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On the Equilibrium of Helical Nanostructures with Ordered Mesopores Lingzhi Zhao, Pei Yuan, Nian Liu, Yifan Hu, Yang Zhang, Guangfeng Wei, Liang Zhou, Xufeng Zhou, Yunhua Wang, and Chengzhong Yu* Department of Chemistry and Shanghai Key Laboratory of Molecular Catalysis and InnoVatiVe Materials, Fudan UniVersity, Shanghai, 200433, P. R. China, and Department of Chemistry and Shanghai Key Laboratory of Molecular Catalysis and InnoVatiVe Materials, Fudan UniVersity, Han Dan Road, 220, Shanghai, 200433, P. R. China ReceiVed: July 18, 2009; ReVised Manuscript ReceiVed: NoVember 5, 2009
Helical conformation exists universally at different length scales. We present a new model to explain the energetics of a helical structure with ordered mesopores and successfully predict their equilibrium state. The formation of the helical structure, which is composed of twisted and hexagonally arrayed one-dimensional pore channels, should be understood at the macromorphology level through the competition between surface free energy reduction and torsion strain energy increase. Our model is established by first reverting a helical rod with experimentally defined parameters to a conjectured straight rod without intrinsic pore channel twisting, and then quantitatively calculating the variation of two competitive energies as a function of twist angle in the torsion process starting from the reverted straight rod. Through our model, a free energy curve is achieved, so that the equilibrium state and the helical structural parameters can be predicted, which are in good agreement with experimental results for helical rods synthesized by different surfactant templates. Moreover, our model can be successfully applied to explain the pitch-radius relationships in previous observations. Our achievement provides unique and fundamental understandings for the spontaneous mesoscopic helix formation, which are different from the microscopic helical structures such as DNA chains. Introduction The charming helical structures are omnipresent in nature and can be found at different length scales: from the helical doublestranded DNA macromolecules to the macroscopic trumpet shell, or even to the galactic nebula which also presents in a circinate form. Scientists from different fields have engaged in the investigation of the origin of helical structures. Generally, mechanisms on the formation of helical structures are related to the equilibrium of energy or forces. For the nanoscale helical structure such as DNA molecules, Snir et al. proposed an entropy driven model to explain the spontaneous formation of helical configuration and the equilibrium was established between the bending energy and entropy gain through the overlapping of excluded volume.1 In daily life, viscous fluid such as honey when poured from a sufficient height may form regular coiling filament at the macroscopic level, in which the counterpoise as well as the helical radius and coiling frequency is achieved between Coriolis force and viscous force of the fluid.2 Similar concepts were also applied to qualitatively explain the helical self-coiling of zinc oxide nanobelts through the minimization of surface area and elastic deformation.3,4 The hint is, therefore, although the helical structures observed at different length scales with versatile compositions have different origins, all of the models have one common feature: the formed helices are ultimately a consequence of the equilibrium of two energies or forces, and are thermodynamically dependent. It is obvious that, to understand the formation of helical structures, the specific energy and forces that should be applied in the theoretical modeling vary significantly, which must be inspected carefully depending on the unique helical structure under study. * To whom correspondence should be addressed. E-mail: czyu@ fudan.edu.cn.
Recently, ordered mesoporous silicas with helical architectures and chiral space have attracted much attention because of their potential applications.5-7 The synthesis of helical mesoporous silica materials has been reported using either chiral or achiral structure directing agents.8-16 However, the origin of such helical nanostructures with ordered mesopores gives rise to much controversy. A key problem is at which level the helical structure should be inspected. Helical nanostructured materials are cooperatively assembled by surfactant templates and siliceous species.17,18 Therefore, the chirality transferability from chiral surfactant molecules or inducing agents to the helical nanostructures has been proposed8,19 starting from the molecular level. In the case of achiral surfactant templated helical mesoporous materials, the staggered wadding of micelle packing20 caused by the tight intramolecular packing of longer alkyl chains21 and the entropy driven model1 were also introduced.22 Nevertheless, helical nanostructures generally have a rod-like morphology which are composed of a bundle of hexagonally arrayed thread-like composite micelles,23 and the removal of surfactants results in the helical rod-like macromorphology with ordered one-dimensional (1D) pore channels. It is noted that the helical curvature of one pore channel is dependent on its location: the curvature for the pore channel right in the middle of the rod is zero and then increases radially with distances apart from the center for the other pore channels. Such helical nanostructure characteristics cannot be well explained by previous mechanisms20,22,24 or mechanisms for other helical morphologies starting from molecules25 and single-stranded helix.9 More importantly, because the helical nanostructure is indeed a helical conformation (the rod-like morphology) composed of ordered mesopores, a mechanism should focus on the origin of the helical conformation itself, rather than the formation of cooperatively self-assembled nanostructure.
10.1021/jp906814b 2009 American Chemical Society Published on Web 11/23/2009
Helical Nanostructures with Ordered Mesopores Previously, we suggested an interfacial interaction mechanism to explain the formation of nanostructured helical morphology, the reduction in surface free energy being the driving force for the spontaneous helix formation.16 To date, however, all of the proposed mechanisms,8,20,22,24 including our own model,16 are indeed qualitative and cannot be used to predict the helical structural parameters, such as the experimentally observed pitch-radius linear relationship of helical rods.15,16 Therefore, it is still an open challenge to investigate the formation of helical structures with ordered mesopores from a thermodynamic concern and by means of equilibrium analysis,1,2 from which the origin of helical structures at the nanoscale can be better understood. Herein, for the first time, we present a new thermodynamic model to explain the energetics for the formation of helical nanostructures and successfully predict their equilibrium structures. The helical nanostructured silica rods studied in this work were prepared by using tetradecyltrimethylammonium bromide (C14TAB) and perfluorooctanoic acid (PFOA) as cotemplates. The formation of helical nanostructures can be modeled as a transformation process starting from a straight cylindrical rod composed of hexagonally arrayed straight 1D pore channels with equal length. By reverting an experimentally obtained helical rod to the conjectural straight rod without intrinsic pore channel twisting and then quantitatively calculating the surface free energy reduction and torsion strain energy increase as a function of the twist angle in the torsion process, the equilibrium state and the helical structural parameters can thus be predicted by our model, which are in good agreement with experimental observations in this study and previous report.16 Our success further demonstrates that the origin of helical nanostructures should be attributed to the competition between surface free energy reduction and torsion strain energy increase, which can be generally applied to understand the spontaneous formation of versatile helical structures at the nano- and macroscales.3,4,26 Experimental Section Synthesis. PFOA, cationic surfactant C14TAB, and cetyltrimethylammonium bromide (C16TAB) were purchased from Aldrich. Other chemicals were purchased from Shanghai Chemical Company. All chemicals were used without purification. Helical nanoporous silica rods were synthesized by using C14TAB together with PFOA as cotemplates under basic conditions. In a typical synthesis in the C14TAB templating system, 0.253 g of C14TAB was dissolved in 120 g of deionized water added with 2.80 g of 28% ammonia under stirring. The temperature of the solution was kept at 303 K, and then, 0.02 g of PFOA and 1.04 g of tetraethyl orthosilicate (TEOS) was added. After stirring for 24 h, the mixture was filtrated and dried at room temperature. The templates were removed by calcination at 823 K for 5 h in air. The synthesis details in the C16TAB templating system were described before.16 Characterization. The X-ray diffraction (XRD) patterns were recorded with a Bruker D4 powder X-ray diffractometer with Ni-filteredCuKRradiation(40kV,40mA).N2 adsorption-desorption isotherms were measured with a Tristar-3000 analyzer at 77 K. Transmission electron microscopy (TEM) images were obtained with a JEOL 2011 microscope operated at an acceleration voltage of 200 kV; the samples were prepared by dispersing the powder samples in ethanol, after which they were dispersed and dried on carbon film on a Cu grid.
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Figure 1. XRD pattern (a) and typical TEM image (b) of calcined silica sample synthesized using C14TAB and PFOA as cotemplates.
Results and Discussion The XRD pattern of calcined mesoporous silica synthesized by using C14TAB and PFOA as cotemplates is shown in Figure 1a. Three well-resolved diffraction peaks are observed at 2θ ) 2.6, 4.5, and 5.2° with a reciprocal d-spacing ratio of 1:3:2, which can be indexed to the (10), (11), and (20) reflections of a two-dimensional (2D) hexagonal mesostructure by combining the XRD pattern and TEM images (Figure 1b).8,27 The cell parameter is calculated to be 3.9 nm on the basis of the p6m symmetry. The scanning electron microscopy studies show that the silica materials prepared by using C14TAB and PFOA as cotemplates possess an exclusive rod-like morphology (Supporting Information, Figure S1). The TEM observation further confirms that these silica rods have helical pore channels. The periodically appearing fringes observed in a typical TEM image (marked by arrows shown in Figure 1b) correspond to the (10) planes, indicating that the hexagonally arrayed 1D pore channels are parallel to the long axis of the rod and twisted along the pore channel right in the middle of the rod, the latter being the only straight one with zero helical curvature among all pore channels in this helical rod.8,23 The pitch size, which is 6 times the spacing between two adjacent (10) fringes, is measured to be 464 nm. The nitrogen sorption isotherm and pore size distribution curve calculated from the adsorption branch using the BJH method is shown in Figure S2 of the Supporting Information. The pore size, pore volume, and surface area of helical silica rods are 2.0 nm, 0.54 cm3/g, and 913 m2/g, respectively. In our previous report, we synthesized helical mesoporous materials by using C16TAB as a template and proposed a surface free energy reduction model to interpret the spontaneous formation of the helical mesostructure.16 However, the previous qualitative model only focuses on the driving force for the formation of helical nanostructure by calculating the surface area reduction. It is not known at which point the helical conformation reaches the equilibrium. Thus, it is our goal to further provide a quantitative and thermodynamic model in this contribution to explain the energetics of helical nanostructures. As shown in Figure 2a, the formation of helical nanostructures can be modeled as a transformation process from a straight cylindrical rod to a twisted helical rod. The straight cylindrical rod is composed of hexagonally arrayed straight 1D pore channels with equal length, as shown in our previous simulation.16 Moreover, an experimentally observed helical rod with
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∆Es ) σ∆S
(4)
where σ and ∆S represent the surface tension of the silica/ solution interface and the surface area reduction during the transformation process, respectively. Now eq 3 can be rewritten as
∆F/G ) π3R4H/P2 - (σ/G)∆S
Figure 2. (a) Transformation from a straight cylindrical rod to a twisted helical rod as a function of the twist angle (R). (b) Geometrical parameters of a helical rod.
defined geometrical parameters (see Figure 2b), which are measured from TEM images, can be reverted to construct the corresponding conjectured straight rod.16 Therefore, it is possible to investigate the variation of the surface free energy reduction and the torsion energy increase as a function of the twist angle in the torsion process starting from the reverted straight rod (Figure 2a). The calculation of the torsion energy now becomes a key issue in order to quantitatively solve the thermodynamic puzzle for the formation of helical nanostructure. The helical nanostructured materials are cooperatively self-assembled by surfactants and siliceous species in solution, thus what we should consider is a helical structure with hexagonally arrayed threadlike composite micelles (before calcination). Theoretically, there are two possibilities to calculate the energy increase for a helical structure: one is to calculate the bending energy of each composite micelle and then sum up the bending energy of all composite micelles with different curvatures in one helical rod. However, this is very difficult in our approach. The other method does not concentrate on one individual micelle. Instead, the rodlike morphology, i.e., the hexagonally arrayed thread-like composite micelles as an integer, is investigated. This method is used in our subsequent modeling. During the transformation process, as shown in Figure 2a, the surface free energy (∆Es) decreases,16 while the torsion strain energy (∆Et) increases; thus, the total change in free energy (∆F) during the formation of a helical rod can be expressed by
∆F ) ∆Et - ∆Es
(1)
The torsion energy of the integral helical rod can be calculated by the following equation28 (see Supporting Information, Modeling and Calculations 1):
∆Et ) Gπ3R4H/P2
(2)
where G is the modulus of shear and R, H, and P are the radius, height, and pitch of the helical rod, respectively (see Figure 2b). It is difficult to measure G of the rod; thus, ∆Et cannot be directly calculated. However, G can be regarded as a characteristic parameter of a given material and thus a constant; therefore, ∆F/G can be calculated to reflect the change in free energy:
∆F/G ) ∆Et /G - ∆Es /G To calculate ∆Es, we have
(3)
(5)
∆S can also be calculated by R, H, and h (see the Supporting Information and more details in ref 16), where h is the lateral height of the rod (Figure 2b). Thus, ∆F/G can be expressed simply with the geometrical parameters and σ/G value. In order to quantitatively investigate how ∆F/G changes during the torsion process, ∆F/G can be calculated as a function of the twist angle R (see the Supporting Information, Figure S3), where R is an independent variable (see the Supporting Information, Modeling and Calculations 3). However, because the σ/G value cannot be directly obtained, a reasonable mathematical treatment should be carried out to achieve such a value. This can be done by the following three steps. First, for one practical helical rod synthesized by using C14TAB as a template (see the Experimental Section for synthesis), we measure the geometrical parameters of a helical rod from the TEM images and then revert the helical rod to an ideal straight cylindrical rod (see the Supporting Information, Modeling and Calculations 2). The twist angle from the reconstructed straight rod to the practical helical rod is defined as R0 (R0 ) 4.35). Second, starting from this reconstructed straight rod, the geometrical parameters for a theoretically converted helical rod as a function of R are calculated. In the third step, the σ/G values are subjectively adjusted in a certain range to obtain their corresponding ∆F/G ∼ R curves. As can be seen from Figure 3a, each curve with a specific σ/G has an R value which minimizes ∆F/G to the lowest point (denoted Rmin), and Rmin increases with σ/G. From a thermodynamic concern, Rmin is the right point where the transformation process from a straight rod to a helical rod reaches equilibrium and R0 ) Rmin should be fulfilled for the practical helical rod. By adjusting σ/G where the corresponding Rmin in its ∆F/G ∼ R curve matches Rmin ) R0, a specific σ/G value (denoted σ/G0, σ/G0 ) 75 nm) is obtained. It is noteworthy that the simulated helical rod at the twist angle Rmin possesses similar geometrical parameters (h, R, and P) to those of the practical rod (Supporting Information, Table S2), indicating that the helical morphology is obtained at the equilibrium point during the formation process as described by our model. The σ/G0 obtained from the randomly selected helical rod is applied to the other helical rods obtained in the same C14TAB synthesis system with the approach described above. Not surprisingly, for each helical rod, R0 ) Rmin is also fulfilled (Figure 3b). Moreover, the geometrical parameters of each rod are similar to the corresponding practical rod (Supporting Information, Table S2), which means the experimentally observed helical structural parameters (R0) can be theoretically predicted by our model (Rmin). The perfect match is a direct support of our proposed mechanism: the formation of helical nanostructures should be understood at the macromorphology level through the competition between ∆Es and ∆Et. As can be seen from Figure 3, the transformation from a straight cylindrical rod to a twisted helical rod is spontaneous during the initial twisting stages (R < Rmin). The equilibrium state is achieved at R ) Rmin because further twisting is energetically unfavorable (R > Rmin). By measuring the geometrical parameters of different helical silica rods, ∆F/G, ∆S, and ∆Et/G can be calculated as a function
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Figure 3. (a) Plots of ∆F/G as a function of the twist angle R beginning with an ideal straight rod reconstructed from a helical rod (R0 ) 4.35) obtained in the C14TAB system while the σ/G value is 45, 60, 75, 90, and 105 nm in plots a-e, respectively. The Rmin (indicated by arrows) in curve c fulfills R0 ) Rmin; thus, σ/G0 ) 75 nm. (b) Plots of ∆F/G ∼ R for other helical rods with different R0 values (indicated by arrows) obtained in the same C14TAB system when σ/G0 ) 75 nm is fixed, where in all plots R0 ) Rmin is observed.
of the surface area (S). As shown in Figure 4a-c, it is found that ∆F/G, ∆S, and ∆Et/G have linear relationships with S, all going through the origin. It is noted that ∆F, ∆S, and ∆Et are calculated using the geometrical parameters (in terms of morphology, e.g., H, R, etc.) and helical parameters (e.g., P) of practical helical rods, which are formed at the equilibrium point based on the discussion before. The linear relationship of ∆F/G versus S indicates the intrinsic relationships between total free energy reduced and surface area, providing a fundamental explanation and direct support for our proposed mechanism that the helical rods are formed at their equilibrium states. Previously, it was reported that the helical nanostructured silica rods showed a linear P/R relationship in different synthesis systems.15,16,29 However, the underlying reason is not well understood until now. Experimental results showed that the P/R value was independent of the stirring rate of the reaction,29 implying that such a relationship is thermodynamically rather than kinetically controlled. Che et al. proposed that the achiral surfactant molecules packed in a helical propeller-like pattern to quantitatively deduce the P/R linear relationship.24 However, on the basis of their hypothesis, this P-R linear function should go through the origin, which is not in agreement with the results. A similar phenomenon can also be observed in our system, where the linear relationship can be expressed by P ) 20.5R 314 nm (Figure 4d). Such a “linear” relationship observed in the above cases might be too simplified. On the basis of our
model through the linear ∆Et/G ∼ S function, the hypostasis of the experimentally observed P/R relationship can be explained satisfactorily, from which a new function of P ) 1.89R1.5 can be deduced (plotted in Figure 4e, curve a) (see the Supporting Information, Modeling and Calculations 5), showing a linear relationship of P versus R1.5 passing through the origin. From Figure 4e curve b, it is also seen that, in the range R ) 36-48 nm, the P ) 1.89R1.5 function can be regarded as a linear equation of P versus R (P ) 18.4R - 254 nm). Both the slope and the intercept at the Y-axis are similar to the practical values obtained in Figure 4d with tolerable derivation, indicating the previously observed linear relationship is a simple expression of our thermodynamic model. Moreover, the plot of P as a function of R1.5 from practical helical rods is shown in Figure 4f (P ) 2.01R1.5), also reflecting a linear relationship passing through the origin. The slope in the equation obtained from experimental data (2.01) is close to that (1.89) obtained from our model calculation (Figure 4e, curve a). It is noted that, when the bottom surface area is neglected and only the side surface area is considered, the calculated value of P/R1.5 based on our model is 2.03 (see the Supporting Information, Modeling and Calculations 5), even closer to the directly measured value of 2.01, indicating that the side surface and bottom surface may have different properties and only the side surface area is important in our model and calculations. Further experiments should be done to confirm this assumption. Therefore, the above
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Figure 4. Plots a-d show linear relationships of ∆F/G versus S, ∆S versus S, ∆Et/G versus S, and P versus R, respectively. c is the linear regression coefficient. In plot e, curve a is the calculated function of P to R, curve b is the calculated linear function of P to R in the range R ) 36-48 nm. Plot f is the linear relationship of P versus R1.5. The samples are from C14TAB samples.
results reveal that the P/R relationship (more accurately, the P/R1.5 relationship) roots in the ∆Et/G ∼ S linear relationship, a genuine reflection of the equilibrium states of all helical nanostructured rods. We have applied the above processes in helical nanostructured rods obtained in the C16TAB templating system.16 The experimental observations are all in good accordance with our model and calculated results (Supporting Information, Figures S4 and S5 and Table S3). In a recent work, the helical silica rods obtained under quite different synthetic conditions also present similar P ∝ R1.5 relationships.30 We also applied the P ∝ R1.5 equation in helical nanostructures obtained by other groups,15 and a near linear function of P versus R1.5 going through the origin is also observed (Supporting Information, Figure S6), indicating that our energetic and equilibrium mechanism is universally applied in different systems to explain the formation of helical nanostructures. Moreover, the surface area reduction and energetic equilibrium model not only predict the helical structure parameters (including the P/R ratio) but also explain the structural characteristics of helical nanostructures. By taking the rod morphology as an integer, the formation of helical nanostructures composed of helical micelles with different curvatures is also a stable conformation by homogenously distributing the torsion energy in the helical rods. The driving force for the formation of helical structures (surface free energy
reduction) applies at the outer surface, leading to helical micelles with decreased curvatures from the outer surface to the center of the rod. Finally, the readers should keep in mind that our surface free energy reduction and energetic equilibrium mechanism for the formation of helical nanostructures aims at the helical rod-like macromorphology, rather than the mesostructure itself, or the chirality of the helical nanostructure. Both the straight rod and the helical rod should have the same hexagonal symmetry, especially when the pitch size of the helical rod is relatively large (see the Supporting Information,Tables S2 and S3). The advantage of the ordered mesostructure (hexagonally arrayed 1D mesochannels) in the helical macrostructure is the occurrence of periodical (10) fringes under TEM observation, through which P can be precisely determined. While P is not related to the hexagonal symmetry, it is one of the important geometrical parameters in our model (Figure 2) to revert a helical rod to a straight one; thus, the surface area reduction and the torsion strain energy can be calculated. Although the formation of mesostructure is considered to be kinetically controlled,17,18 the formation of helical conformation at the macromorphology level, on the other hand, is thermodynamically dependent as revealed by our model, similar to the formation of helical structures at other length scales.1,2 It is also noted that our mechanism is based on the model that the helical mesostructured rod with
Helical Nanostructures with Ordered Mesopores semisphere-like end comes from the straight rod by twisting. Nevertheless, in the solution reaction process, it is not necessarily the case that the hexagonal mesostructured straight rod forms first and then twists into the helical rod. The shaping of the helical morphology may occur simultaneously with the cooperative self-assembly process, as evidenced by our previous study.16 Thus, our model is limited to the understanding of the origin and the equilibrium state for the formation of helical mesostructures, which does not account for the complicated kinetics during this process. Conclusion In conclusion, a surface free energy reduction and energetic competition model is proposed to explain the equilibrium states of helical nanostructured materials and successfully predict their structural parameters. The formation of helical DNA chains, helical nanostructure, and helical coiling filament of viscous fluid should have different origins. However, their helical structures can be understood from the thermodynamic concern and are equilibrium dependent. Our contribution has revealed the connections and differences among the origins of helical structures at different length scales, providing a unique understanding for the formation of mesoscopic materials. Acknowledgment. We thank Dr. Jun Wang for helpful discussions. This work is supported by the 973 Program (2010CB226901, 2006CB932302), the NSF of China (20721063), Shanghai STC (08DZ2270500, 07QH14002), SLADP (B108, B113), FANEDD (200423), and the Ministry of Education of China (20060246010) for their financial support. Supporting Information Available: Characterization of the samples, modeling, and calculation details. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Snir, Y.; Kamien, R. D. Science 2005, 307, 1067. (2) Mahadevan, L.; Ryu, W. S.; Samuel, A. D. T. Nature 1998, 392, 140. (3) Kong, X. Y.; Ding, Y.; Yang, R.; Wang, Z. L. Science 2004, 303, 1348.
J. Phys. Chem. B, Vol. 113, No. 50, 2009 16183 (4) Gao, P. X.; Ding, Y.; Mai, W. J.; Hughes, W. L.; Lao, C. S.; Wang, Z. L. Science 2005, 309, 1700. (5) Bradshaw, D.; Prior, T. J.; Cussen, E. J.; Claridge, J. B.; Rosseinsky, M. J. J. Am. Chem. Soc. 2004, 126, 6106. (6) Davis, M. E. Nature 2002, 417, 813. (7) Gier, T. E.; Bu, X. H.; Feng, P. Y.; Stucky, G. D. Nature 1998, 395, 154. (8) Che, S.; Liu, Z.; Ohsuna, T.; Sakamoto, K.; Terasaki, O.; Tatsumi, T. Nature 2004, 429, 281. (9) Wu, Y. Y.; Cheng, G. S.; Katsov, K.; Sides, S. W.; Wang, J. F.; Tang, J.; Fredrickson, G. H.; Moskovits, M.; Stucky, G. D. Nat. Mater. 2004, 3, 816. (10) Yang, S. M.; Sokolov, I.; Coombs, N.; Kresge, C. T.; Ozin, G. A. AdV. Mater. 1999, 11, 1427. (11) Yang, Y. G.; Suzuki, M.; Owa, S.; Shirai, H.; Hanabusa, K. Chem. Commun. 2005, 4462. (12) Yang, Y. G.; Suzuki, M.; Owa, S.; Shirai, H.; Hanabusa, K. J. Mater. Chem. 2006, 16, 1644. (13) Zhang, Q. H.; Lu, F.; Li, C. L.; Wang, Y.; Wan, H. L. Chem. Lett. 2006, 35, 190. (14) Yang, S. M.; Kim, W. J. AdV. Mater. 2001, 13, 1191. (15) Wu, X. W.; Jin, H. Y.; Liu, Z.; Ohsuna, T.; Terasaki, O.; Sakamoto, K.; Che, S. N. Chem. Mater. 2006, 18, 241. (16) Yang, S.; Zhao, L. Z.; Yu, C. Z.; Zhou, X. F.; Tang, J. W.; Yuan, P.; Chen, D. Y.; Zhao, D. Y. J. Am. Chem. Soc. 2006, 128, 10460. (17) Monnier, A.; Schuth, F.; Huo, Q.; Kumar, D.; Margolese, D.; Maxwell, R. S.; Stucky, G. D.; Krishnamurty, M.; Petroff, P.; Firouzi, A.; Janicke, M.; Chmelka, B. F. Science 1993, 261, 1299. (18) Huo, Q. S.; Margolese, D. I.; Ciesla, U.; Demuth, D. G.; Feng, P. Y.; Gier, T. E.; Sieger, P.; Firouzi, A.; Chmelka, B. F.; Schuth, F.; Stucky, G. D. Chem. Mater. 1994, 6, 1176. (19) Yang, Y. G.; Suzuki, M.; Shirai, H.; Kurose, A.; Hanabusa, K. Chem. Commun. 2005, 2032. (20) Trewyn, B. G.; Whitman, C. M.; Lin, V. S. Y. Nano Lett. 2004, 4, 2139. (21) Gharibi, H.; Razavizadeh, B. M.; Hashemianzaheh, M. Colloid Surf., A 2000, 174, 375. (22) Han, Y.; Zhao, L.; Ying, J. Y. AdV. Mater. 2007, 19, 2454. (23) Ohsuna, T.; Liu, Z.; Che, S. N.; Terasaki, O. Small 2005, 1, 233. (24) Qiu, H. B.; Che, S. N. J. Phys. Chem. B 2008, 112, 10466. (25) Yang, Y. G.; Suzuki, M.; Owa, S.; Shirai, H.; Hanabusa, K. J. Am. Chem. Soc. 2007, 129, 581. (26) Pokroy, B.; Kang, S. H.; Mahadevan, L.; Aizenberg, J. Science 2009, 323, 237. (27) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Nature 1992, 359, 710. (28) Budynas, R. AdVanced Strength and Applied Stress Analysis, 2nd ed.; McGraw-Hill Companies, Inc: New York, 1999; pp 414-415. (29) Jin, H. Y.; Liu, Z.; Ohsuna, T.; Terasaki, O.; Inoue, Y.; Sakamoto, K.; Nakanishi, T.; Ariga, K.; Che, S. N. AdV. Mater. 2006, 18, 593. (30) Hu, Y. F.; Yuan, P.; Zhao, L. Z.; Zhou, L.; Wang, Y. H.; Yu, C. Z. Chem. Lett. 2008, 37, 1160.
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