Supramolecular-jack-like guest in ultramicroporous crystal for exceptional thermal expansion behaviour

The dynamic behaviours of host frameworks and guest molecules have received much attention for their great relevance with smart materials, but little has been developed to control or understand the host–guest interplay. Here we show that the confined guest can utilize not only molecular static effects but also bulk dynamic properties to control the host dynamics. By virtue of the three-dimensional hinge-like framework and quasi-discrete ultramicropores, a flexible porous coordination polymer exhibits not only drastic guest-modulation effect of the thermal expansion magnitude (up to 422 × 10−6 K−1) and even the anisotropy but also records positive/negative thermal expansion coefficients of +482/−218 × 10−6 K−1. Moreover, single-crystal X-ray diffraction analyses demonstrate that the jack-like motion of the guest supramolecular dimers, being analogous to the anisotropic thermal expansion of bulk van der Waals solids, is crucial for changing the flexibility mode and thermal expansion behaviour of the crystal.

On the other hand, the confinement effect of the porous host allows the formation of low-dimensional guest aggregations with abnormal/appealing physical properties 17,39,42 . The overwhelmingly large thermal expansion of the fluidic guest (usually beyond 100 times that of common solids) might be utilized to further drive the thermal expansion of the porous host. When the anisotropic structures of the host framework, pore environment and/or the low-dimensional guest aggregation are appropriately coupled, more exciting microscopic/macroscopic phenomenon could be expected. A key to these goals is to visualize, understand and control the delicate host-guest interplay under external stimulus, in which in situ single-crystal X-ray diffraction (SCXRD) is the most convenient, straightforward and reliable method [43][44][45] . Nevertheless, retaining the sample single-crystallinity after guest removal/absorption/ exchange and temperature cycling treatments is always a great challenge, and the extremely large mobility of guests also impedes determination of their positions 16,17 . Actually, even when the cross-section size of a one-dimensional channel is small enough to fit a single guest molecule well, the guest chain may still show liquid-like mobility 17 . To enable direct observation of thermal expansion of guest aggregations, discrete, isolated or 0D pores with suitable sizes for accommodation of two or a little bit more guest molecules should be optimal 46,47 . However, materials with such pores are generally difficult to change guests, preventing rational modulation of the physical property 20,48,49 .
In this work, we report a PCP possessing not only a threedimensional (3D) hinge-like structure with multimode flexibility but also quasi-0D ultramicropores suitable for adsorption and confinement of pairs of different amide-type guests. SCXRD studies of this material under temperature-and guest-stimuli reveal the largest NTE and PTE among crystalline solids to the best of our knowledge. We also report a drastic guest-modulation effect, and even a change of the main thermal expansion direction since the steric hindrance and thermal expansion effects of the guest dimers are large enough to alter the flexibility mode of the host framework (Fig. 1).
Thermal expansion of the porous crystal. Variable-temperature SCXRD revealed giant temperature-induced crystal deformation property for 1 (Fig. 3, Supplementary Fig. 3, Supplementary Tables 1 and 2 and Supplementary Data 1). While the a-and c-axes decrease by 2.2 and 1.6% from 112 to 300 K, respectively, its b-axis has a significant increase of 9.0%, giving rise to totally 5.8% increase of the unit-cell volume. Concomitantly, its void ratio increases from 20.4 to 24.8%. Such large temperatureinduced crystal deformation has not been observed in coordination networks [15][16][17][18][19]25 . Comparison of the single-crystal structures at 112 and 300 K showed that, similar to other flexible  The red squares and green spires represent two possible responsive modes in a porous crystal encoded with multimode framework flexibility. Without guest, thermal expansion of the host framework is mainly determined by the hinge action across the red fences, which can be restricted by the steric hindrance effect of guest (yellow spheres). Further, the anisotropic thermal expansion effect of the guest dimers (significant change of separation between two yellow spheres), behaving like a jack, can force the host framework to deform in another direction along the green spires.
PCPs, the framework distortions mainly arise from variation of the coordination angles rather than the coordination bonds (Supplementary Fig. 2 and Supplementary Tables 3 and 4). As defined by its bcu topology, the flexible 8-connected building unit can be regarded as a framework hinge and the whole framework can be considered as a 3D hinged rhombic fence consisting of many two-dimensional (2D) rhombic fences running across four crystallographic planes 15,53 . Although this framework topology is highly symmetric (cubic in its highest symmetric form), which allows the crystal to deform in any direction, the real deformation manner should depend on the anisotropy of the coordination network and pore system, as well as the distribution of the guest molecules. As the pores are running along the a-axis of 1, it can be understood that the 3D coordination framework can distort easily on the bc-plane. Actually, there are 2D hinged fence-like motifs (consisting of dinuclear clusters and bent 34pbaligands) running across the bc-plane, whose distortion causes the acute expansion of the b-axis and simultaneous contraction of the c-axis, when the temperature increases. The relative small contraction of the c-axis can be attributed to the nonplanar shape of the bc-plane hinged fence, which transfers some contraction effect to the a-axis.
Host-guest behaviour of the porous crystal. Gas adsorption measurements at low temperatures ( Supplementary Fig. 4) showed that while 1 cannot adsorb N 2 and Ar with kinetic diameters of 3.64 and 3.54 Å, respectively, at 77 K, it can readily adsorb the smaller O 2 (3.47 Å) at the same condition. Nevertheless, the O 2 isotherm exhibits obvious hysteresis and the saturated uptake (32 cm 3 g À1 ) is significantly lower than the value empirically calculated from the crystal structure (146 cm 3 g À1 ), indicating that the adsorption/desorption is very slow due to the high-energy barrier for gas diffusion in the quasi-0D ultramicropores. On the other hand, being similar with some flexible porous coordination polymers 3  ARTICLE difference of the guests, the DMF and DMA supramolecular dimers are distinct in their configurations 54,55 . Specifically, the molecular plane of DMA has an inclined angle of 40.0°with the bc-plane, while that of DMF is only 17.3°, because the small pore forces the larger guest molecule to rotate to avoid significant steric hindrance. As a result of these molecular orientations, the DMF dimer exhibits much larger overlap as compared with those in the DMA dimer ( Supplementary Fig. 8 and Supplementary Supramolecular-jack-like motion of the guest aggregations. Variable-temperature powder X-ray diffraction (PXRD) showed that (Fig. 3), while the (011) peaks of the three compounds gradually move to lower angles in different extents during temperature increase, the (100) peaks of 1 and 1ÁDMF/1ÁDMA move in different directions, indicating that the thermal responses of their a-axes contrast with each other. SCXRD revealed that (Fig. 3, Supplementary Fig. 3, Supplementary Tables 1 and 2 and Supplementary Data 1), while the a-axis of 1 decreases by 2.2% from 112 to 300 K, those of 1ÁDMF and 1ÁDMA increase by 2.8 and 0.7%, respectively. Moreover, the unit-cell volume and the b-/c-axis of 1 changed more largely than those of 1ÁDMF and 1ÁDMA.
The restricted hinge motion of the bc-plane can be explained by the intrinsic steric hindrance effects of the guest molecules. When the quasi-0D cavities, that is, the apertures of the 2D hinged fences on the bc-plane, are filled by guest molecules, the flexibility of the hinged fence is reduced, giving smaller temperature-induced deformation on the b-/c-axis. Though DMF is smaller than DMA, the temperature-induced hinge motion on the bc-plane of 1ÁDMF is the smallest one among the three materials, because the DMF molecules are almost parallel with the bc-plane, which exhibit strong steric hindrance effect with the host framework and restrain the hinge action across this plane ( Supplementary Fig. 9).
More importantly, the reversed directions of changes of the a-axis can be assigned to the thermal expansion of the guest supramolecular aggregation (Fig. 4 Table 6). In 1ÁDMF, the interplanar separation within a dimer significantly increases by 0.45 Å from 112 to 300 K, while this value is only 0.15 Å in 1ÁDMA, which highlights that the thermal expansion of the guest aggregation mainly occurs at the directions of the supramolecular interactions, and the tighter supramolecular contacts between the guest molecules can more effectively response to their local thermal vibrations. Comparison of their temperature-dependent electron density maps can clearly illustrate dynamic behaviours of the guest molecules. On the other hand, the closest interdimer separation decreases by 0.09 Å in 1ÁDMF but increases by 0.17 Å in 1ÁDMA. Since the interdimer interaction is ignorable in the crystal 1ÁDMF, the separation does not expand with increasing temperature. Instead, the large thermal expansion within the DMF dimer reduces the interdimer separation. Nevertheless, the thermal expansion of the dimer mainly transfers to or expands the flexible host framework via host-guest interaction, so that the interdimer separation decreases by much o0.45 Å. In the case of 1ÁDMA, the interdimer supramolecular contact is close enough to show thermal expansion, and the intradimer thermal expansion is not significant enough to compress the interdimer separation. As defined by the directions of the guest-guest interactions, the thermal expansions of the guests are highly anisotropic in the crystals, which is relatively parallel with the a-axis of 1ÁDMF or has a considerable inclined angle with the a-axis of 1ÁDMA. Therefore, the a-axis of 1ÁDMA expands much less than 1ÁDMF, since the thermal expansion of DMA supramolecular aggregations contribute to both the a-and b-axes. What's more, the void volume of 1ÁDMF (from 23.4 to 27.0%) has a larger increase than that of 1ÁDMA (from 27.5 to 28.8%), further indicating that the DMF dimer with much larger overlap can have stronger thermal expansion effect. While the static effects (that is, steric hindrance and supramolecular attraction to the host) of individual guest molecules have been observed to affect the thermal expansion behaviours of a few host frameworks 18,40,41 , this is the first structural evidence of thermal expansion of guest aggregations, which performs like supramolecular jacks to force the deformation of the host framework. It should be also mentioned that the relatively low crystallographic symmetry and suitable pore size (for a pair of amide molecules), as well as the multimode framework flexibility of 1 are decisive for the unambiguous observation of these interesting phenomena.

, Supplementary Figs 8 and 10 and Supplementary
Principal axial thermal expansion of the crystal. Since 1, 1ÁDMF and 1ÁDMA crystallize in the monoclinic crystal system, the axial thermal expansion coefficients of the principal axes were calculated using the programme PASCal (Table 1 and  Supplementary Table 7) 56 . The principal X 2 -axis is the same as the original crystallographic b-axis, while the principal X 1 -and X 3 -axes approximate the original crystallographic a-and c-axes or the [101] and [À101] directions. All the unit-cell parameters of 1, 1ÁDMF and 1ÁDMA change linearly or approximately linearly against temperature, meaning that their axial thermal expansion coefficients are virtually constant in the measured temperature range. Such behaviour is critical for precise thermomechanical actuators and sensors. 1ÁDMF shows huge PTE along the X 1 -axis (a 1 ¼ þ171 Â 10 À6 K À1 ) and moderate PTE and NTE along the X 2 -and X 3 -axes (a 2 ¼ þ60 Â 10 À6 K À1 , a 3 ¼ À56 Â 10 À6 K À1 ), respectively. When DMF is replaced by DMA, the thermal expansion coefficients of the X 1 -and X 2 -axes are approximately halved and doubled (a 1 ¼ þ85 Â 10 À6 K À1 , a 2 ¼ þ103 Â 10 À6 K À1 ), respectively, while that of the X 3 -axis is almost unchanged (a 3 ¼ À51 Â 10 À6 K À1 ). More remarkably, The host frameworks and the guest molecules are shown in green stick and multicolour space-filling modes (carbon, grey; nitrogen, blue; oxygen, red; hydrogen atoms are omitted for clarity), respectively. The enlarged insets compare the relative positions of the two guest molecules (stick mode with oxygen atoms highlighted as spheres) within the supramolecular dimer at 112 (blue) and 300 (red) K, along two representative directions (perpendicular and parallel to the molecular planes). The double-headed arrows represent the vectors of the guestguest movements from 112 to 300 K within each dimer. (c,d) Temperaturedependent electron density maps of (c) 1ÁDMF and (d) 1ÁDMA.
although the PTE of the X 1 -axis of 1 (a 1 ¼ þ61 Â 10 À6 K À1 ) is smaller than those of 1ÁDMF and 1ÁDMA, its X 2 -and X 3 -axes exhibit giant PTE of a 2 ¼ þ482 Â 10 À6 K À1 and NTE of a 3 ¼ À218 Â 10 À6 K À1 , respectively, which are much larger than for other known crystalline materials (Supplementary Table 8). It is noteworthy that the guest-modulation effect among 1, 1ÁDMF and 1ÁDMA are exceptionally enormous, which change the PTE and NTE magnitudes by up to 422 Â 10 À6 K À1 and 167 Â 10 À6 K À1 , respectively. Also interestingly, the X 2 -axial PTE coefficient follows the order 141ÁDMA41ÁDMF, while the X 1 -axial PTE coefficient follows the opposite order 1ÁDMF41ÁDMA41. Consequently, the thermal expansion coefficients of the X 2 -and X 3 -axes of 1 are much larger than that of its X 1 -axis, whereas in 1ÁDMF, the X 1 -axis shows the largest thermal expansion coefficient among three principal axes, meaning that the thermal expansion of the guest dimer can change the main thermal expansion axis or thermal expansion anisotropy of the crystal. Anisotropic physical property, as one of the most important features of crystalline materials, is predominantly determined by the crystallographic symmetry. The guest-dependent anisotropy of thermal expansion of isomorphic 1, 1ÁDMF and 1ÁDMA (same crystallographic symmetry) demonstrates the possibility of controlling and utilizing the host-guest interplay for developing multiresponsive smart materials.

Discussion
In summary, by using mixed linear and bent ligands, we successfully constructed an ultramicroporous flexible framework with a highly connected 3D hinge-like structure and multimode flexibility, which exhibits the largest PTE and NTE coefficients among framework solids. Remarkably, the quasi-0D ultramicropores in this material can accommodate dimers of different small amide molecules, giving unprecedentedly significant guestmodulation effects on both the magnitude and anisotropy of thermal expansion. By virtue of the robustness, low symmetry and suitable pore size of the crystal, the guest-and temperatureinduced structural transformations were directly visualized by PXRD and SCXRD, which revealed that the confined guest dimers can show anisotropic thermal expansion behaviours similar with their bulk forms and force the host framework to drastically change not only the coefficients but also the main axis of thermal expansion. Generally, since the structural transformations of the host framework and the guest aggregations are always observed simultaneously, there is still no rational approach to analyse their relationship or identify which one is the original force. In this context, the multimode framework flexibility of the host framework, which has potential to deform in different ways under different stimuli, is crucial for unambiguous elucidation of the mechanism. Of course, these supramolecular-jack-like dimers and similar guest aggregations should be also effective and applicable for other flexible porous solids, even with only singlemode flexibility.
Measurements. Elemental analyses were performed using a Vario EL elemental analyser. The FT-IR (KBr pellet) spectra were recorded in the range of 400-4,000 cm À1 on a Bruker TENSOR 27 FT-IR spectrometer. Thermogravimetric analyses were carried out using a TA Instruments Q50 thermogravimetric analyser under N 2 at a rate of 10°C/min. PXRD patterns were recorded on a Bruker D8-Advance diffractometer using Cu Ka radiation and a LynxEye detector at room temperature except otherwise stated. Gas sorption isotherms were measured on a volumetric adsorption apparatus (Micromeritics ASAP 2020 M Physisorption Analyzer). Ultrahigh-purity-grade (purity499.999%) N 2 , O 2 and Ar gases were used in all adsorption measurements. As-synthesized samples were degassed under high vacuum at 493 K for 3 h before measurement. Temperatures were maintained by liquid nitrogen.
Synthesis. H34pba (0.40 g, 2.0 mmol) and H44pba (0.40 g, 2.0 mmol) were dissolved in EtOH (80 ml) using a 250-ml scintillation vial, added with a water solution of Cd(NO 3 ) 2 (0.05 mol l À1 , 40 ml). The mixture was then sealed with a screw cap and heated to 90°C for 24 h. Colourless needle-like crystals of X-ray single-crystal structure analyses. Diffraction data were collected on an Agilent SuperNova CCD diffractometer with graphite-monochromated Cu Ka radiation. Single crystals of 1ÁDMF and 1ÁDMA were mounted directly on the top of a glass fibre using minimum amount of glue. A single crystal of 1 was sealed in high vacuum in a glass capillary. The test temperature was controlled by dry nitrogen flow using a Cryostream Plus cooler system, and corrected by a thermal couple at the crystal position. Though thermogravimetry curves of 1ÁDMF and 1ÁDMA showed no weight loss below 350 K, the unit-cell parameters of 1ÁDMF and 1ÁDMA did change above 340 K under the temperature-controlling nitrogen flow after B2 h, which can be attributed to the guest escaping. Nevertheless, under the same measurement conditions, no change of unit-cell parameter or chemical composition occurred for single crystals of 1ÁDMF and 1ÁDMA below 300 K even for one day. The unit-cell parameters at each measurement temperature used for calculation of the thermal expansion coefficients were determined by 30 diffraction images, while those for crystal-structure refinements were determined by 600-900 diffraction images. The reversibility of temperature-induced crystal deformations of the samples were confirmed by the coincidence of data points over a heatingcooling cycle. Absorption corrections were applied by using the multi-scan programme CrysAlisPro 57 . The crystal structures were solved through direct methods and developed by difference Fourier techniques using the SHELXTL software packages 58 . All hydrogen atoms were added geometrically, and anisotropic displacement parameters were used to refine all non-hydrogen atoms.