Computational design of metal–organic frameworks with triangular adsorbaphores for highly selective adsorption of m-xylene

Abstract

Separation of xylene isomers, serving as indispensable feedstock in the petrochemical industry, is important but significantly challenging due to their similar physicochemical properties. With readily tunable network structures and chemical functionalities, metal–organic frameworks (MOFs) are promising for separation and many other potential applications. Here, we computationally design 150 lanthanide-based MOFs with one-dimensional triangular nanopores by varying metal compositions. Compared with p-xylene (pX) and o-xylene (oX), m-xylene (mX) exhibits the strongest interaction with these MOFs, as it can wedge at the vertices of triangular nanopores. Because of such shape-matching, highly selective adsorption of mX is observed, with exceptional mX/oX and mX/pX selectivities. Remarkably, the nanopore size of these MOFs can be systematically adjusted through different metal combinations, achieving efficient xylene separation. The proposed design strategy would facilitate the development of new MOFs and other framework materials for highly selective xylene separation.

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Introduction

Among three xylene isomers, p-xylene (pX) has the highest market value compared to m-xylene (mX) and o-xylene (oX). pX is used to produce terephthalic acid (PTA), which is a key precursor for manufacturing polyethylene terephthalate (PET) resin. Nevertheless, there is a growing industrial demand for mX as a raw material to produce isophthalic acid (PIA).¹ PIA is a modifier in the production of PET, in addition to being used in the manufacturing of many other commodities. Therefore, it is of central importance to separate xylene isomers in the petrochemical industry. Because of the similar physicochemical properties of the isomers, xylene separation by thermally driven distillation is extremely energy intensive. In this context, adsorption turns out to be an efficient technology for xylene separation. A notable example is an industrial unit operation called “MX Sorbex”, which was invented by Honeywell UOP specifically to produce high purity mX, occupying over 90% share of the mX production market.² In industrial xylene separation, zeolite adsorbents are utilized but they offer only modest separation performance.³ There has been a continual quest to develop alternative adsorbents that provide high performance and operational flexibility for xylene separation.

With remarkable tunability in pore size and shape, structural topology, as well as chemical functionality, metal–organic frameworks (MOFs) are intriguing adsorbents for separation and many other potential applications.^4,5 Several experimental^6–10 and computational^11–14 studies have demonstrated the utilization of MOFs for xylene separation, primarily targeting the selective adsorption of pX. However, fewer efforts have been devoted to the separation of mX. The objective of this work is to design MOFs for highly selective adsorption of mX from xylene isomers. We focus on a unique branch of MOFs comprising rare-earth (RE) metals, in which the metal node may consist of a single- or multinuclear metal.¹⁵ Particularly, the high coordination capability of lanthanides (Ln) enables the creation of MOFs with versatile topologies.¹⁶ Ln-MOFs have been tested for adsorbing methanol,¹⁷ sensing xylene isomers,¹⁸ and preferentially recognizing pX.¹⁹

To achieve selective adsorption of mX, we aim to design Ln-MOFs with triangular pores termed adsorbaphores,²⁰ in analogy to pharmacophores in drug design, which favorably interact with mX. Interestingly, the methyl groups of mX can wedge at the vertices of triangular pores and hence mX is more favorably adsorbed over pX and oX. It is noteworthy that a MOF, namely Fe₂(BDP)₃, with triangular pores was reported to selectively adsorb linear hexane against its branched isomers.²¹ However, the existence of triangular pores was revealed to be not a prerequisite for the selective adsorption of hexane isomers.²² In contrast, we envision that the triangular pores (i.e., triangular adsorbaphores) in Ln-MOFs would favor the selective adsorption of mX, as they match well with the shape of mX. As such, in the present study, a large number of Ln-MOFs with tunable pore size are designed for the selective adsorption of mX.

Results and discussion

Experimentally, a handful of Ln-MOFs (Fig. 1a) were synthesized from four different Ln metals (Dy, Er, Gd, and Ho) and H₂pzdc ligand (pyrazine-2,3-dicarboxylic acid) in the presence of Cu ions.^23,24 The resulting MOFs comprise hexanuclear Ln metal nodes and a Cu-centered Hhpzc (3-hydroxy-pyrazine-2-carboxylic acid) linker (Fig. 1b). The rigid Hhpzc linker enforces the central Cu atom to adopt an octahedral geometry, with two water molecules occupying open metal sites, and the removal of water molecules leads to a nearly square planar geometry. These Ln-MOFs possess one-dimensional (1D) triangular pores with a diameter of ∼5 Å.

Fig. 1 (a) Ln-MOFs with triangular adsorbaphores that allow mX to wedge at the vertices. (b) Building blocks in a Ln-MOF consisting of a Ln metal node and a linker with a central metal (CM). (c) Design of 150 MOFs from different Ln–CM combinations, including four experimentally reported structures. Adsorption capacities of xylene isomers in these MOFs were predicted using grand canonical Monte Carlo (GCMC) simulations.

To validate the shape-matching concept, we computationally designed a large number of Ln-MOFs with different metal combinations (Fig. 1c). All 15 Ln elements were used for constructing the metal nodes; meanwhile, 10 different metals (Cu, Pt, Pd, Rh, Ru, Mg, Fe, Mn, Zn and Co) were considered, respectively, as the central metal (CM) atom in the linker. Among the 10 CMs, the Cu-centered linker already existed in the four experimentally reported Ln-MOFs with different metal nodes (Dy, Er, Gd, and Ho).^23,24 Altogether, 146 hypothetical structures were constructed. By adding the four experimentally synthesized MOFs, we had a total of 150 Ln-MOFs. It is worth noting that the synthesizability and stability of the hypothetical Ln-MOFs were not considered in this study. The constructed structures were geometrically optimized with the non-bonded Lennard-Jones (LJ) interactions described by the universal force field (UFF)²⁵ and the bond stretching mimicked by a revised harmonic potential. Details are provided in Computational methods, Fig. S1 and Table S1 (see the SI). This strategy was adopted because optimization at the electronic structure level, e.g., using density functional theory (DFT), is typically challenging for Ln compounds due to their complex electronic structures.^26,27 In addition, performing DFT calculations on 150 structures would be computationally demanding. As presented in Table S2 and Fig. S2, the lattice parameters and bond lengths of our optimized structures are in excellent agreement with the reported experimental values for the four synthesized Ln-MOFs. Then, the optimized structures were used for evaluating their geometric properties (e.g., pore limiting diameter, PLD). Finally, the heats of adsorption for xylene isomers at infinite dilution were calculated using the Widom insertion method. The adsorption capacities of single- and multi-component xylene isomers were predicted using grand canonical Monte Carlo (GCMC) simulations (see the SI).

Fig. 2a shows the heats of adsorption () for xylene isomers in 150 Ln-MOFs at 298 K. The highest , with a mean of 85 kJ mol⁻¹, is observed for mX, followed by pX and oX with mean values of 76 and 72 kJ mol⁻¹, respectively. This implies that mX has the strongest affinity in most Ln-MOFs, as it can wedge at the vertices of triangular pores. The kinetic diameters d_k are 7.1, 7.4 and 6.7 Å for mX, oX and pX, respectively. Apparently, there are obvious variations in , especially for the relatively bulkier mX and oX. To elucidate this, the PLDs of 150 Ln-MOFs were correlated with . As shown at the top of Fig. 2b, the PLDs range from 4.5 to 5.4 Å, with most populated around 5 Å. We should note that d_k is a rough measure of molecular size; even if PLDs are smaller than the d_k of an isomer, many MOFs can still accommodate the isomer. From Fig. 2b, the three isomers exhibit a larger difference in at a smaller PLD, but the difference reduces with increasing PLD. For mX, a higher is seen in a narrower pore, which allows mX molecules to tightly wedge at the pore vertices; however, this tight packing becomes loose when the pore size increases. For oX, increases with PLD, as a wider pore can accommodate bulkier oX molecules. Different from mX and oX, pX shows only weak variation of with PLD, due to its smallest molecular size among the three isomers.

Fig. 2 (a) of xylene isomers in Ln-MOFs. (b) Correlation between and PLD. (c) PLD variation with metal type. (d–f) variation with metal type for mX, pX and oX, respectively. In (c–f), Ln metals are ranked in the descending order of their ionic radii.

Apparently, pore size is crucial in governing the adsorption selectivity of xylene isomers. A narrower pore tends to display higher selectivity, and S_mX/oX is anticipated to be greater than S_mX/pX. Conversely, a wider pore reduces the interaction difference between xylene isomers and is not suitable for separation. To boost xylene selectivity, the pore size can be adjusted. As demonstrated experimentally, the pore size in MFM-300 was tuned upon altering metal type, thus leading to a significant change of xylene selectivity.²⁸ It is instructive to examine how the pore size is affected by the metal type in this study. Fig. 2c shows the PLD variation with metal type for 150 Ln-MOFs. MOFs with La and Ce have the largest PLDs, while those with Yb and Lu have the smallest. Notably, PLD is found to positively correlate with the ionic radius of the Ln metal (Fig. S3a). With descending ionic radius, PLD decreases. This is because a smaller radius of Ln metal induces a shorter coordination bond, a contracted lattice, and a narrower pore. In contrast, there is no apparent correlation between the PLD and the radius of CM (Fig. S3b). The largest PLD is associated with Pd, Cu and Pt, followed by Mg, Zn and Ru, while the smallest PLD is for Rh, Mn, Fe and Co. In 150 Ln-MOFs with different Ln–CM combinations, La and Ce with Pd, Cu, Pt and Mg possess wider pores, while Lu and Yb with Co have narrower ones (Fig. S3c).

Additionally, we analyze the of xylene isomers based on metal combinations. As shown in Fig. 2d for mX, among Ln metals, MOFs with Yb exhibit the highest , followed by Lu. This is because these metals form narrower pores in which mX molecules can wedge at the vertices. Among CMs, Zn possesses the strongest affinity for mX; thus, the MOF with Yb–Zn shows the highest . Interestingly, although MOFs with Lu–Co and Yb–Co have the smallest PLDs, the highest is observed in the MOF with Yb–Zn. The reason is that the interaction of mX with Zn is stronger than with Co, as reflected by the LJ potential parameters (ε) of ∼0.52 and ∼0.06 kJ mol⁻¹, respectively. This observation reveals the important role of metal chemistry, besides pore geometry, in governing adsorption performance. For pX, in Fig. 2e shows a relatively small range of variation (∼8 kJ mol⁻¹) compared to that for mX. Similarly, many of the MOFs with Yb exhibit stronger interaction with pX, particularly those with Yb–Mg. Across the CMs, on average, Zn has the strongest affinity, as explained earlier. For oX, as shown in Fig. 2f, the opposite trend of is observed. Specifically, a Ln metal forming a wider pore favors oX adsorption than its counterpart forming a narrow pore. This is because oX is relatively bulkier and encounters repulsion in a narrower pore, whereas a pore with adequate size (5.2–5.4 Å) maximizes interaction with oX. On one hand, La adjusts the pore to a suitable size for oX adsorption; on the other hand, Zn has the strongest interaction with xylene; consequently, the combination of La–Zn exhibits the highest affinity for oX and hence the highest . Overall, by examining for the three xylene isomers, we can identify which combination of metals allows the selective adsorption of mX over pX and oX. For instance, the combination of an Ln metal (such as Lu, Yb, Tm or Er) forming a narrower pore with a CM possessing strong interaction with mX (such as Zn) is effective in discriminating xylene isomers.

Fig. 3a presents the adsorption capacities of single-component (i.e., pure) xylene isomers at 298 K and 1 bar. Along the x-axis, Ln metals are ranked in the descending order of their ionic radii, and for each Ln metal, there are 10 MOFs with different CMs in the linker. A significant variation in the adsorption capacity of each isomer is observed, signifying the combined effects of both Ln and CM on pore geometry and interaction strength. The capacity decreases with descending ionic radius of Ln metal, originating from the positive correlation between PLD and ionic radius (Fig. S3a), as a wider pore accommodates more molecules. Because of its smallest molecular size, pX exhibits the greatest capacity than mX and oX (Fig. S4a). The difference in capacity between pX and bulkier isomers is especially notable in MOFs with a Ln metal of a larger ionic radius (e.g., La metal) and hence a wider pore. However, this difference diminishes as the pore becomes narrower (e.g., Lu metal). The two bulkier isomers mX and oX display almost identical capacity in MOFs with medium to wide pores. In MOFs with a narrow pore, oX exhibits the lowest capacity. In all cases, the capacity ranges from 0.5 to 1.25 mol kg⁻¹, which is greater than the typical threshold (0.5–0.6 mol kg⁻¹)^12,14 commonly used to identify top-performing MOFs for xylene separation.

Fig. 3 Adsorption of singe-component xylene isomers at 298 K and 1 bar. (a) Adsorption capacities in MOFs grouped by their Ln metal type. (b) Conformations of xylene molecules adsorbed in a representative MOF with Dy–Cu metals. (c) Orientations of xylene molecules in triangular pores.

The conformations of xylene molecules adsorbed in a representative Ln-MOF (Dy–Cu) are illustrated in Fig. 3b. Shape matching is obviously observed for mX, with its methyl groups wedged at the vertices. However, mX molecule adopts an inclined orientation, does not completely face the pore opening, and positions its two methyl groups toward non-opposing Ln metals on either side of the pore (Fig. 3c). This orientation might occur due to the presence of a CM in the linker, which interacts strongly with mX. In contrast, pX and oX tend to lie along the pore direction, because their methyl groups do not match the triangular shape. These observations corroborate the higher of mX compared to those of pX and oX. Nevertheless, xylene separation cannot be determined simply based on the adsorption of pure isomers. As presented below, the competitive adsorption among isomers in a mixture is remarkable and must be taken into account.

Fig. 4a presents the adsorption capacities of multi-component xylene isomers (i.e., an equimolar mixture) at 298 K and 1 bar. For MOFs comprising La and Ce (i.e., Ln metals with the largest radii), pX exhibits the highest capacity. This is because the pores formed by La and Ce are unsuitable for compact packing of mX, thereby losing the merit of triangular adsorbaphores. In such cases, the MOFs are pX selective. When the ionic radius of Ln metal descends, pX capacity decreases, while mX capacity increases. The highest distinction is observed in MOFs with Yb and Lu, where mX can fit tightly in their pores. Notably, the capacities of both pX and mX vary among 10 different CMs in the linker, due to different interaction strengths of CMs. Nevertheless, the variation is marginal in La-MOFs and Ce-MOFs, due to a small interaction strength difference in these MOFs with wide pores. For MOFs with Pr–Tb metals, the variation is significant, as the pore size is intermediate and the energetic factor dominates adsorption. In contrast, in MOFs with narrow pores, the geometric factor (i.e., pore size) plays a vital role in selective adsorption of mX, while metal interaction plays a minor role, minimizing the variation in capacity across different CMs in the linker. It is interesting to observe that oX adsorption is negligible in all the Ln-MOFs with different combinations of metals. This is a result of strong competitive adsorption among the three isomers. With shape matching, mX is the most favorably adsorbed isomer (except in MOFs with La and Ce Ln metals); thus, mX replaces pX, particularly in a narrow pore. With the bulkiest molecular size, oX is the least adsorbed isomer. Therefore, the competition can be attributed to both energetic and entropic effects. Overall, mX has the highest capacity in 150 Ln-MOFs, followed by pX, and the capacity of oX is vanishingly low (Fig. S4b).

Fig. 4 Adsorption of multi-component xylene isomers (equimolar mixture) at 298 K and 1 bar. (a) Adsorption capacities in MOFs grouped by the Ln metal type. (b) S_mX/oXversus S_mX/pX. (c) S_mX/oX and S_mX/pX variation with metal type. Ln metals are ranked in the descending order of their ionic radii.

Fig. 4b presents the selectivity of mX/oX (S_mX/oX) plotted against the selectivity of mX/pX (S_mX/pX) in all the Ln-MOFs. All the MOFs possess S_mX/oX > 10, with many showing exceptionally high S_mX/oX values exceeding 1000. The majority of the MOFs also show significant S_mX/pX, but reverse selectivity is found in MOFs with large pores. It is revealed that the selectivity is largely governed by pore size but also depends on guest–host interaction. Additionally, all the MOFs are pX selective toward oX.Fig. 4c illustrates S_mX/oX and S_mX/pX variation with metal type, where Ln metals of small radii leads to high selectivity.

Conclusion

We have computationally designed a series of Ln-MOFs featuring one-dimensional triangular adsorbaphores. By tuning the metal types in both metal node and linker, the pore size can be adjusted to selectively adsorb mX. From simulations, the affinities of Ln-MOFs for xylene isomers and their adsorption capacities are evaluated. It is confirmed that mX has the strongest interaction among the three isomers with these MOFs. The adsorption of multi-component xylene isomers demonstrates significantly high mX/oX and mX/pX selectivities. The MOFs also exhibit promising pX/oX separation capability. As such, three xylene isomers can be separated completely using a two-step adsorption process, the first step separates mX from pX and oX, and the second one separates pX and oX. Importantly, the selectivities among xylene isomers in these Ln-MOFs can be effectively controlled using different metal combinations. While the present work is entirely computationally driven, we wish that it would trigger experimental investigation. We acknowledge that the synthesis of these Ln-MOFs, especially the hypothetical ones, may pose a challenge due to the complex nature of frameworks and the limited availability of Ln metal precursors, which are less sustainable for mass production. Nevertheless, the design strategy might open a new direction for the efficient separation of xylene isomers and other important mixtures in the chemical industry.

Author contributions

SAM: conceptualization, methodology, investigation, formal analysis, visualization, and writing – original draft. JJ: funding acquisition and writing – review and editing.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

The data supporting this article have been included in the manuscript and the SI. Supplementary Information file contains computational methods, geometric properties, and statistics of adsorption capacities. See DOI: https://doi.org/10.1039/d5nr02310f.

Acknowledgements

We gratefully acknowledge the National Research Foundation Singapore (NRF-CRP26-2021RS-0002) for financial support and the National University of Singapore and the National Supercomputing Centre (NSCC) Singapore for computational resources.

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