Silica Nanoparticle Mass Transfer Fins for MFI Composite Materials

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Silica Nanoparticle Mass Transfer Fins for MFI Composite Materials Xiaoduo Qi, Vivek Vattipalli, Paul J. Dauenhauer, and Wei Fan Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b05400 • Publication Date (Web): 20 Mar 2018 Downloaded from http://pubs.acs.org on March 20, 2018

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Chemistry of Materials

Silica Nanoparticle Mass Transfer Fins for MFI Composite Materials Xiaoduo Qi†, Vivek Vattipalli†, 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 Ave. SE, Minneapolis, MN, 55455 United States of America ABSTRACT: Zeolite nanoparticles have been widely used to overcome diffusion limitations in heterogeneous catalytic reactions. However, the existence of surface barriers for molecular diffusion in zeolites can limit the benefits of using nanoparticles in catalytic reactions. In this study, a set of silica nanoparticle (SNP)/Silicalite-1 composites with different external surface to micropore surface ratios was synthesized to understand the effects of surface-controlled mass transport on molecular diffusion in zeolite nanoparticles. The Zero Length Column (ZLC) technique was used to evaluate the mass transport of cyclohexane in these materials. It was found that the strong sorbate/sorbent interaction at the external surface of Silicalite-1 nanoparticles can cause diffusing molecules to re-enter into micropores and repeat the micropore diffusion process. This pore re-entry step can lead to an unusually long micropore diffusion length. We also demonstrated that this repeated micropore diffusion process can be effectively reduced by mixing the zeolite nanoparticles with secondary, nonporous nanoparticles. This study provides an alternative way to justify the surface mass transfer resistance, and it also introduces a simple strategy to enhance mass transport in zeolite nanoparticles other than surface modification which can damage the integrity of zeolite crystals. Additionally, previous diffusion results were revisited by adjusting the actual micropore diffusion length. It was concluded that the surface resistance in zeolite nanoparticles is likely due to a combination of pore re-entry of adsorbates and pore blockage.

1. INTRODUCTION Zeolites are crystalline aluminosilicates with welldefined microporous structures. Due to their unique molecular sieving and catalytic properties, zeolites have been extensively utilized as catalysts to facilitate chemical reactions in petroleum refinery and petrochemical industries14 . During a typical catalytic cycle within zeolite catalysts, reactant molecules undergo a set of sequential elementary steps including surface adsorption, micropore diffusion and reaction on active sites5. For large zeolite crystals with small micropores, the reaction rate can be limited by slow intra-crystalline mass transport within micropore channels6-8. Considerable effort has been made to reduce the mass transport limitations in zeolite catalysts. Zeolite nanoparticles with short characteristic diffusion lengths have been developed to overcome mass transport limitations9-11. Hierarchical zeolites containing both mesopores and micropores have also been fabricated for this purpose to limit pressure drop in reactors12-14. Mesopores in hierarchical zeolites provide faster molecular transport for molecules to diffuse in and out from the micropores, where the active sites are located. For example, threedimensionally ordered mesoporous imprinted (3DOm-i) hierarchical MFI zeolites were made by using 3DOm carbon as a hard template15-16. These 3DOm-i hierarchical zeolites showed superior catalytic behavior compared to conventional large zeolite particles17. Other hierarchical zeolites exhibited improved catalytic performance in-

cluding the hierarchical MFI zeolite prepared by the desilication method, the monolithic Silicalite-1 consisting of nanosized crystals, the self-pillared pentasil (SPP) zeolite with a “house of cards” structure, and the multilayer MFI zeolite formed by the stacking of MFI nanosheets 11, 14, 18-19. Diffusion studies performed using various techniques (zero length column, frequency response, gravimetric uptake and pulsed-field gradient (PFG) NMR) have shown that the use of zeolite nanoparticles and hierarchical zeolites can indeed improve particle mass transport properties20-22. However, the benefits of using these materials have not been fully realized, and contradictory results have been reported by various researchers. For example, Chang et al. measured the molecular transport of cyclohexane in 200 nm Silicalite-1, SPP zeolite and 3DOm-i Silicalite-1. It was found that even though the diffusion of cyclohexane in these materials was faster than 20 µm Silicalite-1, it was not as fast as expected based on the theoretical calculation using the radius of the zeolites as the characteristic diffusion length23. The presence of a “surface barrier” in small zeolite particles has been used to explain this counterintuitive mass transport behavior24-26. ‘Surface barrier’ is a general term used to describe any additional mass transfer resistance imposed by the external surface of zeolites. For conventional zeolites with large crystal sizes, the effect of such surface resistance is negligible since the external surface only accounts for a

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small portion of the total surface area. However, in the case of zeolite nanoparticles and hierarchical zeolites with high external surface area to volume ratios, the contribution of surface resistance to the overall mass transport becomes more profound than that in large zeolites, resulting in a slower diffusion rate (D/R2). Lercher and co-workers have proposed three elementary steps involved in the mass transport through zeolites: external surface adsorption, pore entering and intracrystalline diffusion27. The overall mass transport could be controlled by any of these three steps depending on which step is the slowest. They compared the diffusion of benzene, toluene and p-xylene in large and small MFI zeolites using the frequency response method with an analysis model consisting of kinetic parameters for both diffusion and surface resistance. It was concluded that for the zeolites larger than 1.0 µm the overall mass transport was governed by intra-crystalline diffusion, whereas for the zeolites smaller than 100 nm the mass transport was surface diffusion controlled28. Gueudré et al. studied the diffusion of cyclohexane in MFI zeolites with different crystal sizes using the gravimetric uptake method. They found that the contribution of surface resistance in small MFI zeolites at low temperature accounted for more than 60% of the overall mass transport29. The origin of surface barriers has been extensively studied by both experimental and computational methods. It has been proposed that surface barriers are likely due to structural defects of zeolite crystals such as surface coking, pore narrowing, internal defects and pore blockage3036 . However, recent computational work carried out by Siepmann and co-workers has shown that even within a defect-free SPP zeolite with a large fraction of mesopores, mass transport of n-hexane is still strongly affected by the presence of a surface resistance. They proposed that the surface barrier in SPP zeolite is caused by the high free energy for relocating molecules from micropores to mesopores37. To explain the effect of surface resistance, our previous work postulated an effective diffusion length for the diffusion of cyclohexane in hierarchical zeolites and mesoporous silicas such as 3DOm-i zeolite and SBA-15. It was proposed that the strong adsorbate/adsorbent interaction at the external surface of these materials distort the actual diffusion length to be significantly longer than the characteristic diffusion length determined from the dimension of the zeolite crystals38. According to this hypothesis, the molecules desorbing from micropore channels during desorption undergo an additional surface diffusion step due to the strong molecule/surface interactions. This surface diffusion step can cause the molecules to re-enter into other micropores due to favorable energetics and diffuse an additional distance before completely desorbing from the zeolite surface. This hypothesis provides an alternative way to describe the surface resistance in a non-structural perspective as opposed to previously proposed mechanisms where the mass transport limitation is attributed to the structure inhomogeneity at the surface39-40.

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In addition to fundamental studies, practical strategies regarding the abatement of surface barriers have also been reported in the literature. One method is to modify the external surface of zeolite crystals including surface structure and composition. Wloch and co-workers applied hydrofluoric acid treatment to etch the external surface, which reduced the extent of surface resistance. After the HF treatment, the uptake rates of n-hexane and isobutane were found to be much higher than those in the untreated crystals24, 41. The study conducted by Lercher and co-workers has also shown that wrapping MFI crystals with a thin layer of silica could enhance their mass transport42. In this structure, the silica layer acted as a funnel to direct diffusing molecules into the configurations with a gradual loss of entropy which can enhance the adsorption uptakes. In this study, we expand our effective diffusion length hypothesis from hierarchical porous materials to zeolite nanoparticles by studying the mass transport of cyclohexane in SNP/Silicalite-1 composite samples. Nonporous silica nanoparticles (SNP) are mixed with microporous Silicalite-1 nanoparticles in varying ratios, and the resulting mixture transport characteristics are quantified by ZLC. The results provide support for the use of an effective diffusion length in zeolite nanoparticles; more importantly, it demonstrates a simple strategy to minimize the surface resistance without any structural modifications during synthesis. 2. EXPERIMENTAL SECTION 2.1. Synthesis of Silicalite-1. Silicalite-1 with a particle size of 80 nm was synthesized using a published method43. First, a tetrapropylammonium hydroxide (TPAOH), tetraethylorthosilicate (TEOS) and water mixture with a composition of 1.00 SiO2: 0.25 TPAOH : 11.00 H2O was placed in a Teflon vessel and aged at 353 K for 24 hr in an oil bath with stirring. Then, the aged mixture was transferred and sealed into a Teflon-lined autoclave for another 24 hr at 443 K. The resulting particles were collected and washed with deionized water by centrifugation until the pH of the solution was below 9. Finally, the sample was dried in the oven at 353 K overnight. Prior to the diffusion measurements, the samples were calcined at 823 K for 12 hr to remove organic compounds. 2.2. Synthesis of SNP. Silica nanoparticle (SNP) with a particle size of 35 nm was synthesized using an existing method 15. In short, 35 nm SNP was prepared by mixing 0.198 g of L-lysine, 13.30 g of TEOS and 180 mL of deionized water at 363 K in a Teflon bottle with a stirring rate of 1000 rpm. An additional amount of 26.60 g of TEOS was added after 24 hr and 48 hr, respectively. The solution was stirred for another 24 hr after adding the last portion of TEOS. The solution was kept in a Teflon sealed centrifuge tube for the preparation of SNP/Silicalite-1 composite. For the ZLC measurement, a small portion of the solution was dried at 373 K overnight and calcined at 873 K for 24 hr. 2.3. Synthesis of composites. SNP/Silicalite-1 composites, denoted as SNP/MFI, with surface area ratios of 0.5, 1, 5, and 10 were prepared by mixing the SNP solution and Silicalite-1 solution with known particle concentrations.


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In this study, the surface area ratio was defined as the total external surface area to the micropore surface area of Silicalite-1 crystals. A detailed synthesis procedure was described in the supporting information. Briefly, 1.0 mL of each compound solution (SNP and Silicalite-1) was added in a glass vial and dried in an oven at 373K overnight. The weight difference between the empty vial and the dried vial was recorded. Then, the external surface area of SNPs and the micropore surface area of Silicalite-1 crystals contained in 1.0 mL of SNP and Silicalite-1 solution were calculated using Eq. S1 and Eq. S2. 1.0 mL of SNP solution was used in the synthesis and the volume of Silicalite-1 solution required for a mixture with a specific surface area ratio was determined from Eq. S3. Finally, two solutions were mixed together and placed into a sonication bath for 20 mins to achieve a homogeneous mixing. The resulting product was dried into an oven at 373 K for overnight and then calcined at 873 K for 20 hr. Before the diffusion measurements, the samples were sieved to 10-20 µm in particle size to eliminate any effects caused by secondary clusters. The cluster size was confirmed by optical microscopy and scanning electron microscopy. These images are available in the supporting information. 2.4. Characterization of materials. The samples were characterized by nitrogen adsorption/desorption isotherms, X-ray diffraction (XRD) and scanning electron microscopy (SEM). Nitrogen sorption isotherms were measured on an Autosorb-iQ system (Quantachrome) at 77 K after outgassing at 573 K until pressure rise in the sample cell was less than 25 mTorr/min. Powder XRD patterns were collected on an X’Pert Pro (PANalytical) diffractometer using Cu Kα radiation with an X’celerator detector. Peaks were collected in 2θ range from 4° to 40°. SEM images were collected on Magellan 400 (FEI) equipped with a field-emission gun operated at 3.0 kV. The sample was sputter coated with Pt before the SEM measurement. 2.5. Zero Length Column for diffusion measurement. The ZLC setup used in this study has been described in our previous publications23, 38. In short, a thin layer of sample (2-3 mg) was placed between two quarterinch porous discs that were mounted in an isothermal gas chromatograph oven (5890 Series II, Hewlett-Packard). Prior to the measurement, the sample was degassed at 523 K for 8 hr in 100 sccm helium to remove any impurities. During the experiments, the samples were first saturated by a dilute stream of cyclohexane in helium. After enough

time to equilibrate, a four-way GC valve was toggled, switching the influent to a pure inert helium stream with a flow rate 100 mL/min. The desorption profile of cyclohexane from the sample was then monitored by measuring the cyclohexane concentration in the effluent using a flame ionization detector (FID). The desorption curve was used to calculate the characteristic diffusion rate (D/R2) with the ZLC long time (LT) method. A detailed derivation of the LT method and data analysis procedure are available in the supporting information. In this work, each experiment was repeated three times to achieve a good reproducibility. All flows were controlled with Brooks 5850E mass flow controllers and gas lines were maintained at 373 K throughout the measurement to avoid any condensation effect. Three criteria (partial pressure of adsorbate, equilibration time and kinetic transport control) were considered to validate the raw data collected from the ZLC setup. A detailed validation procedure is available in the supporting information. 3. RESULTS AND DISCUSSION Figure 1 shows the XRD patterns of all studied samples. The 80 nm Silicalite-1 sample exhibits the diffraction peaks from MFI topology without indication of any impurities. With the addition of SNP, the intensity of zeolite peaks is weakened, indicating a decreased fraction of zeolitic phase in the composite samples. SNP/MFI_10

Reletive intensity (a.u)

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SNP/MFI_5 SNP/MFI_1

SNP/MFI_0.5

80 nm Silicalite-1

5

10

15

20

25

30

2-Theta (Degree) Figure 1. X-ray diffraction patterns for zeolite/SNP samples. Black-80 nm Silicalite-1, red-SNP/MFI_0.5 sample, blueSNP/MFI_1 sample, pink-SNP/MFI_5 sample, greenSNP/MFI_10 sample.



Figure 2. SEM images of (a) 80 nm Silicalite-1 (b) SNP/MFI_0.5 (c) SNP/MFI_1 (d) SNP/MFI_5 (e) SNP/MFI_10 and (f) Silica nanoparticle. Zeolite component in the mixtures is highlighted by a black circle.

As shown in the SEM images (Figure 2), the Silicalite-1 sample shows a coffin-like shape with an average particle size of 80 nm, whereas the SNP sample exhibits an average size of 35 nm. The Silicalite-1 crystals and SNPs are found to be well-mixed in all composite samples. Nitrogen adsorption-desorption isotherms for all the studied samples are presented in Figure 3. For the 80 nm Silicalite-1 sample, a typical type I isotherm of microporous material was observed with a micropore uptake at low relative pressures. In the case of composite samples, hysteresis loops between adsorption and desorption branches were observed, indicating the presence of mesoporous structure corresponding to the interstitial mesopores of SNPs. No micropore volume was observed for the pure SNP sample. The analyzed results from the N2 adsorption isotherms are listed in Table 1. 1200 3

Volume at STP (cm /g)

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SNP

1000 SNP/MFI_10

800 SNP/MFI_5

600 SNP/MFI_1 400

SNP/MFI_0.5

200 80 nm Silicalite-1 0.0

0.2

0.4

0.6

0.8

1.0

Relative Pressure Figure 3. Nitrogen adsorption isotherms of SNP/Silicalite-1 samples at 77 K. Values have been offset on y axis by 200 3 cm /g for each sample.

The micropore volume of the Silicalite-1 sample obtained from the t-plot method is 0.12 cm3/g, which is a typical value for MFI zeolite44. For composites, the value of micropore volume drops from 0.12 cm3/g in Silicalite-1 sample to 0.01 cm3/g in SNP/MFI_10 sample, suggesting a

decrease in micropore fraction with the addition of nonporous SNPs. SNP/MFI area ratios were confirmed using the parameters in Table 1. These values are close to the nominal surface area ratios used in the synthesis. ZLC desorption curves for cyclohexane diffusion in the samples at different temperatures are shown in Figure 4. Dotted lines are experimental data, and solid lines represent the fitting results from the ZLC LT method. In all cases, there is good agreement between the model fitting and the experimental data. The measurements on the SNP samples were conducted at lower temperatures to ensure a transport-controlled desorption process. L values from the LT method are greater than 10 in all the measurements, indicating an internal diffusion-controlled desorption process. The validity of ZLC analysis was further evaluated by a flow study discussed in the supporting information (Fig. S2). The diffusion rate (D/R2) of cyclohexane in the 80 nm Silicalite-1 sample measured in this study is consistent with the values reported in the literature using both frequency response and ZLC method for the same system under similar conditions44-45. In all cases, the linear part of the desorption curves in the long-time region becomes steeper at higher temperatures, indicating a faster diffusion rate (D/R2) based on the LT method used for the ZLC measurement. The diffusion length (R) in the value of D/R2 obtained from the ZLC desorption curves is the actual diffusion path within an individual particle, which depends on the structure of the zeolite and diffusion mechanism. The diffusivity, D, cannot be correctly calculated from the D/R2 value without knowing the actual diffusion length, R. Therefore, instead of using diffusivity, D, the value of D/R2 directly derived from the ZLC desorption curves using the LT method were used to compare the mass transport characteristics of different samples.


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Table 1. Textural properties of the samples used in this study. Values of nominal surface ratio and calculated surface ratio from N2 adsorption/desorption isotherms are also shown. Micropore Vol3 b ume (cm /g)

External Surface 2 b (m /g)

Nominal Surface c Ratio

Calculated Surd face Ratio

323.4

0.120

93.4

SNP/MFI_0.5

272.5

0.073

98.7

0.50

0.57

SNP/MFI_1

183.5

0.026

113.0

1.00

1.60

SNP/MFI_5

125.1

0.006

109.7

5.00

7.10

SNP/MFI_10

132.8

0.001

123.0

10.00

12.50

SNP

131.0

0

130.8

2

Sample

BET Area (m /g)

Silicalite-1

a

a

b

BET area was calculated from the relative pressure between 0.05 and 0.25 of the adsorption curve using BET equation. External c surface and micropore volume were evaluated by t-plot method. Nominal surface ratio was determined using equations listed in d the supporting information. Calculated surface ratio = (External surface)/(BET Area - External Surface).

10-1

100

10-2 10-3 0

200

400

100 10-1

10-3 0

100

100

200 Time (s)

30oC

200 Time (s)

300

SNP/MFI_5

10-2 100

200 Time (s)

300

SNP

SNP/MFI_10

100

10-1

100

10-2 10-3 0

100

10-3 0

300

C/C0

10-1

200 Time (s)

10-2

100

SNP/MFI_1

10-2

10-1

10-3 0

600 800 1000 1200 Time (s)

C/C0

C/C0

SNP/MFI_0.5

80 nm Silicalite-1 C/C0

C/C0

100

C/C0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


40oC

300

50oC

10-1 10-2 10-3 0

70oC

10 Time (s)

100oC

20

125oC

Figure 4. ZLC desorption curves of cyclohexane in all studied samples at different temperatures. Symbols represent experimental data and solid lines are the fitted curves using ZLC LT method. Measurements on SNP sample were conducted under lower temperature to ensure diffusion-controlled mass transport.

The change of diffusion rate (D/R2) as a function of nominal SNP/MFI surface area ratio is presented in Figure 5. Diffusion of cyclohexane in the sample with only SNPs is found to be much faster than those in other samples. This is due to the absence of micropores in the SNP structure, such that mass transport of cyclohexane is entirely governed by surface diffusion. A sharp increase in the value of D/R2 was observed from MFI to the SNP/MFI_0.5

sample, indicating a strong dependence of mass transport with the presence of SNPs. However, the enhancement for the samples with more SNPs is less significant compared to SNP/MFI_0.5.



to hop from one adsorption site to another (the so called hopping mechanism)47-48. The value of activation energy (44.8 kJ/mol) obtained in this study for 80 nm Silicalite-1 sample is in the range of literature values, suggesting a micropore diffusion mechanism49-52. It was observed that the activation energy (20.1 kJ/mol) for cyclohexane diffusion in the SNP sample is much lower than those in mixture samples. This low activation energy obtained from the SNP sample is due to the surface diffusion of cyclohexane on the surface of the nonporous SNPs. Fig. 6(b) shows the change of activation energy with the nominal SNP/MFI surface area ratio. Despite a sharp increase in diffusion rate (D/R2), the value of activation energy remains constant through the first three samples (Silicalite-1, SNP/MFI_0.5 and SNP/MFI_1). This trend suggests that the first increase in diffusion rate as shown in Fig.5 is not from the shift of dominant mass transport mechanism (i.e., from micropore diffusion to surface diffusion). Instead, we conclude that this sharp enhancement in rate is due to a shortened micropore diffusion pathway caused by the presence of SNPs. Starting from SNP/MFI_5, as more external surface from SNPs is mixed with Silicalite-

10-2

D/R2 (s-1)

10-3

10-4

MFI

1

10

SNP

SNP/MFI Area Ratio 30°C

40°C

50°C

70°C

100°C

125°C

2

Figure 5. Plot of diffusion rate (D/R ) versus SNP/MFI area ratio at different temperatures, compared with 80 nm Silicalite-1 and pure SNP sample.

To evaluate mass transport in the composite samples with the addition of SNPs, the activation energy for the diffusion of cyclohexane in each sample was calculated. Molecular diffusion in zeolites has been known to be a temperature-activated process in accordance with the Arrhenius relationship as shown in Fig.6(a)46. The activation energy is the energy required for a diffusing molecule 10-1

10

Activation Energy (kJ/mol)

-2

2

(s-1)

60

80 nm Silicalite-1 SNP/MFI_0.5 SNP/MFI_1 SNP/MFI_5 SNP/MFI_10 SNP

(a)

D/R

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

10-3

10-4 2.4

2.6

2.8

3.0

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3.2

-1 1000/T (K )

3.4

(b) 50

Micropore Diffusion Controlled

40 30 Micropore/Surface Diffusion Controlled

20 10 MFI

1

10

SNP

SNP/MFI Area Ratio

Figure 6. (a) Arrhenius plot of cyclohexane diffusion in all studied samples. (b) The change of activation energy with nominal SNP/MFI area ratio. A transition from micropore diffusion controlled regime to surface diffusion controlled regime was observed. The cross symbol represents the activation energy of surface diffusion of cyclohexane in SNP sample.

1 crystals, the contribution of surface diffusion to the overall mass transport becomes significant, resulting in a decreased activation energy. This suggests a transition from the micropore diffusion-controlled mass transport to the surface diffusion-controlled mass transport. The change in activation energy also suggests that the sharp initial increase in D/R2 is due to a shortened micropore diffusion pathway, whereas further increases are due to the transition of governing diffusion mechanism from the micropore diffusion to the surface diffusion caused by an excess of external surface. It should be noted that surface diffusion can be different between Silicalite-1 and SNP due to different surface characteristics. However, we do not expect this disparity to be significant when compared to the difference between the activation energy of microspore diffusion within Silicalite-1 (44.8 kJ/mol) and the activation energy of surface diffusion on SNP (20.1 kJ/mol).To elucidate the diffusion pathway of cyclohexane in the zeolite nanoparticles and composite samples, the role of surface diffusion has to be considered due to the large external

surface area. In fact, the importance of surface diffusion during mass transport has already been demonstrated for mesoporous silicas. For example, the diffusion study conducted by Bhatia et al. showed that the heat of adsorption of C6 to C10 paraffins (Hexane, Heptane, Octane and Decane) on MCM-41 mesoporous silica at zero loading increased with the carbon number of the molecules53. Due to the large value of the heat of adsorption, the diffusion of C6-C10 paraffin molecules within MCM-41 mesoporous silica was governed by the surface diffusion rather than the Knudsen diffusion. Different from MCM-41 mesoporous silica, we propose that the mass transport of cyclohexane in zeolite nanoparticles is a combination of micropore diffusion and surface diffusion. The proposed diffusion pathways of cyclohexane through 80 nm Silicalite-1 and SNP/MFI composites are visualized as Fig 7. During desorption, cyclohexane molecules diffuse out from the micropores by micropore diffusion. When they reach the micropore mouths, the cyclohexane molecules could travel either by the surface diffu-


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sion along the Silicalite-1 external surface, or the Knudsen diffusion within the interstices between Silicalite-1 crystals. From an energetic point of view, desorption of molecules from a solid surface is an endothermic process, meaning that the molecules need to overcome an energy barrier to desorb from the surface. This energy barrier is associated with the interaction between the adsorbing molecules and the solid surface. In situations where diffusing molecules are not able to obtain sufficient energy to overcome the desorption energy barrier, surface diffusion becomes more favorable than the Knudsen diffusion. While molecules diffuse along the external surface, they can diffuse back into the micropores of the zeolite particles, leading to a longer micropore diffusion length. We call this mechanism as a pore re-entry mechanism since the molecule which has desorbed from one micropore enters another micropore. It should be noted that the pore re-entry step could occur either from the same Silicalite-1 crystal (intra-particle pore re-entry) or adjacent crystals (inter-particle pore re-entry). With the addition of SNPs, the diffusion pathway of cyclohexane in composite samples is altered as shown in Fig. 7 (b). In the composite samples, Silicalite-1 crystals are isolated from each other by SNPs. After the cyclohexane molecules diffuse out from the micropores, instead of diffusing along the external surface of the Silicalite-1 crys-

tals, they travel along the nonporous surface of the SNPs. As a result, it is less likely that this molecule will enter another micropores and repeat the micropore diffusion process. The reduced probability of inter-particle pore reentry step in the composite samples leads to a shortened micropore diffusion length during the overall mass transport process. However, the intra-particle pore reentry from the same zeolite crystal can still occur. For the diffusion measurement using macroscopic methods such as ZLC, frequency response and gravimetric uptake, one limitation is the lack of capability to directly obtain diffusivity (D). In these methods, to obtain the value of diffusivity, the actual diffusion length (R), must be known. As discussed earlier, the actual diffusion length depends on the pore structures of the solids and the diffusion path. From the conventional understanding of the diffusion process in zeolites, the radius of the spherical zeolite crystals was used as the actual diffusion length. For this reason, it was believed that reducing crystallite size can effectively improve mass transport of the zeolites, since the diffusion length is considered to be a monotonic function of zeolite dimensions. For the molecules with weak adsorption on the zeolite surface, this assumption is valid,

Figure 7. Proposed diffusion pathway for the mass transport of cyclohexane molecule during desorption from (a) 80nm Silicalite-1 and (b) SNP/MFI mixture. Solid circle represents secondary cluster because the possibility for diffusing molecules to remain adsorbed on the external surface and re-enter the

(1)

micropore is minimal. On the contrary, for the strongly bonded molecules such as cyclohexane, the strong sorbate/sorbent interaction at the external surface of the zeolites can distort the micropore diffusion pathway, leading to a much longer effective micropore diffusion length38. The effect of pore re-entry on the actual micropore diffusion length was further evaluated using Eq.1. In this study, the actual micropore diffusion length is considered as the sum of two terms: the radius of the Silicalite-1 crystal, R, which describes the conventional understanding of

micropore diffusion length for a spherical crystal; and , which represents the additional micropore diffusion length caused by pore re-entry. is the micropore diffusion time constant that is obtained from the ZLC measurement. is the micropore diffusivity. In this study, the value of was calculated from the diffusion measurement of SNP/MFI_0.5 using the radius of Silicalite-1 crystal (40 nm) as micropore diffusion length. It is based on the approximation that the inter-particle pore re-entry has been eliminated in SNP/MFI_0.5 sample and the overall mass transport is still controlled by micropore diffusion. This condition can be validated from Fig. 5 and Fig. 6(b), where SNP-MFI_0.5 sample shows an improved mass transport with un-


Chemistry of Materials changed activation energy as compared to pure Silicalite-1 sample, and no further increase is observed from SNP/MFI_0.5 to SNP/MFI_1 sample. The obtained values at different temperatures are listed in Table 2. At low temperature (50 oC), the actual micropore diffusion length was observed to be nearly twice as long as the radius of the crystal (40 nm). It should be noted that these values are evaluated only considering the effect of interparticle pore re-entry. If taking both intra-particle pore re-entry and surface barrier (pore blockage) into account, the additional diffusion length should be longer. It is also found that the value of decreases with temperature. High temperature facilitates the desorption of diffusing molecule from the external surface, hence reducing the extent of surface diffusion and pore re-entry on the overall mass transport process. Table 2. Additional micropore diffusion length caused by pore re-entry at different temperatures

Temp. (℃)

(nm)

50

36.8

70

32.2

100

31.0

125

30.5

In our previous studies on the mass transport properties of hierarchal zeolites and zeolite nanoparticles, a strong dependence of apparent diffusivity on the Silicalite-1 crystal size was observed for the cyclohexane/Silicalite-1 system44-45. Within the same zeolite framework, the diffusivity should not vary with crystal size; the discrepancy in the measured diffusivity was explained by the presence of a secondary and sizedependent mass transport limitation generically called a ‘surface barrier.’ To further understand the origin of surface barriers, two different mechanisms were discussed: the narrowing of the pore at the external surface which creates an additional mass transport barrier for the molecules to exit the zeolites (Pore Narrowing Mechanism), and the extension of micropore diffusion length resulting from the total pore blockage near the pore mouth (Pore Blockage Mechanism). The observation of a constant activation energy for the zeolites with different crystal sizes indicates that the surface barrier is likely due to the pore blockage mechanism. However, further Kinetic Monte Carlo simulation on the diffusion of benzene in Silicalite-1 with a particle size over three orders of magnitude showed that if the surface barrier originated exclusively from the pore blockage mechanism, 99.9% of the pores must be blocked54. This counterintuitive result implied

that the pore blockage mechanism alone is not sufficient to justify the dependence of apparent diffusivity on crystal size. In this work, we propose that the pore re-entry effect can provide an alternative explanation to rationalize the size-dependent apparent diffusivity. The effect of pore reentry is similar to pore blockage in the sense of extending the micropore diffusion length. However, unlike the pore blockage mechanism, the pore re-entry effect does not arise from the structural change of the zeolites. It means that even for a “perfect” zeolite with no surface defects such as pore blockage or pore narrowing, the extension of the micropore diffusion can still happen in the presence of strong adsorption on the external surface. To compare the pore re-entry effect with the pore blockage mechanism, the values of obtained in this study were used to re-analyze the diffusion data reported in our previous publication44. Specifically, the micropore diffusion length (R) was adjusted using additional length () to account for the pore re-entry step, and the micropore diffusivity of 80 nm Silicalite-1 crystal was evaluated using the newly defined R. The raw and re-calculated diffusivities of cyclohexane/80 nm Silicalite-1 system are plotted in Figure 8 along with the diffusivity of cyclohexane in 3.0 µm Silicalite-1. As shown in Figure 8, after taking the pore re-entry effect into account, the micropore diffusivity increases almost one order of magnitude. However, this corrected diffusivity is still much lower than that in 3 µm Silicalite-1, suggesting that neither pore blockage nor inter-particle pore re-entry can solely explain the reduction of diffusivity in small zeolite crystals. While this difference can also be caused by the presence of intra-particle pore re-entry (diffusing molecule reenters into micropore from the same zeolite crystal), we conclude that both pore blockage and pore re-entry are present in small MFI zeolites. 10-11 10-12

D (cm2/s) app

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 11

3 µm

10-13

80 nm-Recalculate 10

-14

80 nm

10-15 10-16 2.4

2.6

2.8

3.0

3.2

1000/T (K-1) Figure 8. Corrected apparent diffusivities for the diffusion of cyclohexane in 80 nm Silicalite-1 sample using the additional diffusion length obtained in this study, as compared to pre44 viously published values .

The contribution of different surface resistance mechanisms (inter-particle pore re-entry, intra-particle pore reentry, and pore blockage) to the overall surface resistance can be calculated from the remaining difference between


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the recalculated values of 80 nm Silicalite-1 and 3mm Silicalite-1 as shown in Fig. 8 (between red and blue lines) and Table 3. It can be seen that inter-particle pore reentry accounts for about 4-5% of the total surface resistance, indicating that inter-particle pore re-entry is not the major limitation to slow down mass transport of cyclohexane within the 80 nm Silicalite-1 sample. The intraparticle pore re-entry and pore blockage mechanisms are the dominant limitation for the mass transport process. The identification and reduction of intra-particle pore reentry require further studies. With regard to the pore blockage mechanism, since the kinetic diameter of cyclohexane is close to the micropore size of Silicalite-1, it is not necessary for the pore mouth to be completely blocked in order to block the cyclohexane molecule from exiting the micropore network. Thus, the pore blockage mechanism in this study should also include total pore blockage and partial pore blockage (or pore narrowing). In summary, both pore re-entry and pore blockage mechanisms can limit the mass transport in various ways depending on the property of sorbate and sorbent. Fully unveiling the nature of surface resistance still remains a challenge. Table 3. Contribution of different surface resistance mechanisms. Temp. ( )

Inter-particle pore re-entry (%)

Intra-particle pore reentry and pore blockage (%)

50

5.0

95.0

70

4.3

95.6

100

4.2

95.8

nificantly improve the micropore diffusion rate (D/R2) without changing the diffusion activation energy. An external diffusion path including a pore re-entry step is proposed to explain the experimental observation. It is proposed that the strong adsorption of cyclohexane on the external surface of Silicalite-1 crystals leads to the pore reentry of cyclohexane during the desorption step. Such a pore re-entry step creates a repeated micropore diffusion pathway which significantly extends the micropore diffusion length. With the presence of SNPs, the isolation of Silicalite-1 crystals reduce the probability of the desorbing molecule from inter-particle pore re-entry, resulting in a reduced micropore diffusion length. In addition, further analysis of the experimental diffusion data shows that the pore re-entry mechanism extends the micropore diffusion length to be two-fold longer than the radius of the Silicalite-1 crystal. By revisiting the previous diffusion study, it is proposed that surface resistance in zeolite nanoparticles is likely due to both pore blockage and pore re-entry.

ASSOCIATED CONTENT Supporting Information. The detailed synthesis procedure of SNP/Silicalite-1 composite, SEM and optical microscopy pictures of secondary clusters, ZLC flow study, ZLC data validation procedure, and ZLC model derivation are included in the supporting information.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT

The experiments reported in this study were carried out in the Henry’s law region, which represents a molecular diffusion process under low partial pressure and loading. Understanding the effect of adsorbate concentration on the surface resistance is also worth further study. Higher adsorbate concentrations will introduce the complexity arising from molecule-molecule interactions, which is relevant to applications such as catalytic reactions. At high concentration, the surface resistance could behave differently due to the accumulation of molecules both within the pores and at the pore mouth37. For hierarchical porous materials, the large external surface will adsorb more diffusing molecules than the micropore at high adsorbate partial pressure. This change of distribution of adsorbate within hierarchical porous materials could also alter the nature of the surface resistance. 4. CONCLUSIONS SNP/MFI composites with various external surface area to micropore surface area ratios were prepared. The diffusion of cyclohexane in these samples was studied using the ZLC technique. It was observed that the mixing of Silicalite-1 crystals with a small number of SNPs can sig-

This work is supported by the Catalysis Center for Energy Innovation (CCEI), an Energy Frontier Research Center, funded by U.S. Department of Energy under award number DESC 00001004.

ABBREVIATIONS SNP, silica nanoparticle; ZLC, Zero Length Column; PFGNMR, Pulsed Field Gradient Nuclear Magnetic Resonance.

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SYNOPSIS TOC. The diffusion pathway in zeolite nanocrystals is longer than the conventional understanding (i.e., radius of zeolite crystal). The longer diffusion length is likely caused by the presence of pore re-entry step due to strong surface interaction. By adding silica nanoparticles, the possibility for diffusing molecule to re-enter into micropores is reduced, leading to an enhanced diffusion rate.

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Silica Nanoparticle Mass Transfer Fins for MFI Composite Materials

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