Introduction

Molecules, due to thermal energy, are subject to a continuous irregular movement, referred to as diffusion, in all states of matter1. However, confined diffusion in nanoporous materials is intriguing and exhibits many peculiarities compared with that in the condensed phase2,3,4,5,6. For example, “single-file diffusion”, the restricted motion of interacting particles in narrow micropores with mutual passage exclusion prevalent in many processes, does not obey Fick’s laws7,8. In contrast to the case in homogeneous media with monotonically decreasing diffusion behavior for various alkane molecules, a phenomenon called “resonant diffusion” was presented where the diffusion coefficient varies periodically with the molecular chain length9,10,11. Notably, diffusion is generally faster at a higher temperature, but our previous work has shown the movement of long-chain molecules slows as the temperature increases under confinement, which is due to the “thermal resistance effect”12. Kolokathis et al. studied the diffusion of aromatics in silicalite-1 by quasi-elastic neutron scattering (QENS) and molecular dynamics simulations; they found that the p-xylene diffused faster than benzene due to lower entropic barriers13. Other interesting effects, including the “levitation effect”14,15,16,17,18,19, “incommensurate diffusion”20, “window effect”21,22, and “trapdoor effect”23,24,25,26 have also been found inside the confined space. It is worth noting that only some of the phenomena mentioned above have been experimentally confirmed (Supplementary Table 1).

Transportation of adsorbates in confined channels is controlled by the interplay between adsorbent–adsorbate and adsorbate–adsorbate interactions, and thus molecular diffusion through pores occurs via different mechanisms6,27,28,29,30,31,32. Normally, diffusion is generally slower for larger molecules due to their stronger adsorption energy. For instance, Gao et al. measured the diffusion coefficients of different alkane species in DNL-6 zeolite by pulsed field gradient NMR (PFG-NMR) and found that they followed the order of CH4 > C2H6 > C3H828. Jobic et al. showed that diffusion of branched alkanes (a bulkier molecule) was much slower than the one of linear alkanes (smaller molecule) in ZSM-5 by QENS33. Van Baten and Krishan showed branched isomers of hexane had lower self-diffusivity than n-hexane34, and Schuring et al. reported that the self-diffusion coefficient of n-hexane was higher than 2-methylpentane35. Verploegh et al. predicted the diffusivities of 30 small molecules in various metal-organic frameworks and found that self-diffusivities decreased with the molecular sizes36. DeLuca and other groups predicted the diffusion by adsorption energy, adsorption entropies, and diffusion barriers, which indicated that diffusion was slower for larger molecules in a stronger confined system29,37,38,39. Overall, it was suggested that the diffusion was faster for molecules with small size under a less confined environment.

Symmetry pervades our lives40, which also strongly affects diffusion, especially in the confined environment. For the MOF materials, it was illustrated that the introduction of asymmetry in the pore blocking the diffusion of tetrahedral methane while allowing linear nitrogen to permeate in the process of nitrogen removal from nature gas41. Sharma et al. showed that “levitation effect” (fast diffusion) could only take place for symmetric molecules under confinement42. Several groups tried to recover asymmetric diffusion. For example, Shaw et al. claimed asymmetric diffusion mainly came from an asymmetry in the geometry of the pores43, while Kolomeisky et al. suggested that the interaction potential asymmetry strongly controlled the diffusion44. Other explain to asymmetric diffusion by the fact of the molecular shape, charge asymmetry, and asymmetric jump45,46,47,48,49. Although asymmetric diffusion has been extensively studied, however, the fundamental understanding and quantitative description of molecular asymmetric diffusion under confinement, as well as experimental verifications were still missing.

Zeolites are ideal microporous materials for studying the confinement effect because the channels and pores of these crystalline structures have precise dimensions50,51,52. In this work, the anomalous behavior in diffusion for varied dihalobenzene molecules in zeolites was observed, where the traditional view that the diffusion coefficient is related to the molecular size and molecular weight has been broken, where a smaller molecule with weaker adsorption moved slower than a larger one with stronger adsorption under confinement. The effect of molecule species, the framework, the temperature and loading on diffusion have also been considered, which clearly illustrates the robust to asymmetric rotations slow diffusion under confinement. In addition, several types of experiments were performed to determine molecular diffusion property. The results provide insights into the mechanism of diffusion slowed by asymmetric rotations inside confined systems.

Results

First, the diffusion behaviors of molecules in the bulk phase were studied, and the self-diffusion coefficient (Ds) was used to quantitatively describe the movement of guest molecules6. The initial structure of various m-dihalobenzenes (C6H4F2, C6H4BrF, and C6H4Br2) in the bulk phase is depicted in Fig. 1A and Supplementary Fig. 1 and the parameter sets are listed in Supplementary Table 2. It shows that both the density (Supplementary Table 3) and the molecule size (Supplementary Figs. 2 and 3) follow the order of C6H4F2 < C6H4BrF < C6H4Br2. The Ds were quantitatively determined based on molecular dynamics (MD) simulations and the slope of the mean square displacement (Supplementary Fig. 1) values, which were 2.21 ×10−9, 1.35 ×10−9, and 0.74 ×10−9 m2/s for C6H4F2, C6H4BrF, and C6H4Br2, respectively (Fig. 1D). Then, we performed pulsed field gradient (PFG) NMR (Supplementary Methods) to investigate the diffusion behavior for three molecules in the bulk phase at 298 K. The echo-attenuation from 1H PFG NMR followed a mono-exponential decay model well (Fig. 1B), and the self-diffusion coefficients of three substituted benzene molecules were observed in the following order: C6H4F2 (3.56 ×10−9 m2/s) > C6H4BrF (1.80 ×10−9 m2/s) > C6H4Br2 (0.75 ×10−9 m2/s) (Fig. 1E). The simulated self-diffusion coefficients agree reasonably well with results from PFG NMR, which suggest that the diffusion was strongly related to the size and weight of molecules. In particular, the diffusion was slower for larger molecules in the bulk phase.

Fig. 1: Diffusion in the bulk phase and inside zeolite.
figure 1

A Initial structures of C6H4BrF (1-bromo-3-fluorobenzene) in the bulk phase. B The spin echo-attenuation of PFG NMR as a function of \({{{{\rm{\delta }}}}}^{2}{\gamma }^{2}{g}^{2}\)(\(\Delta -\delta /3\)) on the log-linear scale for C6H4F2, C6H4BrF and C6H4Br2 in the bulk phase. I and I0 are the signal amplitudes with and without gradient strength (g), \(\gamma\) is the gyromagnetic ratio of the 1H nucleus, \(\delta\) is the effective gradient pulse duration, \(\Delta\) is the diffusion time. C Initial structures of C6H4BrF inside AFI zeolite. The dark green, white, cyan and dark red balls represent C, H, F and Br atoms, respectively; yellow represents zeolite framework. Self-diffusion coefficient (Ds) for various molecules in the bulk phase by D MD simulation and E PFG-NMR technique. F Ds for various molecules inside AFI zeolite by MD simulation at 298 K.

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Next, we turned our attention to the diffusion behaviors of these molecules in zeolite with AFI topology (pore size is 7.3 ×7.3 Å2, Supplementary Fig. 4) under confinement (Fig. 1C and Supplementary Fig. 5). The diffusion order differed for dihalobenzene molecules in the bulk phase. As shown in Fig. 1F, the Ds are 1.25 ×10−8, 0.93 ×10−8, and 1.14 ×10−8 m2/s for C6H4F2, C6H4BrF, and C6H4Br2, respectively, which are inconsistent with the molecular size and adsorption energy (Supplementary Fig. 6). For example, the Ds of C6H4Br2 molecule with a bulkier size and stronger interaction (−19.5 kcal/mol) is relatively larger than that of C6H4BrF with smaller size and less interaction (−18.6 kcal/mol). This was a counterintuitive diffusion behavior, and the diffusion mechanism could not be uncovered by adsorption energy38.

To understand the above-mentioned phenomena of different trends of diffusion for dihalobenzene molecules in the bulk phase and inside zeolite, the diffusion trajectories, which can give quantitative information on molecular motion, were obtained28,53,54. Figure 2A–C shows the trajectory of center-of-mass (COM) for various representative molecules along the channel of AFI (direction [001]) zeolite. It clearly shows that C6H4F2 molecular trajectory is the longest, followed by C6H4Br2 and C6H4BrF (statistical results are shown in Table 1). These results agree with the order of Ds, further indicating that the diffusion trajectories can be used to analyze the diffusion behaviors28. Specifically, the maximum diffusion distances for molecules are mainly due to the significant successive jump in the same direction (Supplementary Fig. 7)49,55, such as the jump with long distance for C6H4F2 during 645–655 ps (Fig. 2A, D), as well as for C6H4Br2 during the 515–525 ps (Fig. 2C, F). However, few notable jumps are detected for C6H4BrF molecules; they preferred the back and forth motion (Fig. 2B), which corresponds to the slowest diffusion. In addition, in contrast to the forward rotational motion of C6H4F2 and C6H4Br2, a marked local rotation with less translation is found for C6H4BrF (e.g. 445–455 ps in Fig. 2B, E). These results indicate a large jump of C6H4F2 and C6H4Br2 (Fig. 2D, F) may boost transport, while local dwellings combined with rotation (Fig. 2E) of C6H4BrF hinder diffusion.

Fig. 2: Trajectories inside AFI zeolite.
figure 2

Trajectory of center-of-mass for one representative A C6H4F2, B C6H4BrF, and C C6H4Br2 in AFI zeolite along the direction [001] (Z) for 1000 ps. Diffusion process for D C6H4F2, E C6H4BrF, and F C6H4Br2 along the direction [001] for 10 ps. Three-dimensional trajectory of normalized C‒F and C‒Br bond vector for G C6H4F2, H C6H4BrF, and I C6H4Br2 in AFI zeolite. The dark green, white, cyan and dark red balls represent C, H, F and Br atoms, respectively.

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Table 1 Diffusion parameters
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To evaluate the different rotation behaviors for dihalobenzene molecules, three-dimension (3D) normalized rotational trajectories56,57 for the C‒F (\({{v}^{ \rightharpoonup }}_{{CF}}\)) and C‒Br (\({{v}^{ \rightharpoonup }}_{{CBr}}\)) bonds were obtained. Figure 2G–I shows that the rotational trajectories are symmetric for two \({{v}^{ \rightharpoonup }}_{{CF}}\) and \({{v}^{ \rightharpoonup }}_{{CBr}}\) vectors of C6H4F2 (Fig. 2G and Supplementary Fig. 8A) and C6H4Br2 (Fig. 2I and Supplementary Fig. 8C) with symmetry. In addition, due to the short C‒F bond, C6H4F2 can rotate freely with a wide range of rotational trajectories (Fig. 2G), whereas C6H4Br2 can only swing along the direction Z because two long C‒Br bonds (Fig. 2I and Supplementary Fig. 8C) inhibit rotation. However, there was no symmetry for C6H4BrF transport, along with a local swinging motion of the C‒Br bond as well as more free rotation of the C‒F bond (Fig. 2H and Supplementary Fig. 8B). Overall, it seems that asymmetric rotation can affect diffusion.

Based on the diffusion trajectory profiles (Fig. 2A–C and Supplementary Fig. 7), the diffusion process can be regarded as a jump-like diffusion, which was directly determined by residence time and jump length between two neighboring basins or cages (Supplementary Fig. 9)28,58,59. Table 1 shows the diffusion radius (R) for various molecules in AFI during the diffusion time of 10 ns. Apparently, R follows the order of C6H4F2 (141.6 Å) > C6H4Br2 (136.1 Å) > C6H4BrF (118.1 Å), which is consistent with the order of Ds. Our previous work has shown a continuous-time random-walk (CTRW) coarse graining method can quantitatively investigate the diffusion process by residence time and jump length28,60. Generally, shorter residence time (t) in one basin and longer jump length (d) between two consecutive basins lead to fast diffusion with a longer diffusion radius. As presented in Table 1, the jump length is almost the same, indicating that d is not the main factor for the diffusion differences. Fortunately, the residence time is 62.4, 91.8 and 70.5 ps for C6H4F2, C6H4BrF, and C6H4Br2, respectively, which is inverse to the order of Ds, indicating the increased local residence time slowed the diffusion. However, it should be noted that, due to the lack of correlation between rotation and translation, we could not yet reveal the microscopic mechanism of the slowest translation of C6H4BrF with the longest residence time.

Several investigations have been done to evaluate the diffusion behaviors from both translation and rotation, which indicated that the interaction between guest and host was important to uncover the diffusion mechanism13,61,62,63. The reduced density gradient (RDG) visualization of the iso-surfaces method (Supplementary Methods) was employed to study the interaction between the guest and host (Fig. 3A–C). It shows that the interaction between zeolite and Br atoms (Fig. 3B, C) is much stronger (the large green region representing van der Waals interaction) than that with F atoms (Fig. 3A, B), and thus the anomalous behavior in diffusion is caused by the presence of the specific and selective interaction of the asymmetric guest with the pores. Here, because C6H4BrF is an asymmetric molecule but C6H4Br2 and C6H4F2 possess symmetry, we tried to correlate the asymmetric rotation and translation. First, the 2D contour plots of probability distribution49 between the rotational angle difference (Δθ) and translation displacement (ΔX) at a time interval of 100 ps are shown in Supplementary Fig. 10. We found that Δθ from two halogen atoms is mainly in the region of −90° to 90° for C6H4F2, as well as −60° to 60° for C6H4Br2, indicating a symmetric rotation for symmetric molecules. However, the region of rotational angle difference was different (−90° < Δθ < 30°), demonstrating that some parts of rotation seriously deviated from symmetry because the C‒F bond rotated faster than the C‒Br bond for C6H4BrF. Regardless of the shape of the molecules, the position with the largest translation distance corresponded to the case where the rotation angle difference was zero, indicating marked jumps were present when the angular rotations were symmetrical.

Fig. 3: Interaction energy and two-dimensional free energy.
figure 3

Isosurface plots of reduced density gradient (isovalue = 0.500 a. u.) for (A) C6H4F2, (B) C6H4BrF, and (C) C6H4Br2 in AFI zeolite. The isosurfaces of reduced density gradient were colored according to the magnitude of sign(λ2)ρ, and the RGB scale was indicated. The green region represents van der Waals interaction. The dark green, white, cyan and dark red balls represent C, H, F and Br atoms, respectively. Two-dimensional free energy contour plots correlate rotational angle difference (Δθ) and translational displacement (ΔX) for (D) C6H4F2, (E) C6H4BrF, and (F) C6H4Br2 in AFI zeolite, at a time interval of 100 ps. Kb and T are Boltzmann constant and temperature, respectively.

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Furthermore, to evaluate the hindered diffusion behaviors of probe molecules, the 2D free energy contour plots, which can detect simultaneous rotation and translation, were performed. As listed in Fig. 3D–F, the lowest free energy less than 8 KbT is presented in the region (blue color) where both the rotational angle and translational motion are small, suggesting that molecules are strongly bound in the channel under confinement. In addition, the movement area follows the order of C6H4F2, C6H4BrF, and C6H4Br2, which is the same as the order of molecular size. Specifically, on the iso-free-energy surface (e.g. 9 KbT), the larger the asymmetric rotation (Δθ), the shorter the translational distance (ΔX). Other 2D free energy correlated rotation and translation at different time intervals are shown in Supplementary Fig. 11; these results suggest asymmetric rotations slowed the translation in AFI zeolite. Figure 3D, F shows that there are asymmetric rotations (Δθ ≠ 0) even for symmetric molecules under confinement. And thus, due to the channel of AFI zeolite restricts the asymmetric rotation of C6H4Br2 molecules, the diffusion coefficient for C6H4Br2 is larger than that for C6H4BrF.

The diffusion behaviors of molecules inside the confined channel are strongly correlated with the framework of the zeolite, temperature, loading and molecule species6,30,31,64. Both the mesoporous SBA-15 model and microporous zeolites with VFI and MAZ topologies were chosen to investigate the effect of channel dimension on diffusion under confinement. The topologies and initial structure of molecules are shown in Supplementary Figs. 12–14. All the porous materials possess one-dimensional circular channels with the pore size of 20 × 20, 12.7 × 12.7, and 7.4 × 7.4 Å2 for the SBA-15 model, VFI and, MAZ zeolites, respectively (Supplementary Fig. 4). As shown in Fig. 4A, the diffusion characters are similar for porous materials with a large pore size (i.e. mesoporous SBA-15 model and VFI zeolite), and the Ds follows the order of C6H4F2 > C6H4BrF > C6H4Br2, which is inversely proportional to the adsorption energy (Supplementary Fig. 15) and residence time (Fig. 4B, C, Supplementary Tables 4 and 5). However, as the pore size decreases to sub-nanometer (e.g. MAZ), the order of diffusion changes. As listed in Fig. 4D and Supplementary Table 6, the Ds is 1.32 × 10−8 m2/s for C6H4Br2, which is larger than C6H4BrF (0.76 × 10−8 m2/s) and consistent with the diffusion order in AFI. It is worth noting that, due to the pore roughness and tortuosity factors of SBA-15 model (Supplementary Fig. 12), the self-diffusion coefficient is comparable with AFI and MAZ zeolites. As indicated by the above two different diffusion orders, confinement affected the diffusion. In the tightly confined space, asymmetric rotations increased the residence time and disrupted the order of molecular diffusion.

Fig. 4: Diffusion in other materials.
figure 4

A Self-diffusion coefficient (Ds) for C6H4F2, C6H4BrF, and C6H4Br2 inside SBA-15 model, microporous zeolites with VFI and MAZ topologies at 298 K. Normalized (to C6H4F2) Ds, diffusion radius (R), jump length (d), and residence time (t) for C6H4F2, C6H4BrF, and C6H4Br2 in B mesoporous SBA-15 model, and microporous zeolites with C VFI and D MAZ topologies.

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In addition, we also considered the effect of concentration (loading), temperature, molecule species and shape of the pore size. As shown in Supplementary Fig. 16A and Table 7, due to the more frequent collision hindering the movement, all the diffusion coefficients decrease as the loading increases in AFI zeolite. Thus, the effect of asymmetric rotations was more pronounced at low loading. Besides loading, the diffusion behavior in AFI at different temperatures was analyzed. We found that the effect of asymmetric rotations decreases as the temperature increases (Supplementary Fig. 16B and Table 8). For example, the Ds is 1.81 × 10−8 and 1.94 × 10−8 m2/s for C6H4BrF and C6H4Br2 at 473 K, whereas it reaches 2.96 × 10−8 (C6H4BrF) and 3.11 × 10−8 m2/s (C6H4Br2) at 673 K, which may be caused by the higher temperature increases the momentum of molecules and by weakening the contribution of rotation. Overall, higher loading and temperature reduced the contribution of asymmetric rotation during the diffusion process. We also consider the effect of other molecules such as m-xylene, m-bromotoluene, and m-dibromobenzene (Supplementary Fig. 17) as well as m-difluoropyridine, m-fluorobromopyridine, and m-dibromopyridine (Supplementary Fig. 18), the diffusion anomalous dependence on sorbate size is also present. However, this effect is not fully universal, especially for some large molecules (e.g. 1,2,4-trifluorobenzene, 1,3,5-trifluorobenzene, 1,3-difluoro-5-bromobenzene, 1,3-dibromo-5-fluorobenzene, 1,2,4-tribromobenzene and 1,3,5-tribromobenzene) (Supplementary Fig. 19). Fortunately, as for the elliptical pore size of MOR (6.5 × 7.0 Å2), the Ds is 2.02 × 10−8, 0.97 × 10−8 and 1.34 × 10−8 m2/s for C6H4F2, C6H4BrF and C6H4Br2, respectively. The flexibility of the framework has been considered. The diffusion coefficient of C6H4F2, C6H4BrF and C6H4Br2 in flexible AFI zeolite is 1.12 × 10−8, 0.82 × 10−8 and 1.11 × 10−8 m2/s, respectively. Overall, it clearly illustrates the robust degree to which asymmetric rotations slow diffusion under confinement.

To validate the MD simulations that indicated asymmetric rotations slow diffusion in zeolites, several types of experiments were performed to determine molecular diffusion. Firstly, the diffusion behaviors of C6H4F2, C6H4BrF, and C6H4Br2 in SBA-15 (mesoporous silica) and AlPO4-5 (AFI) zeolite were characterized by dynamic breakthrough curves, which could evaluate the transportation properties of molecules through nanoporous materials65,66,67,68. The X-ray diffraction (XRD) patterns, N2 adsorption–desorption isotherms, scanning electron microscopy (SEM) images, and pore size distribution for zeolite and mesoporous SBA-15 are shown in Fig. 5A, D, as well as Supplementary Figs. 20–22. The SBA-15 possesses well-ordered mesopores, whereas AlPO4-5 has abundant micropores. Due to the large pore size of SBA-15, the diffusion order of the halogenated benzene is C6H4F2 > C6H4BrF > C6H4Br2 (Fig. 5B), which gives a breakthrough time of about 11, 15, and 20 min, respectively. This result agrees well with the size of molecules. However, the diffusion order is altered in microporous AlPO4-5 zeolites (Fig. 5E), which follows the order of C6H4F2 > C6H4Br2 > C6H4BrF, exhibiting the breakthrough time at about 25, 48, and 63 min, respectively. The detailed parameter description for the breakthrough measurements was shown in Methods and the repeatable experiment (Supplementary Methods and Fig. 23) indicated that internal/external diffusion and packing efficiency of adsorbent molecules have no effect on the repetition of breakthrough measurements.

Fig. 5: Experimental results.
figure 5

A SEM image of SBA-15 (mesoporous silica), B breakthrough curves, and C apparent diffusivity (Dapp) of C6H4F2, C6H4BrF, and C6H4Br2 in SBA-15 at 298 K obtained from Intelligent Gravimetric Analyzer (IGA) uptake experiments. The C/C0 represents the relative concentration of the gas. The dark green, white, cyan and dark red balls represent C, H, F and Br atoms, respectively. D SEM image of AlPO4-5 (AFI), E breakthrough curves, and F Dapp of C6H4F2, C6H4BrF, and C6H4Br2 in AlPO4-5 at 298 K obtained from IGA uptake experiments. Dapp is the apparent diffusivity of guest molecules and l is the half thickness of the characteristic length of crystal. Uptake measurements of guest molecules obtained from synchrotron radiation-based infrared microscope (SR-IRM). G Optical view of SR-IRM and selected AlPO4-5 zeolite crystal with large size. Light spot is indicated by the visible light. H Uptake rate curves of C6H4F2, C6H4Br2 and C6H4BrF molecules at 298 K by SR-IRM. I 2H solid-state NMR spectra of C6D4F2, C6D4BrF and C6D4Br2 in AlPO4−5 at 298 K.

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Secondly, the uptake rate measurements, which could quantitate the diffusion coefficient in porous materials69,70, were carried out by an intelligent gravimetric analyzer (IGA). In Fig. 5C, F, the Dapp/l2 was used to represent the effective diffusivity normalized by l2 (l was the half thickness of the characteristic length of crystal). The large Dapp/l2 represented the fast diffusion of guest molecules within zeolite crystal. The trends of apparent diffusivity (Dapp in Fig. 5C, F and Supplementary Fig. 24) in both SBA-15 and AlPO4-5 were in good agreement with the theoretical calculations. Then, highly accurate uptake rates of C6H4F2, C6H4Br2 and C6H4BrF molecules within individual AlPO4-5 (AFI) zeolite crystal (Fig. 5G) at 298 K were measured by synchrotron radiation-based infrared microscope (SR-IRM)71. Uptake rate curves of C6H4F2, C6H4Br2 and C6H4BrF molecules at 298 K were shown in Fig. 5H. The diffusivity also follows: D(C6H4F2) > D(C6H4Br2) > D(C6H4BrF) (Methods and Supplementary Fig. 25). Furthermore, we also performed QENS to get the self-diffusion coefficient (Methods and Supplementary Fig. 26). The long-range self-diffusivity of the C6H4BrF molecule confined in the AlPO4-5 is found to be 2.66 ± 0.65 × 10−9 m2s−1. This value is of the same order of magnitude as predicted from simulations (1.1 × 10−9 to 9.3 × 10−9 m2s−1, Supplementary Table 7).

2H NMR experiments have been widely used for investigating both rotational and translational motions61,62,63,72,73. Recently, we also performed 2H NMR experiments to investigate the dynamical motion of 1,2,4-trimethyl benzene and acetonitrile inside zeolite74,75. In this work, 2H NMR experiments have been utilized to verify symmetric rotations for C6H4F2 and C6H4Br2, in contrast to asymmetric rotation for C6H4BrF. The details of the 2H NMR experimental procedures and simulation methods are provided in Methods. As shown in Fig. 5I, the symmetric molecules (i.e. C6D4F2 and C6D4Br2) present similar Pake doublet spectra, with simulation results aligning closely with the experimental data (Supplementary Fig. 27). This consistency demonstrates that the reorientations for the halogen atoms in C6D4F2 and C6D4Br2 are equivalent, causing similar 2H reorientation processes for each 2H atom within a single molecule. In contrast, the 2H NMR spectrum for C6D4BrF exhibits a distinct lineshape from that of symmetric molecules. Similar pattern can be reproduced by modeling larger-degree reorientation for F atom but smaller-degree reorientation for Br atom, that is asymmetric rotation, which leads to much more varied 2H reorientations compared to symmetric rotation models (Supplementary 2H NMR Simulation Methods).

Discussion

In summary, the combined effort of the molecular dynamics simulation, experimental breakthrough curves, uptake measurement by intelligent gravimetric analyzer, as well as SR-IRM, QENS, and 2H solid-state NMR techniques demonstrated the coupling between rotation and translation during the diffusion process under confinement. In the bulk phase and inside channels with large pore sizes, the diffusivity was determined by the size of molecules and the interaction energy between host and guest. However, since asymmetric rotation significantly slows diffusion, the order of molecular diffusion changes, that is, molecules with larger symmetric shapes may diffuse faster than smaller asymmetric molecules in a tightly confined environment, even if the adsorption energy is stronger. These findings provide fundamental insights into the mechanism of diffusion inside the confined space from both rotation and translation, which could open avenues for catalysis or separation by molecular asymmetry through nanoporous materials.

Methods

Molecular dynamics (MD) simulation

The initial framework of MAZ, AFI and VFI was taken from the International Zeolites Associations (IZA) database51, and the lattice parameters as well as loading number of molecules were shown in Supplementary Table 9. AFI (Supplementary Fig. 4A) and MAZ (Supplementary Fig. 4B) mainly consisted of straight 12-ring channel with a window size of 7.3 × 7.3 Å2 and 7.4 × 7.4 Å2 along [001] direction, respectively, while VFI consisted of 18-ring straight channels with pore sizes of 12.7 × 12.7 Å2 (Supplementary Fig. 4C). In addition, the mesoporous SBA-15 model with the pore size of 20.0 × 20.0 Å2 has also been built (Supplementary Fig. 4D and Model).

MD simulations were performed in the canonical ensemble (NVT), where the number of particles (N), volume (V), and temperature (T) were kept constant. The simulated temperature was 298 K and controlled by a Nosé-Hoover thermostat with a coupling time constant of 0.1 ps. The leapfrog Verlet algorithm was used to integrate the Newton’s equations of motion with a time step of 1.0 fs. Each MD simulation was equilibrated over 1 × 105 steps, and then the following 1 × 107 steps were used to study the diffusion behaviors (e.g. diffusion coefficient and diffusion trajectory) of adsorbate molecules. The COMPASS force field76,77,78,79 was used and the cutoff radius was 12.5 Å. The trajectories were recorded every 1000 steps, and 5–10 independent MD simulations were conducted for better statistics.

A continuous-time random-walk (CTRW) coarse graining method

In coarse-graining time algorithm28,58,59, the center of the k-th dynamic basin of the tagged methane molecule, \(\bar{R}{\left(n\right)}_{k}\), was done iteratively as Eq. (1)

$$\bar{R}{\left(n\right)}_{k}=\frac{\left(n-1\right)\bar{R}{\left(n-1\right)}_{k}+R\left(n\right)}{n}$$
(1)

The average was updated until R (n + 1) walked out of a certain range:

$$\left|R\left(n+1\right)-\bar{R}{\left(n\right)}_{k}\right|\,\left\{\begin{array}{c}\le {D}_{\max }\, {update\; the\; basin\; center\; position}\\ \, > {D}_{\max }\, {start\; the\; new\; basin}\,\hfill\end{array}\right\}$$
(2)

\({D}_{\max }\) was set to 8.5, 8.5, 7.5 and 11.0 Å respectively, which were found to be a reasonable value for the molecules, as a threshold of the basin crossing in AFI, VFI, MAZ, zeolites and SBA-15 model, respectively. The past n snapshots were defined as a dynamical basin centered at \(\bar{R}{\left(n\right)}_{k}\). If the labeled molecule jumped into a new basin according to Eq. (2), the running index n was updated to 1. The residence time τ was defined as the average waiting time of methane within dynamic basin, while the jump length d was the average distance between two consecutive basin centers \(\left\langle {\bar{R}}_{k+1}-{\bar{R}}_{k}\right\rangle\).

Mixed gases breakthrough experiment

The breakthrough experiment was carried out on a Micromeritics Autochem 2920 apparatus with mass spectrum (Supplementary Fig. 30). In a repeatable experiment, the tube (6 mm inner diameter × 190 mm) packed with 50 mg of the sample (40~60 mesh) was first purged with He flow (30 mL/min) for 3 h at 150 °C and then cooled to 25 °C. Subsequently, the room-temperature saturated vapor of adsorbed gas (e.g. C6H4F2, C6H4BrF, and C6H4Br2) was introduced by He flow at 20 mL/min. Outlet gas from the tube was monitored by using mass spectrum (Hiden Analytical, HPR-20 R&D) with an ion source-detector. It should be pointed out that all the chemicals were analytical grade and used directly without further purification.

Uptake measurement

The uptake rate measurements were first carried out by use of the Intelligent Gravimetric Analyzer (IGA-100, Hiden Analytical). Especially, in order to enhance the permeability of probe gas or vapor to samples, homemade mesh type of sample cell was used. About 15 mg AlPO4-5 and SBA-15 samples were added to the chamber, and outgassed until a constant weight was achieved at pressure of 10−6 mbar and temperature of 623 K for at least 6 h. Then a steam of probe vapor was introduced into the system with a carefully controlling quantity in order to ensure the isobaric and isothermal process. Meanwhile, mass change with buoyancy corrections, system pressure and sample temperature were recorded in real-time. The uptake curves of substituted benzene have been performed in AlPO4-5 and SBA-15 at 298 K (0 → 0.25 mbar).

To get more accurate intracrystalline diffusivity, the uptake rate measurements by synchrotron radiation-based infrared microscope has been performed. The AlPO4-5 zeolites with large crystal size were synthesized by the recipe from reference80. The experiments were performed by use of a Fourier transform IR microscope (Bruker Hyperion 3000) composed of a spectrometer (Bruker vertex 80 v) and a 15× optical microscope81,82. The in-situ optical reaction cell with BaF2 window in this device is connected to a saturated vapor system and mounted on a movable platform under the microscope. Such an arrangement facilitates the selection of a reasonably shaped crystallite for subsequent uptake rate measurements. Sample activation was accomplished by heating under air purging at a rate of 10 K/min up to 673 K and kept for 0.5 h, and then the sweeping of nitrogen for 1 h. The total dead-volume of the uptake system (including dead-volume of cell and pipe) is less than 0.5 mL, the flow rate of nitrogen is 40 mL/min, which can avoid the effect of dead-volume on the uptake rate measurements.

Quasi-elastic neutron scattering (QENS)

QENS experiment was performed using the Back-scattering Silicon Spectrometer (BASIS)83 at the spallation neutron source of the Oak Ridge National Laboratory. QENS spectra were collected by spinning the choppers at 60 Hz and selecting the bandwidth of incident neutron centered at 6.4 Å. This configuration of the instrument covers an energy transfer range of ±100 µeV and Q range of 0.2 Å−1–2 Å−1, providing an energy resolution of ~3.4 µeV (Q-averaged full width at half maximum). The sample was placed in an aluminum foil and made a pouch, rolled, and put into an annular aluminum can inside a glove box. The sample was sealed with an indium ring. The sample temperature was controlled using a close cycle refrigerator (CCR). QENS data was collected at 298 K, and the sample specific resolution was measured at 5 K. The data was reduced and analyzed using Mantid84 and DAVE85 software, respectively.

2H NMR experiments

Prior to adsorb deuterated 1,3-halogen-substituted benzene-d4, AlPO-5 zeolites were dehydrated at 693 K and <10−3 Pa for 10 h, weighed and then transferred into rotors within an Ar-filled glovebox. Specified volumes of 1,3-halogen-substituted benzene-d4 were introduced into the rotors using microsyringe, followed by sealing the rotor caps. C6D4F2 was introduced as a CH2Cl2 solution at a concentration of 0.07 g/mL, with a loading for C6D4F2/CH2Cl2 solution of 99 μL/gzeolite. C6D4Br2 and C6D4BrF were used as pure compounds with loading of 11 μL/gzeolite and 12 μL/gzeolite, respectively. The C6D4F2-loaded sample was equilibrated at room temperature overnight, while the C6D4Br2 and C6D4BrF loaded samples were equilibrated at 383 K for 2 h. Before performing 2H NMR experiments, the samples were evacuated at room temperature for 3 min to remove CH2Cl2 and other loosely-bound molecules.

Static 2H NMR experiments were measured at room temperature on a Bruker Avance NEO 400 spectrometer (9.4 T) with a 4 mm HXY MAS NMR probe. The spectra were recorded using the quadrupolar echo (QE) method with a π/2 pulse of 3.5 μs, an echo delay of 35 μs, and a recycle delay of 2 s. 31320 scans were accumulated for each 2H NMR spectrum.