Latent asymmetry of gate opening and closing in a flexible MOF probed by time-resolved in situ XRD

Abstract

Time-resolved in situ X-ray diffraction reveals a latent asymmetry in the gate-type transitions of the flexible metal–organic framework ELM-11. The gate-closing pathways for CO₂ and n-butane are highly asymmetric and distinct from their gate-opening processes. During CO₂ desorption, a unique intermediate phase is formed. The gate closing for n-butane is more complex, involving a continuous structural deformation followed by a sequential, discontinuous transition. This work shows that high-resolution structural mapping across the entire pressure range is crucial for uncovering the true complexity of flexible materials.

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Metal–organic frameworks (MOFs) are widely studied materials due to their high surface areas and tunable pores, making them promising for applications in gas storage, separation, and catalysis.¹ A subclass known as flexible MOFs, or soft porous crystals, exhibit large-amplitude structural transitions in response to external stimuli such as guest molecules, temperature, or pressure.² This dynamic behavior, often termed “breathing” or “gate opening”, results in stepwise changes in porosity. Such transitions can yield step-shaped adsorption isotherms, enabling high working capacities for gas storage and high selectivities in separation processes compared to rigid analogues.³

Understanding the mechanisms and kinetics of these dynamic structural transformations is crucial for the rational design of flexible materials. To this end, advanced in situ characterization techniques are indispensable for observing these frameworks under working conditions.⁴ In particular, synchrotron-based time-resolved in situ X-ray diffraction (TRXRD) enables the direct monitoring of structural evolution during guest adsorption, providing insights into transition pathways.^5–7

Recent TRXRD studies have begun to elucidate the kinetics of these transitions. For instance, the gate-opening kinetics in frameworks like ELM-11 and DUT-8 have been analyzed using the Kolmogorov–Johnson–Mehl–Avrami (KJMA) model.^3,8 Such kinetic analyses have also revealed a strong dependence on crystallite size; for MIL-53(Al), smaller crystals exhibit significantly faster breathing kinetics during n-butane adsorption.⁹ Our group has developed an analytical method based on TRXRD data to derive framework-dependent kinetic models for flexible MOFs such as ELM-11 and MIL-53(Al), revealing that the transition mechanism is intrinsically linked to the framework structure and pathways for gas penetration.¹⁰

Despite these advances in understanding the gate opening, the reverse process—guest desorption and the associated gate closing—has received less attention. With the exception of mechanistically distinct phenomena like memory effects^11,12 and negative gas adsorption,¹³ guest desorption, while often exhibiting hysteresis, is typically assumed to be a fundamentally symmetric process that retraces the adsorption pathway. As a result, there are fewer in-depth studies on gate closing,^14,15 leaving a gap in our understanding of the underlying mechanisms.

Herein, we use TRXRD to investigate the gate opening and closing in the stacked-layer flexible MOF, ELM-11,¹⁶ with two distinct guests: CO₂ at 195 K and n-butane at 273 K. Although both processes were previously considered symmetric based on point-by-point in situ XRD and adsorption isotherm measurements (Fig. S1, SI),^17,18 our TRXRD measurements under continuous pressure changes, which provide a quasi-continuous series of diffraction patterns across the entire pressure range, reveal starkly asymmetric pathways. Specifically, an intermediate phase appears only during CO₂ desorption, while the n-butane system exhibits a more complex transition with mixed continuous-and-discontinuous character upon gate closing.

TRXRD measurements were performed at the BL02B2 and BL13XU beamlines of SPring-8, Japan.¹⁹ A pretreated ELM-11 sample was placed in a glass capillary, and its XRD patterns were recorded every 1 s. For the adsorption process, CO₂ or n-butane gas was introduced at a constant rate of pressure increase using a mass flow controller. The desorption process was performed by evacuating the system through a needle valve connected to a vacuum pump. This experimental setup allows us to treat the time-resolved data as a pressure-resolved map of the structural evolution, revealing thermodynamic phases that may be missed by point-by-point measurements.

Fig. 1 and Fig. S2 in the SI present color-map plots of the TRXRD intensity changes for ELM-11 during CO₂ adsorption and desorption at 195 K. As previously reported based on point-by-point in situ XRD measurements, ELM-11 exhibited the following structural transitions during CO₂ adsorption: (i) a discontinuous gate opening from cp to op-2, (ii) a continuous deformation from op-2 to op-3, and (iii) a second discontinuous gate opening from op-3 to op-6.¹⁷ Here, cp is the closed phase, and op-X denotes an open phase encapsulating X CO₂ molecules per formula unit (Cu(bpy)₂(BF₄)₂; bpy = 4,4′-bipyridine). In contrast, while the desorption process largely follows the reverse path of adsorption, a key difference is the appearance of an intermediate phase, ip, observed within a narrow pressure range of 18 to 8 kPa during the higher-pressure transition upon desorption. Specifically, representing a discontinuous transition as ⇒ and a continuous deformation as →, the overall process is asymmetric: the adsorption path is cp ⇒ op-2 → op-3 ⇒ op-6, whereas the desorption path is op-6 ⇒ ip ⇒ op-3 → op-2 ⇒ cp.

Fig. 1 TRXRD color maps for ELM-11 during (a) CO₂ desorption and (b) adsorption at 195 K.

The pressure range in which ip appears is largely independent of the evacuation speed (Fig. S3, SI), suggesting that ip is a stable phase rather than a kinetically trapped intermediate. Consistent with this view, ip could be isolated by halting the evacuation at 16 kPa, allowing for its structural determination from a XRD pattern with minute-order exposure (Fig. S4, SI). The refined structure has the space group Pc with lattice parameters of a = 11.0917 Å, b = 11.1056 Å, c = 15.6659 Å, and β = 118.727°. Given the similar lattice parameters of op-6 (a = 11.0894 Å, b = 11.1193 Å, c = 15.8201 Å, α = 89.164°, β = 118.253°, and γ = 86.791°),²⁰ ip represents a slightly more symmetric state, involving a transition from a triclinic to a monoclinic system. The crystal structure of ip was determined using our refinement method combining Rietveld analysis and density functional theory (DFT) calculations (Section S1, SI),¹² assuming the encapsulation of five CO₂ molecules per formula unit (namely, ip = op-5) based on the experimental adsorption isotherm (Fig. S1, SI). Fig. 2 and Fig. S5 in the SI compare the framework structure of ip with those of op-3 and op-6. As previously reported, the op-3 ⇒ op-6 transition involves an increase in the layer spacing, Δ, from 5.69 to 6.96 Å, as well as a rearrangement of the grid structure composed of bpy linkers from a zigzag to a sheared conformation.¹⁷ The Δ value of ip is 6.87 Å, indicating that the op-6 ⇒ ip transition is dominated by the grid rearrangement from a sheared to a square conformation, while Δ remains almost unchanged. Consequently, the layer contraction mainly occurs during the ip ⇒ op-3 transition, where the grid rearranges from a square to a zigzag conformation.

Fig. 2 Layer structures of ELM-11 in op-3, ip, and op-6, highlighting the rearrangement of the bpy grid.

The exclusive appearance of ip during the desorption process can be attributed to the interplay between grid rearrangement and layer spacing changes, as illustrated in Fig. S6. In op-3 and more contracted phases (op-2 and cp), each grid-like pore encapsulates two BF₄⁻ anions from the adjacent layers. These anions are sterically interlocked, preventing the grid rearrangement from a zigzag to a sheared conformation because such a rearrangement would require the anions to pass each other, a process that is sterically prohibited at the small layer spacing of op-3. Therefore, for the gate opening (op-3 ⇒ op-6), layer expansion must precede grid rearrangement to unlock this steric hindrance. Conversely, for the gate closing (op-6 ⇒ op-3), the ideal sequence would be grid rearrangement followed by layer contraction. However, the primary driving force for the transition is the desorption of CO₂ molecules, which directly promotes layer contraction rather than grid rearrangement, as the latter has a negligible effect on the pore volume. This creates a mismatch between the driven process (layer contraction) and the required sequence (grid rearrangement first). This conflict likely leads to the formation of ip, a state where the grid has relaxed to a neutral square conformation but significant layer contraction has not yet occurred.

Fig. 3 and Fig. S7 in the SI show color-map plots of the TRXRD intensity changes for ELM-11 during n-butane adsorption and desorption at 273 K. Upon adsorption at 7 kPa, the cp ⇒ op-b transition occurred in a typical manner, characterized by a changing population ratio of the two phases. In contrast, a complex evolution of the XRD patterns was observed during the desorption process. Below 7 kPa, some peaks corresponding to op-b began to shift significantly to higher Q-values. Below 1 kPa, this peak shift occurred simultaneously with the change in the population ratio between cp and op-b. For clarity, we denote the set of continuously deformed structures originating from op-b as {op-b′} and those that coexist with cp as {op-b′′}. Thus, the overall asymmetric process can be described as follows: the adsorption path is cp ⇒ op-b, whereas the desorption path is op-b → {op-b′} → {op-b′′} ⇒ cp.

Fig. 3 TRXRD color maps for ELM-11 during (a) n-butane desorption and (b) adsorption at 273 K.

Fig. 4 shows the changes in the lattice constants and the phase population ratio of the n-butane-encapsulated structure, analyzed with reference to the reported structure of op-b^18,21 (see Section S2, SI). The lattice parameters a, c, and β decreased by 2–5% from the original op-b values, while parameter b remained almost unchanged. The rate of change in the lattice parameters became more gradual below 1 kPa, which coincides with the pressure at which the population ratio of the cp and op-b phases began to change.

Fig. 4 Changes in (a) lattice parameters and (b) population ratio of the n-butane encapsulated structure of ELM-11 with decreasing (c) pressure at 273 K.

The constant b parameter indicates the invariance of the 0k0 reflections. Indeed, the 020 reflection at Q = 1.13 Å⁻¹, though weak in intensity, does not shift at all throughout the process (Fig. 3a). The stability of the b parameter is expected, as the layers of ELM-11 are stacked along the (202̄) plane, and the value of b corresponds to the in-plane length of the Cu–bpy–Cu connection (see Fig. S8, SI). However, intriguingly, other unshifted peaks in Fig. 3a are not 0k0 reflections; for example, the peaks at Q = 0.83 Å⁻¹ and Q = 1.80 Å⁻¹ correspond to the 111 and 131 reflections, respectively. This indicates that the lattice parameters a, c, and β vary in a synchronized manner that preserves the interplanar spacings of specific planes, such as (111) and (131).

A plausible explanation is that during the op-b → {op-b′} → {op-b′′} transformation, the layers of ELM-11 slide along a direction that is simultaneously parallel to both the (111) and (131) planes—that is, the real-space vector [101̄]. To test this hypothesis, we applied a coordinate transformation, a′ = a + c, b′ = b, and c′ = a − c, such that the new c′ axis coincides with the [101̄] direction. In this new basis, the (202̄) layer plane corresponds to the a′-b′ plane. This transformation converts the data in Fig. 4 into Fig. S9 (SI). In the new coordinate system, the change in the c′ parameter (over 6%) is an order of magnitude larger than the minor, secondary changes in a′ (∼0.6%) and β′ (∼1.3%), providing strong evidence for the proposed sliding mechanism.

Using DFT-based geometry optimization, ten representative structures for the op-b → {op-b′} → {op-b′′} evolution were determined with reference to the reported structure of op-b¹⁸ (Section S3, SI). The lack of significant changes in the in-plane structure further confirmed the sliding mechanism; however, a notable discrepancy was found between the simulated and experimental XRD patterns (Fig. S10, SI). The simulated XRD patterns, when normalized to the intensity of the 020 reflection, showed a gradual decrease in the intensities of moving peaks, such as the 002 and 111̄ reflections. In contrast, the experimental results showed the reverse behavior: the intensities of these peaks increased as pressure decreased. This discrepancy suggests that a small amount of n-butane is desorbed during the transformation. Taking the prominent 002 peak as an example, its intensity is determined by the destructive interference between scattering from the Cu-containing planes and the n-butane-containing planes (Fig. S11, SI). A decrease in the occupancy of n-butane molecules weakens this destructive interference, increasing in the net intensity of the 002 peak. Indeed, simulated XRD patterns reproduced the experimental trend when the site occupancy of n-butane was linearly reduced across the ten representative structures, reaching a final value of 0.8 (see Fig. S10, SI).

The molecular picture of ELM-11 upon n-butane desorption is summarized in Fig. 5. In response to decreasing pressure, some n-butane molecules are desorbed from the framework, triggering a gradual contraction of the layer spacing. This contraction occurs via layers sliding along the [101̄] direction while other degrees of freedom, such as in-plane atomic rearrangement, remain almost unchanged. This sliding movement continues, resulting in up to a ∼6% contraction of the layer spacing, accompanied by a 20% desorption of n-butane molecules. Interestingly, the transition to cp does not await the completion of this sliding process. Instead, the {op-b′′} ⇒ cp transition appears to be a staggered process occurring across the ensemble of crystallites. The transition for individual crystallites initiates sequentially once their respective deformation ratio exceeds a threshold of ∼4% (see Fig. S9, SI). Thus, the macroscopic gate closing is a statistical superposition of many discrete transitions, each triggered at a slightly different point along the continuous deformation pathway. This complex, multi-stage nature of the transition further underscores the asymmetry compared to the simple, collective gate-opening process.

Fig. 5 Schematic of the asymmetric gate-opening and gate-closing pathways of ELM-11 with n-butane.

The exact driving force for this asymmetry is not yet clear, but the guest molecule size may be a key factor. To adsorb n-butane, a relatively bulky molecule, ELM-11 must undergo a 47% expansion in cell volume. This large expansion may destabilize the framework, promoting immediate structural relaxation in response to even a small amount of n-butane desorption. In contrast, upon CO₂ adsorption and desorption at 283 K, the cp ⇒ op-2 and op-2 ⇒ cp transitions were found to be completely symmetric, even though the isotherm showed slight CO₂ desorption before gate closing (Fig. S12 and S13, SI). The smaller volume expansion (28%²²) required for CO₂ may enable the op-2 framework to remain stable against slight guest desorption.

In conclusion, we have demonstrated two distinct asymmetric pathways for the gate-type transitions in ELM-11 using TRXRD. A key feature of these phenomena is that they are not predictable from adsorption isotherms, suggesting that similar latent asymmetries may be found in other flexible MOFs. TRXRD under continuous pressure changes is a powerful tool to reveal such behavior, deepening our understanding of the mechanisms of gate opening and closing in flexible frameworks.

This work was supported by JSPS KAKENHI (grant no. 25K01562).

Conflicts of interest

There are no conflicts to declare.

Data availability

Data for this article, including XRD patterns and estimated crystal structures are available at the online repository at https://github.com/2koza/asymmetric-gate-opening.

Supplementary information is available. See DOI: https://doi.org/10.1039/d5cc04347f

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