Aperture Fine‐Tuning in Cage‐Like Metal–Organic Frameworks via Molecular Valve Strategy for Efficient Hexane Isomer Separation

Cage‐like metal–organic frameworks (MOFs) are promising for hexane isomer separation, but their aperture sizes are difficult to control precisely. Herein, a molecular valve strategy is proposed to fine‐tune the aperture of cage‐like MOFs, thereby enhancing their separation performance for hexane isomers. Three novel isostructural cage‐like MOFs, namely Cu‐MO4‐TPA, are synthesized using different oxometallate anions (MO42−, M = Cr, Mo, and W) and the ligand tri(pyridin‐4‐yl)amine (TPA). The different oxometallate anions induce varying degrees of twisting in the TPA ligand, leading to sub‐angstrom tuning in the aperture size of the MOFs. The materials can separate hexane isomers based on their degree of branching, with the smallest aperture material (Cu‐MoO4‐TPA) showing molecular sieving of di‐branched isomers. Adsorption isotherms, kinetic, and breakthrough measurements, Monte Carlo, and density functional theory calculations confirm the aperture size differences result in superior separation of hexane isomers by molecular sieving on Cu‐MoO4‐TPA. The results demonstrate the effectiveness of molecular valve strategy for fine‐tuning MOF aperture size for selective separation applications.


Characterization of Materials
The single crystals of Cu-MO 4 -TPA ([Cu 3 (TPA) 4 (MO 4 ) 3 ] n , M = Cr, Mo, W) were successfully synthesized using the interlayer diffusion method (Figure 1a and S1, Supporting Information).The crystal structures of the resultant MOFs were determined by single crystal X-ray diffraction (SCXRD) measurements (Table S1, Supporting Information), which revealed that Cu-CrO 4 -TPA and Cu-MoO 4 -TPA crystallize in the cubic space group Pm-3 n.However, the space group of Cu-WO 4 -TPA was reduced to P23, likely due to the twisting of oxygen atoms, causing the most pronounced framework deformation among the three materials.Despite this, they remain isostructural, sharing the same ith-d topology.Each Cu(II) cation is squarely coordinated with four pyridine groups from four TPA ligands, and the MO 4 2À pillar anions occupy the two axial positions (Figure 1b).These anions connect adjacent Cu(II) centers vertically, forming the Cu-MO 4 chain structure.Subsequently, these chains interconnect along a, b, and c axes via the three-connected TPA ligands (Figure 1c), ultimately producing the cage-like framework structure of Cu-MO 4 -TPA materials (Figure 1d-f ).
The lattice parameters of Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA are closely aligned, with respective values of 17.552, 17.540, and 17.546 Å.As a result, all three materials feature large cages with respective diameters of 11.08, 11.12, and 11.11 Å, as calculated using Zeoþþ package.However, the cage aperture varied, as determined by the twisting of the pyridine rings in TPA ligands (Figure 1g-l), attributable to the interplay of anion lengths (2.92, 2.73, and 2.86 Å for WO 4 2À , CrO 4

2À
, and MoO 4 2À ) [52] and central metal polarizabilities (W 6þ >Mo 6þ >Cr 6þ ). [53]Cu-WO 4 -TPA possesses the largest pore aperture (4.2 Â 3.1 Å 2 ) among the three materials, courtesy of the minimally twisted pyridine ring of the ligand (24.5°).As the torsion angle increased to 37.3°and 38.0°, the aperture of Cu-WO 4 -TPA and Cu-CrO 4 -TPA contracted further to 4.1 Â 2.6 and 3.8 Â 2.4 Å 2 , respectively.Notably, despite the fact that the measured aperture width (2.4-3.1 Å) of Cu-MO 4 -TPA is smaller than the size of hexane isomer molecules, the rotation of the anion could potentially lead to an expansion of the aperture.Importantly, the separation performance is largely determined by the aperture length, which is primarily defined by the twisting of the TPA ligand.This length aligns well with the dimensional size of hexane isomers, as detailed in Table S2, Supporting Information.These findings underscore that the pore apertures can be fine-tuned via ligand twisting control, embodying the molecular value strategy.
Powder samples of the three MOFs were further synthesized on a larger scale, with their phase purity confirmed by consistent powder X-ray diffraction (PXRD) patterns (Figure S2, Supporting Information).Scanning electron microscope (SEM) images (Figure S3, Supporting Information) and energy-dispersive spectrometer (EDS) measurements made via transmission electron microscope (Figure S4, Supporting Information), evidenced the presence of uniform rhombic dodecahedron microcrystals with diameters of 1-2 μm and MO 4 2À anions in all three materials, respectively.The N 2 and CO 2 adsorption/desorption isotherms at 77 and 195 K (Figure 2a-c) indicate the presence of permanent micropores in the three MOFs.It is worth noting that N 2 can barely enter the cages of Cu-MoO 4 -TPA due to its more restricted aperture compared to the other two materials.Based on the CO 2 adsorption isotherms, the Brunauer-Emmett-Teller (BET) surface areas of the three samples were calculated to be 146, 377, and 217 m 2 g À1 , respectively (Figure S5, Supporting Information).Furthermore, Horvath-Kawazoe (H-K) model analysis was conducted to glean the micropore size distributions (Figure 2d-f ), and the calculated pore diameters of 5.76, 5.43, and 4.96 Å for Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA agree with aforementioned structural analysis.In addition, the thermogravimetric (TG) curves of Cu-MO 4 -TPA (Figure S6, Supporting Information) indicate their good thermal stability, with all three materials remaining intact until 473 K.

Adsorption Isotherms
The single-component vapor isotherms of hexane isomers on Cu-MO 4 -TPA were measured up to 20 kPa at 303 and 318 K (Figure 3a-c and S7, Supporting Information).All three materials strongly adsorb linear n-Hex, displaying type-I isotherms.At 303 K and 10 kPa, the n-Hex capacities on Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA were 0.82, 1.40, and 1.12 mmol g À1 , respectively, indicating effective filling in the comparably large cages of the three materials.Notably, the Cu-WO 4 -TPA, which crystallized in the lower space group P23 and possessed the largest aperture, exhibited slight flexibility in the high-pressure region of the n-Hex isotherm.This flexibility is likely attributable to reduced steric hindrance around the TPA ligand.Furthermore, mono-branched isomers (2-MP and 3-MP) show significantly weaker adsorption than n-Hex on Cu-MO 4 -TPA materials, demonstrating a promising Scheme 1. Schematic illustration of molecular valve strategy: constructing isostructural cage-like MOFs with controllable apertures via ligand twisting.

Kinetics and Adsorption Heats Measurements
To gain a deeper understanding of the adsorption behavior of hexane isomers on Cu-MoO 4 -TPA, the pure-component adsorption kinetic curves (Figure 3d) and DSC exothermic curves (Figure 3e) were synchronously measured on a simultaneous thermal analyzer at 303 K and 15 kPa.The adsorption rates of linear n-Hex and mono-branched 2-MP and 3-MP on Cu-MoO 4 -TPA were found to be similar, with all three isomers rapidly reaching adsorption equilibrium within 10 min.This rapid equilibrium cab be attributed to the presence of large cages in Cu-MoO 4 -TPA.The comparable kinetic profiles suggest that the discrimination between n-Hex and mono-branched isomers on Cu-MO 4 -TPA is primarily thermodynamically driven.This inference is further substantiated by the lower adsorption heats of 2-MP and 3-MP (41 and 37 kJ mol À1 , respectively) compared to n-Hex (72 kJ mol À1 ) on Cu-MoO 4 -TPA.
Conversely, the marginally higher kinetic uptake amounts of di-branched 2,3-DMB and 2,2-DMB, compared to the aforementioned isotherms, can be ascribed to impurity adsorption and surface adsorption.Nonetheless, considering the negligible static adsorption capacity, slow adsorption rate, and the absence of the detectable exothermic peak during DSC measurements, it can be deduced that the di-branched isomers can scarcely penetrate the cages of Cu-MO 4 -TPA due to the presence of confined apertures, particularly in the case of Cu-MoO 4 -TPA.Therefore, the separation of di-branched isomers on Cu-MO 4 -TPA can be achieved via a combined thermodynamic-kinetic mechanism or even through molecular sieving.

Column Breakthrough Experiments
Equimolar five-component vapor breakthrough experiments were conducted on Cu-MO 4 -TPA materials at 303 K to validate their ability to separate hexane isomers.The stainless-steel filling columns with dimensions of 50 mm in length and 4.6 mm in inner diameter were packed with 500, 380, and 420 mg of activated Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA powder samples, respectively (approximately 0.25 mmol for all three materials).As depicted in Figure 4, all three materials exhibited clear separation of hexane isomers based on their branching degrees, namely linear, mono-branched, and di-branched isomers.Cu-MoO 4 -TPA demonstrated the foremost performance for the thermodynamically driven separation of n-Hex and mono-branched isomers among the three materials.This superiority is attributed to the most significant difference in affinity between n-Hex and 2-MP/3-MP on this material (Figure 3c), with Cu-WO 4 -TPA and Cu-CrO 4 -TPA following closely in performance.Furthermore, for the more challenging separation of mono-/di-branched isomers, the three Cu-MO 4 -TPA materials displayed distinct characteristics.Cu-WO 4 -TPA, with the largest aperture, showed separation primarily determined by the thermodynamic differences, resulting in narrow mass transfer zones in breakthrough curves for both mono-and di-branched isomers (Figure 4a).Conversely, in case of Cu-CrO 4 -TPA, the diffusion of di-branched isomers was partially hindered by the smaller aperture, as evidenced by the broadened mass transfer zone (Figure 4b).The difference in diffusion rates between mono-and di-branched isomers facilitated a synergistic effect, further aiding in the separation.Notably, when focusing on Cu-MoO 4 -TPA with the most confined aperture, it was observed that di-branched 2,3-DMB and 2,2-DMB were unable to enter the pores, resulting in a molecular sieving separation on this material (Figure 4c).Thus, Cu-MoO 4 -TPA holds the best overall separation performance for hexane isomers among the three materials.The times taken to yield products with a RON over 95 (RON ≥ 95) were calculated to be 16, 20, and 28 min for Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA, respectively.The stepwise improvement in hexane isomer separation performance, particularly for mono-/di-branched isomers, on Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA effectively demonstrated the efficacy of the molecular valve strategy proposed in this study.

Computational Simulations
CBMC and DFT-D calculations were further performed to elucidate the difference in affinity between n-Hex and 2-MP/3-MP on Cu-MO 4 -TPA materials.The Lennard-Jones (L-J) parameters used during the MC simulation are listed in Table S4 and S5,  Supporting Information.The density distribution of n-Hex and 3-MP on Cu-MO 4 -TPA (Figure 5a,d, S8a,b, and S9a,b, Supporting Information) revealed a clear preference for the adsorption of linear n-Hex over mono-branched 3-MP.However, all three materials show similar adsorption sites, as evidenced by the lowest energy structures obtained during the MC simulations (Figure 5b,e, S8c,d, and S9c,d, Supporting Information).It is important to note that due to the intrinsic lack of consideration given to the accessibility of the cavities and the diffusion pathway of hexane molecules, the hexane isomer isotherms on Cu-MO 4 -TPA are prone to be overestimated by CBMC simulations (Figure S10, Supporting Information).Thus, the simulations should be viewed as offering qualitative results only.Therefore, these lowest energy structures were subsequently optimized using DFT-D method.Figure 5c,f and Table S6, Supporting Information, illustrate that the binding between linear n-Hex and frameworks is the strongest among the three isomers, owing to its appropriate molecular length with respect to the Cu-anion-Cu distance.The binding energies are notably high, reaching 93, 92, and 95 kJ mol  (19), 24 (19), and 26 (19) kJ mol À1 on Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA, respectively.Different from the significant influence of the oxometallate anions on the aperture size of corresponding materials, the binding energy of a given hexane isomer on the three materials shows very limited correlation with the anion type.Instead, the steric effect of differently twisted TPA ligands, generated by different oxometallate anions, remains the primary contributor to the hexane isomer separation performance of Cu-MO 4 -TPA.The combined influence of a more confined aperture and a slightly more pronounced thermodynamic difference on Cu-MoO 4 -TPA synergistically account for its superior n-Hex/3-MP(2-MP) separation performance compared to the other two materials.

Conclusion
In summary, we have successfully constructed three isostructural cage-like MOFs, specifically Cu-MO 4 -TPA (M = Cr, Mo, W), using the three-terminal ligand TPA and oxometallate anions of group-VIB congeners.The pyridine rings of TPA ligands display orderly twisting patterns influenced by different anions, leading to the sub-angstrom variations in the pore apertures of Cu-MO 4 -TPA materials.All three materials have demonstrated the capability to thermodynamically separate n-Hex and its mono-branched isomers, 2-MP and 3-MP, with significant capacities and selectivities.For the more challenging separation of mono-and di-branched isomers, Cu-WO 4 -TPA, with the largest aperture, shows a primarily thermodynamically driven separation.The contracted aperture of Cu-CrO 4 -TPA enhances the separation of mono-and di-branched isomers through a synergistic effect resulting from a more significant difference in diffusion rates.For Cu-MoO 4 -TPA, which has the most restricted aperture, di-branched hexane isomers are unable to enter the pores and are quickly eluted during breakthrough experiments.Consequently, a molecular sieving separation is achieved on this material.Our findings introduce a new class of high-performance adsorbents for the challenging separation of hexane isomers.Moreover, we propose an effective molecular valve strategy for fine-tuning the entrance aperture size of cage-like MOFs by controlling the twisting of organic ligands, thereby paving the way for a broad range of applications.

Figure 1 .
Figure 1.Structure features of Cu-MO 4 -TPA.a) Synthetic scheme of Cu-MO 4 -TPA.b) Coordination environment of Cu 2þ in Cu-MO 4 -TPA.c) Cu-MO 4 chains along a, b, and c axes interconnect with each other by the three-connected TPA ligands.d) Overall framework structure of Cu-MO 4 -TPA: large cage (yellow sphere) interconnected by confined channel (pink cylinder).e) The cage and f ) channel structure of Cu-MO 4 -TPA.g,i,k) The differently twisted TPA ligands in Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA.h,j,l) The van der Waals surfaces of Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA with apertures measuring.Color scheme: Black: C, red: O, blue: N, pale blue: Cu, pink: W, green: Cr, dark blue: Mo, orange: undefined metal atom, the structural disorder and hydrogen atoms are omitted for clarity.

Figure 5 .
Figure 5. CBMC-simulated a) n-Hex and d) 3-MP density on Cu-MoO 4 -TPA at 303 K, 1 kPa, and b,e), corresponding lowest-energy structures, the guest hydrogen atoms are omitted for clarity.DFT-calculated optimum binding sites for c) n-Hex and f ) 3-MP on Cu-MoO 4 -TPA, the structural disorders are omitted for clarity.Color scheme: Black: C, yellow: H on host, red: O, blue: N, pale blue: Cu, dark blue: Mo, dark green: C on n-Hex, pale green: C on 3-MP; white: H on guests.
À1 on Cu-WO 4 -TPA, Cu-CrO 4 -TPA, and Cu-MoO 4 -TPA, respectively.The α-C-H (terminal methyl group) can interact with four pyridine rings from four TPA ligands, with an average C-H•••π distance of 3.18 Å (Cu-MoO 4 -TPA), while the βand γ-C interact with the oxometallate anion, exhibiting an average C-H•••O distance of 2.74 Å (Cu-MoO 4 -TPA).On the contrary, the shorter mono-branched 3-MP can only form three C-H•••O interactions (with an average distance of 2.74 Å on Cu-MoO 4 -TPA) with the frameworks, resulting in lower binding energies of 74, 73, and 76 kJ mol À1 on three materials, respectively.The binding energies of 2-MP are further reduced to 74, 68, and 69 kJ mol À1 .The detailed binding structures of n-Hex, 2-MP, and 3-MP on three materials are shown in Figure S11, Supporting Information.Therefore, the binding energy differences between n-Hex and 2-MP(3-MP) are 19