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Capillary Condensation of Nitrogen in Ordered Mesoporous Silica with Bicontinuous Gyroid Structure Kunimitsu Morishige* and Noriko Tarui Department of Chemistry, Okayama UniVersity of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan ReceiVed: August 2, 2006; In Final Form: October 11, 2006
To know the accurate relationship between pore size and the pressure of capillary condensation or evaporation and also to elucidate the pore-connectivity effects on adsorption hysteresis and pore criticality for the ordered mesoporous silicas (MCM-48 and KIT-6) with bicontinuous gyroid structure, we carried out X-ray structural study of MCM-48 and KIT-6 and measurements of the adsorption-desorption isotherms of nitrogen in comparison with MCM-41 and SBA-15 with unconnected cylindrical pores. The results clearly show that the hydraulic diameter describes incorrectly the mean pore size of these materials expressing the strength of confinement under the assumption of cylindrical pores with no networking effects. In addition, the average pore diameter at the middle point of pore intersections still underestimates the strength of confinement compared to the unconnected cylindrical pores of MCM-41 and SBA-15. Despite a large difference in porous structure, the shape and thermal behavior of the adsorption hysteresis for KIT-6, as well as the sorption scanning behavior, were indistinguishable from those for SBA-15, indicating that interconnections among pores of almost the same size do not have a significant effect on the adsorption hysteresis and pore criticality.
I. Introduction To elucidate the behavior of a fluid in a restricted space and also to establish the fundamentals of pore size analysis by a gas adsorption method, capillary condensation of the fluid in mesoporous materials has been extensively investigated.1,2 This phenomenon is a shifted gas-liquid phase transition resulting from the confinement of the fluid. The pressure at which capillary condensation takes place is often larger than that of capillary evaporation. This hysteresis effect depends strongly on pore geometry and temperature and would be closely concerned with the mechanisms of capillary condensation and evaporation. Knowledge of an accurate relationship between the pore size and the pressure of the capillary condensation or evaporation for the pores of a simple geometry is very important because a pore size distribution (PSD) in porous materials can be obtained on the basis of this relationship. The effects of pore size and geometry on capillary condensation would be most effectively explored by using ordered mesoporous materials because of their well-defined porous structures. For unconnected cylindrical pores, it has become clear that the hysteresis results from the metastability of a confined phase3,4 and a scaling relationship holds between the ratio of molecular size to pore size and the temperature at which the hysteresis disappears (hysteresis temperature, Th).5 The critical temperature of vaporliquid equilibrium in pores (pore critical temperature, Tcp) is different from Th. Very recently, an accurate relationship between the pore size and the capillary condensation and evaporation pressure of nitrogen at 77 K for the cylindrical pores of the ordered mesoporous MCM-41 and SBA-15 silicas has been elaborated.6,7 SBA-15 generally possesses rough pore walls with micromesopores and narrow mesopores that coexist with a regular hexagonal framework of main channels.8,9 Nevertheless, the pore-networking effects for SBA-15 are negligibly small,5-7 because those interconnected pores of SBA-15 are * Address correspondence to this author.
filled with gases at a much lower pressure than the capillary condensation and evaporation pressures within the cylindrical mesopores.10 The structure of the ordered mesoporous MCM-4811-14and KIT-615-17 silicas with a cubic space-group symmetry of Ia3d consists of an amorphous wall following the periodic minimal surface of gyroid. The wall separates two interpenetrating and noninterconnecting channel systems with different chiralities and each forms a three-dimensional (3D) network of pores of almost cylindrical shape. The distance between pore intersections is comparable to the pore diameter. The strength of confinement in the pore channels varies periodically along the pore center, as opposed to the one-dimensional pores of MCM-41 and SBA15. The fluid located in the connecting part of MCM-48 and KIT-6 is less confined than molecules in the cylindrical part. For such a porous structure, Mayagoitia et al.18 have considered the possibility of strong vapor-liquid transitions of an assisted kind taking place during capillary condensation (network effect for adsorption). The possibility of a system-spanning (and therefore first-order) transition appears.19 On the other hand, in one-dimensional idealized pores (cylindrical geometry) only a remnant of a first-order phase transition is present, as it is known that systems infinite in only one dimension cannot exhibit firstorder transitions or critical points. In a previous work,20 we showed that interconnections among pores of MCM-48 would not have a significant effect on capillary condensation, in accord with other works.21-26 Ravikovitch and Neimark25 related topological characteristics of triply periodic minimal surfaces (TPMS) including gyroid to the pore structure parameters evaluated from adsorption measurements and concluded that the mean pore size of MCM-48 can be accurately described by the hydraulic diameter calculated from the capillary condensation region of nitrogen adsorption isotherms by the nonlocal density functional theory method. However, all these studies did not rely on the direct porous structures of the materials and assumed the cylindrical shape
10.1021/jp064946s CCC: $37.00 © 2007 American Chemical Society Published on Web 11/30/2006
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of pore channels with no network effects. In recent years, X-ray structural modeling has been developed to obtain the structural characteristics of the ordered mesoporous materials from a comparison between the experimental and calculated diffraction patterns.14,27 For the ordered mesoporous silicas with bicontinuous gyroid structure, the accurate pore size of the nearly cylindrical part and the hydraulic diameter can be obtained from the structural parameters. The purpose of the present study is to know an accurate relationship between the pore size and the pressure of capillary condensation and the evaporation of nitrogen at 77 K in the interconnected pores of MCM-48 and KIT-6 and to elucidate the connectivity effects on the adsorption hysteresis from measurements of the temperature dependence of the adsorption-desorption isotherm of nitrogen onto KIT-6, as well as primary desorption and adsorption scanning curves at 77 K, in comparison with SBA-15 with unconnected cylindrical pores. II. Experimental Section II.1. Materials. MCM-48 and MCM-41 were prepared by using trimethylstearylammonium chloride and bromide, respectively, as structure directing agents. Sample preparations have been given elsewhere.20,28 KIT-6 was prepared by using P123 triblock copolymer at an aging temperature of 373 K according to the procedure of Kleitz et al.15 The template was removed by extraction in an ethanol-HCl mixture, followed by calcinations at 823 K in a flow of air. The resulting material showed a well-resolved cubic Ia3d XRD pattern of a unit cell length 23.0 nm. SBA-15 was also prepared by using P123 triblock copolymer as a template.29 Preparation and characterization of SBA-15 have been given elsewhere.5 II.2. Measurements. Adsorption isotherms of nitrogen at 77 K were measured volumetrically on a BELSORP-mini II (Bell Japan Inc.). Temperature dependence of adsorption isotherm, as well as sorption scanning curves, was measured volumetrically on a homemade semiautomated instrument equipped with a Baratron capacitance manometer (model 690A) with a full scale of 25000 Torr. The experimental apparatus and procedure have also been described elsewhere.5 The calculation of adsorption at higher pressures took the nonideality of gas into consideration on the basis of a modified BWR equation. Smallangle X-ray diffraction patterns were obtained on a Rigaku NANO-Viewer, using Cu KR radiation.6 II.3. X-ray Data Analysis. X-ray diffraction (XRD) structural investigations were performed by using the continuous density function technique developed by Solovyov et al.14 In this approach, the average density distribution in the material is modeled by flexible analytical function F with adjustable parameters. The density distribution in MCM-48 and KIT-6 having bicontinuous gyroid structure was given by the following functions:11-14,16,17 F(t,δ) ) F(t)[1 + δ(cos 4πx cos 4πy + cos 4πy cos 4πz + cos 4πx cos 4πz)] (1) F(t) )
{
1 for L g |sin 2πx cos 2πy + sin 2πy cos 2πz + sin 2πz cos 2πx| 0 for L < |sin 2πx cos 2πy + sin 2πy cos 2πz + sin 2πz cos 2πx| (2)
where x, y, and z are the fractional coordinates, δ is a variable parameter, and L is a variable constant that determines the pore wall thickness. The multiplier after F(t) in eq 1 is maximal (MCM-48) or minimal (KIT-6) in Wyckoff position 16a of the Ia3d unit cell that corresponds to the centers of the lowest
Figure 1. Adsorption-desorption isotherms of nitrogen at 77 K on MCM-48 (circles) and KIT-6 (squares) in comparison with those on MCM-41 (triangles) and SBA-15 (diamonds). Desorption points are represented by closed symbols.
curvature segments of the pore wall. The silica density was higher in the regions of low wall curvature for MCM-48.14 On the other hand, complementary pores were found to form interconnections between the two main channel systems at the special flat point of the G-surface for KIT-6.16,17 III. Results and Discussion III.1. Relationship between the Pore Size and the Pressure of Capillary Condensation and Evaporation. Figure 1 shows the adsorption-desorption isotherms of nitrogen at liquidnitrogen temperature on MCM-48 and KIT-6, in comparison with those on MCM-41 and SBA-15 having unconnected cylindrical pores. Since Th is lowered with an decrease of pore size, MCM-48 and MCM-41 with smaller pore size showed no appreciable hysteresis, although a distinct step due to capillary condensation was observed. KIT-6 and SBA-15 showed clear hysteresis loops of type H1 in the IUPAC classification.30 Despite the use of similar surfactants, the pressure of the capillary condensation is lower for MCM-48 than for MCM41. On the other hand, the pressures of the condensation and evaporation on KIT-6 were nearly identical with those of the condensation and evaporation on SBA-15, respectively. The pressure of capillary condensation or evaporation was determined at the midpoint of the adsorption step. The pressures of the condensation and evaporation were almost identical for MCM-48 and MCM-41, indicating that the observed pressure represents an equilibrium transition point. In hysteretic isotherms such as the isotherms on KIT-6 and SBA-15, the experimental condensation and evaporation pressures correspond to some pressure points between the equilibrium transition and spinodal condensation pressures and the equilibrium transition and spinodal evaporation pressures, respectively. Figure 2 shows the powder X-ray diffraction patterns of MCM-48 and KIT-6 samples. All the XRD patterns can be indexed to the cubic Ia3d symmetry lattice. The lattice parameter of KIT-6 is significantly larger than that of MCM-48. Further structural information was obtained by X-ray structural modeling, using the continuous density function approach.14 The constant relating to the pore wall thickness (L), the cubic lattice parameter (a), the parameter relating to the density modulation at the special flat point (δ), and the root-mean-square displace-
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Figure 2. Comparison between the experimental and calculated XRD patterns for MCM-48 and KIT-6. The experimental profile is shown by triangles, and the calculated profile is shown by a solid line.
Figure 4. Relationship between the pore size and the pressure of capillary condensation and evaporation of nitrogen at 77 K for MCM48 and KIT-6 in comparison with that for MCM-41 and SBA-15.6 The results for MCM-48 and KIT-6 are shown by diamonds and squares, respectively, while those for MCM-41 and SBA-15 are shown by circles. Open and closed symbols denote capillary evaporation and condensation pressures, respectively.
are 2.2 and 0.6 nm, respectively. The average wall thickness of MCM-48 obtained in the present study is in good agreement with those reported previously by X-ray structural modeling,11,13 but smaller than those obtained by other methods.13,25,28 The following equation relates approximately the parameters of TPMS with a hydraulic pore diameter Dh in bicontinuous structure.25
a/ξ0 ) 〈h〉 + Dh/2
Figure 3. Section of model density distribution for KIT-6. Dotted lines denote the planes perpendicular to the Q230 rods at the middle point of each rod.
TABLE 1: Structural Parameters of the Calculated Forms of the Samples Studied sample
unit cell parameter a (Å)
L
δ
rms displacement u (Å)
MCM-48 KIT-6
90.8 230.4
0.270 0.407
0.025 -0.021
5.5 13.2
ment (u) were varied to obtain the best agreement between the experimental and calculated XRD profiles. Although Solovyov et al.14 have introduced a variable constant, t, that denotes the pore wall thickness for a calcined MCM-48 with empty pores, this constant t does not represent a real pore wall thickness. The real pore wall thickness is smaller than the value of t. As Figure 2 shows, the structure model provides reasonable fits between the experimental and calculated XRD peak positions and intensities for both samples. The final structure parameters obtained are listed in Table 1. It is well-known that the porous structure of the ordered mesoporous silica with bicontinuous gyroid structure can be approximated by the Q230 rod network.12,31 Each end of a rod is grouped with two others; the three rods of each group are coplanar, and are related by a 3-fold axis perpendicular to the plane. The length of each rod is a × 0.3288; 24 rods are contained in one unit cell. This rod network interwines with the gyroid surface. Figure 3 shows the (111) section of model density distribution calculated by using the refined constant L for KIT-6, which is coplanar to one group of the Q230 rods. At the middle point of each rod, the pore is elliptical: 9.2 × 8.7 nm for KIT-6 and 4.0 × 3.6 nm for MCM48. The average wall thicknesses 〈h〉 of KIT-6 and MCM-48
(3)
ξ0 is the dimensionless area per unit cell of TPMS: ξ0 ) 3.0919 for gyroid. Accordingly, the hydraulic pore diameters of KIT-6 and MCM-48 are evaluated to be 10.5 and 4.7 nm, respectively. In Figure 4, we compared the relationship between the pore size and the pressure of capillary condensation and evaporation of nitrogen at 77 K for MCM-48 and KIT-6 with those for MCM-41 and SBA-15 having unconnected cylindrical pores.6 Ravikovitch and Neimark25 have concluded that the mean pore size of MCM-48 can be accurately described by the hydraulic diameter calculated from the capillary condensation region of the nitrogen adsorption isotherm. In other words, the hydraulic diameter equals the mean pore size that was obtained assuming the cylindrical shape of pore channels in MCM-48. As Figure 4 shows, however, the plots of the capillary condensation and evaporation pressures against the hydraulic diameter deviate largely from the relationship between the pore size and the pressure of capillary condensation and evaporation of nitrogen for MCM-41 and SBA-15 having unconnected cylindrical pores. This clearly shows that the hydraulic diameter is not consistent with the mean pore size that is obtained assuming the cylindrical shape of pore channels in MCM-48 and KIT-6. It is evident that the hydraulic diameter describes incorrectly the mean pore size of these materials expressing the strength of confinement under the assumption of cylindrical pores with no networking effects. The average pore diameter (Dav), which was estimated from the elliptical shape of the channels at the middle point of the Q230 rods, still underestimates the strength of confinement compared to the unconnected cylindrical pores of MCM-41 and SBA-15. However, this is reasonable because in the unconnected cylindrical pores an adsorbate molecule experiences only the intermolecular potential due to the walls parallel to the pore axis, whereas in the highly interconnected cylindrical pores of MCM-48 and KIT-6 the molecule experiences extra potential due to the walls perpendicular to the pore axis. This extra
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Figure 6. Temperature dependence of the capillary condensation (adsorption) and evaporation (desorption) pressures of nitrogen onto KIT-6 in comparison with that onto SBA-15.5
Figure 5. Temperature dependence of the adsorption-desorption isotherm of nitrogen onto KIT-6.
potential comes from the fact that the distance between pore intersections is comparable to the average pore diameter for MCM-48 and KIT-6. In the present study, both the hydraulic diameter and the average pore diameter were determined solely based on the X-ray structural modeling. The presence of random complementary pores in the walls of ordered mesopores does not affect the XRD structural modeling results.6,7 In addition, for both samples of SBA-15 and KIT-6, the micropore volume was not detected by the t-plot method.1 III.2. Thermal Behavior of Hysteresis. Figure 5 shows the temperature dependence of the adsorption-desorption isotherm of nitrogen onto KIT-6 in the temperature range 79-122 K. At lower temperatures, the isotherms exhibited hysteresis loops of type H1 in the IUPAC classification. When the temperature was increased, the hysteresis loop shrank and eventually disappeared at ∼107 K, a hysteresis temperature (Th) of this system. The adsorption steps were still nearly vertical above Th. This indicates that Th is lower than a pore critical temperature (Tcp) at which a gas-liquid coexistence in pores vanishes. A theory3 due to a single idealized pore predicts that a jump in adsorption associated with capillary condensation should vanish at Tcp, although there are currently no reliable methods of determining Tcp. We conjecture that Tcp of the present system is ∼120 K because the slope of the adsorption step begins to decrease at around 120 K with increasing temperature. We measured also the temperature dependence of the isotherm of nitrogen onto SBA-15 in the temperature range 74-121 K. The results obtained were almost the same as those reported previously.5 Therefore, the isotherms are not shown. At lower temperatures, the isotherms exhibited hysteresis loops of type H1 similar to those for KIT-6. The thermal behaviors of the hysteresis loop for both materials were also similar: Th and Tcp for SBA-15 were estimated to be ∼107 and ∼120 K, respectively. Figure 6 shows the plots of the capillary condensation and evaporation pressures against temperature for KIT-6 in comparison with SBA-15. Here, 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. The plot for capillary condensation formed an almost linear relationship over a wide temperature range including Th, in accord with the results32 on MCM-41 and SBA-15 with unconnected cylindrical pores. The shape and thermal behavior of the adsorption hysteresis for KIT-6 were indistinguishable from those for SBA15, although the hysteresis loops were wider for SBA-15 than for KIT-6 just below Th. This is compatible with the results of Thommes et al.22 Each particle of KIT-6 contains two interpenetrating and noninterconnecting channel systems with different chiralities. Different pore sections of one channel system of the particle can communicate with each other even at relatively high fillings and thus a system-spanning transition involving fluid molecules in a large number of interconnected channels is possible. On the other hand, the unconnected cylindrical pores of SBA-15 cannot induce a system-spanning transition, that is, a first-order phase transition. In addition, it is sometimes argued2 that interconnections among pores may have a significant effect on the location of Tcp, because near pore connection points the correlation length can grow to lengths greater than the pore width in the direction different from the pore axis, as the Tcp is approached by raising the temperature. When the fluid in pores does not show a real critical behavior at the Tcp, however, the argument is irrelevant. The comparison of the results for KIT-6 with those for SBA-15 indicates that interconnections among pores of almost the same size do not have a significant effect on the adsorption hysteresis and pore criticality. Pore systems of SBA-15 and KIT-6 differ from each other in dimensionality, as well as the pore volume of one channel system in each particle. This suggests that the difference in a system size does not result in an appreciable change in the adsorption hysteresis. III.3. Sorption Scanning Behavior. To compare further the behavior of a fluid confined to the interconnected pores of KIT-6 with that confined to the unconnected pores of SBA-15, we measured the primary adsorption and desorption scanning curves of nitrogen onto KIT-6 and SBA-15 at 77 K. A simple analysis of the shape of the hysteresis loop does not provide reliable information about the topology of the porous material. Adsorption (desorption) scanning curves are obtained by reversing upon desorption (adsorption) the direction of change in the pressure. Figures 7 and 8 show the scanning curves of nitrogen on KIT-6 and SBA-15, respectively. The results for SBA-15 are similar to those reported previously.33,34 Both curves for KIT-6 and SBA-15 are similar. When the volume adsorbed in a reversal was decreased, the shape of the desorption and adsorption scanning curves remained almost unchanged.
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Figure 7. Primary adsorption (upper) and desorption (lower) scanning curves of nitrogen onto KIT-6 at 77 K.
Morishige and Tarui theory consists of presuming that pore domains constitute autonomous entities for which the filling with either liquid or vapor takes place in accordance with their particular x12 and x21 values, and irrespective of the state of their neighboring pore entities. Capillary condensation and evaporation in truly independent domain porous solids develops progressively according to a pore size distribution of the solid. Pore size distribution analysis by a gas adsorption method is usually based on this theory. The scanning curve for independent porous domains must meet the adsorption/desorption branch at a pressure different from the closure points of the hysteresis loop. In contrast, scanning curves for nonindependent systems must meet the hysteresis loop at its closure point,36 although the relationship of the sorption scanning curves with the adsorption and desorption mechanisms is still unclear.37 The scanning curves for SBA-15 observed were different from what was expected from the independent pores of cylindrical shape. The same results have been reported previously and accounted for by single pore-blocking33 or interaction between the pores.34 The scanning curves for KIT-6 with interconnected pores were similar to those for SBA-15 with unconnected cylindrical pores in shape, but the evolution of the scanning curves when the volume adsorbed in a reversal is decreased was different from that expected from the network of pore connections.38 This clearly indicates that the connectivity effects on the adsorption hysteresis are negligible. In the case of the interconnected channels of KIT-6, half the channels in a particle that are interconnected with each other may constitute a single domain. When the boundary scanning curves of both solids are compared, it is found that the adsorption and desorption branches of KIT-6 are steeper than those of SBA-15. Such a difference may come from the fact that the size distribution of pores in a particle of SBA-15 leads to a finite range of condensation and evaporation pressures, whereas the size distribution of channels in a particle of KIT-6 is not recognized in the condensation and evaporation processes. A system-spanning phase transition may actually take place in the interconnected pores of KIT-6. Acknowledgment. We express our sincere thanks to K. Hoshino of Rigaku Corporation for measurement of the smallangle X-ray diffraction patterns for the ordered mesoporous silicas. This research was supported by “High-Tech Research Center” Project for Private Universities: matching fund subsidy from MEXT (Ministry of Education, Culture, Sports, Science and Technology), 2006-2008. References and Notes
Figure 8. Primary adsorption (upper) and desorption (lower) scanning curves of nitrogen onto SBA-15 at 77 K.
In the independent domain theory of adsorption hysteresis, a “pore domain” is assumed as a region of porous space in which capillary condensation and evaporation occurs at well-defined vapor pressure values designated by the notations x12 and x21, respectively.35 Adsorption hysteresis arises by the fact that x12 g x21 for every one of these domains. The main idea of the
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