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Publication Date (Web): October 10, 2016. Copyright © 2016 American Chemical Society. *E-mail: [email protected]...
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Long Walks in Hierarchical Porous Materials due to Combined Surface and Configurational Diffusion Vivek Vattipalli,† Xiaoduo Qi,† Paul J. Dauenhauer,§ and Wei Fan*,† †

Department of Chemical Engineering, University of Massachusetts Amherst, 686 North Pleasant Street, Amherst, Massachusetts 01003, United States § Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States S Supporting Information *

ABSTRACT: Hierarchical materials with porous structures at different length scales (i.e., micropore and mesopore) are an emerging class of materials. However, the lack of fundamental understanding of mass transport properties significantly limits rational development of these materials for applications in catalysis and separation. In this study, we evaluated the mass transport of two probe molecules, cyclohexane and 1-methylnaphthalene, in two different types of hierarchical porous materials, SBA-15 mesoporous silica and three dimensionally ordered mesoporous imprinted (3DOm-i) silicalite-1 zeolite, for comparison with nonmicroporous MCM41 mesoporous silica. It was observed that the apparent diffusion lengths determined for hierarchical porous materials (i.e., SBA15 and 3DOm-i silicalite-1) were significantly longer than predicted by the physical structure (i.e., radius) of the adsorbent particle, indicating that diffusion of molecules in hierarchical porous materials is much longer than expected. The unusually long path length is likely due to diffusion on the external surface, followed by re-entering of diffusing molecules from the external surface into the micropores; the large external surface area of hierarchical porous materials enhances the extent of this phenomenon. The observations reported in the study highlight the importance of surface diffusion in hierarchical porous materials. Enhanced mass transport in hierarchical porous materials can be overpredicted without considering the extent of sorbate−sorbent interaction and the actual diffusion length. microporosity.10−16 Their outstanding catalytic properties have been ascribed to large external surface area and easy access to the active sites located within micropores.17−22 However, the effects of the external surface and the mesopore structure on the mass transport properties of hierarchical porous materials have not been fully understood.23−29 There is an urgent need to establish structure−property−function relationships in order to rationally develop hierarchical porous materials for applications in adsorption, heterogeneous catalysis, and separation. Molecular transport in hierarchical porous materials is a complex process that is dependent on the porous structure and the interconnection of mesopores and micropores.30 When molecules adsorb within micropores, configurational diffusion is the dominant transport mechanism. Configurational diffusion is controlled by micropore structure and sorbate−sorbent interactions. When molecules diffuse out from the micropores and enter the mesopores, either Knudsen diffusion or surface diffusion control the transport process, as determined by the strength of interactions between the molecule and the mesoporous wall. Surface diffusion (i.e., molecular transport along the surface) has been observed for molecular diffusion in systems with a strong sorbent−sorbate interaction. Knudsen

1. INTRODUCTION Hierarchical porous materials exhibit multiple length scale porosity comprising both micropores (2 R2/D) was allowed in all the ZLC experiments.54 The long time analysis was used for all cyclohexane data due to the reliability of the method for large values of L. For 1-methylnaphthalene diffusion, the short time analysis was selected due to strong adsorption of the sorbate and baseline effects. Nevertheless, when possible, the results using both types of analyses were compared and found to agree well.

the surfactant, the sample was calcined at 823 K for 12 h with a ramping rate of 0.5 K/min under flowing dry air. Three samples with different mesopore size and micropore volume are referred to as SBA15 5 nm, SBA-15 6.2 nm, and SBA-15 8.5 nm based on the mesopore diameters obtained from their N2 adsorption isotherms at 77 K (Figure S7). 2.3. Synthesis of MCM-41. MCM-41 was synthesized according to a previously published method.51 Ammonium hydroxide solution was mixed with deionized water and CTAB, and then heated to 353 K under vigorous mixing. Once the surfactant was dissolved in the solution, TEOS was slowly added. This solution was stirred for another 2 h. The final composition was 1 SiO2:0.125 CTAB:69 NH4OH:525 H2O. The obtained product was filtered, dried at 343 K for 10 h, and then calcined at 823 K for 4 h with a ramping rate of 0.5 K/min under flowing dry air. 2.4. Synthesis of 3DOm-i Silicalite-1. 3DOm-i silicalite-1 was synthesized according to a previously published method.52 Threedimensionally ordered mesoporous (3DOm) carbon with a cage size of 35 nm was used as a hard template to synthesize 3DOm-i silicalite1, and then it was removed by calcination at 873 K. 2.5. Characterization of Porous Materials. X-ray scattering data for the SBA-15 samples was collected with a Molecular Metrology SAXS line using Cu Kα radiation and a sample-to-detector distance of 1481 mm. X-ray scattering data for MCM-41 and 3DOm-i silicalite-1 were collected on a SAXSLAB Ganesha instrument using Cu Kα radiation and a sample-to-detector distance of 900 mm. Nitrogen and argon adsorption isotherms were used to characterize the textural properties of all samples. These were measured on a Quantachrome Autosorb-iQ system at 77 and 87 K, respectively, after outgassing at 523 K until pressure rise in the test cell was less than 25 mTorr/min. Pore size distribution and cumulative pore volume were calculated by using the NLDFT (nonlocal density functional theory) adsorption kernel (nitrogen adsorbed in cylindrical pores of silica at 77 K in case of nitrogen isotherms; argon adsorbed in cylindrical pores of silica at 87 K in case of argon isotherms) using AsiQwin v3.01 (Quantachrome). Total pore volumes were evaluated at P/P0 = 0.95. Scanning electron micrographs of the samples were collected using a Magellan 400 XHR-SEM instrument (FEI) equipped with a fieldemission gun operated at 3.0 kV. The samples were sputter coated with platinum before imaging. 2.6. Measurement of Diffusivity. Diffusivity measurements were conducted using the ZLC chromatography technique developed by Ruthven and co-workers.53,54 The design of the setup used in this study has been described in our previous work.39 Further specific information about the conditions used is available in the Supporting Information. Adsorbate probe molecules were cyclohexane and 1methylnaphthalene. In both cases, nitrogen was used as the carrier gas and was bubbled through a liquid column of the probe molecule maintained at a fixed temperature (283 K in the case of cyclohexane; 293 K in the case of 1-methylnaphthalene). The same conditions were used for all the measurements for either of the probe molecules. The piping between the bubbler and the samples was maintained at 323 K to prevent condensation of the probe molecule within the transfer piping. About 2.0 mg of the porous material was placed between two quarter-inch stainless steel frits and contained within a 0.2″ Swagelok union placed in an isothermal gas chromatograph oven (Agilent 7890A). The length of the gas tubing in the isothermal oven was sufficient to ensure that the gas temperature was the same as the sample when contacted with each other. Gas flow rates were regulated using Brooks 5850E mass flow controllers. A FID (Flame Ionization Detector) was used to measure the probe molecule concentration in the gas stream. Prior to measurement, the porous samples were treated at 523 K for 12 h under a nitrogen flow of 50 mL/min to remove any adsorbed water and chemicals. The obtained ZLC data for the diffusion of cyclohexane and 1methylnaphthalene were analyzed using the long-time analysis method and short-time analysis method, respectively.53 Detailed information on the analysis methods is available in the Supporting Information. All measurements were repeated at least once to ensure repeatability of the data (Figure S3). Measurements were also conducted at varying

3. RESULTS AND DISCUSSION 3.1. Textural Properties of Hierarchical Porous Materials. MCM-41 and SBA-15 mesoporous silicas with controllable mesoporosity were synthesized by the selfassembly of surfactants and silicate species under hydrothermal synthesis conditions. The small-angle X-ray diffraction patterns (Figure 2) show three diffraction peaks corresponding to (100),

Figure 2. Small angle X-ray diffraction patterns for (a) MCM-41; (b) three SBA-15 samples; and (c) 3DOm-i silicalite-1.

(110), and (200) reflections of a two-dimensional hexagonal lattice (P6mm), indicating the presence of highly ordered mesoporous structures. The unit cell size for the SBA-15 samples slightly changes with mesopore size and is much larger than MCM-41. 3DOm-i silicalite-1 was prepared by a hardtemplating method. The carbon template (3DOm carbon) was synthesized from the replication of a colloidal silica crystal with a face-centered cubic (fcc) lattice. 3DOm-i silicalite-1 was synthesized within the confined space of 3DOm carbon. Once silicalite-1 was synthesized in the carbon template, the 3DOm carbon was removed by calcination. The formed 3DOm-i silicalite-1 crystal consisted of ordered mesopores, as shown in the small-angle X-ray diffraction pattern (Figure 2). Our previous studies have shown that the 3DOm-i silicalite-1 exhibits a single crystalline feature, indicating that the small zeolite domains are interconnected together with the same crystal orientation. The wide-angle X-ray diffraction pattern (Figure S8) confirms the crystalline nature of the 3DOm-i silicalite-1 sample. Figure 3 depicts the SEM images of the samples used in this study. Figure 3a−c show the rod-shaped morphology of the three SBA-15 samples. The ordered arrangement of mesopores 7854

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isotherms using the NLDFT method. The mesoporous silica samples show much larger BET area compared to 3DOm-i silicalite-1, which is due to the large mesopore volume of the mesoporous silica samples. The mesopore sizes of the SBA-15 samples were controlled from 5.0 to 8.5 nm, which is close to the mesopore size of 3DOm-i silicalite-1, and larger than that of MCM-41. Microporosity was observed in all three SBA-15 samples, while MCM-41 did not exhibit measurable microporosity. However, the micropore size distributions of the SBA-15 samples are much broader than that of 3DOm-i silicalite-1, as shown in Figure 4d. The broad distributions are due to the different formation mechanism of micropores in SBA-15 mesoporous silica relative to zeolites. The presence of micropores in SBA-15 has been ascribed to the use of a nonionic triblock copolymer type of surfactant (poly(ethylene oxide)m−poly(propylene oxide)n−poly(ethylene oxide)m) in the synthesis. It has been proposed that an interpenetrating network of silica and ethylene oxide chains is formed in the mesopore walls of the synthesized SBA-15, leading to the formation of microporous structures on removal of the surfactant by calcination. Furthermore, it has been demonstrated that some of the microporosity in SBA-15 might be generated from stress fractures during the calcination step.55 By making carbon and platinum replicas from SBA-15, it has been found that the mesopores of SBA-15 are interconnected through the disordered micropores located within the mesoporous walls.56,57 Neutron scattering studies also indicated that the density in the mesopore walls of SBA-15 increases from the pore surface toward the center of the wall, resulting in a corona structure.58,59 The micropore volume of the three SBA15 samples varied with the synthesis temperature, ranging from 0.03 cc/g to 0.10 cc/g (Table 1). The SBA-15 sample with the largest mesopore size (SBA-15 8.5 nm) exhibits the lowest micropore volume of the three, which might be due to the relatively small amount of ethylene oxide chains interpenetrating within the silica wall and the reduced pore wall thickness. On the other hand, MCM-41 was synthesized using a cationic alkylammonium surfactant, leading to nonmicroporous silica walls.57,60 Furthermore, the mesoporous silica walls in MCM41 (0.54 nm) are also much thinner than the ones in the SBA15 samples (3.4 to 6.7 nm, Table 1), leading to a much lower possibility for the formation of micropores on account of stress fractures during calcination.58 3.2. Diffusion in MCM-41. Figure 5 depicts the ZLC desorption curves obtained for cyclohexane and 1-methylnaphthalene diffusion in MCM-41. It was observed that the diffusion of cyclohexane in MCM-41 is much faster than that of 1methylnaphthalene. There is a good agreement between the D/ R2 values for cyclohexane diffusion with those obtained in the literature for the diffusion of hydrocarbons with a similar molecular size, such as n-hexane and n-heptane, in MCM-41.42 Interestingly, the diffusivity for both molecules is much lower (by 5−7 orders of magnitude) than Knudsen diffusivity calculated using the kinetic theory of gas molecules (Figure 5), indicating that mass transport is strongly dominated by surface diffusion and hence influenced by the sorbate−sorbent interaction. The dominance of surface diffusion is further confirmed by the higher diffusion activation energy for 1methylnaphthalene compared to cyclohexane (Table 2). This result indicates that these molecules primarily diffuse on the surface of the MCM-41 sample such that the contribution of Knudsen diffusion to overall diffusion is insignificant. This

Figure 3. SEM images of (a) SBA-15 5 nm, (b) SBA-15 6.2 nm, (c) SBA-15 8.5 nm, (d) MCM-41, and (e),(f) 3DOm-i silicalite-1. The inset images for the three SBA-15 samples show the clearly visible mesopores on the surface, which are marked with red lines. Red squares identify the regions on the respective images which are magnified in the inset images.

on the particle surface is visible in these images and marked using red lines. The SBA-15 rods are all of similar size with slight variations in the rod width and length. Figure 3d shows the egg-shaped morphology of MCM-41 synthesized in this study. It is clear that the MCM-41 particles are also of a similar size as the SBA-15 rods. SEM images of 3DOm-i silicalite-1 at different size scales are shown in Figure 3e,f. The particle size of the 3DOm-i silicalite-1 is 2−4 μm, which is close to that of the SBA-15 particles. The image at the smaller size scale shows the ordered arrangement of spherical primary domains of silicalite1 zeolite. The observation is consistent with our previous studies.52 Nitrogen and argon adsorption isotherms were used to analyze the textural characteristics of the materials synthesized in this study (Figure 4, Figure S7, Table 1, and Table S1). It is clear from Table 1 and Table S1 that the total pore volumes measured by the two methods are consistent. The pore size distributions were analyzed from the argon adsorption

Figure 4. (a) N2 adsorption isotherms at 77 K and (b) Ar adsorption isotherms at 87 K for the samples used in this study. The N2 isotherms for SBA-15 6.2 nm, SBA-15 8.5 nm, MCM-41 and 3DOm-i silicalite-1 were shifted 350, 550, 850, and 1450 cm3 g−1 respectively, while the Ar isotherms of SBA-15 6.2 nm, SBA-15 8.5 nm, and MCM-41 were shifted by 300, 600, and 1350 cm3 g−1 respectively. (c) Pore size distributions using the NLDFT model for Ar adsorbed in cylindrical pores of silica at 87 K. 7855

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Chemistry of Materials Table 1. Structural Properties of Materials Obtained from Ar Adsorption Isotherms and X-ray Diffraction sample

BET area (m2 g−1)

total pore volume (cm3 g−1)

micropore volume (cm3 g−1)

mesopore volume (cm3 g−1)

pore wall thickness, 2Rwall (nm)

SBA-15 5 nm SBA-15 6.2 nm SBA-15 8.5 nm 3DOm-i silicalite-1 MCM-41d

661 578 720 343 760

0.54 0.64 1.04 0.31 0.77

0.10 0.09 0.03 0.17 0

0.46 0.54 0.97 0.07 0.77

6.7c 4.4c 3.4c 35 0.54c

a

Cumulative pore volume by NLDFT up to pore size of 2 nm. bCumulative pore volume by NLDFT between pore sizes of 2 and 10 nm. cPore wall thickness = d-spacing − pore size; d-spacing was calculated from the X-ray diffraction data. dData for MCM-41 obtained from nitrogen adsorption isotherm.

cyclohexane, on account of its larger molecular size and aromaticity. 3.3. Diffusion in SBA-15. ZLC desorption curves for the diffusion of cyclohexane and 1-methylnaphthalene in SBA-15 with different mesoporosities and microporosities are shown in Figure 6. The corresponding values of D/R2 at different temperatures in Figure 7 show that the diffusion of both cyclohexane and 1-methylnaphthalene in all three samples of SBA-15 is slower than that in MCM-41 even though the mesopore sizes of SBA-15 are much larger than MCM-41. Because the particle sizes of MCM-41 and SBA-15 samples are similar, it can be concluded that mass transport of cyclohexane and 1-methylnaphthalene in SBA-15 is much slower than in MCM-41. This result suggests that Knudsen diffusion is not kinetically significant in SBA-15 in the low-molecular-coverage regimes used in the ZLC measurement. For cyclohexane diffusion in SBA-15, the D/R2 values are 1− 2 orders of magnitude lower than that in MCM-41 (Figure 7a), strongly indicating that the diffusion of cyclohexane in SBA-15 is dominated by configurational diffusion in the micropores (Figure 7a). This also agrees with the diffusion activation energy (Table 2) being significantly higher in SBA-15. Figure 7a shows that the values of D/R2 for cyclohexane in SBA-15 at a given temperature vary over an order of magnitude between the three SBA-15 samples. Because the diffusion of cyclohexane in the SBA-15 samples is dominated by configurational diffusion, the significant difference in the mass transport of cyclohexane within the three SBA-15 samples is likely due to the different extent of microporosity in the three samples. Such a difference was also observed in the diffusion of cumene and mesitylene in SBA-15 samples with varying microporosities.44 Figure 7b shows that the diffusion of 1-methylnaphthalene in SBA-15 shows a similar trend as cyclohexane diffusion as seen in Figure 7a. The diffusion activation energies of 1methylnaphthalene in SBA-15 are 65−75 kJ/mol (Table 2). These values are higher than the diffusion activation energy of cyclohexane in SBA-15, which is likely due to the stronger interaction of 1-methylnaphthalene with the microporous structures compared to cyclohexane. Due to the higher diffusion activation energy and slower diffusion compared to MCM-41, we conclude that the mass transport of 1methylnaphthalene in SBA-15 is also dominated by configurational diffusion even though its molecular size is much larger than cyclohexane. This is due to the wide size distribution of micropores in SBA-15 which provides a fraction of relatively large micropores to participate in the adsorption/desorption processes and control the overall mass transport (Figure 4d). It was also noticed that D/R2 for 1-methylnaphthalene diffusion in SBA-15 5 nm and SBA-15 6.2 nm are similar (Figure 7b) and

Figure 5. ZLC desorption curves for (a) cyclohexane and (b) 1methylnaphthalene in MCM-41. (c) Arrhenius plot showing the corresponding derived diffusivities for cyclohexane (red circles) and 1methylnaphthalene (green triangles), compared with theoretically calculated Knudsen diffusivities (red line for cyclohexane, green line for 1-methylnaphthalene) under identical conditions.

Table 2. Activation Energies Obtained from the Arrhenius Plots of the Measured Diffusivity Dataa activation energy (kJ mol−1) sample

cyclohexane

1-methylnaphthalene

SBA-15 5 nm SBA-15 6.2 nm SBA-15 8.5 nm 3DOm-i silicalite-1 MCM-41

51.9 44.2 42.0 47.5 35.7

74.9 71.7 67.6 37.1 51.7

a

The standard errors in activation energy from different sets of diffusivity measurements is less than 5%

observation is consistent with the reports from Bhatia et al. where they concluded that the diffusion of paraffins in MCM41 was dominated by surface diffusion, and the activation energy of diffusion and the isosteric heat of adsorption at zero loading increased monotonically with the carbon number of linear paraffins.42 The higher diffusion activation energy observed for 1-methyl-naphthalene in our study is likely due to stronger adsorption on the surface of MCM-41 compared to 7856

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Figure 6. ZLC desorption curves for (a) cyclohexane, (b) 1-methylnaphthalene diffusion in all SBA-15 samples, and (c) corresponding graphs showing short time analysis regions for the 1-methylnaphthalene diffusion cases.

Figure 7. Arrhenius plot showing D/R2(s−1) values for (a) cyclohexane and (b) 1-methylnaphthalene diffusion in all SBA-15 samples (black: SBA-15 8.5 nm; green: SBA-15 6.2 nm; and blue: SBA-15 5 nm), compared against corresponding values obtained for MCM-41 (red).

that mass transport of cyclohexane in 3DOm-i silicalite-1 is significantly slower than the three SBA-15 samples. In addition, the measured activation energy is comparable to that of cyclohexane diffusion in the SBA-15 samples (Table 2), further supporting the inference that neither Knudsen diffusion nor surface diffusion play a significant role in the mass transport of cyclohexane in 3DOm-i silicalite-1. It can be concluded that the diffusion of cyclohexane in 3DOm-i silicalite-1 is dominated by configurational diffusion. Interestingly, although the diffusion of

less than that in SBA- 15 8.5 nm, which could be due to the different micropore volumes in the three samples (Table 1). 3.4. Diffusion in 3DOm-i Silicalite-1. ZLC desorption curves for the diffusion of cyclohexane in 3DOm-i silicalite-1 are shown in Figure 8a. The corresponding D/R2 values (Figure 8d) are significantly smaller than those for cyclohexane in MCM-41, which indicates that Knudsen diffusion and surface diffusion are not the major transport mechanisms for cyclohexane in 3DOm-i silicalite-1. These results also show 7857

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Figure 8. ZLC desorption curves for (a) cyclohexane and (b) 1-methylnaphthalene in 3DOm-i silicalite-1. (c) Corresponding curves showing short time analysis fits for 1-methylnaphthalene diffusion in 3DOm-i silicalite-1. (d) Arrhenius plot for diffusion of cyclohexane (cyan circles) in 3DOm-i silicalite-1, compared with that in MCM-41 (red circles), SBA-15 5 nm (blue circles), SBA-15 6.2 nm (green circles), and SBA-15 8.5 nm (black circles). (e) Arrhenius plot for diffusion of cyclohexane (cyan triangles) in 3DOm-i silicalite-1, compared with that in MCM-41 (red triangles), SBA15 5 nm (blue triangles), SBA-15 6.2 nm (green triangles), and SBA-15 8.5 nm (black triangles).

cyclohexane in the three SBA-15 samples and 3DOm-i silicalite1 is dominated by configurational diffusion, the D/R2 values vary significantly between these two materials. This is likely due to the smaller and narrowed micropore size distribution in 3DOm-i silicalite-1 compared to the SBA-15 samples as well as the difference in micropore volumes among the three SBA-15 samples (Figure 4d). ZLC desorption curves and the derived D/R2 values for 1methylnaphthalene in 3DOm-i silicalite-1 are shown in Figure 8b,e, respectively. D/R2 for 1-methylnaphthalene in 3DOm-i silicalite-1 is similar to that in the MCM-41, and much larger than SBA-15 samples. This indicates that diffusion of 1methylnaphthalene in 3DOm-i silicalite-1 is dominated by surface diffusion within the mesopores rather than configurational diffusion in the micropores. This is expected because 1methylnaphthalene is too bulky to enter the micropores of 3DOm-i silicalite-1. The activation energy for 1-methylnaphthalene diffusion in 3DOm-i silicalite-1 is lower than that in MCM-41, which is possibly due to the different surface structures between the two materials. The mesopore walls of 3DOm-i silicalite-1 are microporous, whereas MCM-41 has nonmicroporous walls. The difference in the surface structure of the mesopores could provide varying strength of interactions with the sorbate resulting in different activation energies for surface diffusion. 3.5. Discussion. The results obtained from this study demonstrate that molecular transport in hierarchical porous materials is closely related to their pore structure and the interactions between the sorbate and sorbent. The transport of cyclohexane and 1-methylnaphthalene in MCM-41, a mesoporous material without micropores, is dominated by surface diffusion. This means that although Knudsen diffusion could

potentially occur, the diffusing molecules spend most of the time traveling on the surface of MCM-41. Since surface diffusion is much slower than Knudsen diffusion, the ratelimiting/dominant diffusion phenomenon for MCM-41 is surface diffusion. This outcome derives from the strong interaction between the substrate and the diffusing molecule which remains adsorbed on the surface while undergoing diffusion. Similarly, when the sorbate molecule is small enough to enter the micropores of the microporous substrates (e.g., cyclohexane in SBA-15 and 3DOm-i silicalite-1, and 1methylnaphthalene in SBA-15), the dominant diffusion mechanism becomes configurational diffusion. In these cases, both surface diffusion and Knudsen diffusion are too fast to observe, and the rate-limiting phenomenon (configurational diffusion) dominates mass transport. Again, the interaction between the substrate and the diffusing molecules is stronger when it is adsorbed in the micropores as compared to when it is adsorbed on the mesopore surface, which leads to the configurational diffusion being the dominant mass transport step. Diffusion of both cyclohexane and 1-methylnaphthalene in the SBA-15 samples is controlled by configurational diffusion. It was observed that the diffusion of both molecules is faster for the SBA-15 sample with lesser micropore volume (SBA-15 8.5 nm). As shown in Figures 6 and 7, the SBA-15 sample with the highest microporosity (SBA-15 5 nm) consistently shows lower diffusivity. This suggests that configurational diffusion within the micropores is dominant for the mass transport of 1methylnaphthalene in SBA-15. Furthermore, our data also show that the diffusion of cyclohexane in 3DOm-i silicalite-1 is slower than that in all of the SBA-15 samples, which is consistent with the observation of decreasing diffusivity with increasing 7858

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temperatures, one would expect that most of the molecules would not have sufficient energy to desorb from the micropores. Under such conditions, the observed mass transport phenomenon would shift from being configurational diffusion-dominated to being surface diffusion-dominated. A shift in the dominant transport mechanism from configurational diffusion to surface diffusion is supported by the observation that the activation energy at the lower temperature regime (right side of Figure 9) is close to the activation energy of the surface diffusion-dominated 1-methylnaphthalene diffusion in MCM-41. To the best knowledge of the authors, this is the first observation of two different kinetic regimes of diffusion in a single porous sorbate−sorbent system using the ZLC method. The fact that two regimes can be observed means that adequate care must be taken during diffusivity measurements for such materials where a significant proportion of the surface area is from the external surface, rather than from micropores. To understand the effects of the micropores on the mass transport in the hierarchical porous materials, we further analyzed the data to determine the characteristic diffusion length of the selected materials. The diffusivity (D) of cyclohexane in 3 μm silicalite-1 and the D/R2 values obtained for 3DOm-i silicalite-1 were used to calculate the diffusion length (R) of cyclohexane in 3DOm-i silicalite-1 (Table S2). In this calculation, we assumed the diffusivity of cyclohexane in the micropores of 3DOm-i silicalite-1 is identical to the large silicalite-1 sample due to the same MFI framework structure. There is a clear difference of more than 3 orders of magnitude between the calculated diffusion length (∼60−120 μm) and the pore wall half-thickness (17.5 nm) of 3DOm-i silicalite-1. This large difference suggests that the actual diffusion length of cyclohexane in 3DOm-i silicalite-1 might be much longer than expected. A different approach to consider the same data would be to calculate the apparent diffusivity of cyclohexane in these materials using the characteristic diffusion length in each

micropore volume. In the case of 1-methylnaphthalene diffusion in SBA-15 5 nm and SBA-15 6.2 nm, the D/R2 values are similar. Despite the total micropore volume of both samples being different from each other, the volume of micropores greater than 0.79 nm (kinetic diameter of 1methylnaphthalene molecule) is similar. The diffusion of 1-methylnaphthalene in the SBA-15 samples was studied between temperatures of 343 and 463 K to investigate the temperature dependence of diffusion. Aforementioned results were collected at temperatures higher than 403 K. Interestingly, at measurement temperatures above and below 403 K, two different kinetic regimes were observed in Figure 9. Due to the significant mesopore surface area as well as

Figure 9. Observation of temperature-dependent regimes in the diffusion of 1-methylnaphthalene in different SBA-15 samples.

micropore volume in hierarchical porous materials such as SBA15, both surface diffusion and configurational diffusion can occur. As discussed earlier, the dominant diffusion mechanism is determined by the strength of the interactions between the adsorbed species and the substrate. In the case of configurational diffusion, the sorbent/sorbate interaction is much stronger as compared to surface diffusion. Thus, at low enough

Figure 10. Apparent diffusivities in 3DOm-i silicalite-1 (a) and SBA-15 8.5 nm (b) calculated using R as the particle size, Rpart and pore wall halfthickness, Rwall. The experimentally measured values for diffusivities in 3 μm silicalite-1 are also included for comparison. (c) Visualization of diffusion in the three types of materials under the conditions investigated. 7859

DOI: 10.1021/acs.chemmater.6b03308 Chem. Mater. 2016, 28, 7852−7863

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Chemistry of Materials

structural surface barrier mechanisms alone cannot entirely account for the observed variation in diffusivity.41 The “effective diffusion length” mechanism proposed here, of surface diffusion and reuptake into the micropores, represents a “non-structural” surface barrier mechanism which can account for secondary transport limitations. This calls into question one of the most common assumptions that are made with diffusion measurement techniques or in general when mass transport phenomena are considered. It is commonly assumed that chemical species diffuse through a micropore/mesopore and then immediately desorb/leave the system by diffusing out of the pore and into the bulk gas phase. This is not the case when molecules adsorb into the mesopores/micropores as lower energy states. Desorption to the higher energy bulk gas state becomes the primary rate limitation, and molecules stay within the particle (either on the surface or in the micropore) until desorption occurs. The time molecules reside in the particle randomly moving through the micropores and mesopore surface results in the “effective diffusion length” that is significantly larger than the characteristic length. The thermodynamics of adsorption phenomena as well as the inherent randomness of diffusion result in the “effective diffusion length” scale which needs to be considered rather than a characteristic diffusion length based purely on the pore structure of the sorbate. Unfortunately, the effective diffusion length is not immediately obvious upon inspection/characterization of particles and can currently be determined only computationally41 or experimentally by the approaches taken herein. The difficulty in elucidating the actual diffusion path length taken by molecules in real, complex particles means that quantification of molecular transport by different techniques (e.g., ZLC and frequency response) will be limited by the lack of knowledge of the contributions of configurational, surface, or Knudsen diffusion. In other words, simple single-measurement (“one-point”) characterization of transport in hierarchical materials is not feasible. The rates of mass transport of molecules evaluated in this work are sufficiently different that one can envision the potential for diffusion-based gas separations, assuming that competitive adsorption effects are not unfavorable. For the materials used in this study, the “selectivity” has been calculated as a ratio of the D/R2 values and is shown in Figure 11.

sample. Two physical values may be used to represent the diffusion length (R) as shown in Figure 1: (i) Rwall or the pore wall half-thickness, which represents the radius of individual primary domains in 3DOm-i silicalite-1 and pore wall halfthickness in SBA-15; and (ii) Rpart, or the particle radius. Table S3 shows the calculated apparent diffusivities (Dapp) for cyclohexane diffusion in 3DOm-i silicalite-1 and SBA-15 samples based on the two different options for characteristic diffusion length. Figure 10a compares the apparent diffusivities in 3DOm-i silicalite-1 with that in 3.0 μm silicalite-1. The apparent diffusivity of cyclohexane is significantly different between the two silicalite-1 materials, suggesting that there must exist additional transport phenomena which were unaccounted for, when considering the diffusion of cyclohexane in the hierarchical porous materials. Therefore, an “effective diffusion length” is proposed to explain this difference. This mechanism may be visualized as follows: a molecule escaping from one micropore can travel either by surface diffusion (either on the mesopore surface or external surface of the particle) or by Knudsen diffusion (in the mesopore). Based on the energetics of sorbent/sorbate interaction, surface diffusion is the favorable mechanism. While traveling on the surface, there is a high probability that the molecule eventually finds another micropore and enters it, again due to favorable energetics. As this process repeats itself a number of times, the diffusion length would become much higher than the value of micropore length, which is represented by the pore wall half-thickness (Rwall). This leads to effective diffusion lengths that are much larger than the radius of the primary domain (17.5 nm) of the 3DOm-i silicalite-1. The value of the effective diffusion length would thus depend on the proportion of external surface area in the porous materialsif the proportion of the external surface area is higher, the likelihood of molecules entering more micropores from the external surface would be higher. This is true for hierarchical zeolites, zeolite nanoparticles, and mesoporous silica with microporosity due to the high proportion of external surface area (i.e., surface area not attributed to micropores). Conversely, this effect would be less significant in large zeolite crystals due to the small proportion of external surface area in comparison to the micropore surface area. For systems such as the hierarchical materials studied here, the effective diffusion length would be significantly different from the physical values commonly used to represent characteristic diffusion length (e.g., Rwall and Rpart). The probability of reuptake into the micropores would also depend on the extent of microporosity of the samples. A higher micropore volume would lead to an increased likelihood of reuptake and thus, an increased effective diffusion length. This explains the observation of varying values of D/R2 in SBA-15 samples with varying microporosity, as seen in this study (Figure 7) as well as others.44 The concept of “surface barrier” has been widely used in literature to explain variation of diffusivity between different particle sizes of zeolite and other porous materials.40,61−66 Surface barriers are a generic term used to explain different types of resistances to molecular transport occurring at the mouth of the pore due to structural aspects such as pore narrowing or pore blockage.63−66 Our calculation of effective diffusion length assumes that such structural resistances are absent, while one can expect that such structural resistances would be present. However, recent work has suggested that the

Figure 11. Diffusion-based selectivities of cyclohexane over 1methylnaphthalene at 383 K in the different porous materials used in this study, as compared to calculated theoretical Knudsen selectivity. All the D/R2 values used, except for cyclohexane diffusion in MCM-41, were measured directly using ZLC; the value for cyclohexane in MCM-41 was obtained by extrapolation of values measured using ZLC between temperatures of 303 and 343 K. 7860

DOI: 10.1021/acs.chemmater.6b03308 Chem. Mater. 2016, 28, 7852−7863

Article

Chemistry of Materials Notes

Diffusion of the bigger molecule (1-methylnaphthalene) is favored over the smaller one (cyclohexane) due to the molecular sieving effect in the micropores of 3DOm-i silicalite-1. On the other hand, diffusion of the smaller molecule is favored in both SBA-15 and MCM-41 because the dominant diffusion mechanism for both molecules within these systems are the same. In the three SBA-15 samples, due to differences in the relative micropore and mesopore volumes, the sample with the lowest micropore volume among the three (SBA-15 8.5 nm) shows an almost 4-fold improvement in selectivity compared to the one with highest micropore volume. This shows that careful design of hierarchical materials can greatly enhance the difference in diffusion of different molecules within them. Hierarchical materials can, thus, be designed in such a manner that the transport of specific molecules of interest is favored over others.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by National Science Foundation Grant No. CBET 1403542. The authors would like to thank Prof. Peter Monson, Prof. David Ford and Ashutosh Rathi for insightful discussions. The authors would also like to thank Hong Je Cho for synthesis of 3DOm-i silicalite-1 and ChunChih Chang for help with the characterization of 3DOm-i silicalite-1.

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ABBREVIATIONS ZLC, Zero Length Column; PFG-NMR, Pulsed Field Gradient Nuclear Magnetic Resonance

4. CONCLUSIONS The ZLC chromatography technique was used to study the diffusion of cyclohexane and 1-methylnaphthalene in both hierarchical (SBA-15 and 3DOm-i silicalite-1) and conventional (MCM-41 and silicalite-1) types of porous materials. It was observed that the strongest possible sorbate−sorbent interaction governs the diffusion mechanism. Similar thermodynamic drivers are proposed to cause the existence of an effective diffusion length which is significantly higher than a characteristic diffusion length determined from the physical structure of the materials. These long diffusion lengths are likely due to molecules exiting a micropore going through an intermediate surface step, thus causing the molecules diffusing on the mesopore or external surface to re-enter into other micropores before undergoing desorption. This effective diffusion length, coupled with previously proposed structural surface barrier mechanisms such as pore blockage or pore narrowing, could account for the significantly low diffusivities observed in the hierarchical porous materials due to their high external surface area. The existence of such a nonstructural surface barrier implies that there may be an upper bound for the enhancement of mass transport by size reduction or the use of hierarchical materials even if the structural surface barriers are eliminated by employing different synthetic strategies. The observation of a wide range of diffusivities for the two probe molecules in the different materials investigated in this study gives further insights into the rational design of hierarchical porous materials. Such materials can be potentially used in gas separations based purely on the different rates of mass transport of molecules rather than on a molecular sieving mechanism.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b03308. Details of ZLC model, validation of the ZLC setup, pore size distribution of MCM-41 and SBA-15 based on N2 adsorption isotherms, wide-angle X-ray diffraction pattern for 3DOm-i silicalite-1, cumulative pore volumes, and calculated effective diffusion lengths (PDF)

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REFERENCES

(1) Wei, Y.; Parmentier, T. E.; de Jong, K. P.; Zecevic, J. Tailoring and visualizing the pore architecture of hierarchical zeolites. Chem. Soc. Rev. 2015, 44, 7234−7261. (2) Ivanova, I. I.; Knyazeva, E. E. Micro-mesoporous materials obtained by zeolite recrystallization: synthesis, characterization and catalytic applications. Chem. Soc. Rev. 2013, 42, 3671−3688. (3) Möller, K.; Bein, T. Mesoporosity - a new dimension for zeolites. Chem. Soc. Rev. 2013, 42, 3689−3707. (4) Parlett, C. M. A.; Wilson, K.; Lee, A. F. Hierarchical porous materials: catalytic applications. Chem. Soc. Rev. 2013, 42, 3876−3893. (5) Luan, Z.; Hartmann, M.; Zhao, D.; Zhou, W.; Kevan, L. Alumination and ion exchange of mesoporous SBA-15 molecular sieves. Chem. Mater. 1999, 11, 1621−1627. (6) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Triblock copolymer syntheses of mesoporous silica with periodic 50 to 300 angstrom pores. Science 1998, 279, 548−552. (7) Zhao, D.; Huo, Q.; Feng, J.; Chmelka, B. F.; Stucky, G. D. Nonionic triblock and star diblock copolymer and oligomeric surfactant syntheses of highly ordered, hydrothermally stable, mesoporous silica structures. J. Am. Chem. Soc. 1998, 120, 6024−6036. (8) Corma, A. From microporous to mesoporous molecular sieve materials and their use in catalysis. Chem. Rev. 1997, 97, 2373−2419. (9) Hartmann, M. Hierarchical zeolites: A proven strategy to combine shape selectivity with efficient mass transport. Angew. Chem., Int. Ed. 2004, 43, 5880−5882. (10) Egeblad, K.; Christensen, C. H.; Kustova, M.; Christensen, C. H. Templating mesoporous zeolites. Chem. Mater. 2008, 20, 946−960. (11) Choi, M.; Na, K.; Kim, J.; Sakamoto, Y.; Terasaki, O.; Ryoo, R. Stable single-unit-cell nanosheets of zeolite MFI as active and longlived catalysts. Nature 2009, 461, 246−249. (12) Na, K.; Jo, C.; Kim, J.; Cho, K.; Jung, J.; Seo, Y.; Messinger, R. J.; Chmelka, B. F.; Ryoo, R. Directing Zeolite Structures into Hierarchically Nanoporous Architectures. Science 2011, 333, 328−332. (13) Groen, J. C.; Moulijn, J. A.; Pérez-Ramirez, J. Desilication: on the controlled generation of mesoporosity in MFI zeolites. J. Mater. Chem. 2006, 16, 2121−2131. (14) Mehlhorn, D.; Inayat, A.; Schwieger, W.; Valiullin, R.; Kärger, J. Probing Mass Transfer in Mesoporous Faujasite-Type Zeolite Nanosheet Assemblies. ChemPhysChem 2014, 15, 1681−1686. (15) Zhang, X.; Liu, D.; Xu, D.; Asahina, S.; Cychosz, K. A.; Agrawal, K. V.; Al Wahedi, Y.; Bhan, A.; Al Hashimi, S.; Terasaki, O.; Thommes, M.; Tsapatsis, M. Synthesis of Self-Pillared Zeolite Nanosheets by Repetitive Branching. Science 2012, 336, 1684−1687. (16) Tao, Y.; Kanoh, H.; Abrams, L.; Kaneko, K. Mesopore-modified zeolites: Preparation, characterization, and applications. Chem. Rev. 2006, 106, 896−910. (17) Xiao, F.-S.; Wang, L.; Yin, C.; Lin, K.; Di, Y.; Li, J.; Xu, R.; Su, D. S.; Schlögl, R.; Yokoi, T.; Tatsumi, T. Catalytic properties of hierarchical mesoporous zeolites templated with a mixture of small

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Corresponding Author

*E-mail: [email protected]. 7861

DOI: 10.1021/acs.chemmater.6b03308 Chem. Mater. 2016, 28, 7852−7863

Article

Chemistry of Materials organic ammonium salts and mesoscale cationic polymers. Angew. Chem., Int. Ed. 2006, 45, 3090−3093. (18) Č ejka, J.; Centi, G.; Perez-Pariente, J.; Roth, W. J. Zeolite-based materials for novel catalytic applications: Opportunities, perspectives and open problems. Catal. Today 2012, 179, 2−15. (19) Fernandez, C.; Stan, I.; Gilson, J.-P.; Thomas, K.; Vicente, A.; Bonilla, A.; Pérez-Ramirez, J. Hierarchical ZSM-5 Zeolites in ShapeSelective Xylene Isomerization: Role of Mesoporosity and Acid Site Speciation. Chem. - Eur. J. 2010, 16, 6224−6233. (20) Kim, J.-C.; Ryoo, R.; Opanasenko, M. V.; Shamzhy, M. V.; Č ejka, J. Mesoporous MFI Zeolite Nanosponge as a High-Performance Catalyst in the Pechmann Condensation Reaction. ACS Catal. 2015, 5, 2596−2604. (21) Cho, H. J.; Dornath, P.; Fan, W. Synthesis of Hierarchical SnMFI as Lewis Acid Catalysts for Isomerization of Cellulosic Sugars. ACS Catal. 2014, 4, 2029−2037. (22) Wang, Z.; Dornath, P.; Chang, C.-C.; Chen, H.; Fan, W. Confined synthesis of three-dimensionally ordered mesoporousimprinted zeolites with tunable morphology and Si/Al ratio. Microporous Mesoporous Mater. 2013, 181, 8−16. (23) Schneider, D.; Kondrashova, D.; Valiullin, R.; Bunde, A.; Kärger, J. Mesopore-Promoted Transport in Microporous Materials. Chem. Ing. Tech. 2015, 87, 1794−1809. (24) Kärger, J.; Valiullin, R. Mass transfer in mesoporous materials: the benefit of microscopic diffusion measurement. Chem. Soc. Rev. 2013, 42, 4172−4197. (25) Valiullin, R.; Kärger, J. The Impact of Mesopores on Mass Transfer in Nanoporous Materials: Evidence of Diffusion Measurement by NMR. Chem. Ing. Tech. 2011, 83, 166−176. (26) Mehlhorn, D.; Inayat, A.; Schwieger, W.; Valiullin, R.; Kärger, J. Probing Mass Transfer in Mesoporous Faujasite-Type Zeolite Nanosheet Assemblies. ChemPhysChem 2014, 15, 1681−1686. (27) Mehlhorn, D.; Valiullin, R.; Kärger, J.; Cho, K.; Ryoo, R. Intracrystalline Diffusion in Mesoporous Zeolites. ChemPhysChem 2012, 13, 1495−1499. (28) Bonilla, M. R.; Valiullin, R.; Kärger, J.; Bhatia, S. K. Understanding Adsorption and Transport of Light Gases in Hierarchical Materials Using Molecular Simulation and Effective Medium Theory. J. Phys. Chem. C 2014, 118, 14355−14370. (29) Mehlhorn, D.; Valiullin, R.; Kärger, J.; Cho, K.; Ryoo, R. Exploring the hierarchy of transport phenomena in hierarchical pore systems by NMR diffusion measurement. Microporous Mesoporous Mater. 2012, 164, 273−279. (30) Kärger, J.; Ruthven, D. M.; Theodorou, D. N. Diffusion in Nanoporous Materials; Wiley-VCH: Weinheim, Germany, 2012. (31) Bhatia, S. K.; Bonilla, M. R.; Nicholson, D. Molecular transport in nanopores: a theoretical perspective. Phys. Chem. Chem. Phys. 2011, 13, 15350−15383. (32) Bhatia, S. K.; Nicholson, D. Some pitfalls in the use of the Knudsen equation in modelling diffusion in nanoporous materials. Chem. Eng. Sci. 2011, 66, 284−293. (33) Christensen, C. H.; Johannsen, K.; Törnqvist, E.; Schmidt, I.; Topsøe, H.; Christensen, C. H. Mesoporous zeolite single crystal catalysts: Diffusion and catalysis in hierarchical zeolites. Catal. Today 2007, 128, 117−122. (34) Jobic, H. Diffusion of linear and branched alkanes in ZSM-5. A quasi-elastic neutron scattering study. J. Mol. Catal. A: Chem. 2000, 158, 135−142. (35) Liu, Y.; Zhang, W.; Liu, Z.; Xu, S.; Wang, Y.; Xie, Z.; Han, X.; Bao, X. Direct observation of the mesopores in ZSM-5 zeolites with hierarchical porous structures by laser-hyperpolarized Xe-129 NMR. J. Phys. Chem. C 2008, 112, 15375−15381. (36) Valiullin, R.; Kärger, J.; Cho, K.; Choi, M.; Ryoo, R. Dynamics of water diffusion in mesoporous zeolites. Microporous Mesoporous Mater. 2011, 142, 236−244. (37) Liu, Z.; Fan, W.; Ma, J.; Li, R. Adsorption, diffusion and catalysis of mesostructured zeolite HZSM-5. Adsorption 2012, 18, 493−501. (38) Remi, J. C. S.; Lauerer, A.; Chmelik, C.; Vandendael, I.; Terryn, H.; Baron, G. V.; Denayer, J. F.; Kärger, J. The role of crystal diversity

in understanding mass transfer in nanoporous materials. Nat. Mater. 2016, 15, 401−406. (39) Chang, C.-C.; Teixeira, A. R.; Li, C.; Dauenhauer, P. J.; Fan, W. Enhanced Molecular Transport in Hierarchical Silicalite-1. Langmuir 2013, 29, 13943−13950. (40) Teixeira, A. R.; Qi, X.; Chang, C.-C.; Fan, W.; Conner, W. C.; Dauenhauer, P. J. On Asymmetric Surface Barriers in MFI Zeolites Revealed by Frequency Response. J. Phys. Chem. C 2014, 118, 22166− 22180. (41) Teixeira, A. R.; Qi, X.; Conner, W. C.; Mountziaris, T. J.; Fan, W.; Dauenhauer, P. J. 2D Surface Structures in Small Zeolite MFI Crystals. Chem. Mater. 2015, 27, 4650−4660. (42) Qiao, S. Z.; Bhatia, S. K. Diffusion of linear paraffins in nanoporous silica. Ind. Eng. Chem. Res. 2005, 44, 6477−6484. (43) Qiao, S. Z.; Bhatia, S. K. Diffusion of n-decane in mesoporous MCM-41 silicas. Microporous Mesoporous Mater. 2005, 86, 112−123. (44) Hoang, V.-T.; Huang, Q.; Eić, M.; Do, T.-O.; Kaliaguine, S. Structure and diffusion characterization of SBA-15 materials. Langmuir 2005, 21, 2051−2057. (45) Huang, Q.; Eić, M.; Xiao, H.; Kaliaguine, S. Characterization of the diffusion path in micro- and meso-porous materials from ZLC analysis. Adsorption 2010, 16, 531−539. (46) Teixeira, A. R.; Chang, C.-C.; Coogan, T.; Kendall, R.; Fan, W.; Dauenhauer, P. J. Dominance of Surface Barriers in Molecular Transport through Silicalite-1. J. Phys. Chem. C 2013, 117, 25545− 25555. (47) Galarneau, A.; Guenneau, F.; Gedeon, A.; Mereib, D.; Rodriguez, J.; Fajula, F.; Coasne, B. Probing Interconnectivity in Hierarchical Microporous/Mesoporous Materials Using Adsorption and Nuclear Magnetic Resonance Diffusion. J. Phys. Chem. C 2016, 120, 1562−1569. (48) Coasne, B.; Galarneau, A.; Gerardin, C.; Fajula, F.; Villemot, F. Molecular Simulation of Adsorption and Transport in Hierarchical Porous Materials. Langmuir 2013, 29, 7864−7875. (49) Breck, D. W. Zeolites Molecular Sieves: Structure, Chemistry, and Use; John Wiley & Sons, Inc.: Hoboken, NJ, 1973. (50) Sayari, A.; Han, B.-H.; Yang, Y. Simple Synthesis Route to Monodispersed SBA-15 Silica Rods. J. Am. Chem. Soc. 2004, 126, 14348−14349. (51) Cai, Q.; Luo, Z.-S.; Pang, W.-Q.; Fan, Y.-W.; Chen, X.-H.; Cui, F.-Z. Dilute Solution Routes to Various Controllable Morphologies of MCM-41 Silica with a Basic Medium. Chem. Mater. 2001, 13, 258− 263. (52) Fan, W.; Snyder, M. A.; Kumar, S.; Lee, P.-S.; Yoo, W. C.; McCormick, A. V.; Penn, R. L.; Stein, A.; Tsapatsis, M. Hierarchical nanofabrication of microporous crystals with ordered mesoporosity. Nat. Mater. 2008, 7, 984−991. (53) Hufton, J. R.; Ruthven, D. M. Diffusion of light alkanes in silicalite studied by the zero length column method. Ind. Eng. Chem. Res. 1993, 32, 2379−2386. (54) Brandani, S.; Ruthven, D. M. Analysis of ZLC desorption curves for gaseous systems. Adsorption 1996, 2, 133−143. (55) Hsu, Y.-C.; Hsu, Y.-T.; Hsu, H.-Y.; Yang, C.-M. Facile Synthesis of Mesoporous Silica SBA-15 with Additional Intra-Particle Porosities. Chem. Mater. 2007, 19, 1120−1126. (56) Ryoo, R.; Ko, C. H.; Kruk, M.; Antochshuk, V.; Jaroniec, M. Block-Copolymer-Templated Ordered Mesoporous Silica: Array of Uniform Mesopores or Mesopore−Micropore Network? J. Phys. Chem. B 2000, 104, 11465−11471. (57) Jun, S.; Joo, S. H.; Ryoo, R.; Kruk, M.; Jaroniec, M.; Liu, Z.; Ohsuna, T.; Terasaki, O. Synthesis of New, Nanoporous Carbon with Hexagonally Ordered Mesostructure. J. Am. Chem. Soc. 2000, 122, 10712−10713. (58) Pollock, R. A.; Walsh, B. R.; Fry, J.; Ghampson, I. T.; Melnichenko, Y. B.; Kaiser, H.; Pynn, R.; DeSisto, W. J.; Wheeler, M. C.; Frederick, B. G. Size and Spatial Distribution of Micropores in SBA-15 using CM-SANS. Chem. Mater. 2011, 23, 3828−3840. (59) Zickler, G. A.; Jähnert, S.; Wagermaier, W.; Funari, S. S.; Findenegg, G. H.; Paris, O. Physisorbed films in periodic mesoporous 7862

DOI: 10.1021/acs.chemmater.6b03308 Chem. Mater. 2016, 28, 7852−7863

Article

Chemistry of Materials silica studied by in situ synchrotron small-angle diffraction. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 184109. (60) Silvestre-Albero, A.; Jardim, E. O.; Bruijn, E.; Meynen, V.; Cool, P.; Sepulveda-Escribano, A.; Silvestre-Albero, J.; Rodriguez-Reinoso, F. Is there any microporosity in ordered mesoporous silicas? Langmuir 2009, 25, 939−943. (61) Micke, A.; Bülow, M.; Kocirik, M. A Nonequilibrium Surface Barrier for Sorption Kinetics of p-Ethyltoluene on ZSM-5 Molecular Sieves. J. Phys. Chem. 1994, 98, 924−929. (62) Bülow, M.; Struve, P.; Finger, G.; Redszus, C.; Ehrhardt, K.; Schirmer, W.; Kärger, J. Sorption kinetics of n-hexane on MgA zeolites of different crystal sizes. Study of the rate-limiting transport mechanism. J. Chem. Soc., Faraday Trans. 1 1980, 76, 597−615. (63) Zhang, J.; Xiao, P.; Li, G.; Webley, P. A. Effect of flue gas impurities on CO2 capture performance from flue gas at coal-fired power stations by vacuum swing adsorption. Energy Procedia 2009, 1, 1115−1122. (64) Ruthven, D. M.; Vidoni, A. ZLC diffusion measurements: Combined effect of surface resistance and internal diffusion. Chem. Eng. Sci. 2012, 71, 1−4. (65) Gueudré, L.; Jolimaite, E.; Bats, N.; Dong, W. Diffusion in zeolites: is surface resistance a critical parameter? Adsorption 2010, 16, 17−27. (66) Ford, D. M.; Glandt, E. D. Steric hindrance at the entrances to small pores. J. Membr. Sci. 1995, 107, 47−57.

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