New Insight into Ordered Cage-Type Mesostructures and Their Pore

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A New Insight into Ordered Cage-Type Mesostructures and Their Pore Size Determination by Electron Tomography Pei Yuan, Jie Yang, Hongwei Zhang, Hao Song, Xiaodan Huang, Xiaojun Bao, Jin Zou, and Chengzhong Yu Langmuir, Just Accepted Manuscript • Publication Date (Web): 08 Feb 2015 Downloaded from http://pubs.acs.org on February 9, 2015

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A New Insight into Ordered Cage-Type Mesostructures and Their Pore Size Determination by Electron Tomography Pei Yuan, [a, b]‡ Jie Yang, [b]‡ Hongwei Zhang, [b] Hao Song, [b] Xiaodan Huang, [b] Xiaojun Bao, [a]

Jin Zou[c] and Chengzhong Yu[b]*

[a]State Key Laboratory of Heavy Oil Processing, China University of Petroleum, No. 18 Fuxue Road, Beijing 102249, P. R. China [b]Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, Brisbane, QLD 4072, Australia [c]Materials Engineering and Centre for Microscopy and Microanalysis, The University of Queensland, Brisbane, QLD 4072, Australia ‡These authors contribute equally to this work. *Email: [email protected]

KEYWORDS. Ordered cage-type mesostructures, Pore size, Pore connectivity, Nitrogen adsorption analysis, Electron tomography

ACS Paragon Plus Environment

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ABSTRACT. In this work, a new approach based on electron tomography (ET) has been developed to measure the pore size, through which a new insight into cage-type ordered mesostructures and their pore size determination has been obtained. It is demonstrated that the accurate pore diameter, especially for cage-type cubic mesoporous materials, can only be determined through our ET approach by considering the pore geometry is a real 3D space. We use the established ET method to revisit the applicability of different models for the pore size calculation in nitrogen adsorption analysis. Different from the overwhelming understanding that the nonlocal density functional theory (NLDFT) and Derjaguin-Broekhoff-de Boer (BdB) model are recommended to calculate the pore size of cage-type cubic mesoporous materials while the Barret-Joyner-Halenda (BJH) model should not be used, a new understanding is gained through this study. The choice of a suitable model for pore size determination depends on the precise pore structure. For a cage-type cubic mesoporous material with an fcc symmetry and large entrance connecting the cages, BJH model is more accurate while the other two methods both overestimate the pore size (up to 40% higher). The DFT model is more appropriate when the pore shape is a perfect sphere than BJH and BdB models, which underestimates and overestimates the pore size, respectively. It is our opinion that the unique ET approach should be used to revisit a vast number of large-pore cubic mesoporous materials to provide genuine structural information.


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Introduction Ordered mesoporous materials (pore size in the range of 2-50 nm according to IUPAC classification) have received great scientific and industrial interest due to their large surface area, tunable pore structure as well as potential applications including separation, adsorption, filtration, and catalysis.1-11 In particular, more attention has been paid to ordered cage-type mesoporous silica materials (OCMSMs) with controlled cages and entrance dimensions, such as SBA-16, FDU-1, KIT-5 and FDU-12,1, dimensional structures.2,

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3, 8, 11

due to their fascinating interconnected three-

During the last ten years, the synthesis of ordered cage-type

mesoporous materials with tailored unit cell sizes, pore sizes and pore connectivity has been well reported.1,

4, 7

Hydrothermal treatment is an efficient method to finely control the structure

parameters, including the enlargement of pore size and entrance size that connects adjacent pores.1, 2, 8, 12 One crucial aspect in the characterization of ordered cage-type mesoporous materials is the investigation of the structural parameters, such as the pore size and connectivity properties including the size, arrangement and shape. Firstly, the precise control of the pore size distribution in OCMSMs is necessary to achieve the desirable function in a particular application.7 Secondly, the size and arrangement of the connectivity is critical for those applications requiring mass diffusion and transportation.1 Thirdly, the shape of the connecting pores is crucial for applications where the final topology is important, such as in the process of growing porous crystals templated by OCMSMs as the hard template.13 Therefore, these structural properties should be carefully characterized. Nitrogen sorption analysis is a well-known technique for the pore diameter measurement, in which the calculation of pore size distribution is dependent on the model chosen.14, 15 Barret-


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Joyner-Halenda (BJH) method,16 nonlocal density functional theory (NLDFT)17 and DerjaguinBroekhoff-de Boer (BdB) theory18 are commonly used models for the calculation of pore size distribution curves. However, it should be pointed out that the above-mentioned three models have their own pitfalls according to previous studies. The BJH method based on Kelvin equation was developed for the pore size calculation of cylindrical mesopores,19 and this method may underestimate the pore size of cage-type mesopores up to 100%.20 The NLDFT method also has its limitation. This method can only calculate the pore size of materials with given pore geometry (slits/cylinders/spheres) and surface properties.19 While such information is not available, the results provided by NLDFT may be misleading. The BdB theory is one sophisticated approach for the measurement of pore size distribution.20,

21

However, this method was reported to

significantly underestimate the pore size because of the neglect of the surface tension changes in mesopores.22 For ordered mesoporous materials synthesized at high hydrothermal treatment temperature, it is frequently observed that the pore size determined by nitrogen adsorption is surprisingly larger than the cell parameter, and this phenomenon occurs in not only hexagonal mesostructures23-25 but also OCMSMs.7 In the case of hexagonal mesostructures, this observation was explained by the coalescence of adjacent mesopores26 as confirmed by electron tomography (ET) technique.25 However, for OCMSMs, this abnormal phenomenon is not well explained, further showing the limitation of nitrogen adsorption analysis in the determination of pore size. Therefore, in addition to nitrogen adsorption analysis, an alternative method for pore size determination is needed to answer questions that have not been addressed. The size and shape of the connecting pore of OCMSMs are also crucial parameters. Generally, the connectivity size could be characterized by nitrogen adsorption with the assumption that the connecting pores are cylindrical. However, the connectivity with the size


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smaller than ~ 5 nm cannot be determined due to the delay of capillary evaporation of nitrogen at 77 K to the lower limit of the hysteresis.6,

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There are other methods to solve this problem,

including the pore surface modification with ligands of different alkyl chain lengths,4 and by electron crystallography (EC).2,

9, 10, 27, 28

However, these methods require the use of ideal

geometrical models, thus cannot be applied some well-defined OCMSMs with considerable structural disorders and defects. Ersen and co-workers reported the direct observation of pore connections in FDU-12 by ET also assuming the interconnectivity with cylindrical shape.29 There are few reports in which the shape of connectivity can be experimentally determined. Transmission electron microscopy (TEM) has been widely used for the interior structural determination and is the most efficient method to explore pore arrangement at present. However, the traditional 2D TEM can only provide a projective image of a 3D object, thus it is hard and sometimes even impossible to determine accurate parameters, such as the pore size, shape and connectivity due to the overlapping effect resulted from the sample thickness. The limitation of the traditional TEM technique can be conquered by a rapidly developing technique, ET. Unlike 2D TEM, ET technique not only can provide the reconstructed complex 3D structures from a tilt series of TEM images,30-36 but also can reveal particular characteristics of the object hidden inside the materials from a set of ultrathin tomographic silices.25, 37-39 We have demonstrated in previous studies that ET can be used to measure the pore diameter in order to minimize the thickness and overlapping effect which is common in TEM images.25, 37-39 However, how to accurately measure the pore size of OCMSMs with a 3D structure from selected 2D ET slices needs to be improved. In this report, we have developed a new approach based on (ET) to measure the pore size of OCMSMs by considering their structures in a 3D space. With this technique, we demonstrate


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that the choice of pore size calculation models in N2 sorption analysis depends on the real pore shapes and structures rather than the structure symmetry determined by bulk characterizations. It is found that the pore diameters of FDU-12 materials synthesized at higher hydrothermal treatment temperatures (> 120 °C) are generally overestimated by nitrogen sorption analysis with either DFT or BdB models. Surprisingly, the BJH model is more suitable because the pore shape has changed to cylindrical pores. This knowledge may provide answers to many questions that have not been addressed in literature. Experimental Section Synthesis of FDU-12 mesoporous materials: In the typical synthesis, 2.0 g of triblock copolymer F127 and 10 g of KCl were completely dissolved in 120 mL of 2 M HCl at 15 °C, then 2.4 g of TMB was added and the mixture was stirred at 15 °C for 6 h. Then, 8.32 g of tetraethylorthosilicate (TEOS) was added to the previous mixture, which was left to stir for another 24 h at 15 °C. The solid products were collected by filtration, washed with water, then added to a solution consisted of 1 g of triblock copolymer F127 and 120 mL of 0.01mol/L HCl. The pH value of the solution was adjusted to 2 using HCl and aqueous ammonia. The mixture with a final volume of about 130 mL was transferred into an autoclave for hydrothermal treatment at a given temperature (100, 120, 160 and 180°C) for 24 h. The final as-synthesized product was collected by filtration, washed with water and dried in air, then calcined at 550 °C for 5 h to remove the templates. The final samples synthesized under different conditions were named as FDU-12-T, where T denotes the hydrothermal treatment (HT) temperature. Characterization: The small angle X-ray scattering (SAXS) profiles were obtained from BrukerNanoSTAR with a 2-D detector (HiSTAR) and X-ray beam pinholecollimated (40 kV, 30 mA). The N2 adsorption-desorption isotherms were measured at 77 K on a nitrogen adsorption


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apparatus (Quadrasorb SI, Quantachrome) after degassing the samples at 180 °C for 6 hours. The Brunauer–Emmett–Teller (BET) surface areas were determined from the adsorption branch of the isotherm in a relative pressure range from 0.05 to 0.30. The pore size distribution (PSD) was determined using BJH, NLDFT method with cylinder/sphere pore model, and BdB method. ET was performed with a FEI Tecnai F30 electron microscope operating at 300 kV. All TEM images were recorded at a given defocus in a bright-field mode to show the thickness contrast. The ET specimens were prepared by dispersing the powder samples in ethanol by ultrasonication for 5 min and then depositing them directly onto copper grids (2000×1000 slot, Proscitech) with Formvar supporting films. Colloidal gold particles (5 nm) were deposited on both surfaces of the grid as fiducial markers for the subsequent image alignment procedures. The tomographic tilt series were carried out by tilting the specimen inside the microscope around a single axis under the electron beam. All TEM images were recorded over a tilt range of +60 to -60° at increments of 1°. Data processing was carried out by using IMOD software.40

Results Pore size and cell parameter determination by ET approach. To demonstrate the principle of our approach, Scheme 1A shows two consecutive cage-type pores arrayed along [100] direction in a FDU-12 type face-centered cubic mesostructure (space group: Fm3m). The pores are modeled as identical and perfect spheres (in blue color) with a diameter of D. The cross sections of the spherical pore (shown by shadowed ellipsoids in yellow color) perpendicular to the [100] direction are indeed circles (shown in Scheme 1B), and their diameter (d) changes at


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different positions. For example, at positions a and b as indicated in Scheme 1A, the diameters of corresponding cross sections, da and db, are not equal as shown in Scheme 1B. To allow for a quantitative determination, a two-dimensional coordinate system is built as shown in Scheme 1C, where the x-axis is the [100] direction and the y-axis represents the diameter (dx) of circular cross section located at the position x. The origin is set so that the centre of the left sphere in Scheme 1C is located at (D/2, 0). Theoretically, dx is a function of x, which can be expressed by the following equation:

[x − (D / 2 + na )]2 + d x2 D2 (D / 2)2

= 1 (n = 0, 1, 2, 3….)

As shown from the curve of dx(x) function in Scheme 1C, dx has the maximum of D only when x = D/2, which is the actual pore diameter. This value can be experimentally determined by tracing one pore in a number of ET slices corresponding to the yellow circles in Scheme 1B. A maximum diameter of the circle as indicated by db in Scheme 1 can be measured as the real pore diameter (D). As shown in Scheme 1A, the distance along the x-axis between two adjacent cross sections with the maximum diameter of D corresponds to the cell parameter (a). In our process, a can be measured by the production of the slice thickness and slice numbers going from one slice with the peak diameter of D to another. As a result, both D and a can be determined by the ET method. Moreover, a obtained from SAXS profile can be used to calibrate a and D values measured from ET. FDU-12-100 treated with the hydrothermal temperature of 100 °C was selected as an example to show how ET approach works for the pore size and cell parameter determination. Figure 1A shows the SAXS pattern for the calcined FDU-12-100 mesoporous material collected from q = 0.2 to 2.0 nm-1. Five well-resolved diffraction peaks with q-values of 0.375, 0.610, 0.718, 0.945 and 1.302 nm-1 can be clearly observed. Based on the relationship between the peak


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positions with the d-spacing ratios of √3: √8: √11:√19:√36, they can be indexed as 111, 220, 311, 331 and 442 reflections with an Fm3m symmetry and a = 29.0 nm. Figure 1B displays the N2 sorption isotherm and the pore size distribution calculated from the adsorption branch using DFT model (inset) of FDU-12-100. The sample exhibits a type IV nitrogen sorption isotherm and H2 hysteresis loop, indicating a typical cage-type mesoporous material. A narrow pore size distribution centered at 10.2 nm can be observed. The BET surface area and total pore volume are 521 m2/g and 0.56 cc/g, respectively. Desorption branch is declined steeply at the lower limit of adsorption–desorption hysteresis (relative pressure of 0.4–0.5 for nitrogen at 77 K). As discussed elsewhere, the delay of capillary evaporation of nitrogen at 77 K to the lower limit of hysteresis indicates that entrances to the cage-type pores of these samples are of diameter below about 5.0 nm.5, 8, 20 Therefore, the desorption branches are not suitable to determine the size of connectivity in this case. Figures 1C and D are the typical TEM images for a selected area of FDU-12-100 taken along [100] zone axis and a corresponding (100) tomographic slice (thickness of 0.19 nm) extracted from its tomogram volume. The well ordered face-centred cubic (fcc) mesostructure with uniformly arrayed pores can be clearly seen. A unit cell is indicated by red squares in Figure 1C and D. The a values measured from two different images are 27.0 and 28.5 nm, thus the deviation of the value compared with SAXS data (29.0 nm) is 6.90% and 1.72%, respectively. This discrepancy should be due to the overlapping effect resulting from sample thickness in TEM projective image. It should be noted that the mesostructure given in the tomographic slice (Figure 1D) do not show the well ordered pore arrangement in the entire selected area as demonstrated by TEM image (Figure 1C). That is because the different sample height or the defects existed in the interior of sample (as the pores and ordered structure are originated from


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the self-assembly of surfactants and silica sources, it is no surprising to have some defects inside of the materials), which may not be reflected by projective TEM image with several hundreds of nm thickness, but can be clearly revealed by tomographic slice with thin thickness. The ET technique is also used to determine the pore size as described in Scheme 1. In practice, a continuous series of ET slices with a thickness of 0.19 nm was extracted from tomogram volume. As illustrated by a spherical pore model in Figure 2A, the pore size can be determined by tracing one pore to find its maximum position. The images of a pore sliced at different positions expressed by various Z numbers are displayed in Figure 2B. As shown in Figure 2C, the value of dx(x) measured from Figure 2B changes as a function of x (x is the distance from Zx to Zy, which can be calculated by the production of slice thickness and slice numbers Zy-Zx). By monitoring one pore, the diameter of the circles increases from 0 (Z = 79) to a maximum of 10.0 nm (Z = 106), then decrease to 0 again (Z = 133). The maximum value of 10.0 nm represents the actual pore size as illustrated in Scheme 1. The distance from slice Z = 79 to Z = 133 (totally 54 slices), which represents the pore diameter of the sphere from another direction (perpendicular to the yellow cross-section in Scheme 1), is 10.26 nm (54 × 0.19 = 10.26 nm), similar to the pore size directly measured from Z = 106 slice. This suggests that the shape of pores in FDU-12-100 is indeed a sphere. In addition, the measured pore change as a function of x displayed by grey lines in Figure 2C fits well with the theoretical equation we proposed in Scheme 1 (red line), indicating our method to determine the pore size is reasonable. Moreover, according to the accumulated length between two adjacent maximum circles along [100] direction as shown in Scheme 1, a value can also be calculated to be 28.12 nm (totally through 148 slices) which have a 3.03% deviation from SAXS data.


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In addition, another sample area along [111] direction was also performed on ET as shown in Figure S1 and the 3D model was reconstructed in order to get the 3D mesostructure showing the ordered ABCABC stacking with an fcc symmetry (Figure S1c). The pore size is measured to be 10.64 nm which is similar to that obtained from [100] direction (Figure 2). The cell parameter can be determined by the distance from Z = 51 to Z = 180 with the slice thickness of 0.38 nm in this case, which is calculated to be 28.30 nm with a 2.41% deviation from SAXS data. We use the above method to measure 120 different pores and plot a pore size distribution curve. For comparison, we also plot a pore size distribution curve using conventional methods by randomly statistical evaluation of 120 pores measured in 2D ET slices (as shown in Figure 1D). If the pore size was only measured from 2D ET slices, the pore size distribution is very broad, ranging from 4 to 12 nm (Figure 3A). However, if all the pores are measured using the protocol established in this study, a narrow pore size distribution curve with the pore size centered at 10.0 nm can be obtained (Figure 3B), which is in good agreement with the pore size distribution curve obtained from DFT model (Figure 1B inset).

The effect of hydrothermal treatment temperature. To investigate the evolution of primary mesopores / connectivity with increasing hydrothermal treatment temperature and apply our method in the analysis of pore sizes of various samples, a series of FDU-12-T (T = 120, 160 and 180 ˚C) materials were synthesized. The SAXS patterns of FDU-12-T are shown in Figure 4 and the peak positions and peak assignment are also given in the inset. These three samples have similar diffraction patterns and the space groups can be assigned to the same Fm3m (fcc structure) as FDU-12-100. With the increase of hydrothermal treatment temperature, the reflection shifts to lower angle; accordingly, a value increases from 29.0 (FDU-12-100, Figure 1A) to 36.8 nm (FDU-12-160 and 180). It is worthy of noting that the reflection, which is


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perpendicular to the direction of the connectivity, cannot be observed in FDU-12-100 (Figure 1A) but appears and gradually increases its peak intensity with the temperature raising from 120 to 180 ˚C (Figure 4), indicating the occurrence and enlargement of the pore connectivity.10 In addition, 111, 220, 311, 420 and 442 reflections can still be detected in FDU-12-180 (Figure 4C), indicating the highly ordered structure is well maintained even after the high temperature hydrothermal treatment. Typical TEM images of FDU-12-T taken along [100] (T = 100, 120 and 160 ˚C) and [110] directions (T = 180 ˚C) are shown in Figure S2. Under the TEM observation, the highly ordered lattice array of FDU-12-T can be clearly seen, in accordance with the SAXS results. Figure 5 shows the N2 adsorption/desorption isotherms of calcined samples FDU-12-T samples treated at 120, 160 and 180 ˚C, respectively. Based on the N2 sorption analysis, the values of surface area, pore volume, pore size calculated from adsorption branch using BJH, BdB and DFT models are determined and summarized in Table 1. FDU-12-120 and FDU-12-160 exhibit type IV nitrogen adsorption-desorption isotherms and a large H2 hysteresis loop, similar to FDU-12-100 (Figure 1B) and those cage-like mesoporous silicas such as SBA-16, FDU-1, KIT-5, etc.3, 8, 11 It is noteworthy that when the hydrothermal treatment temperature increases to 180˚C, the hysteresis loop becomes smaller and shows typical H1 hysteresis loop. The shift of the desorption branch to the higher relative pressure (0.7-0.8) indicates the enlargement of pore entrances, which is calculated from the desorption branch to be 11.6 nm (as shown in Table 1). The highest BET surface area of FDU-12-T is observed when T=160 ˚C. It is possible that some pores are closed

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at a relatively lower hydrothermal treatment temperature of 100 and 120 ˚C,

while increasing the temperature to 160 ˚C may open up those closed pores and result in accessible surface areas. The dramatic decrease in surface area at T=180 ˚C is attributed to the


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formation of cylindrical-like pores. The total pore volume increases from 0.56 to 1.07 cc/g as temperature raises from 100 to 180 ˚C, which are mainly due to the enlargement of mesopores.

Connectivity. The ET approach can be applied to determine the size and shape of primary mesopores. We extend this method to the study of connectivity. Due to the limitation of the resolution of ET, it is difficult to quantitatively measure the size of micropores, therefore we focus on the shape and size of entrances with large sizes. In the ET slices of FDU-12-100 (Figure 1D), almost no connections can be observed between the primary pores. For FDU-12-120 (Figure 6A), the pore size is increased. Further increasing the hydrothermal treatment temperature to 160 ˚C, the average size of isolated pores has almost no change but the connectivity is enlarged obviously with the size of approximately 4.5 nm (as indicated by the arrows in Figure 6B). In the case of FDU-12-180 (Figure 6C), the high hydrothermal treatment temperature leads to the formation of more connectivity between the primary pores with larger sizes. As indicated by a rectangle and arrows, the pores are no longer spherical in shape but changed to irregular cylindrical one due to the existence of abundant connections. ET slices in large area for samples FDU-12-120, FDU-12-160, and FDU-12-180 are provided in Figure S3, in agreement with the above observation. 3D reconstruction was processed to study of the shape, size as well as direction of the connecting pore in FDU-12-180. The 3D models of connected cages indicated by a rectangle in Figure 6C is displayed in Figure 6D. The sizes of the connecting pores (1-3) indicated by the arrows are 6.81, 12.34 and 8.51 nm, respectively, indicating the non-uniform sizes of the entrance connecting primary mesopores. Figures 6E and F show the reconstructed structures viewing from [100] and [111] directions of one unit cell selected from the tomogram of FDU-12180, respectively. As discussed in our previous work,25 ET has irreplaceable advantage to reveal


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the interior structure hidden inside the materials such as the "local disorder" accumulating to "long-range ordered structure" for 3D-SBA-15. For FDU-12-180 as shown in Figures 6E and F, most of the connectivity may be overlapped by the silica wall thus ordered cubic mesostructure can be observed from projective TEM image and also in the 3D reconstructed models. However, it can be seen that the connections are along directions (Figures 6E and F), which is the shortest distance between two adjacent pores.10, 28 This trend is different compared to 3D-SBA15 in which the connections between pore channels are randomly orientated.28 Connections along other directions than direction may also have chance to develop as indicated by the red arrows in Figure 6C, but such connections are not dominant compared to those grown along the directions.

Discussion An abnormal phenomenon is frequently observed for ordered mesoporous materials with either hexagonal23-25 or cage-type cubic mesostructures7 after high hydrothermal temperature treatment, that is, the pore size determined by nitrogen adsorption is larger than the cell parameter. This leads to negative value of silica walls, which is not reasonable. Such abnormal results raise a question: how to measure the pore size accurately? In the case of ordered hexagonal mesostructure, we have employed ET technique to give an explanation.25 The coexistence of main pore channel size and connections between channels has been revealed by ET slices. When the hydrothermal treatment temperature exceeds a certain degree, the size of main pore channels has little change while the pore connections make a dominant contribution to the enlarged pore size calculated by N2 sorption with BJH model. It is concluded that N2 sorption only provides an overestimated average pore size, but not the real pore channel size.


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With regard to ordered cage-type cubic mesostructures, the situation is more complicated because there are various models to calculate the pore size distribution in nitrogen adsorption analysis. Researchers tend to choose one model for spherical pores to calculate a series of samples prepared with different hydrothermal temperatures, regardless of the pore shape and structure change during the high temperature treatment process. To compare different pore calculation models, the pore sizes of FDU-12-T materials hydrothermally treated at 100, 120, 160 and 180 °C were obtained by BJH, DFT, BdB models and also our ET approach. The results are listed in Table 1 and shown in Figure 7 for a direct comparison. The pore size distributions acquired by ET approach for FDU-12-120, 160 and 180 are shown in Figure S4, showing pore diameters centered at 17.2, 17.5 and 19.8 nm, respectively. As shown in Figure 7, the pore sizes measured by DFT method using cylinder/sphere model gradually increase with temperature from 10.2 to 27.4 nm in the temperature range of 100-180 ˚C, while the pore sizes calculated by BJH and BdB methods increase from 9.3 to 20.6 and from 15.2 to 25.0 nm, respectively. At the lowest hydrothermal treatment temperature of 100 ˚C, cagetype mesostructure is highly ordered (Figure 1A) and the shape of pores is nearly ideal spherical (see Figure 2) without any connections between the pores. In this case, the pore size obtained from DFT model (10.2 nm) is consistent with that from ET measurement (10.0 nm), while BJH model slightly underestimates (9.3 nm) and BdB model overestimates the pore size (15.2 nm). The difference in pore sizes measured by four methods changes with the hydrothermal treatment temperature. When the hydrothermal treatment temperature is 160 and 180 ˚C, it is found that both DFT and BdB methods overestimate the cage size measured by ET, the BJH pore size is more close to that determined by ET.


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Both FDU-12-160 and FDU-12-180 have a long-range ordered cage-like mesostructure (Figure 4), however the pore shape is no longer perfect spherical due to the development of connectivity around the primary mesopores (Figure 6). The ET method measures the pore size directly, in contrast to DFT, BdB and BJH models in the pore size calculation. It is noted that both DFT and BdB models are based on the assumption of ideal spherical pores, however the pore shape has changed into irregularly cylindrical-like (more evident for FDU-12-180, see Figure 6 and S3), leading to a high derivation of both DFT and BdB pore sizes from the real one. On the other hand, the BJH model is designed and corrected for cylindrical-like pores, thus more suitable to measure the pore size in cage-type mesostructure with large entrance sizes. The micropores in FDU-1210 and other copolymer-templated silicas2, 8 originate from the occlusion of the hydrophilic poly (ethylene oxide) chains (EOn) in the silica walls during the formation of silica-copolymer composites. Higher hydrothermal treatment temperature leads to a higher degree of aggregation of EOn blocks in the silica wall. This aggregation, in one hand, causes the increase of the hydrophobic segment volume and results in pore size enlargement. In the other hand, the aggregation of EOn blocks in the silica wall possibly causes the formation of connecting pores, which are formed after the removal of the copolymer templates. With increasing size of pore connectivity at high hydrothermal treatment temperatures, some adjacent connecting pores could preferentially merge together into channel-like pores (Figure 6). Using the 3D reconstruction ET technique, the connectivity with different shapes and the connection directions can be determined. Such information cannot be detected by other bulk techniques such as SAXS, TEM or N2 sorption analysis.

Conclusion


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We have demonstrated the unique advantage of electron tomography technique in the detailed structure determination of cage-type mesoporous materials, specifically for pore size measurement. Taking advantage of a continuous series of tomographic ultrathin slices, the cell parameter, pore size, pore shape and pore connectivity can be directly determined. It is shown that for cage-type mesoporous materials, a suitable model for the pore size calculation in nitrogen sorption analysis relies on the information of pore connectivity. While the DFT model is recommended for materials with ordered structures and nearly perfect spherical pores, the BJH model should be used when the connecting pores (or entrance connecting cages) have large sizes, even the overall structure is still an ordered cubic mesostructure. In case the ET approach is not available for general users and the detailed information of pore connectivity is unknown, caution should be taken in nitrogen sorption analysis to choose a suitable calculation model. It is recommended that one may estimate the sizes of pores and entrances from the adsorption and desorption branches (either BJH or DFT), and then compare the difference to judge which model is suitable. Under most circumstances the BJH model is recommended when the entrance size is enlarged to a certain degree. However, only the ET technique could provide an unambiguous answer. It is expected that our ET approach can also be used for materials with other pore structure and symmetry to retrieve genuine structural information for designed synthesis and applications.

Acknowledgments This work was financially supported by the National Natural Science Foundation of China (Grant 21106182) and the Australian Research Council. The authors acknowledge the Australian National Fabrication Facility and the Australian Microscopy and Microanalysis Research Facility at the Centre for Microscopy and Microanalysis, The University of Queensland.


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Supporting Information Available. This information is available free of charge via the Internet at http://pubs.acs.org/.

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Scheme 1. Illustration of the 3D geometric resolving approach to determine the pore size by ET reconstruction.


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Figure 1. SAXS pattern (A) and nitrogen adsorption-desorption isotherm (B) of calcined FDU12 materials hydrothermally treated at 100 °C and the inset of (B) is the pore size distribution calculated from the adsorption branch by NLDFT method using the spherical model; (C) Typical TEM image for a selected area of FDU-12-100 taken along [100] zone axis; (D) a corresponding thin tomographic slice with the thickness of 0.19 nm. A unit cell is indicated by a red square in (C) and (D).


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Figure 2. (A) A spherical pore model to demonstrate how ET works to measure the accurate pore size with thin tomographic slices indicated by dashed lines and the Z slices indicate the different positions of the tomogram; (B) the pore size change of anarbitrarily selected pore from Figure 1D as increasing Z slices from 79 to 133; (C) the pore size measured from different Z slices (dx) as a function of x, where x is calculated by the production of slice thickness (0.19 nm) and slice numbers regarding Z = 79 as 0. For example, when Z = 106 (the seventh image in (B)), the pore size is measured to be 10.0 nm as dx and x is calculated by the following equation (10679) × 0.19 nm = 5.13 nm.


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Figure 3. Histograms showing the pore size distributions of FDU-12-100 measured by one randomly selected slice as shown in Figure 1D (A) and by a series of ET slices to find the max value by tracing each pore as demonstrated in Figure 2 (B). Totally 120 pores in Figure 1D are statistically evaluated.


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Figure 4. SAXS patterns for calcined FDU-12 materials hydrothermally treated at 120 (A), 160 (B) and 180 ˚C (C).

Figure

5. Nitrogen

adsorption-desorption

isotherms

of

calcined

FDU-12

materials

hydrothermally treated at 120, 160 and 180 ˚C. The adsorption isotherms for FDU-12-160 and 180 samples are shifted up by 100 and 400 cc/g (STP), respectively.


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Figure 6. (A)-(C) are the ET slices of FDU-12-120, FDU-12-160 and FDU-12-180, respectively. (D) is the reconstructed 3D structures of connected pores indicated by a rectangle in (C). (E) and (F) are the reconstructed 3D structure of one unit cell in FDU-12-180 viewing from [100] and [110], respectively. All scale bars are 20 nm.


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Figure 7. Evolution of the pore size calculated by ET and different N2 sorption calculation methods as a function of the hydrothermal temperature.


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Table 1. The summary of structural parameters of FDU-12 synthesized at different HT temperature determined by SAXS, nitrogen adsorption and ET.

SBET

Vt

We

a

aET

WBJH

WDFT-S

WBdB

WETC

(m2/g)

(cm3/g)

(nm)

(nm)

(nm)

(nm)

(nm)

(nm)

(nm)

FDU-12-100

521

0.56

New Insight into Ordered Cage-Type Mesostructures and Their Pore

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