Langmuir 1998, 14, 3079-3081
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Prediction of Hysteresis Disappearance in the Adsorption Isotherm of N2 on Regular Mesoporous Silica Satoru Inoue, Yoko Hanzawa, and Katsumi Kaneko* Physical Chemistry, Material Science, Graduate School of Natural Science and Technology, Chiba University, 1-33 Yayoi, Inage, Chiba 263, Japan Received November 17, 1997. In Final Form: March 11, 1998 The thermodynamic Saam-Cole approach including the molecule-surface interaction was applied to explain the critical pore width at which the adsorption hysteresis of N2 on regular mesoporous silica disappears. The difference of the critical thickness of physisorbed layers on the pore wall upon condensation and evaporation was associated with the pore wall roughness inherent to the atomic structures, showing that the critical pore width for the disappearance of the adsorption hysteresis is in the range of 3.6 to 3.8 nm.
Introduction Solids with a regular pore structure are expected to elucidate the interaction of gas with pores to develop new chemical processes and materials.1,2 IUPAC classified pores into micropores, mesopores, and macropores using the pore width w (micropores: w < 2 nm; mesopores: 2 nm < w < 50 nm, and macropores; w > 50 nm).3 Physical adsorption mechanism changes with this pore width. Recently, adsorption on mesopores has gathered much attention. Even below the saturated vapor pressure, vapor is condensed in the mesopore space of which walls are covered with the adsorbed layer. This mechanism is called capillary condensation. Capillary condensation has been explained by the Kelvin equation for many years.4,5 The Kelvin equation determines the condensation (Pc) and evaporation (Pe) pressures that are governed by the mean radius rm of the curvature of the meniscus of the condensate in the mesopore. When Pc and Pe are different from each other because of the different rm values for the meniscus on condensation, then evaporation, adsorption, and desorption branches do not overlap each other to give rise to an adsorption hysteresis. This capillary condensation theory predicts that the adsorption isotherm of N2 on cylindrical mesopores that are open at both ends has a clear adsorption hysteresis of IUPAC H1. Regular mesoporous silica, such as FSM6 and MCM-41,7 with a honeycomb structure of straight cylindrical mesopores has provoked an essential question about the origin of the adsorption hysteresis. Many physical adsorption studies on the regular mesoporous silica have been done all over the world.8-15 A clear dependence of the adsorption hysteresis of N2 adsorption * Corresponding author. Fax: 81-43-290-2788. E-mail: kaneko@ pchem1.nd.chiba-u.ac.jp. (1) Kaneko, K. J. Membr. Sci. 1994, 96, 59. (2) Huo, Q.; Margolese, D. I.; Stucky, G. D. Chem. Mater. 1996, 8, 1147. (3) Sing, K. S. W.; Everett, D. H.; Haoul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603. (4) Everett, D. H. In The Solid-Gas Interface; Flood E. A., Ed.; Marcel Dekker: New York, 1967; Chapter 3. (5) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic: London, 1982. (6) Inagaki, S.; Fukushima, Y.; Kuroda, K. J. Chem. Soc., Chem. Commun. 1993, 680. (7) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chue, C. T.-W.; Olson. D. H.; Sheppard, E.W.; MacCullen, S., B.; Higgins, J. B.; Schelender, J. L. J. Am. Chem. Soc. 1992, 114, 10824.
isotherms at 77 K on w was explicitly shown by Llewellyn et al.;7 the mesopores of w e 4 nm provide no adsorption hysteresis, whereas the adsorption isotherm of pores w g4 nm has an adsorption hysteresis. We do not understand the reason for the disappearance of the adsorption hysteresis and the presence of the critical pore width of ∼4 nm for N2 adsorption isotherm. Hence, we need a new analytical method that can predict the adsorption hysteresis inherent to each molecule/solid system instead of the Kelvin equation. Analytical Method The Kelvin equation takes into account the moleculesolid and intermolecular interactions through the contact angle and the surface tension, respectively. However, the Kelvin approach is not appropriate for description of adsorption on small mesopores. In particular, the contact angle term should be replaced with a more microscopic description of the molecule-solid interaction. Saam and Cole developed the thermodynamic theory with the average molecular potential for liquid helium in a cylindrical pore to understand unusual properties of liquid helium.16,17 Findenegg et al. have applied the SaamCole theory to elucidate fluid phenomena near the critical temperature.18,19 The Saam-Cole theory includes the molecule-solid dispersion interaction in a form of the sum of pair interactions. Therefore, the Saam-Cole theory can be applicable to describe adsorption phenomena in (8) Branton, P. J.; Hall, P. G.; Sing, K. S. W. J. Chem. Soc., Chem. Commun. 1993, 1257. (9) Llewellyn, P. L.; Grillet, Y.; Schu¨the, F.; Reichert, H.; Unger, K. K. Microporous Mater. 1994, 3, 345. (10) Branton, P. J.; Hall, P. G.; Sing, K. S. W.; Reichert, H.; Unger, K. K. J. Chem. Soc., Faraday Trans. 1994, 90, 2965. (11) Schmidt, R.; Sto¨cker, M.; Hansen, E.; Akporiaye, D.; Ellestad, O. H. Microporous Mater. 1995, 3, 443. (12) Ravikovitch, P. I.; Domhnaill, S. C. O.; Neimark, A. V.; Schu¨th, F.; Unger, K. K. Langmuir 1995, 11, 4765. (13) Branton, P. J.; Kaneko, K.; Setoyama, N.; Sing, K. S. W.; Inagaki, S.; Fukushima, Y. Langmuir 1996, 12, 599. (14) Morishige, K.; Fujii, H.; Uga, M.; Kinukawa, D. Langmuir 1997, 13, 3494. (15) Kruk, M.; Jaroniec, M.; Sayari, A. J. Phys. Chem. 1997, 101, 583. (16) Cole, M. W.; Saam, W. F. Phys. Rev. Lett. 1974, 32, 985. (17) Ball, P. C.; Evans. R. Langmuir 1989, 5, 714. (18) Michalski, T.; Benini, A.; Findenegg, G. H. Langmuir 1991, 7, 185. (19) Keizer, A.; Michalski, T.; Findenegg, G. H. Pure Appl. Chem. 1991, 63, 1495.
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Inoue et al.
∆µs ) -
γVm R 3 a (R - a)
(3)
If ∂∆µs/∂l < 0, the adsorbed film grows. In the case of ∆∂µs/∂l > 0, the film growth becomes unfavorable, giving rise to the capillary condensation. Hence, ∆∂µs/∂l ) 0 determines the critical thickness lc from the symmetryto-asymmetry transformation. On the other hand, the chemical potential of the asymmetrical state (∆µa) for the asymmetry-to-symmetry transformation is given by
∆µa ) -
2γVm R 3 a (R - a)
(4)
Equation 4 is true because the radius of the mean curvature of the meniscus of the condense is different from that of the asymmetry-to-symmetry transformation. Evaporation needs the conditions of ∆∂µs/∂l > 0, whereas ∆∂µs/∂l ) 0 leads to the critical thickness le for evaporation. The asymmetric state transforms into the symmetric one at l ) lc. If le ) lc, the adsorption isotherm has an adsorption hysteresis. If lc > le, an adsorption hysteresis can be observed. To determine the critical thickness difference ∆lc () lc - lc), ∆µs and ∆µa must be calculated as a function of l using the FHH plot of the adsorption isotherm, the pore width, and the literature values of γ and Vm. Both lc and le values are obtained from the top of the ∆µs versus l and ∆µa versus l curves. Figure 1. Adsorption model in a cylindrical mesopore.
Experimental Section
mesopores.20 The necessary outline of the Saam-Cole theory is described in the following. The chemical potential change of the multilayer adsorbed film of the thickness (l) on a flat surface is given by the Hill’s approximation21
∆µ ) U(l) ) -
R l3
(1)
where U(l) is the net attractive interaction energy between the adsorbed molecule and surface and R, which can be determined by Frenkel-Halsey-Hill (FHH) analysis of the adsorption isotherm, is an interaction parameter depending on the molecule and solid. Figure 1 shows the model state of adsorption in a cylindrical mesopore whose pore width is R. The symmetrical state in Figure 1A expresses multilayer adsorption, whereas Figure 1B shows the asymmetrical state due to a partial capillary condensation. The chemical potential change ∆µ of the adsorbed molecules in the cylindrical pore is generally given by the summation of the gas/solid surface (∆µgs) and the interfacial (∆µi) chemical potential terms
∆µ ) ∆µgs + ∆µi
(2)
Here, ∆µgs is expressed by eq 1, and ∆µi depends on the shape of the meniscus in the pore. For the transformation of multilayer adsorption to capillary condensation (symmetry-asymmetry transformation), ∆µi is given by -γVm/ a, where γ and Vm denote the surface tension and molar volume of the condensate, respectively (a ) R - l). Hence, the chemical potential change of the symmetrical state, ∆µs, is expressed by (20) Hanzawa, Y.; Kaneko, K. Adsorption, in press. (21) Hill, T. L. Adv. Catal. 1952, 4, 211.
We used mesoporous silica called FSM-16, which was supplied by Toyota Central Research Center. The detailed N2 adsorption isotherms were measured gravimetrically at 77 K with computeraided equipment.22 The samples were preevacuated at 383 K and 1 mPa for 2 h prior to the adsorption experiment. These adsorption data were used for determination of the necessary parameters just described.
Results and Discussion The adsorption isotherm of N2 on FSM-16 was the same as reported earlier.13 The R value was determined from the observed N2 adsorption isotherm. Figure 2 shows chemical potential diagrams of N2 adsorption isotherm of FSM-16 (w ) 3.4 nm) at 77 K. The upper and lower curves show ∆µs(l) and ∆µa(l), respectively. The solid line denotes the stable or metastable path, whereas the broken line indicates an unstable path. Therefore, adsorption proceeds along the allowed multilayer adsorption path from left to right and reaches a maximum at lc, transferring a downward condensation path. Desorption proceeds on the lower curve from right to left and comes at the maximum at lc, which is different from lc. The asymmetrical condensed state changes into the symmetrical state at le. Thus, we can determine lc, le, and ∆lc for different pore widths using the chemical potential diagram. We calculated lc, le, and ∆lc values for cylindrical pores with different pore widths from 3 to 5 nm. Figure 3 shows the of lc (∆lc) with the increase of w. The ∆lc increases with w; therefore, we can associate the ∆lc value with the disappearance of the adsorption hysteresis. Even the regular mesoporous silica has a slight pore size distribution inherent to the atomic structure. The pore walls of mesoporous silica are composed of oxygen atoms. The pore wall is not perfectly smooth and it can be approximated by the enveloping surface. The effective pore width depends on the interaction of the adsorbed (22) Kakei, K.; Ozeki, S.; Suzuki, T.; Kaneko, K. J. Chem. Soc., Faraday Trans. 1991, 86, 371.
Disappearance of Hysteresis of N2
Langmuir, Vol. 14, No. 11, 1998 3081
Figure 2. Chemical potential changes of symmetric and asymmetric models with the thickness of physisorbed layers. Key (b) ∆µs; (2) ∆µa. Figure 4. The structural reason for the intrinsic pore width distribution of silica for N2 molecules. Si atoms are not shown.
Figure 3. The relationship between ∆lc () lc - le) and w/2 () R) for N2 adsorption on mesoporous silica at 77 K.
molecule with the pore wall. Therefore, the atomic structure of the pore wall is essentially important. If we assume the atomic structure of crystalline silica,23 the center of a triangular site of three partially ionic oxygens (Si-O distance ) 0.162 nm), and a spherical N2 molecule (radius ) 0.180 nm), the mesopore width has the distribution of 0.09 nm arising from the top and the bottom of the enveloping surface, as shown in Figure 4. The radius (23) Kingery, W. D. Introduction to Ceramics; John Wiley & Sons: New York, 1967; Chapter 4.
of an ionic oxygen provides the distribution of 0.10 nm. The intrinsic pore size distribution (∆wt) leads to an ambiguity in the ∆lc value that determines the symmetryasymmetry transformation. If ∆lc > ∆wt, lc and le can be distinguished from each other, giving an adsorption hysteresis. On the contrary, if ∆lc < ∆wt, lc and le should be regarded as an identical value, giving no adsorption hysteresis. Thus, the pore width distribution inherent to the structure of the regular mesoporous silica should determine the adsorption hysteresis. Because the surface component is not pure oxygen, but hydroxyl, the ∆lc value should be greater by 0.01 nm. Therefore, the total ∆lc becomes 0.10 nm. The pore width corresponding to ∆lc ) 0.10 is w ) 3.6-3.8 nm; that is, the mesopore width of more than ∼4 nm is requisite for the adsorption hysteresis of N2/siliceous pore systems. This analytical method can be widely applied to the prediction of the critical pore width for disappearance of an adsorption hysteresis in adsorption isotherms of other adsorbate/adsorbent systems. Acknowledgment. K.K. is grateful to Dr. Slash for a fruitful discussion. The FSM samples were given by Drs. S. Inagaki and Y. Fukushima. This work was funded by the Grant in-Aid for Scientific Research on Priority Areas No. 288 “Carbon Alloys” from the Japanese Government. LA971256U
