Nature of Adsorption Hysteresis in Cylindrical Pores: Effect of Pore

Sep 15, 2016 - Rémy Guillet-Nicolas , François Bérubé , Matthias Thommes , Michael T. Janicke , and Freddy Kleitz. The Journal of Physical Chemistry C...
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Nature of Adsorption Hysteresis in Cylindrical Pores: Effect of Pore Corrugation Kunimitsu Morishige* Department of Chemistry, Okayama University of Science, 1-1 Ridai-cho, Kita-ku, Okayama 700-0005, Japan ABSTRACT: To examine the effect of pore corrugation on the nature of adsorption and desorption branches due to capillary condensation in cylindrical pores, we measured the adsorption subloops and temperature dependence of the adsorption−desorption isotherms for oxygen on ordered mesoporous silicas COK-11 and MCM-41. Although the two samples give very sharp steps due to capillary condensation in the isotherms, the pores of COK-11 are corrugated, whereas the amplitude of the pore corrugation in MCM-41 synthesized with the pH adjustment is negligibly small. The pore corrugation affects significantly the nature of adsorption hysteresis. The temperature dependence of capillary condensation/evaporation pressure of oxygen on the MCM-41 synthesized very carefully is perfectly consistent with the theoretical prediction for a pore of cylindrical shape open at both ends. On the other hand, the hysteresis temperature, above which the adsorption hysteresis disappears, is not appreciably affected by the pore corrugation.

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INTRODUCTION When mesoporous materials are exposed to a gas at a subcritical temperature, capillary condensation of the gas inside the mesopores takes place at a pressure less than the saturation pressure of the bulk liquid (P0) depending on the pore size and shape. It is very often observed that the condensed liquid can only evaporate when the pressure of the gas surrounding the materials is decreased to below that of capillary condensation. The nature of hysteresis in pressure between capillary condensation and evaporation may depend on the morphology and topology of the mesopores and has continued to attract much attention in surface science for many years.1−6 For a pore of cylindrical shape open at both ends, a series of theoretical and simulation studies5,7−16 has clearly indicated that capillary condensation takes place through a cylindrical meniscus of the adsorbed film formed inside the cylindrical pore at a metastable state, while capillary evaporation takes place by a mechanism via a hemispherical meniscus receding from the pore ends close to an equilibrium transition. Experimental verification of such a prediction concerning the adsorption hysteresis, however, is by no means easy because the equilibrium condensation pressure in the hysteresis region in experiments is very difficult to be determined. In addition, direct observation of the meniscus associated with capillary condensation/evaporation is confronted with great difficulty in the implementation even with a leading-edge technique.17 Very recently, in situ X-ray diffraction measurements have been successfully used to verify the growth process (a cylindrical meniscus) of the adsorbed film inside cylindrical pores before onset of capillary condensation with increasing pressure.18−20 In our previous study,21 we tried to verify the theoretical prediction in a thermodynamic way. Ordered mesoporous silicas MCM-4122 and SBA-1523 possess almost cylindrical © 2016 American Chemical Society

mesopores of uniform size arranged parallel in a honeycombtype lattice and thus can be regarded as model adsorbents of cylindrical pores. The adsorption isotherms of simple gases on these materials at low temperatures show hysteresis loops of type H1 according to the 1985 IUPAC classification.24 The hysteresis loop shrinks in width with increasing temperature and eventually disappears at the hysteresis temperature (Th).21 Above Th, the isotherm is reversible, and thus, the capillary condensation pressure represents an equilibrium-phase-transition pressure. Therefore, the condensation and evaporation pressures were plotted in the form of T ln(P/P0) as a function of temperature over a wide temperature range including Th. For both types of the ordered mesoporous silicas, however, the plots for capillary condensation always connected smoothly into the equilibrium transition range at higher temperatures, while the plots for evaporation had a kink at Th, being in disagreement with the theoretical consideration.21 The present method does not require a comparison between experimental and theoretical isotherms for the same pore size,25−28 in order to examine the nature of the adsorption hysteresis. Since the pore size of the experimental isotherm depends on the method used and the pore model assumed,20,28,29 the comparison cannot avoid a problem due to ambiguity of the pore size for the experimental isotherm. In addition, the pore model used in the theoretical isotherm is only an approximation to the pores of the corresponding material. It is now known that SBA-15 synthesized from polymer templates in usual ways possesses a variety of pore imperfections such as pore connections, constrictions, and Received: August 1, 2016 Revised: September 14, 2016 Published: September 15, 2016 22508

DOI: 10.1021/acs.jpcc.6b07764 J. Phys. Chem. C 2016, 120, 22508−22514

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The Journal of Physical Chemistry C undulations.30−33 In particular, the pore constrictions and undulations may strongly affect the nature of adsorption and desorption branches.32−38 On the other hand, it is generally believed that the amplitude of the pore imperfections for MCM-41, which is synthesized from surfactants of low molecular weight, is less than for SBA-15.2,39 The situations in MCM-41 are still unclear. The amplitude of the pore imperfections for SBA-15 can be significantly reduced by the proper selection of the synthesis conditions.33 Since the pore size of SBA-15 thus synthesized is relatively large, however, the temperature range where the equilibrium-transition pressure can be observed is narrow. This leads to less reliability for the extrapolation of the equilibriumtransition pressures obtained at high temperatures to lower temperatures. As the pore size of MCM-41 is smaller than SBA15 it is highly desirable to synthesize MCM-41 and related material almost free of pore imperfections. In this respect, COK-11 synthesized recently is promising.40 It has a porous structure similar to MCM-41 and yet a pore size distribution narrower than MCM-41. On the other hand, the quality of MCM-41 can be improved by maintaining a constant pH during hydrothermal synthesis.41 Both types of silicas give sharp steps due to capillary condensation in the adsorption isotherms of nitrogen at 77 K, although the hysteresis is not observed because of the relatively small mesopores. Liquid oxygen has a molar volume smaller than liquid nitrogen, and the triple point of oxygen is exceedingly lower than that of nitrogen. These properties operate in favor of oxygen as an adsorbate for characterization of the porous structures of these silicas as well as measurements of the adsorption−desorption isotherms in a wide temperature range. The purpose of the present study is to examine the relationship between the pore imperfections and the nature of the adsorption/desorption branch by measuring adsorption/ desorption subloops at 70 K and the temperature dependence of hysteresis loops in a wide temperature range for oxygen on COK-11 and MCM-41 in order to give experimental verification for the nature of adsorption hysteresis obtained on the basis of theory and simulations.

homemade semiautomated instrument equipped with a closed cycle refrigerator. Measurements of subloops consist of performing adsorption/desorption cycles on adsorption and desorption branches in the same pressure range. The experimental apparatus and procedure have been described in detail elsewhere.33,43

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RESULTS Figure 1 presents the adsorption−desorption isotherms of nitrogen on COK-11 and MCM-41 measured at 77 K. Both

Figure 1. Adsorption−desorption isotherms of nitrogen at 77 K on COK-11 (open red circle, closed red circle) and MCM-41 (open blue box, closed blue box). Open and closed symbols designate adsorption and desorption points, respectively.

isotherms are almost reversible and exhibit sharp steps due to capillary condensation at P/P0 slightly below 0.4. The adsorption step of COK-11 is somewhat sharper than for MCM-41, suggesting that the pore size distribution of COK-11 is slightly narrower than for MCM-41. This is in good agreement with the previous results.40 The independent domain theory developed by Everett44 and subsequently other researchers45−47 indicates that two subloops taken in the same range of relative pressure on adsorption and desorption branches will always be congruent when the pore system behaves as an assembly of independent porous domains. For a powder of perfect cylinders that has a distribution of diameters, an analytical relationship between the condensation and the evaporation pressures in individual pores is held. In this case, the pores empty in the exactly reverse order of that in which they fill, that is, the plots of the evaporation pressures versus the condensation pressures in individual pores are linear. As a result, the scanning curve will be a straight line across to a main hysteresis loop.45,46 If the pore geometry is more complicated and individual pores are still independent from each other, however, an analytical relationship between the condensation and the evaporation pressures is not necessary, and other distributions between the condensation and the evaporation pressures can be considered. It is well known that capillary condensation and evaporation pressures of a fluid in pores are controlled not only by the pore size but also by the pore geometry. If capillary condensation took place in a cylindrical pore of one particular length and in a pore of different length or different geometry at the same pressure, capillary evaporation from the two different pores would occur at different pressures, because the relationship between the condensation and the evaporation pressures depends on the pore length48 and pore geometry.49 Woosters and Hallock45

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EXPERIMENTAL SECTION Materials and Characterization. COK-11 was synthesized according to the procedure of Verlooy et al.40 The washed and then dried product was calcined at 573 K (heating rate 0.5 K/min) for 1 h in air. MCM-41 was synthesized in a manner similar to that reported in our previous study,42 except for the use of the pH adjustment.41 In brief, 2.4 g of stearyltrimethylammonium chloride was mixed with 3.0 g of sodium silicate, 0.7 g of pyrogenic silica, and 50.0 g of water with stirring. After receiving ultrasonic agitation for 1 h at room temperature, the mixture was heated at 373 K for 24 h. Then it was cooled to room temperature, and the pH of the mixture was adjusted to 10 with acetic acid. The mixture after pH adjustment was heated again at 373 K for 48 h. The procedure of pH adjustment and subsequent heating was repeated once more. The washed and dried product was calcined at 813 K (heating rate 1 K/min) for 8 h in air. Adsorption isotherms of nitrogen at 77 K were measured volumetrically on a BELSORP-mini II. Measurement of Adsorption Hysteresis and Subloops. The adsorption isotherms and subloops of oxygen at 70 K as well as the temperature dependence of the adsorption isotherm of oxygen were measured volumetrically on a 22509

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subloops strongly suggests that the pores are not necessarily perfect cylinders that have a distribution of diameters as commonly assumed in the independent domain theory.45 The plots of the capillary condensation and evaporation pressures as a function of temperature over a very wide temperature range including Th can give important information as to the nature of the adsorption hysteresis. Figure 4 presents a

have clearly shown that in this case the scanning subloops are not reversible anymore, and yet two subloops on adsorption and desorption branches taken in the same pressure range will always be congruent. In the present study, the term “corrugation” denotes a variation of the pore diameter along the pore axis. Coasne et al.46 in molecular simulations and Bruschi et al.38 in experiments have clearly shown that the pore corrugation results in noncongruence of the subloops. Figures 2 and 3 compare the two subloops that were measured in the same range of P/P0 for oxygen at 70 K on

Figure 4. Change of the adsorption−desorption isotherm of oxygen on COK-11 with temperature. Figure 2. Hysteresis loop and two subloops for oxygen at 70 K on COK-11. Dashed line represents the subloop on the adsorption branch that was corrected for the adsorbed film on the pore walls47 for comparison.

change of the adsorption−desorption isotherms for oxygen on COK-11 in a wide temperature range of 76−116 K. At lower temperatures, the isotherms showed H1 hysteresis loops according to the 1985 IUPAC classification.24 The hysteresis loop shrank in width with increasing temperature and eventually disappeared at Th of ∼100 K. Figure 5 shows the

Figure 3. Hysteresis loop and two subloops for oxygen at 70 K on MCM-41. Dashed line represents the subloop on the adsorption branch that was corrected for the adsorbed film on the pore walls47 for comparison.

Figure 5. Plots of the capillary condensation and evaporation pressures as a function of temperature for oxygen in the cylindrical pores of COK-11. Open and closed triangles designate capillary condensation and evaporation pressures, respectively. The explanation of the straight line is given in the text.

COK-11 and MCM-41, respectively, together with the adsorption−desorption isotherms. Here, the subloops taken on the adsorption branch were corrected for a difference in thickness of the adsorbed film on the pore walls between the two subloops.46,47 The two subloops for COK-11 are not congruent, while on the other hand, the two subloops for MCM-41 are almost congruent. This implies that on adsorption and desorption the cylindrical domains in COK-11 depend on each other and the pores consist of alternating wide and narrow sections.33,38,46 Despite the very narrow distribution of pore size, the pores of COK-11 are corrugated. On the other hand, it is very likely that the pores of MCM-41 consist of an assembly of independent porous domains, that is, the amplitude of corrugations in the cylindrical pores of MCM-41 synthesized very carefully is negligibly small. In addition, the shape of the

plots of the capillary condensation and evaporation pressures in the form of T ln(P/P0) as a function of temperature. Here, the condensation and evaporation pressures were determined at the midpoint of the adsorption and desorption branches, respectively. T ln(P/P0) is the difference of the chemical potential with respect to the bulk liquid. The straight line in the figure represents a fitting curve to the data points of capillary evaporation at temperatures below Th and the extrapolation of the linear relation to higher temperatures. It is apparent that the plots of T ln(P/P0) as a function of temperature for capillary evaporation do not connect smoothly into that for the 22510

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takes place at the metastable state, while capillary evaporation takes place at the equilibrium state. The same figure also includes the plots for capillary condensation/evaporation pressure that have previously been reported on MCM-41 synthesized in a similar manner without the pH adjustment.21 For both MCM-41 samples the condensation pressures in the reversible isotherms at high temperatures are almost identical, indicating that the pore sizes of the two MCM-41 samples are almost the same. The plots in the hysteresis region clearly indicate that neither condensation nor evaporation takes place at the equilibrium for the MCM-41 synthesized conventionally. This will be certainly associated with the presence of pore corrugation in MCM-41 synthesized in the conventional way. The slope of the plots in the equilibrium transition range for COK-11 is slightly different from that for MCM-41 of similar pore size. This suggests that the natures of the pore walls of COK-11 and MCM-41 differ, although at present we do not know the physical meaning of the slope for the plots in the form of T ln(P/P0) versus T. Indeed, COK-11 is synthesized based on a concept of zeolitization of the mesopore walls, different from MCM-41. Room-temperature, hydrothermal, and thermal stability of the COK-11 material is superior to MCM-41 materials.40 On the other hand, the slope of the plots in the equilibrium transition range for MCM-41 synthesized in the conventional way nearly coincides with that for MCM-41 synthesized with pH adjustment, because the natures of pore walls of the two MCM-41 samples are expected to be almost the same except for the different amplitude of pore corrugation. For both materials of MCM-41 synthesized in the conventional way and COK-11, the plots of T ln(P/P0) as a function of temperature for capillary evaporation have kinks at Th, indicating that evaporation in the hysteretic region does not occur at the equilibrium.

equilibrium transition range at higher temperatures. This is consistent with the results of our previous study21 that was carried out using MCM-41 and SBA-15 synthesized in conventional ways. However, the situation is altered on MCM-41 synthesized very carefully. Figure 6 presents a change of the adsorption−

Figure 6. Change of the adsorption−desorption isotherm of oxygen on MCM-41 with temperature.

desorption isotherms for oxygen on MCM-41 in a wide temperature range of 76−118 K. The hysteresis loop shrank with increasing temperature and eventually disappeared at Th of ∼100 K as well. Figure 7 shows the plots of the capillary

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DISCUSSION The present two samples, COK-11 and MCM-41, gave very sharp steps due to capillary condensation in the adsorption isotherms of oxygen. One usually imagines that the cylindrical pores of both samples are very uniform not only in diameter but also in size along the pore axis. However, a comparison of the two subloops taken in the same range of P/P0 on the adsorption and desorption branches clearly indicates that the variation in diameter along the pore axes for MCM-41 is indeed negligibly small, while on the other hand, the pores of COK-11 are corrugated. The steepness of the adsorption steps does not necessarily guarantee that the pore walls of the materials are smooth. This is consistent with the previous results on SBA1532,33 and nanoporous anodic aluminum oxide.38 The channels in MCM-41 synthesized with the pH adjustment are uniform, i.e., their variation along the channel axis is negligible, and thus, the pore size distribution in the MCM-41 is solely due to a distribution of the channel diameters. On the other hand, the pore size distribution in COK-11, namely, the slope of adsorption or desorption branch, is due to the combined effect of a distribution of the channel diameters and a variation of the channel diameter along the channel axis. For a powder of perfect cylinders that have a distribution of diameters, the pores empty in the exactly reverse order of that in which they fill. The resulting scanning curve will be a straight line across a main hysteresis loop.45 As Figure 3 shows, this is not the case for MCM-41 synthesized very carefully, suggesting that the pore geometry of MCM-41 is more complicated than

Figure 7. Plots of the capillary condensation and evaporation pressures as a function of temperature for oxygen in the cylindrical pores of MCM-41 synthesized with pH adjustment (open red circle, closed red circle). Triangles designate the data on MCM-41 reported previously.21 Open and closed symbols designate capillary condensation and evaporation pressures, respectively. The explanation of the straight line is given in the text.

condensation and evaporation pressures as a function of temperature. Similarly, the straight line in the figure represents a fitting curve to the data points of capillary evaporation in the irreversible isotherms at low temperatures and the extrapolation of the linear relation to higher temperatures. As opposed to the case of COK-11, the plots of T ln(P/P0) as a function of temperature for capillary evaporation connect smoothly into that for the equilibrium transition range at higher temperatures, whereas the plots for capillary condensation have a kink at Th. This is fully consistent with the behavior predicted theoretically for fluids in a cylindrical pore, that is, capillary condensation 22511

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anodic aluminum oxide, narrow sections of the pores play an important role for the appearance of capillary condensation and evaporation.38 MCM-41 and SBA-15 that are synthesized in conventional ways seem to possess the corrugated pores of an almost cylindrical shape. Although for cylindrical pores the nature of the experimental adsorption and desorption branches is altered by the pore corrugation, Th is not appreciably affected. Very recently, Wilms et al. suggested from Monte Carlo simulations that Th in cylindrical pores is the temperature above which an axially inhomogeneous multidomain state of liquidlike and vaporlike domains appears.51 In other words, Th is the temperature at which the disappearance and formation of a nanobubble in a liquid confined to the cylindrical pores begins to take place reversibly. The pore corrugation does not seem to affect appreciably the onset of such a multidomain state of alternating liguidlike and vaporlike domains. In our previous study52 we examined the hysteresis critical points for nitrogen in many kinds of mesoporous silicas with ordered networks of cagelike pores and cylindrical pores, which are defined as a threshold of temperature (Th) and pressure above which capillary condensation and evaporation takes place reversibly in a given size and shape of pores. They formed a common line in a temperature−pressure diagram irrespective of the pore morphology. This suggests that Th is the temperature at which the formation and disappearance of nanobubbles in the liquid confined to the pores begins to take place reversibly irrespective of the pore geometry.

has been assumed hitherto. It is well known that capillary condensation and evaporation pressures of a fluid in pores are controlled not only by the pore size but also by the pore geometry. If capillary condensation took place in a cylindrical pore of one particular length and in a pore of different length or different geometry at the same pressure, capillary evaporation from the two different pores would occur at different pressures, because the relationship between the condensation and the evaporation pressures depends on the pore length48 and pore geometry.49 This will lead to other distributions between the condensation and the evaporation pressures. In this case, the scanning subloops are not reversible anymore, and yet the two subloops on adsorption and desorption branches in the same pressure range will always be congruent.45 There will be a distribution of pore length48 and deviation49 in pore geometry from a perfect cylinder. Nevertheless, individual pores behave independently on capillary condensation and evaporation. The amplitude of pore constrictions and undulations in the sample will be negligibly small, and thus, the present MCM-41 sample can be virtually regarded as a model adsorbent in that the results obtained represent the properties expected for a single pore of almost cylindrical shape. For a pore of cylindrical shape open at both ends, the theory and simulations predict that capillary condensation takes place through the cylindrical meniscus at the metastable sate, while evaporation takes place by a mechanism via the hemispherical meniscus receding from the pore ends close to the equilibrium state.5,7−16 In contrast, the nature of the adsorption hysteresis on MCM-41 and SBA-15 having almost cylindrical pores is still controversial.21,25−28,32,43,47,50 The present study shows that for cylindrical pores the nature of the experimental adsorption and desorption branches is significantly affected by the pore corrugation. For MCM-41 that is synthesized very carefully and thus almost free of pore imperfections, the relationship between capillary condensation/evaporation pressure of oxygen and temperature is perfectly consistent with the theoretical prediction for a single pore of cylindrical shape open at both ends. To the best of our knowledge, the present system is the first experimental verification for the Foster−Cohan model7,8 of the adsorption hysteresis for a cylindrical pore, that is, it is clearly indicated that in the cylindrical pores of MCM-41 synthesized in a sophisticated manner capillary condensation of a fluid takes place at a pressure greater than the equilibrium transition pressure, i.e., at the metastable state, while capillary evaporation takes place close to the equilibrium state. COK-11 as well as MCM-41 that is synthesized in a conventional way possess cylindrical pores of varying diameter. For the corrugated pores, capillary condensation takes place at a certain pressure between the equilibrium transition and the spinodal capillary condensation pressures, while evaporation takes place at a certain pressure between the equilibrium transition and the spinodal capillary evaporation pressures. For MCM-41 and related materials that were synthesized in conventional ways, therefore, evaluation of pore size from the adsorption and desorption branches in the irreversible isotherms is inevitably inaccurate. Figure 7 shows that for the corrugated pores of MCM-41 both the pressures of capillary condensation and evaporation of oxygen in the irreversible isotherms are definitely lowered compared to those for the noncorrugated pores. This is in good agreement with the occurrence of advanced adsorption and single pore blocking in corrugated pores as assumed previously.34 Indeed, in the corrugated pores of nanoporous

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CONCLUSIONS For cylindrical pores, steepness of the adsorption step due to capillary condensation does not necessarily indicate the uniformity of the pore diameter along the pore axis. The pore corrugation affects significantly the nature of the adsorption hysteresis. The amplitude of corrugation in the cylindrical pores of MCM-41 can be diminished considerably with the pH adjustment. Capillary condensation of oxygen in the cylindrical pores with smooth walls takes place at the metastable state higher than the equilibrium-transition pressure, whereas capillary evaporation takes place close to the equilibrium state. This is in good agreement with the model of Foster−Cohan.7,8 On the other hand, for the corrugated pores, both the pressures of capillary condensation and evaporation of oxygen in the irreversible isotherms are definitely lowered compared to those for the noncorrugated pores. On the other hand, the hysteresis temperature (Th) above which the adsorption hysteresis disappears is insensitive to the pore corrugation.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +81-86- 256- 9494. Fax: +81-86- 256- 9757. E-mail: [email protected]. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS We thank Ms. M. Imai and Mr. K. Takahara for their technical assistance in the development of software for adsorption measurements and in the preparation of MCM-41 samples, respectively. 22512

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