York, 1986; p 89. (7) Kaneko, K.; Nakahigashi, Y.; Nagata, K. Carbon 1988, 26, 327. (8) Kaneko, K.; Suzuki, T.; Kuwabara, H.; Kakei, K. In 3rd International Conference on Fundamentals of Adsorption; Mersmann, A. B., Scholl, S. E., Eds.; American Institute of Chemical Engineering: New York, 1989; p 345. (9) Kakei, K.; Ozeki, S.; Suzuki, T.; Kaneko, K. J. Chem. Soc., Faraday Trans. 1990, 86, 371. (10) Kaneko, K.; Shimizu, K.; Suzuki, T. J. Chem. Phys. 1992, 97, 8705. (11) Matsumoto, A.; Kaneko, K.; Ramsay, J. D. F. Stud. Surf. Sci. Catal. 1993, 80, 405.

ACFs would be suitable model substances for study of adsorption in a micropore. Strength of adsorption is essentially dependent on the interaction between a solid surface and vapor adsorbates and can be compared experimentally by adsorption calorimetry. Especially, the measurement of the differential heats of adsorption with consecutive change of adsorption uptake gives information on the adsorbed state of molecules at each adsorption stage.12 In this study, ACFs of different pore widths are characterized by nitrogen adsorption and adsorption behavior of hydrocarbons on ACFs are examined by measurements of differential heats of adsorption. Effects of the pore widths of the ACFs and the sizes of the hydrocarbons on the differential heats of adsorption are discussed. 2. Experimental Section Pitch-based activated carbon fibers (Osaka Gas Co.) of various microporosity, which are designated by P-7, -10, -15, and -20, were used in this study.7 The sample number stands for the order of pore width; the sample designated with a greater number has wider pores. The nitrogen adsorption isotherm was measured volumetrically at 77 K using a laboratory-made automatic adsorption apparatus equipped with two pressure transducers ranged from 10-1 to 105 Pa. Differential heats of adsorption and adsorption isotherms of hydrocarbons on the ACFs were measured by a twin-conduction-type calorimeter (Tokyo Riko Co.) equipped with a volumetric adsorption system at 303 K. The heats of adsorption and the adsorption isotherms were simultaneously determined by dosing consecutively a small amount of hydrocarbon vapor. The hydrocarbons n-hexane, n-octane, cyclohexane, neopentane (2,2-dimethylpropane), and benzene were used after purification by proper methods. Approximately 50 mg of sample was used in each experiment, and the sample was evacuated at 383 K and 1 mPa for 10 h prior to these measurements.

3. Results and Discussion 3.1. Microporosity. Figure 1 shows adsorption isotherms of nitrogen on ACFs. The isotherm on P-7 was of Type Ia; the adsorption isotherm on P-7 had a sharper “knee” at p/p° ) ca. 0.01 and came to a limiting value (12) For example, see: Tsutsumi, K.; Nishimiya, K. Thermochim. Acta 1989, 299, 143. Tsutsumi, K.; Mizoe, K. Colloids Surf. 1989, 37, 29. Reichert, H.; Mu¨ller, U.; Unger, K. K.; Grillet, Y.; Rouquerol, F.; Rouquerol, J.; Coulomb, J. P. Stud. Surf. Sci. Catal. 1991, 62, 311. Tsutsumi, K.; Matsushima, H.; Matsumoto, A. Langmuir 1993, 9, 2665. Matsumoto, A.; Tsutsumi, K. J. Chem. Soc., Faraday Trans. 1995, 91, 1707.

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nation of the monolayer capacity for microporous solids. Sing et al. proposed using the amount adsorbed at a fixed relative pressure of 0.4 as a normalizing factor, which is called the Rs method.17 The specific surface areas aR and the micropore volumes WR determined from the Rs-plots were compared with those from the t-plots, and each micropore parameter determined by these different methods was almost identical. Therefore, the determination of micropore parameters by the t-plot would be reliable in the present case. Micropore filling of vapors can be described using the Dubinin-Radushkevich (DR) equation18,19 Figure 1. Adsorption isotherms of nitrogen on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 2. t-plots applied to the adsorption isotherms in Figure 1: 2, P-7; O, P-10; b, P-15; 0, P-20.

manifested in a plateau region. The isotherms on the other ACFs were of Type Ib, which had round knees around 0.01 < p/p° < 0.3 with a gradual approach to the plateau.2 It has been known that adsorption on a microporous solid leads to an isotherm of Type I and that the microporous solid of narrower pore width of molecular dimensions shows Type Ia character coming to saturation at a lower p/p°. The micropore width of P-7 is the narrowest among these ACFs. Isotherms of microporous solids with wider micropores have been reported to have round knees at higher p/p° (to ca. 0.2) due to cooperative filling of nitrogen (Type Ib character).2,13 Therefore, P-10, -15, and -20 have wider pores of widths of a few molecular layers.8,9,13 The adsorption isotherms expressed p/p in a logarithmic form are often useful to reveal the differences in the data for a low p/p region; however, there were no remarkable differences in the nitrogen adsorption. The t-plots applied to the adsorption isotherms in Figure 1 are shown in Figure 2. The standard thickness of adsorbed N2 layer, t, on the graphitized nonporous carbon was used.14,15 The t-plot of each ACF is linear, passes through the origin, and bends near the t-region of 0.350.6 nm to reach a plateau at higher t. Since the inflection points correspond to one-half of the pore width, all of the ACFs are microporous.16 The specific surface area at, the micropore volume (Wt) and the pore width of the ACFs calculated from the t-plots are compiled in Table 1. Values of at and Wt varied from 870 to 2000 m2/g and from 0.3 to 1.1 mL/g, respectively, with an increase in the pore width from 0.7 to 1.1 nm. Applicability of the t-plot analysis to the micropore system has been criticized with regard to the determi(13) Carrot, P. J. M.; Roberts, R. A.; Sing, K. S. W. Stud. Surf. Sci. Catal. 1988, 39, 89. (14) Rodriguez-Reinoso, F.; Martin-Martinez, J. M.; Prado Burguete, C.; McEnaney, B. J. Phys. Chem. 1987, 91, 515. (15) Carrot, P. J. M.; Roberts, R. A.; Sing, K. S. W. Carbon 1987, 25, 769. (16) Gregg, S. J.; Sing, K. S. W. Adsorption Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982; Chapter 2.

W ) Wo exp(-/βEo)2 where W is the amount adsorbed at a p/p°, Wo is the amount of micropore volume filled with vapor, and β and Eo are an affinity coefficient and a characteristic adsorption energy which relate to the adsorbent, respectively. The term  is the adsorption potential and equal to RT ln(p°/p), where R and T are the gas constant and temperature, respectively. Figure 3 shows the DR-plots for the N2 adsorption on ACFs. These plots exhibit good linear relationships at [ln(p°/p)]2 > 10 (viz. p/p° < 0.04), which also suggests that the micropore filling of N2 is nearly completed at this region. In the DR-plots, upward deviations were observed at [ln(p°/p)]2 < 10, which would be ascribed to multilayer adsorption on relatively large pores, mesopores and macropores, and defects.20 Little upward deviation was observed in the DR-plot of P-7. This suggests that the pores of P-7 consist mainly of micropores of uniform size. The amount of micropore volume filled with N2, Wo, was estimated by the DR-plot as listed in Table 1, with the assumption that N2 adsorbed as a liquid with a density of 0.8085 g/mL at 77 K. Each Wo value in units of milliliter per gram is comparable to the pore volume estimated by t- and Rs-plots. In the cases of P-7 and P-10, the Wo value was almost identical to Wt or WR values. However, Wo values were less than Wt or WR values in the cases of P-15 and P-20. The Wt or WR value consists of the pore volumes of both micropores and more larger pores, although Wo is equal to micropore volume only. Therefore, P-15 and P-20 with larger pores gave the discrepancy between Wo and Wt or WR. 3.2. Adsorptivity of Hydrocarbons. Figures 4-8 show adsorption isotherms of hydrocarbons on ACFs at 303 K. The adsorption isotherm of neopentane shown in Figure 6 could not be measured at higher p/p° (over ≈0.2) because of the much higher saturation vapor pressure of 186.9 kPa compared to the atmospheric pressure at 298 K. Each isotherm was of typical Type I, and almost all adsorption completed at p/p° less than 0.2 for each adsorbate. These results suggest that micropores of ACF were filled with the hydrocarbon vapors. Especially, the isotherms of P-7 were of Type Ia showing a strong interaction between the ACF surface and the hydrocarbon molecules. The Langmuir and DR equations applied to each isotherm gave good linear curves, and the saturation amounts of adsorption in millimoles per gram, designated as WL and WDR, were determined. Values of WL and WDR (17) Carrot, P. J. M.; Sing, K. S. W. Stud. Surf. Sci. Catal. 1988, 39, 77. (18) Dubinin, M. M. In Chemistry and Physics of Carbon; Walker, P. L., Ed.; Marcel Dekker: New York, 1966; Vol. 2, p 51. (19) McEnaney, B.; Mays, T. J. In Introduction to Carbon Science; Marsh, H., Ed.; Butterworths: London, 1989; Chapter 5. (20) Stoeckli, H. F. In Porosity in Carbons: Characterization and Applications; Patrick, J. W., Ed.; Edward Arnold: London, 1995; Chapter 3.

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Table 1. Microporosity of ACFs Determined from t rs and DR-Plots

sample

surface area (Rt) (m2 g-1)

t-plots pore volume (Wt) (mL g-1)

pore width (nm)

P-7 P-10 P-15 P-20

870 1350 1850 2000

0.29 0.56 0.96 1.06

0.7 0.9 1.0 1.1

Rs-plots surface area (aR) pore volume (WR) (m2 g-1) (mL g-1) 860 1330 1830 2050

0.30 0.57 0.96 1.05

DR-plots pore volume (Wo) (mL g-1) 0.32 0.58 0.83 0.87

Figure 3. DR-plots for the N2 adsorption on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 6. Adsorption isotherms of neopentane on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 4. Adsorption isotherms of n-hexane on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 7. Adsorption isotherms of cyclohexane on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 5. Adsorption isotherms of n-octane on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 8. Adsorption isotherms of benzene on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

are listed in Table 2. The WL values increase with an increase in the pore widths of the ACFs as well as the change of the saturation uptake of N2, WR. The value of WL, which is based on the monolayer adsorption, was almost identical to WDR (within the range of (0.1 mmol/g) even though the adsorption in micropores would proceed by micropore filling rather than monolayer adsorption. The βEo in the DR equation, which was already mentioned in the previous section, is associated with the isosteric heat of adsorption at the fractional filling of 1/e, qst,θ)1/e, expressed as

relates to the differential heat of adsorption, qd, as qst ) qd - RT. Consequently, the change in qst corresponds to that of qd. Around θ ) 1/e, the qd of each adsorbate scarcely changed the change in adsorption uptake as shown in Figures 10-14, which correspond to the micropore filling process for each hydrocarbon in the micropores.22 Therefore, the qst,θ)1/e reflect the enhancement of adsorption in micropore filling. Figure 9 shows the relationship between the pore width and qst,θ)1/e. The qst,θ)1/e of the ACFs of narrower pore widths are higher than those of wider ones, and they are comparable with the changes in qd and the integral heats of adsorption. The higher qst,θ)1/e of the ACFs of narrower pore widths are ascribed to the enhancement of adsorption due to overlapping of adsorption potential of opposite sides of walls. The enhancement will be mentioned later in relation to qd.

qst,θ)1/e ) βEo + ∆Hliq where ∆Hliq is the heat of liquefaction (for ∆Hliq of each hydrocarbon, see Table 3).21 Thermodynamically, the qst (21) Kaneko, K. J. Membr. Sci. 1994, 96, 59.

(22) Wang, Z.; Kaneko, K. J. Phys. Chem. 1995, 99, 16714.

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Figure 9. Relationship between the isosteric heat of adsorption estimated from the DR-plots and the pore widths of the ACFs. Table 2. Saturated Amounts of Adsorption of Hydrocarbon Vapors on ACFs hydrocarbon n-hexane

WL WDR n-octane WL WDR neopentane WL WDL cyclohexane WL WDR benzene WL WDR

P-7 P-10 P-15 P-20 (mmol g-1) (mmol g-1) (mmol g-1) (mmol g-1) 2.8 2.8 2.3 2.2 2.9 2.9 3.3 3.2 3.3 3.4

4.2 4.2 2.9 2.8 5.0 5.1 4.9 5.0 5.2 5.3

7.1 7.1 5.0 5.1 6.2 6.3 6.0 6.3

7.5 7.4 5.3 5.3 7.6 7.4 6.5 7.1 7.6 7.4

3.3. Heat of Adsorption. The calorimetrically determined differential heats of adsorption, qd, of hydrocarbons are plotted against the adsorption amount as shown in Figures 10-14, respectively. The qd of n-hexane are shown in Figure 10. The qd on the ACFs of narrower pores are higher than those on ACF of wider ones. Especially, the initial heats of n-hexane on P-7 attained more than 80 kJ/mol, which are 1.3-1.8 times as much as those on other ACFs, and the high-heat evolution of 73 kJ/mol was observed from the adsorption of 1.2 to 2.8 mmol/g of n-hexane. The differential heat on P-7 decreased steeply at the adsorbed amount of 2.8 mmol/g which corresponded to the sharp “knee” in the adsorption isotherm or the saturation uptake shown in Figure 4, whereas the heats of the other ACFs decreased gradually with an increase in the adsorption uptake. Even at the end of adsorption, the differential heats of adsorption on P-7 of 60 kJ/mol were about twice those on other ACFs. In the case of vapor adsorption on microporous carbon, the higher qd at the initial stage are observed regardless of the polarity of adsorbates.22,23 Wang et al. suggested that the high heat evolution with SO2 adsorption at this stage is ascribed to the strong adsorption on the surface functional groups and to the additional interaction of the SO2 dipole with the surface functional groups through the surface electric field. However, n-hexane is nonpolar so that the dispersion interaction would play a dominant role in the adsorption rather than the polar ones. In the N2 adsorption on micropores, Sing et al. pointed out that the initial heats of adsorption of the primary micropore filling are 1.5-2 times greater than those of the secondary micropore filling.17 Therefore the high qd at the initial stage would be due to micropore filling in ultramicropores which may be present in the ACFs. The continuous heat evolution of 73 kJ/mol would arise from micropore filling in micropores of 0.7 nm in width, and the high heat evolution at the end of adsorption (23) Tsutsumi, K.; Matsushima, H.; Matsumoto, A. Langmuir 1993, 9, 2665.

would also suggest the strong adsorption of n-hexane molecules in the micropore of P-7. The qd of n-hexane on other ACFs decreased gradually until the saturated adsorption and approached to ∆Hliq of n-hexane, 29 kJ/mol. In the case of adsorption on the ACFs of wider pore sizes, the evolution of high heat was not observed since the enhancement of potential from both side of pore walls was not so pronounced. The same tendency was observed in the adsorption of n-octane shown in Figure 11. The qd values of these n-alkanes, as well as their integral heats, were relatively higher than those of cyclohexane and neopentane shown later. In the case of n-alkane adsorption, the flexible hydrocarbon chain of the n-alkanes would be adsorbed along pore walls of graphite layers and each segment in n-alkanes, methyl, and methylene groups could interact, respectively, with carbon atoms on graphite layers. Therefore, the heat evolution with adsorption of these n-alkanes was higher than that of cyclohexane and neopentane because these have a more rigid structure. As shown in Figures 12 and 13, the qd of neopentane and cyclohexane decreased monotonously with an increase in the adsorption amount until the saturation point was reached, and qd approached ∆Hliq of each adsorbate as tabulated in Table 3. The differences in the qd of these adsorbates were small for all ACFs. The qd of benzene, shown in Figure 14, are higher than those of cyclohexane although the changes in qd with an increase in the uptake showed the same tendency. This arises from the π-electron interaction between the benzene molecules and the graphite planes of the ACFs. The relationships between the integral heat of adsorption of each adsorbate and the pore widths of the ACFs are shown in Figure 15. The integral heat of adsorption is calculated by integrating the differential heats of adsorption from the initial stage of adsorption to the completion of adsorption saturation and subtracting the contribution of ∆Hliq of each adsorbate. The integral heat is represented in joules per unit area of each ACF to compare the effect of pore width. The integral heats tend to decrease with an increase in the pore width, which coincides with the change in qst,θ)1/e. This result also suggests the existence of a stronger adsorbate-adsorbent interaction in the ACFs having narrower pores. 3.4. Molecular Potential and Heat of Adsorption. In the case of adsorption in micropores, the micropore filling takes place. The micropore filling of overlapping of the potential would be estimated by the potential profile in the micropores. Although the potential is not corresponding to qd or the adsorption potential, the potential profile would give useful information on the strength of the adsorbate-adsorbent interaction in the micropores and would often correspond to the change of qd.22 When nonpolar molecules adsorb on the basal plane of graphite, the nonpolar interaction, such as the dispersion interaction, would be dominant rather than the polar one. Therefore, in this study, the nonpolar interaction was described by the Lennard-Jones potential. Estimating of the Lennard-Jones potential of polyatomic molecules of cylindrical (n-alkanes), round (neopentane) and disk (cyclohexane) shapes is more difficult than estimating the potential of small spherical molecules because of the difficulty in estimating the orientation of these adsorbates in micropores. Therefore, the one-center calculation was adopted in the present calculation. In the case of adsorption on a smooth graphite surface, the total interaction (Φ) would be a pairwise sum of

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Table 3. Reference Data for the Hydrocarbon Adsorptives n-hexane

n-octane

neopentane

cyclohexane

benzene

31.4 28.9 423 0.59 109 0.47

2.46 35.0 333 0.74 97 0.54

101.3 22.8 193 0.70 74 0.52

16.2 33.0 323 0.61 95 0.48

15.9 31.7 440 0.53 111 0.43

saturated vapor pressure at 303 K26 (kPa) heat of liquefaction at 303 K27 (kJ mol-1) gg24b(K) σg,g24b (nm) g,s (K) σg,s (nm)

Figure 10. Heats of adsorption of n-hexane on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 13. Heats of adsorption of cyclohexane on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 11. Heats of adsorption of n-octane on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 14. Heats of adsorption of benzene on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 12. Heats of adsorption of neopentane on ACFs: 2, P-7; O, P-10; b, P-15; 0, P-20.

Figure 15. Relationship between the integral heat of adsorption and the pore widths of the ACFs.

an adsorbate molecule and solid atoms, and Φs,g is represented as

Lennard-Jones parameters of adsorbate molecules (energy parameter, g,g, and size parameter σg,g) and of carbon atoms (s,s, σs,s) and are listed in Table 3. Parameters Fs and ∆ represent the solid number density of graphite, 114 nm-3, and the distance between graphite layers, 0.335 nm, respectively.26 In the micropore, the adsorption potential would be the sum of the interaction potential, Φs,g, from both pore walls. When the distance between

[( ) ( )

Φs,g(z) ) A

2 σg,s 5 r

10

-

σg,s r

σg,s4

4

-

]

3∆(r + 0.61∆)3

A ) 2πFsg,sσ2g,s∆ where r is the distance between the center of an adsorbate molecule and the graphite surface and g,s and σg,s are energy and size parameters of the Lennard-Jones (126) potential between a carbon atom and an adsorbate molecule, respectively.21,24a,25 Therefore, g,s and σg,s values are calculated from Lorentz-Berthelot rule by use of the (24) Hirschfelder, O. J.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954; (a) Chapter 3, (b) Appendix. (25) Steel, W. A. Surf. Sci. 1973, 36, 317.

(26) Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir 1994, 10, 4606. (27) Chemical Society of Japan. Kagaku Binran (Handbook of Chemistry), 2nd ed.; Marzen: Tokyo, 1984; pp II-118. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. (28) Chemical Society of Japan. Kagaku Binran (Handbook of Chemistry), 2nd ed.; Marzen: Tokyo, 1984; pp II-271. Rossini, F. D. Selected Values of Chemical Thermodynamic Properties, U.S. GPrintingO: Washington, DC, 1952. Landolt-Bo¨rnstein Tabellen; 6 Aufl., II Band, 4 Teil. Springer-Verlag: Heidelberg, 1961. Stull, D. R.; Westrum, E. F., Jr.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds; Wiley: New York, 1967.

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Figure 16. Profile of the interaction potential between an adsorptive molecule and the pore walls.

graphite surfaces of the micropore and that between an adsorbate molecule and the center of the micropore are denoted by 2d and z, respectively, the total potential Φ could be represented by Φ ) Φs,g (d + z) + Φs,g(d - z). The profiles of interaction potential between an adsorptive molecule and pore walls for each ACF are shown in Figure 16. The potential axis is normalized by g,s of each adsorbate. The ACFs of wider pore widths gave shallower potential minima or a minimum. In the adsorption on P-7, the interactive potential of each adsorbate overlap and the two potential minima coalesce giving a single minimum with increasing depth. The ratios of the potential minimum for P-7 to those for other ACFs having wider pores are 1.2-1.7:1, which correspond well to the ratio of the qst,θ)1/e for P-7 to those for the other ACFs of 1.1-1.4:1. As already mentioned in the previous section, the qst,θ)1/e would reflect the enhancement of adsorption in micropore filling. Therefore, the comparison of qd around θ ) 1/e would give an approximate prediction of the potential depth or the microporosity of solids, and vice versa, though the calculated energy standing for the molar energy is not the partial molar energy such as qd.22 The difference between the ratios of qst,θ)1/e and those of qd would arise from the estimation of the interaction parameters g,g and σg,g. It should be noted that these parameters used in the present study are not the data of

gas phase in restricted space like micropores but those of bulk liquid. The proper estimation of the interaction parameters by considering molecular configuration in the restricted space such as micropores would give more consistent results. 4. Conclusion ACFs of different pore widths were characterized by nitrogen adsorption, and it was confirmed that the ACFs are microporous materials having high surface areas and pore volumes. In the case of the adsorption of condensable hydrocarbon vapors, adsorbed amounts and heats of hydrocarbons on ACFs were affected by the pore width of ACFs and the size of the hydrocarbons; adsorption amounts on ACFs became greater with an increase in the pore widths of the ACFs; however, heats of adsorption became less with an increase in the micropore widths. These results showed that the micropore filling plays an important role in the hydrocarbon adsorption in the microporous ACFs. Estimation of the potential profile of intermolecular potential could possibly be used to predict the adsorption behavior of hydrocarbons. Interpretation of the calorimetrically determined heats of adsorption by use of theoretical calculation will be further studied. LA950958L