Diffusion anisotropy descriptor revealing morphology effect of H-ZSM-5 zeolite for olefin catalytic cracking

Zeolite morphology is vital in determining catalytic activity, selectivity and stability in zeolite catalysis, while quantitative description of morphology effect is great challenging but highly desirable. Herein, a descriptor to elucidate the morphology effect is proposed by revealing the diffusion anisotropy in straight and sinusoidal channels of H-ZSM-5 zeolite for olefin catalytic cracking. A series of H-ZSM-5 zeolites with similar nano-sheet morphology were precisely synthesized in which only the length in c-axis varies. It is unexpectedly demonstrated that the catalytic activity and stability can be obviously improved by employing samples with longer length in c-axis. Combining time-resolved in-situ FT-IR spectroscopy with molecular dynamic simulations, we revealed that the difference in catalytic performance can be attributed to the intracrystalline diffusive propensity in different channels. This work not only provides a clear descriptor revealing morphology effect, but also offers deep insight into design of highly effective zeolite catalysts for olefin catalytic cracking.


Introduction
The molecules like methanol, xenon, methane etc. are small enough to diffuse randomly through the network of two intersecting channel systems without configuration limitations [15][16][17] . However, as the size of guest molecules further increasing, such as long chain hydrocarbons (C3, C4) or aromatic molecules, an anisotropic diffusion would occur, where the escape rates of the adsorbate in the intersecting pores of ZSM-5 zeolites are diverse in different channels segments (scheme 1b) 9,15,18,19 . Therefore, differentiating diffusivities in straight and sinusoidal channels for these anisotropic molecules over H-ZSM-5 zeolites are benefit to the understanding of activity, stability or product distribution in catalysis and the guidance of catalyst design with designated morphology. The catalytic cracking of low-value C4+ olefins fractions (OCC), deriving from fluid catalytic cracking (FCC) and methanol to olefins (MTO) processes 7,[20][21][22] , represents a meaningful route to improve the ethylene and propylene production (important to the polymer industry) using H-ZSM-5 catalysts in industrial application [23][24][25][26][27] . Herein, the olefin catalytic cracking process was employed to clarify the descriptor of morphology effect in catalysis process by revealing the diffusion anisotropy in straight and sinusoidal channels of H-ZSM-5 zeolite.
In this work, several H-ZSM-5 zeolites with controllable nano-sheet morphology were precisely designed: various lengths along c-axis with comparative textures, acidities, lengths of a-axis and thicknesses of b-axis, suggesting equiform diffusion path lengths but different exposed percent of pore channels to defined crystal-facets. A home-made time-resolved in situ FT-IR spectroscopy was developed to study the diffusion properties of zeolites catalysts. Combined with experimental evidences and molecular dynamics simulations, the relationship between morphologies, catalysis behaviors and diffusion properties will be discussed in detail. The key descriptor for the morphology effect in OCC reaction was investigated. For the first time, the diffusion anisotropy behavior is studied by precise morphology adjustment to modulate the catalytic performances.
work. The X-ray diffraction patterns (XRD) in Fig. S1a displays the diffraction peaks of MFI topological structure with considerable crystallographic intensity, indicating a high and similar relative crystallinity over the samples 5,28 . All the Ar physisorption isotherms of the samples show similar shapes (Fig. S1b), indicating a comparable pore structure. The pore volumes, BET surface areas and detailed textural parameters over the samples are provided in Table S1. There are no obvious distinctions in BET surface areas and pore volumes over the selected samples. Brønsted acid sites, as shown at 1545 cm -1 in Fig. S1c, are deemed to be the active sites for olefin catalytic cracking reaction, and their numbers are summarized in Table S1h, in which the total amounts of active sites for various samples are comparative. The SEM images of these H-ZSM-5 samples are shown in Fig. 1a-f. All of the samples exhibit a coffin-like nano sheet shape, which is a typical morphology of MFI type zeolites 5,28 . The average lengths of a-, b-and c-axis over corresponding zeolites were counted from Fig. 1a-c by statistics of 100 specimens. As shown in Fig. 1a-f and Fig. S2, the samples present similar lengths of crystal along a-and b-axis, with the average size of ~250 nm and ~100 nm respectively, whereas the lengths of c-axis are apparently diverse. Z-cS presents the smallest length of c-axis with a medial of 548 nm, while the mean lengths for Z-cM and Z-cL are 970 nm and 1530 nm respectively. According to the TEM and aberration-corrected STEM images, the characteristic 10-membered ring straight channels which run along b-axis can be distinguished along the [010] plane ( Fig. 1g-j), and the sinusoidal channels which parallel to a-axis could be observed along the  Table 1b, and the detailed calculation procedures are displayed in the methods section. All of these sheet-like zeolites exhibit a dominant exposed plane of [010].
Longer c-axis results in a higher exposed degree of [010] plane and Z-cL presents the highest exposed degree up to 68.9%. Furthermore, the lattice parameters for the H-ZSM-5 crystal unit cell have been decided from X-ray diffraction methodology, and the diameters of a-, b-, c-directions in one unit cell are considered as 20.07, 19.92, and 13.42 Å in the Pnma space group (orthorhombic), as shown in the databases of IZA structure. The same results were reported in some early papers 15,16,18 . Therefore, the cross section parameters of a unit cell in various crystal facets could be presented. The [010] plane in one unit cell exhibits two pores follow the straight channel path, with a cross section of 20 Thus, the degree of exposed pore channels per unit area (/n 2 ) in corresponding exposed plane can be calculated, as listed in Table S2. Then, the proportions of the two types of channels in the selected H-ZSM-5 samples can be explicitly computed, as presented in Table 1c and d, and the detailed calculation processes are displayed in Table 1 and methods section. It can be found that as the exposed degree of [010] plane increased, the more percent of straight channels are revealed.

Catalytic behaviors over H-ZSM-5 catalysts with various morphology.
In this work, the catalytic behaviors on the cracking of C4 olefin (OCC) were explored over H-ZSM-5 catalysts with various sheet-like morphology, and the results are displayed in Fig. 2. The OCC reactions were performed with a high weight hourly space velocity of pure butene (30 h -1 ) at 550 o C, as shown in Fig. 2a and b. In the initial few hours, all of these catalysts presented a relatively stable performance, the C4 = conversion and yield of the main products C2-3 = over Z-cL are slightly higher than these over the other two catalysts. As reaction processing, the activities of these catalysts become significantly disparate, with decreased sequence of Z-cL > Z-cM > Z-cS.
To directly find out the explicit catalytic distinctions over the catalysts, the detailed C4 = conversions and C2-3 = yields at various reaction time are displayed in Fig. 2c and d. At initial 10 hours reactions, C4 = conversions are kept above 70%, with lower olefins yields of almost 30% over all catalysts. The activity of Z-cL is slightly higher than that of other two catalysts. After reacting for 50 hours, Z-cL presents a much slow decreasing tendency, of which C4 = conversion and C2-3 = yield could retain 40% and 18% after reacting for 50 h, which is obviously higher than that of other two catalysts. Generally, the reduction of particle size helps to ensure stability regarding catalyst deactivation for long-term catalytic reactions [8][9][10] . However, our experimental facts in Fig. 2 unexpectedly point out an obviously opposite result that enlarging the size along c-axis in H-ZSM-5 catalyst can result in a higher OCC catalytic activity and a better stability. It is well known that many factors in H-ZSM-5 crystal can influence the catalysis properties, such as acidities 26,29 , textural structures 27 and morphology 9-12 . On one hand, the influence of the textural structures and acid sites in our disquisitive catalysts can be excluded due to the similarity in these zeolites, as presented in Fig. S1 and table S1. On the other hand, the characters of morphology are significantly different over those selected catalysts, as shown in Fig. 1 and Table 1, which could be attributed to the probable influencing factor for the unnatural catalytic performance.

Diffusion behaviors of morphology effect over H-ZSM-5 catalysts.
To obtain better cognition of the relationship between the catalytic properties and the morphology, the uptake rates of C4 molecules (the kinetic diameter is comparable to the pore sizes of H-ZSM-5) over those three samples were compared using our home-made time-resolved in situ FTIR spectroscopy. Detailed exploratory operation conditions about this measurement as well as the original uptake curves are shown in Fig. S3 and S4. The diffusion rate (Deff/L 2 ) was applied to evaluate the diffusion resistance of these analytic samples, which can be fitted from the normalized uptake curves with Eq. 6 in methods section. Lower Deff/L 2 represents a stronger diffusion resistance in zeolite pore systems. Fig. 3a-c displays the normalized uptake curves of C4 molecules adsorption over various zeolites respectively, the uptake rates are increased in the order  Table S3), and the activation energy of Z-cS (26.4 kJ mol -1 ) is 30% higher than that of Z-cL (20.3 kJ mol -1 ).
These results further demonstrate the increase of [010] exposure degree in H-ZSM-5 crystal can reduce the diffusion resistance, resulting in a lower active energy barrier to a certain extent. The results presented in Fig. 3 have quantificationally indicated that the exposed degree of crystal-facet orientation is responsible for the various diffusion barriers in H-ZSM-5 crystals. It is worth noting that the diffusivity derived from the time-resolved in situ FTIR spectroscopy is actually the apparent diffusive rates reflecting the combination of surface and intracrystalline diffusion in the nano sheet H-ZSM-5 crystals 30,31 . The surface diffusive mechanism, though remaining unrevealed, is closely related to the external surface characteristics of H-ZSM-5 crystals 31,32 . The intracrystalline diffusion is directly attributed to the properties of nanoporous intracrystalline pore systems 33,34 . Recently, Gao et al 35,36 have proposed an approach to directly quantify dual resistance model (DRM) by deducing an approximate expression relying solely on surface permeability from the initial uptake rate (α/L): And the intracrystalline diffusivity can be fitted by the following approximation 35,37,38 : Where Deff represents the apparent diffusion coefficient, Dintra is the intracrystalline diffusive coefficient, α is the surface permeability, and L is the diffusion path length.
In order to reveal the intrinsic diffusive mechanism of the morphology effect, initial normalized uptake curves presented in Fig. 3a-c were fitted with Eq. 1 and Eq. 2. The fitted curves and the corresponding results of Dintra/L 2 and α/L are displayed in Fig. 4a-d, Fig. S7. Therefore, It can be considered that the diffusion rate in straight channels is obviously faster than that in sinusoidal channels for olefins molecules, which can explain the reason why the percent of straight channels accelerating the intracrystalline diffusivity significantly.
According to the results presented above, it can be seen that the diffusion barriers over H-ZSM-5 zeolites are significantly determined by controlling the morphology with various exposed facets degrees after excluding the influence of the textural compositions and active sites.
The diffusion anisotropy in intracrystalline channels of H-ZSM-5 crystal is considered to be the essential factor for morphology effect. Due to the preferred diffusive pathway, increasing the straight channels percent by enlarging the [010] plane degree is an efficient route to accelerate the internal diffusive rate.  Table S4 and Table S5.
Herein, the ratio of Dself-xx/Dself-yy was employed to describe the diffusion anisotropy of guest molecules in the straight and sinusoidal channels (see Fig. 5c). It is seen that these ratios for propene and 1-butene diffusion increase monotonously with the temperature and the values are smaller than 0.6, indicating that the contribution the sinusoidal channels for the diffusion of both olefins could be enhanced with temperature. In addition, the contribution the straight channels for the diffusion of higher olefins increases as the ratio for propene is higher than that of 1-butene.
These simulation results clearly demonstrate the diffusion anisotropy of olefins in MFI-structured zeolite, which depends on the temperature of diffusion and structure of guest molecules.

Catalysis-diffusion relationship.
The understanding of the relationship between the catalysis and the diffusion behavior is crucial to future H-ZSM-5 catalyst design for industrial catalysis. The experimental facts in Fig. 2 have pointed out an unexpected result that enlarging the particle size along c-axis over H-ZSM-5 catalyst can prolong the catalytic lifetime in OCC reaction. It was revealed that the intracrystalline diffusive rates of reactants over those selected catalysts are different due to the diverse characters of two-channels network, as shown in Fig. 3 and 4, which could lead to the differences of catalytic properties. Therefore, the catalytic properties, expressed by the deactivation rates of C4 = conversion and C2-3 = yield, were correlated with the intracrystalline diffusive rates of reactant molecules in internal pore channels over H-ZSM-5 catalysts, as displayed in Fig. 6a. It can be seen that the deactivation rate distinctly slowed down with the increasing of Dintra/L 2 , indicating that the intracrystalline diffusive rate plays a pivotal role in the catalytic cracking reaction over H-ZSM-5 zeolite. For the lower olefins selectivity, as shown in Fig. S8, Z-cL with faster intracrystalline diffusivity exhibits higher C2-3 = selectivity, while Z-cS with stronger internal diffusion resistance shows a lower products selectivity.
In order to further investigate how intracrystalline diffusivity is related to the catalytic lifetime and products selectivity, the three H-ZSM-5 catalysts were comparatively analyzed using TGA and Ar adsorption after 50 h of reaction ( Fig. S9 and Table S6). Particularly, the locations and the amounts of coke formation calculated using the method reported by Ryoo et al. 39 , were studied as a function of the intracrystalline diffusivity. As the result in Fig. 6b shows, although the total coke contents are similar among these three catalysts, it is of interest that the ratios of external and internal coke species are quite different. It was suggested that the coke species deposited inside the micropores is believed to induce the quick deactivation in catalysis 39,40 . The acceleration of Dintra/L 2 increased the fraction of external coke species rather than that of internal cokes inside the micropores, and decreased the microporous blockage degree, hence contributing to prolonging the catalytic lifetime. Thus, a faster intracrystalline diffusive rate would promote the reactants and products move outward the crystals during OCC reaction and delay further transformation of light olefins to heavy cokes in the micropores, which increases the resistance to deactivation and lower olefins selectivity. It has been demonstrated that the intracrystalline diffusion in H-ZSM-5 crystal, which significantly impacts the catalytic performance, is closely related to the percent of straight channels due to their molecules diffusive propensity. Therefore, we consider that the anisotropic diffusion behavior in two-channels network of H-ZSM-5 crystal is the essential mechanism for morphology effect in olefin catalytic cracking. The controlling of the percent of straight channels by prolonging the c-axis morphology in H-ZSM-5 could be applied to modulate catalyst lifetime and products yield in olefin catalytic cracking.

Discussion
In this work, A series of H-ZSM-5 zeolites with controllable nano-sheet morphology were precisely designed: the acidities, the textures, the sizes along a-and b-axis are comparative, but the lengths of c-axis are variable, suggesting that the compositions and the diffusive path lengths over these zeolites are constant, but the percents of pore channels are diverse. Then, the catalytic performances of these H-ZSM-5 zeolites in olefin catalytic cracking were investigated. It was pointed out that enlarging the particle size along c-axis in H-ZSM-5 catalyst will unexpectedly improve the catalytic activity and stability, which is distinct from the conventional rules of mass transfer behaviors in zeolites. Furthermore, based on the time-resolved in-situ FTIR spectroscopy, It was found that the apparent diffusive rates of the guest molecules were significantly boosted with the increase of exposed [010] plane degrees over H-ZSM-5 zeolites. According to the analysis of the dual resistance model (DRM), it was demonstrated that the morphology effect of diffusive properties was essentially related to the anisotropic diffusion in different channels of H-ZSM-5 zeolite. The intracrystalline diffusive rate in straight channels is faster than that in sinusoidal channels for olefins molecules, which was further confirmed by molecular dynamic simulations (MD). Therefore, the diffusion anisotropy in different channels was proposed as the descriptor for the morphology effect in olefin catalytic cracking. The controlling of the intracrystalline diffusive rate via changing the proportion of pore channels could modulate the catalytic activity and stability due to the differences in the location of the coke species in OCC reaction. In short, this work not only provides a clear diffusion anisotroy descriptor to reveal the morphology effect, but also offers a deep insight into design of highly effective zeolite catalysts for OCC process.

Synthesis of H-ZSM-5 catalysts.
The zeolite materials were prepared by hydrothermal synthesis according to previously reported conventional method 11   Products were analyzed by an online gas chromatography (Agilent 7860). The calculation of C4 = conversion was based on the moles of C4 = at inlet and outlet gases, the product selectivity was calculated on a molar carbon basis.

Measurements
Where mt is the amount adsorbed at time t (in s), m∞ is the amount adsorbed at equilibrium coverage, Deff represents the apparent diffusion coefficient, and L represents the diffusion length of H-ZSM-5 crystal. In this work, the diffusion rate, Deff/L 2 was chosen for evaluated the diffusion property of H-ZSM-5 sample.
Computational methods. molecular dynamics (MD) simulations by Forcite module in materials studio 8.0 with COMPASS-II force field were performed to investigate the diffusion properties in two-channels network over MFI type zeolite. Guest molecules loadings in pure silica zeolite were set at 32 and 24 molecules per supercell (2×2×2) for propene and butene molecule respectively, ensuring that the number of heavy atoms in each simulation was consistent. The initial structural model for each MD simulation was obtained by the Packing technology in the Amorphous Cell module. All MD simulations were performed in NVT ensemble and the temperatures were maintained by the Nose thermostat. The long-range interaction was calculated by Ewald summation method with a cutoff radius 15.5 Å. The velocity Verlet integrator is used with a time step of 1 fs. Snapshots of the positions were recorded at every 0.5ps. The simulations studies were performed at various temperatures of 323, 373, and 423 K, each for 5 ns, following an equilibration of 0.3 ns. According to the dynamic trajectory of each system, the mean square displacement (MSD) of an adsorbate molecule during a time interval τ was calculated by the following equation: Where Nm corresponds to the number of olefin molecules considered in the calculation of the MSD. Therefore, the self-diffusion coefficient Dself was obtained by fitting the MSD plots respecting to the time range 0.3~2.5ns.
Where b is the offset at time zero. In addition to the isotropic average, the anisotropic components of MSD (i.e., xx, yy, zz,) were also produced with the following equation: The self-diffusion coefficient Dself-xx and Dself-yy in the x-(sinusoidal channels of MFI type zeolite) and y-(straight channels of MFI type zeolite) directions could be respectively obtained by fitting the separate plots MSDxx and  (11)

Data availability
The data supporting the findings of this study are available from the corresponding authors on reasonable request.