Langmuir 2004, 20, 4503-4506
4503
Nature of Adsorption and Desorption Branches in Cylindrical Pores Kunimitsu Morishige* and Yuka Nakamura Department of Chemistry, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan Received November 12, 2003. In Final Form: March 22, 2004 To examine the nature of the adsorption and desorption branches in hysteretic adsorption isotherms of gases on mesoporous materials, we measured the temperature dependence of the adsorption and desorption isotherms of argon, oxygen, and carbon dioxide onto MCM-41 with a pore diameter of 4.4 nm. The results clearly show that in the open-ended cylindrical pores of MCM-41, capillary condensation rather than evaporation takes place near a thermodynamical equilibrium transition, as opposed to the general statement that capillary evaporation can occur via a meniscus formed at the pore mouth, and, thus, takes place at equilibrium.
I. Introduction Capillary condensation of gases within mesoporous materials is a shifted gas-liquid-phase transition resulting from the confinement of the fluid. The pressure at which capillary condensation (adsorption) takes place is often larger than that of capillary evaporation (desorption).1 This hysteresis effect depends strongly on pore morphology and temperature2 and would be closely concerned with the mechanisms of capillary condensation and evaporation. The adsorption-desorption hysteresis is one of the long-standing problems in the field of surface science. For unconnected cylindrical pores, it has become clear that the hysteresis results from the metastability of a confined phase3,4 and a scaling relation holds between the ratio of molecular size to pore size and the temperature at which the hysteresis disappears (hysteresis temperature, Th).5-7 The critical temperature of vapor-liquid equilibrium in pores (pore critical temperature, Tcp) is different from Th.4,6,7 Most of the theoretical considerations3,4,8-12 strongly suggest that capillary evaporation can occur via a meniscus formed at the pore mouth and, thus, takes place at a thermodynamical equilibrium transition, although in principle metastability is thermodynamically feasible on either branch. Cohan13 first suggested this model. The view that experimental hys(1) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic: New York, 1982. (2) Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; SliwinskaBartkowiak, M. Rep. Prog. Phys. 1999, 62, 1573. (3) Evans, R.; Marconi, V. M. B.; Tarazona, P. J. Chem. Soc., Faraday Trans. 2 1986, 82, 1763. (4) Ravikovitch, P. I.; Domhnail, S. C. O.; Neimark, A. V.; Schuth, F.; Unger, K. K. Langmuir 1995, 11, 4765. (5) Morishige, K.; Fujii, H.; Uga, M.; Kinukawa, D. Langmuir 1997, 13, 3494. (6) Morishige, K.; Shikimi, M. J. Chem. Phys. 1998, 108, 7821. (7) Morishige, K.; Ito, M. J. Chem. Phys. 2002, 117, 8036. (8) Heffelfinger, G. S.; van Swol, F.; Gubbins, K. E. J. Chem. Phys. 1988, 89, 5202. (9) Marini Bettolo Marconi, U.; van Swol, F. Phys. Rev. A 1989, 39, 4109. (10) Papadopoulou, A.; van Swol, F.; Marini Bettolo Marconi, U. J. Chem. Phys. 1992, 97, 6942. (11) Neimark, A. V.; Ravikovitch, P. I.; Vishnyakov, A. Phys. Rev. E 2000, 62, R1493. (12) Vishnyakov, A.; Neimark, A. V. J. Phys. Chem. B 2001, 105, 7009. (13) Cohan, L. H. J. Am. Chem. Soc. 1938, 60, 433.
teresis in cylindrical pores occurs mainly on the adsorption branch, however, is not based on any direct experimental evidence. In previous works,7,14 we have shown that the nature of the adsorption and desorption branches can be examined by plotting the condensation/evaporation pressure in a form of T ln(P/P0) against temperature over a wide temperature range including both regions of irreversible and reversible isotherms. The principle of this method relies on the simple idea that the equilibrium phasetransition pressures in the hysteretic isotherms would be obtained by the extrapolation of the plot for reversible capillary condensation to lower temperatures. The method was successfully applied to indicate that for SBA-16 with well-defined ink-bottle pores capillary condensation in the hysteretic isotherms takes place near the equilibrium, whereas capillary evaporation from large cavities is delayed.14 On the other hand, the results for the cylindrical pores of MCM-41 and SBA-15 were not clear, though they strongly suggested that irreversible capillary condensation rather than evaporation took place near the equilibrium similarly to the ink-bottle pores.7 The previous results for cylindrical pores were obtained for nitrogen adsorption on one kind of MCM-41 and four kinds of SBA-15. The pore wall of SBA-15 is more corrugated than that of MCM41,15 and, thus, the effect of constrictions in channels cannot be completely ruled out for SBA-15. In addition, the temperature region in which reversible capillary condensation takes place was narrower for SBA-15 than for MCM-41, leading to less reliable justification of this method for SBA-15. The purpose of the present study is to examine the nature of the adsorption and desorption branches in cylindrical pores by measuring the temperature dependence of the adsorption and desorption isotherms of argon, oxygen, and carbon dioxide onto MCM41 with well-defined cylindrical pores. II. Experiment Sample preparation and characterization have been given elsewhere.5,7 The BET surface area and total pore volume are 865 m2/g and 0.896 mL/g, respectvely. The diameter of the (14) Morishige, K.; Tateishi, N.; Fukuma, S. J. Phys. Chem. B 2003, 107, 5177. (15) Imperor-Clerc, M.; Davidson, P.; Davidson, A. J. Am. Chem. Soc. 2000, 122, 11925.
10.1021/la030414g CCC: $27.50 © 2004 American Chemical Society Published on Web 05/01/2004
4504
Langmuir, Vol. 20, No. 11, 2004
Figure 1. Temperature dependence of the adsorptiondesorption isotherm of argon onto MCM-41.
Morishige and Nakamura
Figure 3. Temperature dependence of the adsorptiondesorption isotherm of carbon dioxide onto MCM-41.
Figure 2. Temperature dependence of the adsorptiondesorption isotherm of oxygen onto MCM-41. cylindrical pores was estimated to be 4.4 nm from a comparison of the experimental capillary condensation pressure of N2 at 77 K with the equilibrium transition pressure for the cylindrical pores of silica calculated as a result of nonlocal density functional theory (NLDFT).16 Adsorption isotherms were measured volumetrically on a homemade semiautomated instrument equipped with a Baratron capacitance manometer (model 690A) with a full scale of 25 000 Torr. The experimental apparatus and procedures have also been described elsewhere.7 The calculation of adsorption at higher pressures took the nonideality of gas into consideration on the basis of a Benedict-Webb-Rubin (BWR) equation (CO2) or a modified BWR equation (Ar and O2).
III. Results The temperature dependence of the experimental capillary condensation/evaporation pressure over a very wide temperature range including both regions of the irreversible and reversible isotherms can give direct evidence as to the nature of the adsorption and desorption branches. Figures 1-3 show the adsorption-desorption isotherms of Ar, O2, and CO2 on MCM-41, respectively. At lower temperatures, all the isotherms exhibited hysteresis loops of type H1 in the IUPAC classification,17 typical of cylindrical pores. When the temperature was increased, the hysteresis loop always shrank and eventually disappeared at Th, well below the corresponding bulk critical temperature (Tc). Figure 4 shows the plots of the capillary condensation and evaporation pressures against temperature for these three gases on MCM-41. Here, the (16) Neimark, A. V.; Ravikovitch, P. I. Microporous Mesoporous Mater. 2001, 44, 697. (17) Sing, K. S. W.; Everett, D. H.; Haul, R. A.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603.
Figure 4. Temperature dependence of the capillary condensation and evaporation pressures of argon, oxygen, and carbon dioxide onto MCM-41. Open and closed circles denote capillary condensation and evaporation pressures, respectively.
condensation and evaporation pressures were determined at the midpoint of the adsorption and desorption branches, respectively, and P0 is the saturated vapor pressure of the bulk liquid. At lower temperatures, T ln(P/P0) is the difference of the chemical potential with respect to the bulk liquid. This figure includes the data of Th5 and Tcp.
Adsorption and Desorption Branches in Pores
Langmuir, Vol. 20, No. 11, 2004 4505
Tcp was determined from the inflection point in a plot of [∂(P/P0)/∂V]T estimated at the midpoint of the adsorption step against temperature. As Figure 4 shows, all the plots of T ln(P/P0) versus T for capillary condensation form an almost linear relationship over a wide temperature range spanning Th, whereas the same plots for capillary evaporation always break at Th. Therefore, it is evident that below Th capillary condensation rather than capillary evaporation takes place near the equilibrium. IV. Discussion There are many discussions3-13,18-28 on the origin of the adsorption hysteresis and the nature of the adsorption and desorption branches in cylindrical pores. From simulations about the effects of pore ends on the shape of hysteresis. Papadopoulou et al.10 have shown that in open-ended cylindrical pores a metastable liquidlike state would not be observed on desorption because, as the vapor pressure decreases, evaporation occurs near the equilibrium via formation of the meniscus at the pore ends. As far as we know, however, this view that in open-ended cylindrical pores capillary evaporation occurs at the equilibrium transition does not rely on any direct experimental evidence. Very recently, Neimark and co-workers11,12 have also reported that in the cylindrical pores of MCM-41 and SBA-15 desorption takes place at the equilibrium. Their conclusion is based on the arbitrary assignment of the NLDFT equilibrium transition to the desorption branch of the hysteresis loop of an experimental isotherm and the NLDFT metastable adsorption branch to the experimental adsorption branch. Kruk and Jaroniec29 have examined the relation between the pore size and capillary condensation/evaporation pressure of N2 and Ar in MCM-41 and SBA-15 and questioned the assignment of the experimental capillary evaporation to the equilibrium transition. The present results clearly indicate that capillary condensation rather than capillary evaporation takes place near the equilibrium, as opposed to many of the theoretical considerations. We now reexamine the temperature dependence of the capillary condensation and evaporation pressures of nitrogen in the cylindrical pores of MCM-41 and SBA-15 reported previously.7 Figure 5 reproduces the plots of T ln(P/P0) against temperature for one kind of MCM-41 and three kinds of SBA-15 with different pore sizes. The pore size of each sample was estimated from a comparison of the experimental capillary condensation pressure of N2 at 77 K with the NLDFT equilibrium pressures.16 In our previous paper,7 the SBA-15 samples with pore radii of 4.7 and 18 nm were incorrectly reported to have pore radii of 3.9 and 11 nm, because we misunderstood that in these samples capillary evaporation took place near the equilibrium. Only the data points below Tcp are shown in this (18) Derjaguin, B. V. Acta Physicochim. URSS 1940, 12, 181. (19) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1967, 9, 8. (20) Everett, D. H.; Haynes, J. H. J. Colloid Interface Sci. 1972, 38, 125. (21) Saam, W. F.; Cole, M. W. Phys. Rev. B 1975, 11, 1086. (22) Celestini, F. Phys. Lett. A 1997, 228, 84. (23) Sonwane, C. G.; Bhatia, S. K. Chem. Eng. Sci. 1998, 53, 3143. (24) Inoue, S.; Hanzawa, Y.; Kaneko, K. Langmuir 1998, 14, 3079. (25) Pellenq, R. J.-M.; Denoyel, R. P. O. In Fundamentals of Adsorption 7; Kaneko, K., Kanoh, H., Hanzawa, Y., Eds.; IK International: Chiba, 2002; p 352. (26) Schreiber, A.; Reinhardt, S.; Findenegg, G. H. In Studies in Surface Science and Catalysis 144; Rodriguez-Renzo, F., McEnancy, B., Rouquerol, J., Unger, K., Eds.; Elsevier: New York, 2002; p 177. (27) Gelb, L. D. Mol. Phys. 2002, 100, 2049. (28) Kornev, K. G.; Shingareva, I. K.; Neimark, A. V. Adv. Colloid Interface Sci. 2002, 96, 143. (29) Kruk, M.; Jaroniec, M. J. Phys. Chem. B 2002, 106, 4732.
Figure 5. Temperature dependence of the capillary condensation and evaporation pressures of nitrogen in the cylindrical pores of MCM-41 and SBA-15. Open and closed symbols denote capillary condensation and evaporation pressures, respectively.
figure, because above Tcp capillary condensation does not take place. The plot for capillary condensation always connects smoothly into that for reversible capillary condensation measured above Th, and the slope for capillary condensation decreases progressively with increasing pore size. The regular change of the slope with pore size is natural, although at present we have no intuitive explanations for it.30,31 On the other hand, the same plot for capillary evaporation does not connect smoothly into that for reversible condensation above Th. Therefore, the temperature dependence of capillary condensation and evaporation pressures of nitrogen for the cylindrical pores of different sizes give further support to the view that capillary condensation in the hysteretic isotherms takes place near the equilibrium transition, whereas capillary evaporation from the cylindrical pores is delayed. The present results indicate that in the open-ended cylindrical pores of MCM-41 and SBA-15 capillary condensation rather than capillary evaporation takes place near the equilibrium. This, however, does not necessarily deny the general statement that evaporation occurs by the receding of the meniscus formed at the pore mouth. Very recently, Gelb27 has suggested from a series of simulations of adsorption and desorption of xenon in cylindrical pores of a silica-like material that the chemical potential at which desorption occurs in the open-ended pore is mediated by the structure of the pore mouth and its interaction with the liquid-vapor meniscus. Capillary condensation is a first-order phase transition between a liquid filled in a pore and the vapor coexisting with the liquid film adsorbed on the pore wall. In principle, the experimental capillary condensation and evaporation pressures correspond to some pressure points between the equilibrium transition and spinodal capillary condensation pressures and the equilibrium transition and spinodal capillary evaporation pressures, respectively. When there is no adsorption-desorption hysteresis, the equilibrium transition corresponds to both adsorption and desorption branches of experimental isotherms. In the hysteretic isotherms, the position of the adsorption/ desorption branch is controlled by the height of the energy barrier between the full liquid pore and the vapor coexisting with the liquid film.12,22 The barrier height depends strongly on the mechanisms of the phase (30) Gross, S.; Findenegg, G. H. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1726. (31) Schreiber, A.; Bock, H.; Schoen, M.; Findenegg, G. H. Mol. Phys. 2002, 100, 2097.
4506
Langmuir, Vol. 20, No. 11, 2004
change.20,28 In a spherical cavity, a spherical meniscus is always held during the phase change, and, thus, we were able to estimate the barrier height as a function of vapor pressure and temperature for a fixed pore size.32 On the other hand, in the case of a cylindrical pore, the mechanisms of the phase change and the effect of the pore mouths on the chemical potential of the confined phase are not certain. Further studies by means of other techniques such as small-angle scattering are needed to (32) Morishige, K.; Tateishi, N. J. Chem. Phys. 2003, 119, 2301.
Morishige and Nakamura
elucidate the processes of capillary condensation and evaporation in cylindrical pores. In a very recent report,33 Qiao et al. have obtained the same conclusion by comparing the equilibrium transition pressure calculated on the basis of the Broekhoff and de Boer treatment19 with the experimental adsorption and desorption branches of nitrogen on MCM-41 at 77 K. LA030414G (33) Qiao, S. Z.; Bhatia, S. K.; Zhao, X. S. Microporous Mesoporous Mater. 2003, 65, 287.
