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Framework disorder and its effect on selective hysteretic sorption of a T-shaped azole-based metal–organic framework

The effect of framework (pore) disorder on gas sorption of azole-based isoreticular Cu(II) MOFs with rtl (rutile) topology and characteristic 1D tubular pore channels is investigated for the first time.


Introduction
Porous materials such as zeolites, molecular cages, activated carbons, covalent organic frameworks and metal-organic frameworks (MOFs) have been utilized as adsorbents for gas capture (e.g. CO 2 ). Among these materials, MOFs with high surface area, tunable pore size and modifiable pore surfaces are receiving great interest because they show unique flexibility and dynamic behaviors (e.g. phase change) and also offer significant improvements in separation performance (Horike et al., 2009;Schneemann et al., 2014;Alhamami et al., 2014;Zhang et al., 2017). For example, their corresponding hysteretic gas adsorption/desorption behaviors are able to decrease the pressure of gas storage.
According to the isoreticular MOF concept introduced by Yaghi and others (Eddaoudi et al., 2002;Wilmer et al., 2012;Deng et al., 2012;Ma et al., 2010), a MOF structure is determined by the connectivity of the rigid bridging ligand, the secondary building unit (SBU) and the framework topology. By fixing a specific topology, the isostructural frameworks can be readily fine-tuned via organic ligand manipulation and metal ion selection (Yuan et al., 2010;Caskey et al., 2008). Analogous ligands with different functionalities can be especially employed to produce desired frameworks (Colombo et al., 2012;Sumida et al., 2013). Along these lines, the effect of some subtle factors on the pore properties can be investigated and analyzed by designing isoreticular MOFs (McDonald et al., 2012;Li, Zhang et al., 2012;Das et al., 2012;Zhang et al., 2012;Bae et al., 2012). However, much of the research emphasis remains on developing and characterizing highly ordered framework materials with regularly repeating crystal structures where all the pores have exactly the same size, shape and functionality. This ignores disorder and/or defects which are often concomitant with the growth of a long-range periodic framework. The introduction of defects may alter the regular porous interior and behavior of MOFs. Defects may play a crucial role in enhanced accessibility of the porous network and higher basicity of the metal centers. Defects in regular MOFs have been shown to impart unusual and useful physical properties to these framework materials (Cairns & Goodwin, 2013;Tucker et al., 2005;Goodwin et al., 2009;Cheetham et al., 2016;Fang et al., 2015;Tahier & Oliver, 2017;Cliffe et al., 2014;Li et al., 2013). Fundamental correlations between defects and properties of the resulting defective materials have been shown in some examples. Partial interpenetration of MOF NOTT-202a was observed by Schrö der and co-workers to provide defect sites for gas recognition and storage, and to show selective hysteretic sorption of gas molecules . The mixed linker approach was reported by Zhou and co-workers to introduce functionalized disordered mesopores into MOFs Yuan et al., 2016). Missing-linker defects were shown to be extensively present [e.g. in the UiO-66 series (Trickett et al., 2015)], increasing the gas adsorption capacities (Rodríguez-Albelo et al., 2017) and enhancing the proton mobility Taylor, Komatsu et al., 2015). Herein, we report a unique example to demonstrate how structural disorder can lead to unusual changes in the properties of MOFs (e.g. the sorption property) based on a series of isoreticular azole-based MOFs with rtl (rutile) topology (denoted rtl-MOFs).

Syntheses and crystal structures
The T-shaped ligand 5-(1H-imidazol-1-yl)isophthalate acid (denoted as T imi ) used to introduce hetereocyclic imidazole was synthesized by acid-catalyzed ester hydrolysis of dimethyl 5-(1H-imidazol-1-yl)isophthalate, which was obtained via cyclization of formaldehyde with the diazabutadiene intermediate formed from a reaction of molar equivalents of dimethyl 5-aminoisophthalate, ammonium chloride and glyoxal. A mild solvothermal reaction of T imi with CuCl 2 Á2H 2 O at 353 K in a mixture of DMF/EtOH (v:v 3:1) led to the new rtl-MOF member, herein denoted as T imi -Cu.
The structure of T imi -Cu was determined and checked by single-crystal X-ray diffraction at 150, 195 and 273 K with several randomly selected crystals, all displaying disordered character. In general, T imi -Cu crystallizes in the monoclinic space group P2 1 /c, which is isostructural to the previously reported T triaz -Cu (Eubank et al., 2011) and T tetraz -Cu   (Fig. 1, Table S1 of the supporting information). In contrast, the reaction of T imi with CuCl 2 Á2H 2 O at 353 K in acidified DMF yields a different topological structure (Zhu et al., 2015). The reaction of T imi with CuBr 2 at 353 K in acidified DMF-H 2 O yields the same topological structure, but no framework disorder is located (this structure is not stable during a sorption study) (Cheng et al., 2017). Therefore, regardless of the disorder in T imi -Cu, these azole-based rtl-MOFs have the same overall unit cell, building block geometry and lattice porosity. As shown in Fig. 2, the basic structural units are the dicopper paddle-wheel SBUs bonded together by four T-shaped ligands via carboxylate groups. The axial sites are occupied by the N donors of imdazole. Each Cu 2 SBU joins six ligands and each ligand bridges three different Cu 2 SUBs, thus generating the (3,6)-connected 3D framework of rtl topology. The tubular channels run along the a axis and have an opening of 11.9 Â 14.5 Å (b Â c, b ? c) along the diagonals of the quadrangle cross section. The solvated DMF and H 2 O molecules are disordered and reside in the channels. Based on calculations using the program PLATON, the total potential solvent-accessible void volume is about 885.1 Å 3 per unit cell with a pore volume ratio of 50.3%.
The detailed structural analysis of T imi -Cu reveals that the coordination framework is actually disordered in a specific fashion (Figs. 3 and S1). In a statistical sense, each Cu 2 paddle-wheel SBU is distributed over two fractional positions in an approximate 3:1 ratio, and some local areas can be imagined to superimpose two partial rtl-MOFs in an offset way. In reality, each Cu 2 SBU has a definite orientation in the individual asymmetric unit, and is closely related to the neighboring SBUs owing to the rigidity of the isophthalate moiety and consequently fixed Cu 8 L 4 square-grid conformation. This is due to the fact that, in the rtl topology, sql sheets are formed via the isophthalate moiety in a predetermined 1,2-alternating fashion (up-up down-down). Thus, local primary 2D Cu 8 L 4 square-grid layers are inherently inert to dynamic disorder. In the contrast, local interlayer gliding is relatively easy ( ligands, (ii) the Cu-N binding between imidazole N donors and axial positions of Cu 2 SBUs is relatively labile, and (iii) the imidazole ring is freely rotatable along the N-C bond to the isophthalate moiety so as to adapt to the layer motions.
Therefore, the disorder in T imi -Cu may be considered to originate from local random interpolated movement of the 2D Cu 8 L 4 square-grid layers. This might also account for the observation of two isomerized T triaz -Cu structures (Eubank et al., 2011;Wen et al., 2012) which differ only in the arrangement of the 2D Cu 8 L 4 square-grid layers in one direction. The crystal packing in the other two directions and the framework porosity are similar. However, as for T teraz -Cu, noticeable disorder was not detected in T triaz -Cu, meaning that the chemical nature of heterocycles in this azole-based isoreticular rtl-MOF has a subtle influence on crystallization habit and framework isomerization (Makal et al., 2011;Lü et al., 2006). In the reaction of T imi with CuBr 2 at 353 K in acidified DMF-H 2 O, the product has no noticeable disorder as well, showing that guest solvent molecules or ions may have a subtle effect on the disorder.
To further probe the structure of T imi -Cu, X-ray photoelectron spectroscopy (XPS, Fig. S2) and X-ray absorption fine-structure (XAFS, Fig. S3 and Table S2) measurements were investigated. XPS confirms the presence of copper(II) in T imi -Cu. Cu 2p core-level photoelectron spectra for imi-Cu    displayed doublets i.e. Cu 2p 3/2 and Cu 2p 1/2 at 935.8 and 955.0 eV, respectively. The Cu 2p 3/2 and Cu 2p 1/2 main doublets were separated by 20 eV and their satellite peaks present at binding energies of 943.0 and 964.0 eV are characteristic of the unfilled orbitals. The study of the Cu LMM signal also supports the presence of Cu(II), and the Cu LMM signal with a kinetic energy of 916.0 eV is assigned to Cu(II). Although being the most common technique for structure determination/identification and measurement of long-range order, powder X-ray diffraction (PXRD) generally provides little information on defects. XAFS was expected to provide some local order information. XAFS data show that Cu(II) is present and the average Cu-O/N bonds are calculated to be 1.97 AE 0.01 Å . However, the data of T imi -Cu are comparable with the data of Cu-T triaz and Cu-T tetraz , which have no disorder. It can be concluded that T imi -Cu and the other two MOF materials have similar short-range coordination spheres.
The above results show that a unique structural feature of T imi -Cu is that the disorder does not cause absence of crystallinity. In other words, the disorder occurs in a crystallographically 'regular' way to a certain extent. Various comparisons of the disordered structures of T imi -Cu with those of notionally ordered counterparts are depicted in Figs. 3, 4 and S1. It is speculated that partial Cu 8 L 4 square-grid layers shift exactly half a unit cell along the c direction, leading to offset stacking of these 2D sql sheets along the a direction. In this way, all Cu 2 SBUs need not change conformation except for a 180 rotation of the imdazole rings to adapt to the new axial coordination (Fig. 4). Since orientation of the Cu 2 SBUs in every layer is fixed, gliding of the 2D sheet along any other direction will cause a severe geometry and connectivity mismatch. This is evident from observations of the nearly identical packing modes of the ordered and disordered frameworks in both the b and c directions (Fig. S1). Such a disorder phenomenon is distinct from the topological disorder in well known amorphous silica glass (-SiO 2 ) with a continuous random network (Cairns & Goodwin, 2013;Tucker et al., 2005). It is also distinct from the 2D layered square grids Ni(CN) 2 , which lack long-range order in the perpendicular direction (Cairns & Goodwin, 2013;Goodwin et al., 2009), although in a short-range or local environment they might be comparable. It is worth noting that some framework defects like coordination mismatch or connectivity distortion should also be present.
Therefore, the disordered T imi -Cu is a new member of the azole-based isoreticular rtl-MOFs containing different fivemembered-ring heterocycles (imidazole, 1,2,4-triazole and tetrazole). A study of T imi -Cu may offer the following advantages: (i) T imi -Cu has a comparable pore volume regardless of chemical or structural variation. For the azolebased rtl-MOFs, the heterocycles protrude into the channels and slightly reduce the pore sizes in comparison with the pyridyl rtl-MOF (Xiang et al., 2011). However, the similar Cu 8 L 4 square grids and pillaring nature of three fivemembered azole rings principally decide the total comparable pore volume. (ii) The inner pore surfaces are modified by different heterocyclic azole rings. Two C-H moieties point into the channel in T imi -Cu, one C-H and one N donor in T triaz -Cu, while there are two N donors in T tetraz -Cu (Fig. 1). (iii) Framework disorder in T imi -Cu produces different pore permeability from that in T triaz -Cu and T tetraz -Cu. As seen from Figs. 3, 4 and S1, partial gliding of sql sheets does not cause significant pore changes along the b and c axes but does along the a axis. The main pore channels along the a axis in T imi -Cu become distorted in contrast to the straight channels with long-range order in T triaz -Cu and T tetraz -Cu. (iv) The propensity for disorder and framework defects in T imi -Cu probably results in sorption dynamics compared with the more static frameworks in T triaz -Cu and T tetraz -Cu.

Thermal stability
As-synthesized bulk samples of T imi -Cu display sharp PXRD patterns that closely resemble those simulated from the single-crystal data (Fig. S4), indicative of phase purity and air stability. Thermogravimetric analysis (TGA) of T imi -Cu reveals similar thermal stability to that reported for T tetraz -Cu (Wen et al., 2012;Zhang et al., 2010). The TGA plot of assynthesized T imi -Cu shows a weight loss of 26.2% from room temperature to ca. 513 K, corresponding to the release of solvent molecules (1.5 DMF and 0.5 H 2 O per formula unit; calculated weight loss 28.8%) residing in the pore channels (Fig. S5). Rapid decomposition occurs upon further heating above 543 K. The thermostability of the desolvated material is further revealed by PXRD experiments at various temperatures (Fig. S6). PXRD results reveal that the framework structure is unchanged up to 373 K and transforms into a new structure with a different framework topology between 383 and 443 K (the new structure will be reported in due course). This further indicates that the Cu 2+ -T imi system is rather sensitive to synthetic parameters including solvent, counteranions and temperature.

Permanent porosity
To evaluate the permanent porosity, nitrogen physisorption measurements were performed at 77 K. Prior to analysis, pore activation was performed by evacuating T imi -Cu by thermal activation under vacuum at 358 K following surface cleaning by EtOH. This gives rise to a partially desolvated sample, in which the DMF molecules occluded within the channels were not removed completely (Seo et al., 2010;Hijikata et al., 2013;Wang et al., 2013Wang et al., , 2015. FT-IR spectra confirm the presence of residual DMF (Fig. S7). An N 2 adsorption isotherm of T imi -Cu reveals a steep uptake in the low-pressure region and the profile displays a type-I curve that is typical of microporous materials (Fig. 5). The Langmuir and BET surface areas are calculated to be 1145 and 771 m 2 g À1 , respectively, and the total pore volume is 0.31 cm 3 g À1 (Table S3, Figs. S8-S10). Surprisingly T imi -Cu shows a double-peak pore size distribution centered around 5.1 and 6.8 Å according to the Horvath-Kawazoe method. The main pore size at 5.1 Å is consistent with other rtl-MOFs , while 6.8 Å is unprecedented (see the discussion below). For comparison, T triaz -Cu has Langmuir and BET surface areas of 893 and research papers IUCrJ (2019). 6, 85-95 768 m 2 g À1 , while those of T tetraz -Cu are 1055 and 766 m 2 g À1 , consistent with the reported data . The total pore volumes are 0.29 and 0.30 cm 3 g À1 , respectively, and the pore sizes are comparable at around 4.9 Å .
The pore enlargement of T imi -Cu is unexpected and can reasonably be related to the framework disorder. On one hand, the disorder in T imi -Cu causes the pore channels to become distorted; on the other hand, appearance of structural disorder in the crystal structure always implies concomitance of local defects due to coordination mismatch or topological distortion caused by interlayer gliding. Hence, enlargement of partial pores in T imi -Cu is understandable. The defects (probably containing uncoordinated metal centers) may be readily occupied by solvated DMF molecules. Moreover, the N 2 sorption isotherms show an obvious H2-type hysteresis loop which is usually considered to be a characteristic of mesoporosity (Li et al., 2013;Fang et al., 2010;Zhao et al., 2011;Qiu et al., 2008), but we believe that this may also be attributed to the structural disorder. The clustering of numerous local defects may result in larger-scale mesoporosity, so the existence of some mesopores in the disordered framework is to be expected.

CO 2 capture and framework dynamics
Low-pressure and high-pressure CO 2 sorption has been studied. As depicted in Fig. 6, T imi -Cu adsorbs significant amounts of CO 2 at various temperatures (195,263,273,283 and 298 K). At 195 K, the isotherms are type I, which is typical for microporous materials. T imi -Cu displays an uptake capacity CO 2 adsorption-desorption isotherms for T imi -Cu measured at (a) 195 K (insert shows an enlargement of the low-pressure section); (b) 263, 273, 283 and 298 K; and (c) CO 2 , N 2 , H 2 and CH 4 adsorption-desorption isotherms for T imi -Cu measured at 273 K, and CO 2 , N 2 and CH 4 adsorption-desorption isotherms for (d) T imi -Cu, (e) T triaz -Cu and ( f ) T tetraz -Cu measured under various pressures at 298 K. (a) N 2 adsorption-desorption isotherms for T imi -Cu measured at 77 K and (b) Horvath-Kawazoe micropore size distribution. of 7.3 mmol g À1 (32.0 wt%) for CO 2 at 1 bar. A striking feature is that T imi -Cu also shows high CO 2 uptake at 273 K. T imi -Cu has CO 2 storage capacity of 4.2 mmol g À1 (18.7 wt%) at 273 K, 1 bar. The adsorption isotherm of CO 2 up to 30 bar at 298 K indicates that T imi -Cu shows a CO 2 uptake capacity of 3.2 mmol g À1 (14.1 wt%) at 30 bar. The high CO 2 uptake capacity of T imi -Cu, which has no open metal/N-donor sites on the inner pore surface revealed by the X-ray structure, hints at other contributions, namely framework disorder (see the discussion below).
Another noteworthy feature is that T imi -Cu shows remarkable hysteretic sorption behavior toward CO 2 , while the isostructural T triaz -Cu and T tetraz -Cu do not show obvious hysteresis loops (Fig. 6). The stepwise sorption usually indicates filling of different types of pore sites, originating from the gate effect or dynamic nature (Kitaura et al., 2002;Thallapally et al., 2008;Chen, Ma, Hurtado et al., 2007;Nouar et al., 2012;Suzuki et al., 2016;Carrington et al., 2017;Taylor et al., 2016;Choi & Suh, 2009;Llewellyn et al., 2006) and framework defects . Careful examination reveals that T imi -Cu exhibits stepwise adsorption under low pressure at 195 K (Fig. 6a). Surprisingly, such adsorption/desorption hysteresis becomes more prominent at elevated temperatures up to 273 K (Fig. 6b). Note that a higher pressure is needed to initiate the hysteresis as temperature increases. The inducing pressure of P/P 0 = 0.01 at 195 K increases to 0.37 at 263 K and 0.54 at 273 K.
The adsorption isotherms of CO 2 up to 30 bar at 298 K further reveal the temperature-gating pressure relationship (Fig. 6). T imi -Cu exhibits a distinct stepwise adsorption isotherm, while the desorption branch does not trace the adsorption branch, forming a remarkable hysteresis loop. At low pressure, only a small amount of CO 2 (0.5 mmol g À1 ) is adsorbed. A sudden rise in the isotherm occurs at an inducing pressure of 125 kPa, which is higher than that at 273 K. This confirms the low-pressure observations that a higher pressure is needed to initiate the hysteresis as temperature increases.
Considering the above temperature-dependent variations of CO 2 sorption capacity and hysteresis, and comparing the structural nature of these isoreticular rtl-MOFs, we believe that the framework disorder in T imi -Cu imparts an essential effect on the CO 2 sorption behavior. As discussed above, the structural disorder causes the pore channels to become too distorted for gas molecules to permeate through, and renders some local defects which might be partly maintained by the solvated DMF molecules. If gas molecules have a tendency to interact with the pore surface (protruding heterocycles) and defect sites (such as uncoordinated metal centers), gas uptake may induce framework dynamics. For T imi , the blocking/ shielding DMF molecules can facilitate and affect the structural transformation, thus making hysteresis pronounced. At low temperature, i.e. 195 K, the coordination framework and shielding DMF molecules are relatively static, and the hysteretic steps are therefore relatively inexplicit. As the temperature increases, the kinetically hindered pores in the disordered framework become easier to break through, thus displaying a larger hysteresis loop. However, once the temperature rises above 283 K, hysteresis turns indistinctive again (Fig. 6b), implying facile and expeditious structural conversions above this temperature. Additionally, the inducing pressure of hysteresis increases with rise in temperature, which may be due to higher thermal vibration of the framework, hindering DMF and adsorbed CO 2 molecules at elevated temperature and resulting in weaker adsorbent/ adsorbate interactions, thus requiring a larger pressure to push the motion of the framework. This may also account for the observation that the CO 2 uptake capacity of T imi -Cu decreases as temperature increases relative to that of T triaz -Cu and T tetraz -Cu. The CH 4 isotherm also exhibits a broad hysteresis loop with an inflection point at 298 K and a higher pressure of ca. 940 kPa, which may relate to its larger polarizability (25.93 Â 10 À25 cm 3 ) (Li et al., 2009;Sircar, 2006). This offers a new strategy for hysteretic sorption of CH 4 (Taylor et al., 2016;Mason et al., 2014).
According to the above discussion, the present CO 2 uptake process may represent a distinct strategy to drive adsorption/ desorption hysteresis that is inherently related to framework (pore) disorder. In contrast to the gate effect and interpenetrating dynamics (Kitaura et al., 2002;Thallapally et al., 2008;Chen, Ma, Hurtado et al., 2007;Nouar et al., 2012;Suzuki et al., 2016;Carrington et al., 2017;Taylor et al., 2016;Choi & Suh, 2009;Llewellyn et al., 2006), the present CO 2 (and CH 4 ) hysteresis is temperature dependent, originating from the propensity of structural disorder which can be affected by guest intrusion. The structure dynamics can be induced selectively by CO 2 (and CH 4 at higher pressure) but not by N 2 or H 2 .
In order to have further insight into the structure dynamics, PXRD investigation was performed. PXRD patterns of T imi -Cu remain unchanged under a high-pressure CO 2 atmosphere up to 3.0 MPa even if accompanied by pulverizing of the crystal sample (Fig. S11). Moreover, the XRD patterns of T imi -Cu show no change after tablet compression with a tablet press from 0 to 20 MPa (Fig. S12). The results reveal that the long-range order of T imi -Cu is generally maintained under high pressure. The XRD signals become weak above 30 MPa, showing partial loss of long-range order under high pressure. Therefore, either no phase transformation occurs or the structural change is tiny under high pressure.
Two possible factors may contribute to the CO 2 hysteresis. (i) Penetration of CO 2 and CH 4 through the disordered pore channels offers a greater driving force than through the straight 1D channels, and interactions of CO 2 with the protruding imidazole rings facilitate their rotation along N-C bonds. Simulation of the CO 2 adsorption isotherms at 263 K shows that a slight rotation of the imidazole ring of 5.448 has a dramatic effect on the adsorption results (Fig. S13). (ii) DMF guest molecules in the framework perhaps block the pore entrance, which becomes dynamic when the temperature and/ or pressure increases. Such framework dynamics may result in partial loss of long-range order, as shown by the broadened PXRD pattern after sorption. Therefore, the framework dynamics are responsive to CO 2 uptake depending on feasible conditions created by proper temperature. This is analogous research papers IUCrJ (2019). 6, 85-95 with the partially interpenetrated NOTT-202a which shows temperature-dependent adsorption/desorption hysteresis only below the triple point of CO 2 (216.7 K), corresponding completely to the framework defects. In our case, the framework dynamics may be more related to the topological disorder, because the disordered structure model established by single-crystal analysis prefers topological distortion to defect formation. Nevertheless, interaction of CO 2 with the defect sites should also contribute to the dynamics of the disordered framework.
The CO 2 adsorption capacity around room temperature is essential for potential industrial usage, such as CO 2 capture and separation in upgrading of natural gas (natural gas cleanup, CO 2 /CH 4 ), post-combustion (flue gas, CO 2 /N 2 ) and precombustion (shifted synthesis gas stream, CO 2 /H 2 ) (Sumida et al., 2012;Li, Sculley & Zhou, 2012;Nugent et al., 2013;. To investigate the sorption selectivity of T imi -Cu, CO 2 , N 2 , H 2 and CH 4 low-pressure adsorption isotherms were measured at 273 K, and CO 2 , N 2 and CH 4 high-pressure adsorption isotherms at 298 K, and compared in Figs. 6(e) and 6( f ). For T imi -Cu, considerably larger amounts of CO 2 are adsorbed than N 2 , H 2 and CH 4 , suggesting that the gas uptake capacity drops remarkably for N 2 , H 2 and CH 4 but remains significant for CO 2 at elevated temperatures (see Figs. S8-S10 for low-temperature data).
The above results verify that T imi -Cu has a high and general gas sorption selectivity for CO 2 over H 2 /CH 4 /N 2 ; the question is then how such sorption behavior happens. Various effects have been reported in the literature that enforce strong interactions between the host framework and CO 2 under ambient conditions, e.g. immobilization of open metal sites or polarized functional groups (Yuan et al., 2010;Sumida et al., 2012;Cui et al., 2012;Gu et al., 2010;Demessence et al., 2009;McDonald et al., 2011;Banerjee et al., 2009). In particular, aromatic ligands containing uncoordinated N donors (e.g. tetrazole-based ligands) were found to improve the selective adsorption behavior for CO 2 Cui et al., 2012;Lin et al., 2010Lin et al., , 2012Qin et al., 2012). In the present azole-based rtl-MOF, no purposely introduced open metal sites exist on the pore surface and T imi -Cu has no polarized functional groups (open N-donor sites). So, the good selectivity of T imi -Cu probably relies on the above-described structural disorder, as well as the tubular pore channels characteristic of rtl-MOFs containing pillaring T-shaped ligands.
First of all, the tubular channels of narrow size in the present rtl-MOF have proved important (Du et al., 2013;An & Rosi, 2010). It is argued that, for MOFs with bigger pore sizes (>6 Å ), substitution of C-H moieties with N donors does not significantly affect the adsorption capacity for H 2 and CO 2 (Park et al., 2011). The pore sizes of T imi -Cu justify this assumption well. Second, the quadruple moment of CO 2 renders a stronger interaction with the host framework, which contributes excess energy for CO 2 to enter the pore channels. Since CO 2 is well known to have stronger adsorbent/adsorbate interactions due to strong polarizability (29.11 Â 10 À25 cm 3 ) and quadruple moment (4.30 Â 10 À26 esu cm 2 ) (Li et al., 2009;Sircar, 2006), selective hysteretic sorption of CO 2 over N 2 , H 2 and CH 4 is understandable at low pressure. Third, the structural disorder may cause defects in the coordination framework, thus creating open metal sites. Such defects may exist in a small portion of the framework (see above). On the other hand, the framework disorder enables distorted pore channels as well as straight channels. The distorted channels with narrow size are appropriate for holding gas molecules kinetically within the channels, which increases the van der Waals interactions between the host framework and gas molecules (Wen et al., 2012). Most importantly, as temperature rises, CO 2 uptake towards such disordered pores amplifies the framework dynamics, resulting in selective sorption hysteresis. Such adsorption/desorption hysteretic behavior at room temperature is rare (Hijikata et al., 2013;Wang et al., 2013Wang et al., , 2015; it greatly improves the adsorption selectivity for CO 2 at ambient temperature, similar to observations of selective CO 2 capture by flexible or dynamic MOFs under different conditions (Choi & Suh, 2009;Llewellyn et al., 2006;Mohamed et al., 2012;Burd et al., 2012;Eguchi et al., 2012). In addition, the present framework disorder induces hysteretic sorption in a much broader range from 195 K to room temperature. This allows the capture of CO 2 at high pressure, but leaves CO 2 trapped in the pores at low pressure, thus facilitating the separation of CO 2 from H 2 /CH 4 /N 2 under more industrially applicable conditions.

Conclusions
A unique rtl-MOF (T imi -Cu) with framework disorder was prepared by incorporating an imidazole ring into a T-shaped ligand and the gas sorption properties were evaluated. In contrast to other azole-based rtl-MOFs with five-memberedring heterocycles (triazole, T triaz -Cu; tetrazole, T tetraz -Cu), T imi -Cu does not integrate open N-donor sites while containing only two C-H moieties in its characteristic tubular pores. Remarkably, T imi -Cu displays crystallographically identifiable disorder of the framework. Considering the interesting effects induced by structural disorder on framework materials (Cairns & Goodwin, 2013;Tucker et al., 2005;Goodwin et al., 2009;Cheetham et al., 2016;Fang et al., 2015;Tahier & Oliver, 2017;Cliffe et al., 2014;Li et al., 2013;Amirjalayer & Schmid, 2008), T imi -Cu provides a unique example to investigate the effect of framework pore disorder on sorption properties. As a defective derivative, T imi -Cu retains the long-range order and topology of the parent framework of rtl-MOFs, while it exhibits pore disorder and a relatively large percentage of defects in an otherwise highly crystalline material. Single-crystal analyses establish the disordered structural model in relation to porosity, featuring distorted 1D tubular channels and DMF-guestremediated defects. These factors endow T imi -Cu with good gas sorption capacity. Importantly, temperature-dependent hysteretic CO 2 (and CH 4 ) sorption is shown up to 298 K, which dramatically enhances selective adsorption of CO 2 (and CH 4 ) at elevated temperatures. Therefore, the present azolebased rtl-MOF shows strong binding with CO 2 and high selectivity for CO 2 over H 2 /CH 4 /N 2 at ambient temperature. Furthermore, the results imply the significance of structure disorder (defects) on the modification of the performance of framework materials, providing a viewpoint for expanding the properties of framework materials.

Materials and methods
All starting materials and solvents were obtained from commercial sources and used without further purification unless otherwise indicated. Dimethyl-5-(1H-imidazol-1yl)isophthalate was prepared according to the published procedure . PXRD data were recorded on a Bruker D8 Advance diffractometer at 40 kV and 40 mA with a Cu-target tube and a graphite monochromator. Infrared spectra were measured on a Nicolet/Nexus-670 FT-IR spectrometer with KBr pellets. Thermogravimetric analysis was performed under N 2 at a heating rate of 10 K min À1 on a Netzsch Termo Microbalance TG 209 F3 Tarsus. The sorption isotherms were measured with a Quantachrome Autosorb-iQ or Autosorb-iQ2 analyzer.

Synthesis of T imi -Cu
A solution of T imi (6.0 mg, 0.025 mmol) in DMF (3 ml) and a solution of CuCl 2 Á2H 2 O (8.5 mg, 0.05 mmol) in EtOH (1 ml) were mixed. The resultant clear solution was heated in a closed vial at 353 K for 3 days. Green crystals were collected using filtration (7 mg, 70%). Microanalysis found (calculated) for C 11 H 6 O 4 N 2 CuÁ1.5DMFÁ0. 4.4. X-ray structure determination X-ray reflection data were collected at 150 (2) K on an Oxford Gemini S Ultra diffractometer equipped with a graphite-monochromated Enhance (Cu) X-ray source ( = 1.54178 Å ). An empirical absorption correction was applied to the intensity data using spherical harmonics implemented in the SCALE3 ABSPACK scaling algorithm (Agilent, 2012). The structure was solved by direct methods following difference Fourier syntheses and was refined by the full matrix leastsquares method against F o 2 using SHELXTL software (Sheldrick, 2015). The whole framework is disordered over two positions with an occupancy ratio of 0.694:0.306. The unit-cell volume includes a large region of disordered solvent (1.5 DMF and 0.5 H 2 O molecules). One DMF molecule is disordered over two positions with an occupancy ratio of 0.679:0.321. There are 0.25 water and 0.25 DMF molecules located at the inversion center. Modeled refinements were applied to the disordered parts including the imidazole ring, solvated water and DMF molecules to make them geometrically reasonable, resulting in a total of 1074 restraints.

Related literature
The following references are cited in the supporting information: Vitillo et al. (2008); Zhou et al. (2008).