Main

Many structurally flexible porous materials swell reversibly in response to the uptake and release of small volatile compounds in their surroundings. For example, carpenters must anticipate and compensate for cross-grain expansion and contraction of wooden boards with fluctuations in relative humidity1. When immersed in liquid water, clays expand anisotropically2 whereas hydrogels swell isotropically3. Coal beds also swell isotropically under high pressures of methane (CH4) or carbon dioxide (CO2) gas4. Indeed, the influence of external stimuli on strain in one or more of the three principal directions has been studied extensively for a wide variety of responsive materials. Although crystals are generally considered to be brittle chemical cemeteries5 in which the components are frozen into static three-dimensional arrays, recent research efforts have revealed that some are capable of a surprising level of dynamic behaviour6. Exerting control over dynamic strain with a view to develop new potential applications of crystals as mechanical, electrical or optical components has been termed crystal adaptronics7. This relatively young area of research is primed for the discovery of material properties, accompanied by the development of innovative approaches to quantification and molecular-level elucidation of the underlying dynamic mechanisms.

In recent years, much attention has been focused on the structure–property relationships of porous materials, particularly metal–organic frameworks8 and covalent organic frameworks9. However, the lesser-known porous molecular crystals have yielded several surprising findings; some examples of these from our own work, and that are relevant to the current report, include transient porosity (that is, the transport of guest molecules within a flexible host framework devoid of permanent channels10) and low-temperature uptake and release of water vapour11. The porosity of crystalline molecular materials may result from inefficient packing (extrinsic voids that form between host molecules) or molecular design (intrinsic voids in host molecular cavities)12.

Our research on the host–guest chemistry of molecular crystals has primarily centred on cyclic hosts, such as metallocycles and organic macrocycles, which are designed to contain clefts or cavities that can form intrinsic or hybrid intrinsic–extrinsic zero-dimensional (0D) lattice voids. In this context, we recently reported a detailed in situ structure–property study of a trianglimine macrocycle T1 (ref. 11; Fig. 1), which crystallizes to form both one-dimensional (1D) channels and seemingly inaccessible 0D voids. The 0D voids are initially too small to accommodate gas molecules such as CO2 if the crystal structure remains rigid. However, by using a combination of in situ techniques, we demonstrate that CO2 gas molecules can be forced into the 0D voids under pressure. This process is facilitated by structural flexibility, which allows the voids to swell individually in response to increasing gas pressure without damaging the overall integrity of the crystal. The swelling mechanism causes one of the crystallographic axes to undergo pressure-dependent expansion, which also manifests macroscopically, thereby providing a new type of stimulus for crystal adaptronics.

Fig. 1: Various representations of trianglimine T1.

a, Schematic of T1. b, Capped-stick model showing intramolecular hydrogen bonds (dotted red lines), which rigidify the open conformation of the molecule. c, Space-filling model showing the molecular cleft of T1. d, Trigonal arrangement of six molecules of T1 to form a 1-nm-wide 1D extrinsic channel (brown surface) propagating along [001], and six hybrid intrinsic–extrinsic 0D voids; the blue and green surfaces represent the two crystallographically unique void spaces at the centroids of the T1 molecules. The models shown in b–d are based on the structure of anhydrous crystals of T1, determined at 298 K. Atom colours: white, hydrogen; grey, carbon; blue, nitrogen; red, oxygen. All void spaces were mapped using a probe with a radius of 1.5 Å.

Crystal packing and guest-accessible space

The enantiopure chiral host T1 (Fig. 1a–c) crystallizes to form acicular crystals with space group R3; the asymmetric unit comprises two host molecules, each situated on a general position. Application of three-fold rotational symmetry yields a hexameric ring (Fig. 1d) in which the molecules associate via relatively weak dispersion interactions. The rings stack according to unit-cell translational symmetry to form conceptually infinite 1-nm-wide channels that propagate along [001], which is also the needle axis of the crystal. In addition to the extrinsic space represented by open channels, a map of the probe-accessible space (Supplementary Text 3) reveals the presence of two crystallographically distinct 0D cavities in the structure, each of which is centred on the aperture of a trianglimine host molecule. At relative humidity levels above 55%, the crystals of T1 readily and reversibly absorb water; the water molecules aggregate in the open channels, which contain hydrophilic binding sites, but do not access the 0D voids.

Since the open-channel crystal form of T1 (T1****0) is stable in the absence of water molecules, we investigated its ability to also absorb CO2 gas at various pressures. We first evaluated the potential guest-accessible space in T1****0 in silico using structural data (Cambridge Structural Database REFCODE BIJLIT01) obtained during our previous work11. The two crystallographically unique 0D voids are formed in a similar fashion, and therefore, it is only necessary to describe one such assembly (Supplementary Text 4). The trianglimine molecule is relatively rigid; strong intramolecular hydrogen bonds within the bridging arms orient the hydroquinone rings approximately perpendicular to the mean plane of the molecule, and there is limited capacity for the rotation of linkers to consume the cavity. The molecular aperture is capped at each end by a cyclohexane moiety of a neighbouring host molecule, one oriented edge on and the other almost coplanar with the trianglimine. This arrangement results in the formation of 0D hybrid intrinsic–extrinsic voids that are close to but isolated from the open channels and, thus, seemingly impervious to guest intrusion. Moreover, under ambient conditions, the probe-accessible volumes of the two crystallographically distinct voids are 37 Å3 and 45 Å3, as calculated using MSRoll13,14. According to the 50% rule of thumb15, each guest molecule in an inclusion compound nominally requires space equal to at least twice its van der Waals volume. Although originally formulated for solvates, we believe that this rule can also be applied to estimate the upper limit of guest occupancy for the inclusion of a gas in a porous crystalline material16. On the basis of this postulate, neither of the discrete voids in T1****0 is large enough to accommodate a molecule of CO2, for which we estimate a van der Waals volume of 33.3 Å3 (Supplementary Text 5). However, using the program Mercury17 and using a probe radius of 1.5 Å, we determined the total probe-accessible volume per extrinsic channel per unit cell of T1****0 to be 1,032 Å3. This is sufficient space to accommodate a maximum uptake of approximately 2.6 molecules of CO2 per T1 molecule15; if we assume that the crystal structure is rigid, this value represents the expected experimental limit of CO2 uptake by the material.

Gas sorption analysis

A sorption/desorption isotherm was recorded for the inclusion of CO2 by T1 crystals at 20 °C over the pressure range of 0–20 bar (Fig. 2 and Supplementary Text 6). The isotherm follows a type I trajectory18 with negligible hysteresis, and the absence of inflections in the data implies that the uptake of CO2 does not require a breathing or gate-opening structural transformation19,20. At almost 20 bar (the upper pressure limit of the instrument), gas loading reached 2.64 molecules of CO2 per host molecule. However, from the shape of the isotherm, it is apparent that CO2 uptake does not plateau at 20 bar, and modelling the data using the Langmuir–Freundlich equation21 predicts a maximum guest–host molar ratio of nmax = 3.98 at infinite pressure (Supplementary Table 1). Since the CO2 capacity of the material exceeds our prediction based on structural data, and the isotherms do not suggest an abrupt change in the crystal structure of the host, we undertook a series of in situ variable-pressure crystallographic studies with a view to locate the preferred binding sites of the gaseous guest and to elucidate the reason for the seemingly incongruous CO2 sorption data.

Fig. 2: Sorption isotherm for the uptake and release of CO2 gas by T1 crystals at 20 °C.

Experimental absolute adsorption (filled circles) data for CO2 in the pressure range of 0–20 bar. The solid line represents the corresponding optimized Langmuir–Freundlich model21 for adsorption. Gas uptake is shown in moles of gas per mole of T1 to rationalize the data in terms of guest–host stoichiometries.

Source data

In situ crystallography

On the basis of the shape of the sorption isotherm, in situ variable-pressure single-crystal X-ray diffraction data were recorded for crystals of T1 in the pressure range of 0–32 bar of CO2 (experimental details are provided in Supplementary Text 7.1 and selected data are summarized in Table 1 and Supplementary Table 3). Typical for in situ crystallographic characterization of porous crystals under gas pressure, it was not possible to reliably model the sorbed gas molecules. However, we were able to extract important and detailed structural information regarding the pressure-dependent response of the host structure to gas loading. At 32 bar, the unit-cell volume of T1****C32 was approximately 5.3% larger than that determined under vacuum (Supplementary Fig. 8a). Although published in situ structural data are still relatively rare, the slight unit-cell expansion of a porous crystalline material due to guest inclusion is intuitive22,23,24,25, and has been observed previously (Supplementary Text 8). Relative to the structure under vacuum, the crystallographic a axis initially expands slightly (peaking at 2 bar) and then contracts by approximately 1.5% over the range of 2–32 bar (Supplementary Fig. 8b). Concomitantly, the crystallographic c axis expands dramatically (Table 1 and Supplementary Table 3), stretching by 8.6% between 0 and 32 bar (Supplementary Fig. 8c and Supplementary Text 7.3).

It is important to note that a crystal structure determination only yields a time-averaged structural model for the irradiated part of the sample under a well-defined set of experimental conditions. Thus, the model might not accurately represent a precise molecular arrangement at a specific location within the crystal at any moment. Below, we first discuss the overall changes in structural features of the time-averaged models derived from our variable-pressure single-crystal X-ray diffraction data (Supplementary Text 9), after which we propose a molecular-level mechanism to account for structural adaptation by T1 crystals to gas inclusion.

Surprisingly, over the pressure range of 0–32 bar, the 1D channels of **T1Cx expand in volume by 19.7% (Supplementary Table 3 and Supplementary Fig. 8d) despite the slight contraction of a and expansion of c by 8.6%. Probe-accessible maps (Supplementary Video 1) show that both crystallographically distinct 0D voids grow substantially and in unison with increasing pressure, reaching average volumes of 84 Å3 in T1****C32 (Fig. 3). In sharp contrast to the structure of T1****0, this provides sufficient space to accommodate one CO2 molecule per cavity, adding additional CO2 uptake capacity of one molecule per T1 molecule. Indeed, electron counts based on a difference electron density map (Supplementary Text 10) strongly suggest that each of the 0D voids is almost fully occupied by a molecule of CO2 at 32 bar. Owing to the conformational rigidity of the trianglimine molecule, a substantial expansion of a 0D void in its crystal structure can only occur if the capping cyclohexane groups of neighbouring T1 molecules are drawn or pushed away. This can be achieved by both tilting and shifting the host molecules along [001], thereby shortening the a and b axes and elongating the c axis (Supplementary Video 6). Thus, our proposed mechanism for the insertion of a CO2 molecule into a 0D void is as follows. The gas molecule enters the channel but cannot bind strongly to the channel walls. However, coordinated thermal motion of the T1 molecules creates a short-lived pore that both enlarges a void and connects it to the channel. Under favourable geometric and dynamic conditions, the CO2 molecule can exploit this fleeting metastable state to enter the void (analogous to ingestion by phagocytosis), thereby locking the local arrangement of T1 molecules to accommodate guest binding. The energetic penalty for moving the host molecules apart is offset by the omnidirectional dispersion interactions between the guest and host molecules that define the void. The resulting increased periodicity along [001] with increased gas loading creates convex indentations in the channel walls, thereby also increasing the volume of the channel as a direct result of accommodating guest molecules in the 0D voids (Supplementary Video 4). Indeed, under 32 bar of CO2 pressure, the channels expand to enclose a volume of 1,192 Å3 per unit cell; according to the 50% rule, this expansion is sufficient to increase the capacity of each channel to three molecules of CO2 per T1 molecule. This channel capacity, in combination with the inclusion of up to one CO2 molecule per 0D void, is consistent with the maximum total uptake capacity of four CO2 molecules per T1 molecule, as predicted by applying the Langmuir–Freundlich model to the experimental sorption data.

Fig. 3: Adaptation of 0D voids of T1 crystals to CO2 inclusion.

a,b, Perspective views along [001] of T1****0 (a) and T1****C32 (b). T1 molecules are shown in capped-stick representation and probe-accessible (rprobe = 1.5 Å) cavities as blue surfaces.

Although the variable-pressure crystallographic models show an incremental expansion of 0D voids, it is important to note that a specific void can assume only one of two possible states, that is, it can be either occupied or unoccupied at any moment. At 0 bar, all the voids are unoccupied, and at the maximum loading, all of them are presumably occupied, that is, these two extreme situations are nominally represented by our structural models for T1****0 and T1****C32, which also provide the lower and upper limits of the length of the c axis. At equilibrium, we can consider any one of the intermediate states **T1Cx to be a solid solution comprising a dynamic but randomly distributed ensemble of T1 monomers and T1‧CO2 heterodimers, where the T1:T1‧CO2 ratio is dependent on the external CO2 pressure x. At the unit-cell level, the periodicity of the c axis is governed by the spacing along [001] of two successive supramolecular assemblies, each consisting of a ring of 6 T1 molecules that form a part of a column that encloses a 1D channel. For zero and full loading, both local and global c-axis lengths are governed by the periodicities of two (T1)6 or (T1‧CO2)6 rings, respectively. However, at any equilibrium loading, the ensemble of 12 molecules considered can instantaneously assume any of the stoichiometries (T1)n:(T1‧CO2)12–n (n = 0 to 12). Each ensemble has a local periodicity dictated by n, as well as by the states of surrounding ensembles, and each unit cell is furthermore traversed by three columns of host molecules. The crystal structures of **T1Cx represent the time-averaged permutations of the various configurations described above, and the global length of the c axis, thus, approximates a pressure-dependent continuum between the two extremes measured for T1****0 and T1****C32. Owing to the link between pressure and guest–host stoichiometry, there also exists a link between the measured length of the c axis and the overall guest occupancy, which probably accounts for the Langmuirian trend in the pressure-induced elongation of c (Fig. 4a and Supplementary Text 11). Indeed, the elongation of c with pressure for the structures **T1Cx in the range x = 0–32 bar was modelled using the more versatile Langmuir–Freundlich equation, which predicts the maximum extension at full loading of approximately 10%, relative to the guest-free form. We do not ascribe any significance to the Langmuir–Freundlich parameters beyond that they provide purely empirical relationships between the linear extension of c and CO2 pressure.

Fig. 4: Elongation of a crystal along [001] in response to CO2 gas loading.

a, Plot of percentage elongation of the crystallographic c axis of T1 crystals with increasing CO2 pressure. Percentage elongation is calculated relative to the length of c at 0 bar. The filled circles represent the experimental data and the optimized Langmuir–Freundlich fit is shown as a solid line. b, In situ photomicrographs of a crystal of T1 in its forms T1****0 (bottom) and T1****C32 (top). The dashed vertical line on the left indicates where the crystal is attached to a glass fibre and the dashed vertical line on the right facilitates observation, relative to T1****0, of gas-induced elongation along [001].

Photomicroscopy

It is reasonable to assume that a pronounced change in one or more of the unit-cell dimensions of a crystal might be observable at the micro- or macroscopic level26,27,28,29. To this end, we constructed an apparatus consisting of a microscope-mounted pressure cell attached to an electronic pressure valve (Supplementary Text 12). Bespoke software was used to automatically record the time-lapse photomicrographs and controlling the pressure within the cell according to a predefined pressure–time ramp rate. A series of micrographs was recorded for several crystals of T1 exposed to CO2 in the pressure range 0 → 32 → 0 bar and at a rate of 0.2 bar min−1 (Supplementary Videos 8–12). Indeed, the micrograph recorded at 32 bar of CO2 shows elongation of the needle [001] axis of the crystal consistent with stretching of the crystallographic c axis for T1****C32 (Fig. 4b). Moreover, the measurement of the lengths of several crystals at various CO2 pressures confirmed our hypothesis that the same Langmuir–Freundlich trend in gas-induced elongation experienced by the crystallographic c axis can be observed at the macroscopic scale (Fig. 5). Indeed, the photomicrographs show that the needle axis expands and contracts with increasing and decreasing pressure, respectively, with little hysteresis displayed over a relatively wide pressure range (Supplementary Figs. 17, 18, 20 and 21), and that the response of a crystal is repeatable over multiple pressure cycles (Supplementary Figs. 19 and 22) with its single-crystal integrity maintained. We also established that the crystals become friable at approximately 45 bar of CO2 pressure (Supplementary Fig. 23 and Supplementary Video 11), indicating that the maintenance of crystal singularity is subject to lattice distortion limits.

Fig. 5: Elongation of T1 along [001] with increasing pressure.

Langmuir–Freundlich models of the percentage elongation of the needle axes of five different crystals of T1 in the range of 0–30 bar as measured from the in situ photomicrographs. The black circles represent the relative elongation of the crystallographic c axis of the sixth crystal in the range of 0–32 bar, with the corresponding Langmuir–Freundlich model shown as a solid black line.

Source data

A limited set of experiments, similar to those described above for CO2, was carried out with CH4 gas to investigate the effect of a different guest on T1 crystals (Supplementary Text 14). Elongation of the crystallographic c axis in the pressure range of 0–60 bar of CH4 was only approximately half that observed for the range of 0–32 bar of CO2, despite indications (cavity volumes and electron counts) that the 0D pockets are fully occupied by CH4 at 60 bar. This result can be rationalized based on the smaller molecular volume and approximately spherical shape of CH4 compared with CO2.

Discussion

Our in situ crystallographic studies indicate that the gas molecules become lodged within the 0D cavities of the host molecules despite the absence of permanent pathways to these sites. Indeed, such transient porosity was first recognized more than two decades ago for the single-crystal-to-single-crystal inclusion of vinyl bromide into an apohost form of p-tert-butylcalix[4]arene30 and, subsequently, reaffirmed for the inclusion of CO2 and other gases into the same host system16. Although the overall packing arrangement of T1 does not change during gas loading (that is, no phase transition occurs), the host molecules undergo subtle adjustment of their positions and orientations to accommodate the guests within their 0D pockets, accompanied by a concomitant swelling of the 1D channels. These molecular rearrangements cause a Langmuirian elongation of the crystallographic c axis, which manifests as comparable changes in the macroscopic dimensions of the crystal, as confirmed by in situ photomicroscopy (Supplementary Videos 8–12). Thus, the expansion of the channel volume is a direct result of the accommodation of gas molecules in the adjacent 0D voids of **T1Gx rather than the gas loading of the channel. These results are a proof-of-concept demonstration of control over the dimensions of a crystalline material using gas pressure as a stimulus, although in an extreme environment. Similar control has been reported extensively for other extreme environments, involving concepts such as thermal expansion and hydrostatic compressibility (for which the coefficients are given as α and β, respectively). Indeed, it is possible to borrow further from these fields by quantifying expansion along c using the equation:

$${\delta }_{{\rm{c}}}=\frac{1}{L}{\left(\frac{\partial L}{\partial P}\right)}_{{\rm{T}}},$$

where we define δc as the sorption-induced ‘linear swelling coefficient’, L is the length of c at 0 bar and ({\left(\frac{\partial L}{\partial P}\right)}_{{\rm{T}}}) represents the pressure-dependent elongation of c at a constant temperature; the linear swelling coefficient δc = 2.69 × 10−8 Pa−1 (that is, ~27 GPa−1) for T1****C32. We have also demonstrated that our data for swelling along c (both crystallographically and macroscopically) can be modelled using the Langmuir–Freundlich equation, thereby providing an empirical relationship between gas pressure and length of the crystallographic c axis. We have demonstrated that a porous material with flexible pockets that are initially too small to accommodate gas molecules can inflate substantially as gas molecules accumulate in these spaces under the influence of increasing pressure. These results add an additional stimulus to the growing arsenal of stimuli that can be used to control the dimensions of crystalline materials, and may have implications for diverse applications that include sensors and actuators, as well as those requiring optical components with tunable refractive indices.

Methods

Materials

All commercially available reagents were obtained from commercial suppliers and used in reactions without further purification, unless otherwise specified. The 1H and 13C nuclear magnetic resonance (NMR) spectra were recorded on a Bruker 300-MHz or Bruker 400-MHz spectrometer at the ambient temperature. The NMR spectra are reported in parts per million (ppm) downfield of the tetramethylsilane signal and were measured relative to the residual signals for CDCl3 (7.27 and 77.0 ppm, respectively, for 1H and 13C NMR). The 13C NMR spectra were obtained with 1H decoupling. Mass spectra were recorded on an AB Sciex TripleTOF 5600+ system. Melting points were measured using open glass capillaries in a Büchi Melting Point B-545 apparatus. The infrared spectra were measured using a Thermo Scientific Nicolet iS50 FTIR spectrometer.

Single-crystal X-ray diffraction

Data were recorded using a Bruker D8 Venture equipped with a PHOTON II CPAD detector and an Oxford Cryosystems Cryostream 800Plus cryostat. Mo Kα X-rays (λ = 0.71073 Å) were generated using a multilayer Incoatec microfocus (IµS) source. A crystal-to-detector distance of 37 mm was used for all experiments. Data reduction was carried out using the Bruker SAINT31 software; absorption and other corrections were made using SADABS32 as implemented in the Bruker APEX 3 software package. Crystal structures were solved either using SHELXD33 or SHELXT34 via the X-Seed35,36 graphical user interface. Non-hydrogen atoms of the host were refined anisotropically using SHELXL37 using full-matrix least squares minimization. Host hydrogen atomic positions were calculated using riding models. The absolute structure of the investigated crystals was assumed from the known absolute configuration of (R,R)-1,2-diaminecyclohexane, which was used as a starting material in the syntheses.

Variable-pressure in situ X-ray crystallography

Variable-pressure single-crystal X-ray diffraction experiments were carried out using an environmental gas cell developed in-house. Intensity data were recorded for samples exposed to CO2 in the pressure range of 0–32 bar. Since it is not possible to control the temperature of the entire gas cell using a conventional cryostat, the temperature of each data collection was taken to be the temperature of the diffractometer cabinet, which ranges between 26 and 27 °C.

In a typical experiment, a suitable crystal was attached to the end of a thin glass fibre by means of epoxy. The fibre was then inserted into a 0.3-mm Lindemann glass capillary, which was epoxy-sealed to a modified stainless steel barb fitting, which, in turn, was attached to a bespoke miniature valve. A high-pressure manifold equipped with calibrated test gauges was used to pressurize the gas cell before each diffraction experiment; in each case, the sample was allowed to equilibrate overnight at the desired pressure, with the temperature maintained at 27 °C. After equilibration, the gas-cell assembly was attached to a modified goniometer head, which was mounted onto the goniometer of the diffractometer.

Crystallographic software

Probe-accessible extrinsic channel and intrinsic cavity volumes were calculated using MSRoll38 using a probe radius of 1.5 Å, and visualized using Mercury39. The Cambridge Structural Database40 (v. 5.46; database: November 2024) was accessed using Conquest41.

Gas sorption analysis

Gravimetric sorption isotherms were recorded for an ~25-mg sample of T1 crystals by means of an Intelligent Gravimetric Analyser (IGA-002) supplied by Hiden Isochema42,43,44,45,46. The instrument facilitates the precise measurement of mass change and the control of pressure and temperature. The pressure is monitored using a pressure transducer within a range of 0–20 bar and buoyancy effects are corrected by the control software. During each experiment, the temperature was maintained at 20 ± 0.05 °C using a Grant refrigerated recirculating bath. Data collection was controlled by real-time processing computer software that continually predicts the equilibrium pressure using least squares regression to extrapolate a value for the asymptote. A linear driving force relaxation model was used, with each point recorded once a 99% fit to the model was achieved. CO2 (99.995%) gas cylinders were purchased from Afrox. The sample was initially evacuated in situ for 2 h to ensure that it was fully activated.

Variable-pressure in situ photomicroscopy

In situ microscopy experiments were carried out to record macroscopically visible changes in the dimensions of single crystals exposed to gas pressure at variable-pressure ramp rates. The apparatus required for these experiments (Supplementary Fig. 10) was developed in-house and consisted of a gas supply connected to a software-controlled electronic gas valve, which was, in turn, connected to a stainless steel pressure chamber equipped with 6-mm-thick quartz windows. The pressure chamber is attached to the sample stage of a microscope fitted with a USB camera. Experiments were controlled and monitored using bespoke software (Pressure_Valve, developed by L.J.B.). For the current study, photomicrographs were recorded at 30-s intervals and exposing crystals to gas at a ramp rate of 0.2 bar min−1. In a typical experiment, the pressure was increased from 0 bar to a selected maximum pressure, followed by a decrease in pressure back to 0 bar.

Data availability

The main data supporting the findings of this study are available within the article and its Supplementary Information. Crystallographic data are tabulated in Supplementary Information and archived at the Cambridge Crystallographic Data Centre (CCDC) under reference numbers CCDC 2404628 to 2404641. Source data are provided with this paper.

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