Balancing Effect between Adsorption and Diffusion on Catalytic

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Balancing Effect Between Adsorption and Diffusion on Catalytic Performance inside Hollow Nanostructured Catalyst Dawei Yao, Yue Wang, Katherine Hassan-Legault, Antai Li, Yujun Zhao, Jing Lv, Shouying Huang, and Xinbin Ma ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.9b00282 • Publication Date (Web): 25 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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Balancing Effect between Adsorption and Diffusion on Catalytic Performance inside Hollow Nanostructured Catalyst Dawei Yao,† Yue Wang*†, Katherine Hassan-Legault,‡ Antai Li†, Yujun Zhao†, Jing Lv†, Shouying Huang†, and Xinbin Ma*†

†Key

Laboratory for Green Chemical Technology of Ministry of Education, Collaborative Innovation

Center of Chemical Science and Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People’s Republic of China

‡Department

of Chemical and Biological Engineering, University of Ottawa, Ontario K1N 6N5, Canada

Keywords: adsorption • heterogeneous catalysis • mesoscale • copper-based catalyst • mass transfer

Abstract: Hollow nanostructured materials are widely used in catalysis. Besides the large surface area, well-defined active sites and delimited cavities, the favorable catalytic performance of hollow nanostructured catalysts can be ascribed to the enrichment of reactant molecules around active species implemented by the hollow chambers. Previous studies found the enrichment of reactant is induced by surface curvature, but understanding of the structural effect still needs quantitative discussion. Herein, we elucidate the curvature effect by building nanotube assembled hollow spheres with controllable morphology. By using experimental and computational method, we demonstrate that with the increasing in hollow-sphere size, the reactant concentration inside hollow sphere decreases while the diffusion flux

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increases, which both affecting the reaction rate. This balancing effect between adsorption and diffusion induced by surface curvature suggests a unique strategy to design more efficient and selective hollow nanostructured catalysts.


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INTRODUCTION Hollow nanostructured materials with adjustable structures and delimited nanochambers have been employed in plenty of emerging research fields,1 such as catalysis,2-4 adsorption,5-6 pharmaceutical compound containers7-8 and batteries.9-10 Particularly, the unique properties of hollow nanostructure, such as large specific area, discrete hollow chambers and high porosity, have been harnessed in catalysis. These specific structural features of hollow-nanostructured catalysts exhibit superior catalytic performance, especially in high activity, favorable selectivity or stability for cascade reactions4, 11 or tandem reactions.1213

With adjustable morphologies, hollow-nanostructured catalyst not only becomes an appropriate model

for the rational design of catalyst, but also provides a facile way to investigate structural effect in catalytic reaction. Typically, the hollow-nanostructured catalysts exhibit high performance in several ways.14 First of all, the large surface area of hollow nanostructures provides a large quantity of accessible surface sites with high unsaturated-coordination, which enhances the activity.15-16 Active species can also be trapped on the interior surfaces, as well as the pores and channels on the wall of hollow structure, which is responsible for preventing sintering.17-18 Meanwhile, the delimited nanochambers easily separate multiple active sites for cascade reactions.4, 11 For catalysis inside hollow structures, the diffusion of reactant into the hollow chamber is important for the catalytic performance. The uniform channels on the wall of nanochamber are constructed to enhance the mass transfer19-20 or filter molecules to increase the selectivity.21-22 Besides, the hollow-nanostructured materials trend to adsorb more reactant molecules and concentrate inside hollow structures, resulting in an accelerated reaction rate.23-24 Theoretical studies from Prof. Pan and


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Prof. Bao demonstrated that the small molecules are prone to be concentrated inside hollow structures by Monte Carlo studies.25 Meanwhile, density functional theory further proved that the concave surface is more feasible for adsorption than the convex surface.25-26 However, the relationship among surface curvature, concentration of reactant inside hollow chamber and reaction rate needs further investigation by quantitative experiments. Recently, we reported a copper silicate nanotube-assembled hollow sphere (NAHS) to catalyze the hydrogenation of dimethyl oxalate (DMO),23 which is a key step in the synthesis of methyl glycolate (MG), ethylene glycol (EG), and ethanol from syngas (Scheme S2). We found that H2 molecules trend to enrich inside the hollow chambers, resulting in an enhanced catalytic performance. In this work, we fabricated a series of NAHSs with different hollow-sphere size, while other structural properties and active species were precisely controlled to be similar. The relationship between surface curvature and reaction rate is further investigated. By combining experimental and computational methods, a balancing effect between adsorption and diffusion inside hollow nanostructured catalysts was demonstrated. This balancing effect produces a unique approach for designing intricate hollow nanostructured catalysts. RESULT AND DISCUSSION 1. Controllable fabrication of NAHS Notably, our previous work found that the length of nanotubes in NAHS influences catalytic performance by controlling the diffusion path in continuous hydrogenation, consequently affecting the production distribution.23 Thus, to investigate the effect of hollow-sphere size on catalytic performance, the nanotube-length of NAHS must be controlled. It is widely accepted that the formation mechanism of


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NAHS is a dissolution-precipitation process, implying the dissolution of silica sphere and growth of nanotube happens simultaneously.27-28 As a result, it is difficult to separately control the hollow-sphere sizes and nanotube lengths. For instance, the NAHS with small hollow sphere could only have short nanotubes due to the lack of dissolved silicate ions (Figure S1). Meanwhile, to assemble short nanotubes on a large hollow sphere, the hydrothermal time needs to be short, which leads to an incomplete dissolution of silica core (Figure S1). Due to this growing mechanism, the traditional hydrothermal method is not appropriate to fabricate NAHSs with the same nanotube length and different hollow-sphere size, which hinders further investigation of the hollow-sphere size effect on catalytic performance.

Figure 1. The modified NAHS fabrication process. Herein, we report a modified hydrothermal treatment (Figure 1) to easily control the morphology of NAHS. Firstly, the size of hollow sphere is determined by the size of silica sphere (Figure 1A), which can be controlled by varying the proportion of water, ethanol and ammonia in Stöber method. Then the length of the nanotubes on NAHSs can be adjusted by the time of hydrothermal treatment (Figure 1B). Finally,


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the copper ion is removed to prevent further growth of the nanotubes, while extra ammonia is added to dissolve the rest silica core (Figure 1C). According to this modified method, NAHS materials with hollow-sphere sizes from 69 nm to 361 nm were fabricated (Figure 2). The nanotubes assembled on NAHSs have similar lengths of 72±4 nm and similar diameters of 4±0.1 nm (Figure S2). During hydrothermal treatment, the octahedral [Cu(OH2)6]2+ accompanied with (SiO4) tetrahedron anionic group forms the clay-type copper silicate structure.6 The [Cu(OH2)6]2+ octahedron need to rotate and warp with a certain degree to suit to (SiO4) tetrahedron, resulting in a fixed curvature of copper silicate layer and a fixed diameter (~4 nm) of all the single-layer copper silicate nanotubes.29-30 This also consists with the identical nanotube-diameters of NAHSs (Table 1). Meanwhile, the structural and physical properties of NAHSs were also characterized by nitrogen adsorption-desorption (Figure S3). All the isotherms can be attributed to type IV isotherms with hysteresis loops, indicating that the NAHSs are typical mesoporous materials. And the shape of hysteresis loops can be ascribed to cylinder-shaped pores,31 corresponding to the shape of nanotube. The pore-size distributions of these NAHSs (Figure S3B) are calculated by the BJH method, which demonstrates the uniform pore size in all the NAHSs. Except for the hollow-sphere size, the other structural and physical properties of NAHSs, such as pore volume, pore size and specific surface area, were maintained similarly (Figure S3 and Table S1). Before catalyst evaluation, all the NAHSs were reduced at 573 K in a H2 flow. The TEM images of the reduced NAHSs (Figure 2) demonstrate that although copper clusters are generated after reduction, the structures of both nanotubes and hollow spheres are completely maintained. Due to the


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similarity of structural properties, especially in length and diameter of nanotube, the NAHSs are selected here for investigating the hollow-sphere size effect on catalytic performance.

Figure 2. TEM images of reduced NAHSs with different hollow-sphere sizes. 2. Similarity of active species on NAHSs. The quantity of surface active species on NAHS were also precisely adjusted to easily investigate the effect of different surface curvature on catalytic performance. Previous studies have demonstrated that surface Cu0 and Cu+ are both active species to catalyze C–O bond hydrogenation reactions.32-35 Thus, the surface area of Cu0 and Cu+, as well as their molar ratio, have a great impact on catalytic performance. All


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the NAHSs contain copper silicate, which is verified by Fourier-transform Infrared (FTIR, Figure S4) spectroscopy with the appearance of a νSiO peak at 1040 cm-1 and a δOH vibration at 670 cm-1.36-37 With the uniform chemical compositions and copper loadings (Table S2), the active copper species of all the NAHSs should have similar surface area. The XRD patterns (Figure 3A) show broad peaks at 36.4 o and 43.3o, which can be ascribed to the Cu2O(111) plane (JCPDS 65-3288) and Cu(111) phase of metallic Cu (JPCDS 65-9743), respectively. The copper particle size is calculated using the Scherrer equation and the Cu(111) peak at 43.3o, then listed in Table S2. The dispersion of metal copper (DCu(0)) measured by N2O titration is around 22%~24% on all the NAHSs. It is apparent that the NAHSs surface area of Cu0 is also maintained due to the same copper loading and Cu0 dispersion across samples. Furthermore, no Cu2+ is present on the surface of all the NAHSs, proven by the absence of the Cu 2p satellite peak at 942-944 eV in XPS (Figure 3B). Consequently, the surface-distribution ratio of Cu0 and Cu+ can be calculated by deconvoluting the two overlapping peaks in the Cu LMM AES (Figure 3C) at binding energies of 569.8 eV and 573.1 eV, respectively. The results of Cu+/(Cu0+Cu+) shown in Table 1 vary from 21.1% to 23.2%, indicating that the distribution of surface Cu0 and Cu+ is also similar in all NAHSs. Obviously, the SCu(I) of all the NAHSs, which is calculated from the SCu(0) and Cu+/(Cu0+Cu+), is also similar. The SCu(I) is also verified by performing an in-situ FTIR CO adsorption, where the integral areas of peaks assigned to Cu+CO species at 2100-2200 cm-1 are equal (Figure 3D).32, 37 In conclusion, there is no obvious change in the surface areas of Cu0 and Cu+, as well as the ratios of these two species in all reduced NAHSs, which leads us to directly investigate the influence of different surface curvature on activity.


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Figure 3. Characterization of active species of reduced NAHSs with different hollow-sphere size. A. XRD patterns; B: Cu 2p XPS; C: Cu LMM AES (origin data: black, fitted data: red, background: green, fitted peak of Cu0: emerald, fitted peak of Cu+: blue); D: in situ FTIR spectra of CO adsorption. Table 1. Properties of structure and active species of NAHSs. Hollow Length of Diameter of nanotubesa SCu(0)b SCu(I)c Cu+/(Cu0+Cu+)d sphere nanotubesa 2 2 (nm) (m /g) (m /g) (%) size (nm) (nm) 69 69 4.08 33.6 8.9 21.1 140 68 3.96 30.4 9.3 23.5 211 70 4.04 30.3 9.1 23.1 258 72 4.10 31.8 9.0 22.2 325 76 3.92 33.4 10.1 23.2 361 75 3.95 33.5 9.7 22.5 aAverage size that measured from more than 100-200 hollow spheres or nanotubes in TEM images bDetermined by N O titration. cCalculated on the basis of S 2 Cu(0) and XCu(I) and verified by in situ FTIR spectra of CO adsorption. dCalculated from Cu LMM AES spectra.


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3. Relationship between hollow-sphere size and reaction rate. All the NAHS catalysts with different hollow-sphere sizes are evaluated for DMO hydrogenation. During this reaction, the copper active species contribute to convert DMO to MG as well as to further convert MG to EG.34-36 We use the apparent reaction rate, which is calculated from the DMO conversion rate normalized by reaction time and total number of surface Cu0 and Cu+ sites, to reveal the relationship between the hollow-sphere size and catalytic performance. The weight hourly space velocity (WHSV) is set as high as 6.4 gDMO·h-1·gcat-1 to guarantee all the active sites are solely used convert DMO to MG, with no further conversion of MG to EG. Thus, the relation between apparent reaction rate and hollow-sphere size of NAHSs is shown in Figure 4. It is notable that with the increase of hollow-sphere size, the apparent reaction rate rises at low hollow-sphere size, reaches a maximum at 211 nm, and then decreases with further increase of size. The parabolic curve indicates the reaction rate may be influenced by different effects, which are induced by changing the surface curvature of hollow sphere.

Figure 4. Apparent reaction rates of NAHSs with different hollow-sphere size. Reaction conditions: 463 K, 2.5 MPa, H2/DMO=20, WHSV=6.4 h-1.


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4. Effect of surface curvature on hydrogen adsorption We first investigate the relationship between surface curvature and hydrogen adsorption capacity to elucidate the possible effect on catalytic performance. By measuring hydrogen adsorption isotherm (Figure 5A) at reaction conditions (2.5 MPa, 463 K), the concentration of H2 inside hollow sphere is calculated via equation (1)： 𝑄𝑝

𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝐻2 = 𝑉𝑡 =

Q 𝑡 ― 𝑄𝑐 𝑉𝑡

(1)

where Qp (mol·gcat-1) is the amount of physisorbed at 2.5 MPa (reaction pressure); Qt (mol·gcat-1) is the total amount of absorbed hydrogen at 2.5 MPa calculated from the hydrogen adsorption isotherm; Qc (mol·gcat-1) is the quantity of chemisorbed hydrogen (Table S3); and Vt (m3·gcat-1) is the total volume of hollow sphere in per gram of NAHS. As we aforementioned, the lengths of the nanotubes on NAHSs are similar, as are specific surface area (Table S1) of all the NAHSs. Thus, it is reasonable to believe that the nanotubes are well-distributed on the surface of hollow sphere, resulting in a directly proportional relation between the weight of single NAHS nanostructure and the surface area of a hollow sphere. In this case, we assumed that the weight of hollow sphere surface per unit area is α (g·m-2) and the Vt can be calculated via equation (2) 1

𝑉𝑡 = 𝑁 × 𝑉𝑠 = 𝜋𝛼𝑑2 ×

𝜋𝑑3 3

𝑑

= 3𝛼 (2)

where N (g-1) is the total quantity of hollow spheres per gram catalyst, Vs (m3) is the volume of a single hollow sphere, m (g) is the weight of catalyst, and d (m) is the diameter of hollow sphere. Combining the


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equation (1) and (2), the concentration of H2 inside all the NAHSs are calculated and shown in Figure 5B. It’s worth noting that the concentration of H2 increases with increasing of surface curvature.

Figure 5. A: Hydrogen adsorption isotherms under 463 K. B: Effect of hollow-sphere size and surface curvature on hydrogen concentration inside hollow sphere. To further understand the mechanism of the curvature effect, the adsorption energies of H2 on silica surface with different curvature are studied by using density functional theory (DFT). The curved silica surfaces are obtained by twisting a SiO2 (111) surface with different angles (Scheme S1). The adsorbed hydrogen molecules are sitting above the –OH group on the curved silica surface. The distance between the hydrogen molecules and silica surface is around 3 Å, which is the equilibrium distance of the Lennard-


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Jones potential.25 Optimized structures of the silica surface and absorbed hydrogen molecule are shown in Figure 6. With increasing curvature of the silica surface, the adsorption energy decreases from -9.51 kJ/mol to -10.95 kJ/mol, indicating a stronger intermolecular force between H2 molecule and the surface. The strong intermolecular force results in the increased concentration of hydrogen molecules inside the hollow spheres. Therefore, one of the effects influencing the reaction rate is the adsorption of hydrogen. When the hollow-sphere size decreases from 361 nm to 211 nm, the H2 concentration increases, which accelerates the reaction rate and consequently enhances the catalytic performance.

Figure 6. Effect of surface curvature on hydrogen adsorption energies calculated by density functional theory. 5. Effect of hollow-sphere size on DMO diffusion Additionally, when the size of hollow sphere further decreases from 211 nm to 69 nm, an unusual decreasing of the apparent reaction rate appears. To further investigate the reason for this decline, we measured the Arrhenius plot (Figure 7A). Theoretically, the data corresponds to the Arrhenius equation


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when the fitted curve is linear, indicating that the reaction is in the kinetic control regime, and the diffusion limitation is negligible.38 However, the relations between the logarithmic of the apparent reaction rates (Rapp) and 1000/T are not linear. The fitted curve of NAHSs with 69 nm to 258 nm hollow-sphere size are curvy, indicating that the reaction is in the regime of diffusion control.38-39 Meanwhile, when reaction temperature rises, the accelerated activity induces a more severe diffusion limitation, which causes a gentler slope of the fitted curve.39-40 In the case of NAHSs with 325 nm and 361 nm hollow-sphere size, the fitted curves are relatively linear, indicating that with the increasing of hollow-sphere size, the reaction moves from diffusion control regime to kinetic control.38-39 Furthermore, the Carberry number41-42 and Wheeler-Weisz criterion43-44 are calculated to verify the influence of external and internal mass transfer limitation as well, which is detailed in Section 7 of Supporting Information. The Carberry numbers of all the NAHSs are smaller than 0.05, but the Wheeler-Weisz criterions are higher than the value of 0.1 (Table S4). These two values demonstrate that the reaction is not limited by the external mass transfer,41-43 but limited by internal mass transfer.44-45 Evidently, the limited internal mass transfer causes the decreasing of apparent reaction rate when surface curvature is increased. Thus the internal diffusion flux of DMO in all the NAHSs was calculated to quantify the effect of diffusion on catalytic performance. With the increasing of diffusion flux, the apparent reaction rate increases and no longer be restricted by the mass transfer limitation. The diffusion flux (ND, mol·m-2·s-1) of DMO can be calculated by multiplying the diffusion coefficient (Dp, m2·s-1) and the concentration gradient (dCi/dx, mol·m-3·m-1): 𝑑𝐶𝑖

( )

𝑁𝐷 = ― 𝐷𝑝

𝑑𝑥

(3)


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In the reaction condition, the ratio of mean free path and pore diameter of NAHS is 7.81 (in the range of 0.01 to 10), thus the diffusion limitation is both caused by the collision between molecules as well as the collision between the molecule and pore wall.39 The diffusion coefficient is influenced by the pore diameter of catalysts, the size of reactant molecules and the reaction conditions (see equation S8-1 to S8-4 of the supporting information). Due to the identical pore size (proved in Table 1) and same reaction conditions, the diffusion coefficients of DMO in all the NAHSs should be same. Therefore, changing of concentration gradient may be the only reason for the different DMO diffusion flux. Due to the uniform structure of NAHSs, the DMO molecules diffuse and react through the nanotube and enter the hollow sphere. Thus, the equation (3) can be changed to: 𝐶𝑜 ― 𝐶𝑖

𝑁𝐷 = 𝐷𝑝

𝑙

(4)

where Co and Ci (mol·m-3) respectively represent to the DMO concentrations outside and inside the NAHS, and l (m) is the length of nanotube on NAHS. Co is equal to the feed DMO concentration. Due to the uniform length of nanotubes as well as the well-dispersed copper active sites, catalytic ability of every nanotube on all the NAHSs should be the same. Consequently, the amount of converted DMO after passing through the nanotube is directly proportional to the surface area of hollow sphere. To calculate Ci, we here assume the remaining amount of DMO on per unit area of hollow sphere surface is β (μmol·m-2). Thus, Ci can be calculated by: 𝐶𝑖 =

𝛽𝑆𝑠 𝑉𝑆

𝜋𝑑2𝛽

=1

3 6𝜋𝑑

(5)

where SS (m2) and VS (m3) represent the surface area and inner volume of one single NAHS, respectively, and d (m) is diameter of hollow sphere.


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Then, equation (4) can be changed to: 𝐶𝑜 ―

𝑁𝐷 = 𝐷𝑝

10 ―7𝜋𝑑2𝛽 1 3 𝜋𝑑 6

𝑙

(6)

According to equation (6), the DMO diffusion flux of all the NAHSs is shown in Figure 7B. Notably, DMO concentration inside the hollow sphere decreases with the increasing hollow-sphere size, while the DMO concentration outside of NAHSs is the same. Consequently, the concentration difference between the inside and outside of the hollow sphere increases with increasing hollow-sphere size, leading to a more intensified diffusion flux. Therefore, the concentration gradient of the larger hollow sphere is much higher than that of the smaller size, resulting in a higher diffusion flux in the NAHSs with increased hollowsphere size. Furthermore, when the hollow sphere is large enough, the inner concentration of DMO is extremely low. As such, the diffusion flux is close to the maximum of 12.2 (10-3 mol·m-2·s) and increases slightly with the growing of hollow-sphere size. This is consistent with Figure 7A, in which the reaction of NAHS with large hollow sphere is demonstrated to be slightly limited by diffusion.


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Figure 7. A. Relationship of the logarithmic apparent reaction rate (lnRapp) as a function of 1000/T. Reaction conditions: 2.5 MPa, H2/DMO = 20. B. Effect of hollow-sphere size on DMO diffusion flux. 6. Balancing effect between adsorption and diffusion inside NAHSs As we aforementioned, both physical properties and accessible active sites across all the NAHSs is the same. According to the different trends between hydrogen concentration and DMO diffusion flux of NAHSs (Figure 8), it is concluded that the size of hollow chambers affects two crucial factors, adsorption and diffusion of reactant molecules, which directly influence catalytic performance. The increasing hollow-sphere size causes both a decrease of hydrogen concentration and an increase of DMO diffusion flux. These two opposing effects on catalytic performance result in a parabolic trend between apparent


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reaction rate and hollow-sphere size. Moreover, the hollow sphere with extremely small or large size hampers the mass transfer of DMO or decreases the concentration of hydrogen, leading to an unsatisfying activity.

Figure 8. Balancing effect between adsorption and diffusion inside hollow sphere. 7. Influence of the reactant molecular size on adsorption-diffusion effect As we previously demonstrated, the diffusion coefficient is also influenced by the molecular size of reactant. To investigate the influence of reactant molecular size on the balancing effect of adsorption and diffusion, we chose two other straight-chain esters, methyl acetate (MA) and diethyl oxalate (DEO), for


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hydrogenation to evaluate the catalytic performance of NAHSs with different hollow-sphere size. The results are compared in Figure 9. When the hollow-sphere size increases, the apparent reaction rate of MA hydrogenation decreased linearly, while those of DMO and DEO hydrogenations changed according to volcano trends. Based on the evaluation results, the Carberry numbers and W-W groups of MA and DEO were calculated as well (Table S4). It is found that the diffusion limitation is not present in MA hydrogenation, while the DEO and DMO hydrogenations are limited by internal diffusion. Thus, there are two possible situations governing catalytic performance for differing hollow-chamber size, dependent on the reactant molecular size. For small molecules, such as MA, decreasing the hollow-chamber size enhances the adsorption, and linearly enhances the activity (Figure 9A). In comparison, for reactants of larger molecular size, such as DMO and DEO, decreasing the hollow-chamber size enhances adsorption but inhibits diffusion, resulting in the volcano trend between reaction rate and hollow-sphere size. Moreover, the optimized hollow-sphere size for DEO hydrogenation (258 nm) is larger than the optimized one for DMO hydrogenation (211 nm). The larger size of DEO caused a decreased the diffusion coefficient (Dp), which leads to a stronger diffusion limitation. Accordingly, the hollow-sphere size needs to be larger to increase the concentration gradient and subsequently enhance diffusion. In designing the hollow nanostructured catalysts, the molecular size of reactant should therefore be considered. When the mass transfer is not limited, the size of hollow nanostructured catalysts should be small to concentrate the reactant and enhance the activity. Conversely, when the diffusion limitation exists, the designed void of hollow chamber should be larger to enhance the diffusion. In order to obtain the highest activity, the


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balancing effect between adsorption and diffusion, which are both induced by the hollow-chamber effect, should be seriously considered.

Figure 9. The relationship between apparent reaction rate (RAPP) and hollow-sphere size in different hydrogenation reactions. A: methyl acetate hydrogenation. B: Dimethyl oxalate hydrogenation. C: Diethyl oxalate hydrogenation. Reaction conditions: 463 K, 2.5 MPa, H2/reactant=20

CONCLUSIONS In summary, we demonstrate the influence of surface curvature on catalytic performance by precisely fabricating NAHSs with different sizes of hollow spheres. The similarity of other physical properties, as well as accessibility of active sites, are accurately controlled to exclude their influences on activity. With


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the hollow sphere size rises, the reaction rate increases at first and then decreases. Combining experimental and computational methods, we proved this volcano-trend catalytic performance is induced by a balancing effect between reactant concentration inside hollow sphere and diffusion flux. The hydrogen concentration is increased with decreasing hollow-sphere size, while the reactant diffusion is accelerated with increasing hollow-sphere size. The mid-sized hollow chamber is appropriate for both reactant adsorption and mass transfer, leading to an excellent catalytic performance. Meanwhile, when the diffusion coefficient decreases, the optimized hollow-sphere size shifts to a larger size to enhance the diffusion and obtain the highest activity. We first propose this general balance effect between adsorption and diffusion induced by surface curvature and hollow structures, and demonstrate a new progress in studies of the morphological effect in catalysis reaction. This balancing effect produces more effective and conscious approaches for the design and fabrication of intricate hollow nanostructured catalysts.

ASSOCIATED CONTENT The Supporting Information is available free of charge on the ACS Publications website.

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


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ACKNOWLEDGMENTS We gratefully acknowledge support from the National Key R&D Program of China (2018YFB0605803), the National Natural Science Foundation of China (21325626, 21706814), Natural Science Foundation of Tianjin City (18JCQNJC06100) REFERENCES 1.Zhu, W.; Chen, Z.; Pan, Y.; Dai, R.; Wu, Y.; Zhuang, Z.; Wang, D.; Peng, Q.; Chen, C.; Li, Y. Functionalization of Hollow Nanomaterials for Catalytic Applications: Nanoreactor Construction. Adv. Mater. 2018, 1800426. 2.Pan, X.; Fan, Z.; Chen, W.; Ding, Y.; Luo, H.; Bao, X. Enhanced Ethanol Production inside Carbonnanotube Reactors Containing Catalytic Particles. Nat. Mater. 2007, 6, 507-511. 3.Yin, Y.; Rioux, R.; Erdonmez, C.; Hughes, S.; Somorjai, G.; Alivisatos, A. Formation of Hollow Nanocrystals Through the Nanoscale Kirkendall Effect. Science 2004, 304, 711-714. 4.Yang, Y.; Liu, X.; Li, X.; Zhao, J.; Bai, S.; Liu, J.; Yang, Q. H. A Yolk-Shell Nanoreactor with a Basic Core and an Acidic Shell for Cascade Reactions. Angew. Chem. Int. Ed. 2012, 51, 9164-9168. 5.Zhang, Y.; He, Z.; Wang, H.; Qi, L.; Liu, G.; Zhang, X. Applications of Hollow Nanomaterials in Environmental Remediation and Monitoring: A review. Front. Environ. Sci. Eng. 2015, 9, 770-783. 6.Wang, X.; Zhuang, J.; Chen, J.; Zhou, K.; Li, Y. Thermally Stable Silicate Nanotubes. Angew. Chem. Int. Ed. 2004, 43, 2017-2020.


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Balancing Effect between Adsorption and Diffusion on Catalytic

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