Low-entropy supramolecular crystals elucidating the inhomogeneity of interfacial water molecules at atomic resolution

Abstract

Water at interfaces plays crucial roles in various natural phenomena and in the material sciences. Therefore, understanding the structure and hydrogen-bonding network at such interfaces is essential. Recent advances in porous crystalline materials, combined with single-crystal X-ray diffraction techniques, have enabled the visualization of molecular structures on pore surfaces at atomic resolution. Herein, we report the formation of a supramolecular porous crystal composed of a resorcin[4]arene and a rigid cationic coordination complex, stabilized by hydrogen bonds and noncovalent interactions. This specific arrangement creates a porous framework with anisotropic, information-rich surfaces, accommodating water molecules to form multi-layered water channels. The analysis reveals clustering motifs and hydrogen-bonding patterns in the water molecules at interfaces, supported by molecular dynamics simulations and spectroscopy studies. These findings advance our understanding of the structure–property relationship of water at interfaces in low-entropy crystalline materials, offering insights into their behavior on complex surfaces.

Water at interfaces plays crucial roles in various natural phenomena and in material sciences. Here, the authors report the formation of a supramolecular crystal forming a porous framework with anisotropic, information-rich surfaces, accommodating water molecules to form multi-layered water channels.

Introduction

Water molecules at interfaces play critical roles in numerous natural phenomena and in the material sciences^1,2. For example, water-mediated forces enable large biomolecules to form complex three-dimensional structures that are essential for biological activity, mediating ligand–receptor binding, enzymatic reactions, and material transport^3,4. Similarly, the water at the interface between the aqueous phase and both organic and inorganic materials affects the chemical and physical properties, influencing biomaterial adhesion, aqueous chemical reactions, water harvesting systems and clathrate hydrate formation^5–7. Vibrational and photoelectron spectroscopic measurements have provided averaged information about interfacial water, such as information about the arrangement of the first hydration layer at different material surfaces^8–10. To achieve the atomic-scale resolution of water molecule alignment, scanning tunneling microscopy (STM) and non- contact atomic force microscopy (AFM) have proven invaluable. These techniques reveal hydrogen-bonding networks of adsorbed water molecules templated on well-ordered, highly symmetric metal substrates^11,12. However, visualizing the 3D alignment of water clusters and hydrogen-bonding networks on organic polymer surfaces at atomic resolution remains challenging. This difficulty stems from the complexity of tailoring polymer surface structures. Furthermore, analytical methods to characterize multilayered water channels have yet to be developed.

Crystalline porous materials, which have well-defined inner spaces in terms of size and shape, have been extensively studied as potential analytical tools because of their large surface areas, which are suitable for capturing gas and organic molecules within crystal frameworks via noncovalent interactions^13–15. Typically, these materials have highly symmetric skeletons with chemically equivalent surfaces, and their structures are typically resolved through diffraction studies. However, this symmetry often complicates the identification of water-molecule cluster motifs and their hydrogen-bonding networks because of dynamic and static disorder within the pores; that is, analysis is possible only when the molecular symmetry of the water clusters matches the symmetry of the host framework^16–20.

Conversely, recent advancements in low-symmetry porous crystals have enabled the visualization of molecules and their orientations trapped at crystal pore surfaces through single-crystal X-ray diffraction (SCXRD)^21–23. The anisotropic surfaces of these crystals possess high structural information within a periodic pattern, effectively suppressing the static disorder of the guest molecules and enabling the periodic organization of these guests inside the pores through multiple noncovalent interactions with the framework. This enables a method to visualize the absolute configuration of chiral molecules and dynamic behavior, such as cluster motifs and site exchange, on the pore surface, using crystalline porous materials^24–26. This technique, applicable without a time-consuming crystallization process, offers a straightforward procedure for structural determination at atomic resolution. Therefore, the development of porous crystals has drawn interest in various research fields for monitoring a range of chemical and physical phenomena on pore surfaces.

In the context of information theory, high-entropy materials exhibit considerable ambiguity because their many configurational states result in low observable structural information, often reflected in averaged spectra or featureless signals²⁷. Here, the terms ‘low entropy’ and ‘high entropy’ are used qualitatively to describe the relative degree of structural order, with ‘low entropy’ indicating a highly ordered, directional arrangement with high structural detail that is observable, while ‘high entropy’ denoting a more disordered, flexible configuration with ambiguous structural features. In other cases, when molecular components are positioned in a chemically equivalent manner, the distinguishability of each component reduces because of symmetry. This situation also leads to a decrease in local structural information and an increase in structural ambiguity (higher information entropy).

Recent research in supramolecular chemistry has focused on achieving low-symmetry assemblies with added functionality and complexity, inspired by the activity of biological systems resulting from their low-symmetry and well-defined (low-entropy) structures²⁸. We have reported the formation of a defined C₁-symmetric supramolecular structure from C_4v and C₂ molecular fragments that shows unique symmetry-breaking photophysical properties in solution²⁹. Such a supramolecular structure is achieved because of the combined effects of hydrogen bonds and noncovalent interactions between rigid and dynamic components, reminiscent of those in natural systems. The synergistic effect of these weak interactions between components promotes assembly toward a low configurational entropy state. Additionally, the balance of weak interactions is highly dependent on reaction conditions, allowing the isolation of “out-of-equilibrium” and “local equilibrium” solution structures as crystalline forms via solid-state driven assembly, which can be visualized at atomic resolution via SCXRD analysis.

Resorcin[4]arene units with short lower rims have been reported to afford supramolecular crystals accommodating various organic salts stabilized by multiple hydrogen bonds and cation–π interactions in their concave cavities^30–37. This host typically forms a sandwich-type 1:2 inclusion complex with small organic cations in the crystalline state. In contrast, large guest cations destabilize the dimeric hosts, promoting unique aggregated structures in crystalline form^29,30.

In this study, we attempted to isolate an “out-of-equilibrium” structure and its hierarchical assembly motif via solid-state driven assembly. A combination of a flexible resorcin[4]arene and a rigid coordination complex salt yielded a supramolecular crystal. Interestingly, its specific arrangement of the components creates large pore channels in the crystal lattice, stabilized by multiple noncovalent interactions. The structure is sufficiently stable to undergo solvent exchange via a single-crystal-to-single-crystal (SCSC) process, creating well-defined 1D water channels. These pores, surrounded by a specific arrangement of molecular components, provide an anisotropic and highly ordered surface, enabling the visualization of specific cluster motifs in the first water layer and hydrogen-bonding networks of water pentamers along the surface through SCXRD analysis. Furthermore, molecular dynamics calculations and spectroscopic studies elucidated the dynamic characteristics of water molecules in the second hydration region. Thus, this supramolecular crystal is a “low-entropy supramolecular crystal” with low configurational entropy and high structural information content. Further, the fluxional nature of the secondary hydration layer is revealed by variable-temperature SCXRD studies, demonstrating structural information transfer from the material surface. Molecular simulations based on the X-ray crystal structure and statistical analysis confirmed unique temperature dependencies of water molecule mobilities, consistent with experimental results. Further, spectroscopic analysis revealed the characteristic properties of water molecules in the second hydration layer on the concave surfaces, and their fluxional dynamics were attributed to their unusual hydrogen-bonding features. These results suggest that self-assembly from noncovalent interactions among molecular components can produce unique supramolecular crystals with low-entropy, information-rich pore surfaces, showing information transfer to provide insights into the properties of water at interfaces at atomic resolution.

Results

Formation of the supramolecular crystal and water channel in the infinite pore channels

The supramolecular crystal 3•EtOH was obtained via co-crystallization from an EtOH–H₂O mixed solution of the organic host 1 and the Ir complex salt [2]Cl (Fig. 1a). Slow evaporation of the solution at room temperature yielded yellow rod-shaped crystals in 39% isolated yield. SCXRD at 90 K revealed a 1:1 stoichiometry of 1 and [2]⁺ in the crystal, forming a supramolecular framework with large cell parameters (C2/c, a = 34.764(6) Å, b = 29.640(4) Å, c = 19.842(3) Å, β = 92.556(3)°, V = 20,425(5) ų). In the 1:1 structure, one ^tBu group of [2]⁺ fits into the concave cavity of 1 via cation–π and CH–π interactions (Fig. 1b). The supramolecular crystal has a porous framework with 36% void volume, as estimated using the PLATON VOID algorithm, containing polar solvent molecules. These polar molecules face the polar components, such as the OH groups of 1 and the coordination complex salt [2]Cl, whereas the hydrophobic lower rims of 1 remain away from polar 1D channels. This suggests the driving forces for the formation of this supramolecular crystal are multiple noncovalent interactions between the components, such as cation–π, CH–π, hydrophobic, and van der Waals interactions, unlike the reversible bond formations in metal-organic frameworks (MOFs), covalent organic frameworks (COFs), and hydrogen-bonded organic frameworks (HOFs). These results strongly suggest that the concerted effects of weak noncovalent interactions add complexity and functionality to the supramolecular structure in both solution and crystalline states²⁹. Thus, the supramolecular framework created low-entropy, information-rich surfaces, enabling the visualization of the positions and conformations of counter anions and solvent molecules adsorbed on the pore surface (Fig. 1b). SCXRD analysis at 90 K revealed the presence of Cl^– ions and EtOH molecules on the pore surface (Supplementary Fig. 5). The Cl^– anion and three EtOH molecules are located near the OH groups in 1 within 3.1 and 2.7 Å, respectively, suggesting hydrogen-bond trapping by the framework, and one EtOH molecule, which does not form a hydrogen-bond with the surface, is trapped in the hydrophobic pocket of the pore surface. This demonstrates that the supramolecular crystal contains multiple recognition sites on its asymmetric surface, binding the guest molecules in specific conformations. In contrast to the well-resolved solvent molecules on the pore surface, those in the central area of the 1D channel showed signs of static disorder, characterized by a diffuse, low electron density (Fig. 1c). This is likely because of the lower hydrogen-bonding ability of EtOH.

Fig. 1. Schematic of the supramolecular crystal, 3•EtOH, comprising an organic host and the chloride salt of an Ir complex.

a The supramolecular crystal contains one-dimensional infinite pores (0.9 nm × 0.9 nm) in the crystal lattice. b, c Molecular alignment of Cl^– ions and EtOH towards surface molecules (b), and viewed along the pore channel axis (c). Colors: N, blue; Cl, green sphere; O, red; Ir, dark green; the carbon atoms of 1 and 2 are shown in gray and yellow, respectively.

The porous crystals of 3•EtOH underwent solvent exchange with water in the pore channels via SCSC (Supplementary Fig. 2), as observed in rigid MOFs^21,22, even though this framework is built on concerted noncovalent interactions similar to HOFs³⁸. Specifically, when 3•EtOH was immersed in water at room temperature for one day, the EtOH molecules were completely exchanged with H₂O, forming 1D water channels in the supramolecular crystal. SCXRD analysis of 3•H₂O at 298 K showed no significant change in the lattice parameters (C2/c, a = 35.128(6) Å, b = 29.686(5) Å, c = 19.878(3) Å, β = 91.774(3)°, V = 20,719(6) ų) after solvent exchange (Fig. 2a). Although the pores were filled with H₂O molecules, electron densities corresponding to oxygen atoms were observed only near the pore surfaces (Supplementary Fig. 7). Thus, under ambient conditions, the water molecules in the confined pore channels behaved more like bulk water than like the water of crystallization typically observed in hydrated compounds. The dynamic character of the water molecules in the 1D water channel is supported by impedance measurements of 3•H₂O, revealing a medium proton conductivity of 3.6 × 10^–8 S cm^–1 at 308 K and 95% relative humidity (RH), corresponding to that of bulk water (Supplementary Fig. 18a)³⁹. Variable-temperature (VT) conductivity measurements indicated an activation energy (E_a) of 0.5–0.7 eV for the proton migration pathway (Supplementary Fig. 18b), suggesting a vehicle-type proton migration mechanism⁴⁰. These results suggest that water molecules in the pore channels of 3 exhibit fluxional behavior under ambient conditions and function as proton carriers, being reminiscent of a superfluid phenomenon of ⁴He in a one-dimensional pore⁴¹.

Fig. 2. Variable-temperature X-ray analyses of 3•H₂O.

a–c Single-crystal X-ray structures of 3•H₂O viewed along the pore channel axis, and d–f oxygen atoms of water molecules around Cl^– ions at 298 (a, d), 90 (b, e), and 170 K after measurement at 90 K (c, f). The sticks between oxygen atoms represent hydrogen bonds with atomic distances below 3.4 Å.

In principle, crystal growth yields dense structures because intermolecular interactions provide an enthalpy increase that overcomes the loss of entropy on self-assembly. Thus, multi-component assembly yielding a low-symmetry structure with large solvent voids in the crystal lattice is rare. However, once large solvent voids form, the solvent molecules in the pore channels of 3 are highly dynamic, resulting in an increase in entropy, even in the confined pore spaces, thus compensating for the entropy loss upon crystallization.

VT X-ray analyses of water at interfaces

The solvent molecules in the low-entropy framework were structurally dynamic (high-entropy state) in the pore channels of 3•H₂O under ambient conditions. However, the highly dynamic water molecules showed temperature-sensitive behavior, forming structurally defined water clusters on the pore surface of 3 at low temperatures (Fig. 2). Interestingly, the low-symmetry, information-rich pore surface of 3 allowed the visualization of the cluster motifs of water at the interface with 3 through SCXRD analysis. The X-ray structure of 3•H₂O at 90 K was solved in the space group C2/c (a = 35.358(8) Å, b = 29.128(7) Å, c = 19.546(4) Å, β = 91.323(3)°, V = 20125(8) ų), and strong electron densities corresponding to the oxygen atoms of water near the pore surfaces were observed (Supplementary Fig. 9). The positions of the hydrogen atoms of the water molecules could not be determined because of the low electron density of hydrogen atoms and the dynamic nature of the water molecules, even at low temperature. However, the distances between oxygen atoms were <3.4 Å, strongly suggesting the presence of hydrogen bonds between water molecules along the pore surface. The Cl^– anion and water molecules identified by SCXRD analysis at 298 K acted as cluster cores, extending the hydrogen-bonding network upon cooling, where water molecules formed tetrahedral structures (Supplementary Fig. 13). In addition, the clusters formed cyclic water pentamers (H₂O)₅, a structural motif typically observed in clathrate hydrates⁴².

The well-defined pore surface of the complex formed by 1 and [2]⁺ could be a good model of organic polymeric surfaces and the hydrogen-bonding patterns in the first hydration layer, whose precise structures are challenging to determine at atomic resolution because of the high entropy and low periodicity. The X-ray analysis of 3•H₂O suggests that organic polymeric surfaces are also covered by cyclic water oligomers, similar to clathrate hydrates. In contrast, the water molecules in the second hydration layer, located at the center of the pore, were not observed (Fig. 2b), likely because highly dynamic water molecules with low tetrahedrality^43–45 readily formed a kinetic amorphous ice phase having a disordered hydrogen-bonding network and low periodicity during rapid freezing from room temperature to 90 K for the X-ray measurement.

The amorphous ice-like structure in the pore center at 90 K showed thermal reorganization of the hydrogen-bonding network of the second hydration layer, even below 273 K (Fig. 2c and f). After increasing the measurement temperature from 90 to 170 K, a transformation from C2/c at 90 K to P2₁/n (a = 19.556(2) Å, b = 29.145(3) Å, c = 35.596(5) Å, β = 91.104(3)°, V = 20,285(4) ų) was observed, and electron densities corresponding to water molecules were observed at the pore centers (Supplementary Fig. 11), indicating the thermal rearrangement of disordered water molecules forming a periodic structure detectable by XRD (Supplementary Fig. 14). The rearrangement of a periodic structure of H₂O molecules triggered significant changes in the cell parameters from those at 90 K. The new periodic structure at the pore channel center was derived from water clusters on the pore surface because the thermal rearrangements of kinetically trapped amorphous ice formed a thermodynamically stable hydrogen-bonding network with pre-organized water clusters on the pore surface. After cooling the crystal from 170 to 90 K during SCXRD measurements, the space group remained P2₁/n, and water molecules did not rearrange further, indicating their thermodynamically favored positions in the pore channels of 3. However, the water molecules at the pore center, treated as a secondary hydration layer, showed fluxionality and large anisotropic displacement parameters, medium occupancies, and deviation from a tetrahedral hydrogen-bonded structure, indicating disorder.

The low-entropy, information-rich crystal framework formed of multiple noncovalent interactions clearly demonstrated information transfer from the information-rich surface to the first and second hydration layers in the confined space via hydrogen-bonding networks, elucidating the inhomogeneity and dynamic character of water at the interfaces. Such long-range information transfer via hydrogen bonds at the molecular level is also essential in biological systems^46,47. Although our system is artificial and structurally rigid compared to biological systems, the observed propagation of structural information through ordered hydrogen-bond networks provides a conceptual model for understanding how molecular-level information can be spatially transferred in a controlled fashion. This analogy highlights the potential of low-entropy materials as model platforms for studying interfacial molecular recognition and unique arrangement.

Theoretical Investigation of water molecules in the pore channel of 3

Molecular dynamics (MD) simulations reveal the real-time motion of molecules, unlike the static results obtained by SCXRD analysis^48,49. MD simulations starting from the initial structures based on the X-ray results obtained at 170 K showed that, below 170 K, the water molecules had uniformly low mobilities (Fig. 3a). These results suggest the formation of a kinetically trapped hydrogen-bond network with low periodicity because hydrogen bonds between water molecules suppress their dynamics at low temperature, consistent with the SCXRD results obtained at 90 K (Fig. 2b). As the system temperature was increased in the MD simulation, the mobility of the water molecules was increased. Interestingly, between 203 and 263 K, the effect of temperature on water mobility depended on the distance of the water molecules from the material surface (Fig. 3b). The MD simulations showed that water molecules at the pore center (second hydration region) had higher mobility than those in the first hydration layer because of the hydrogen bonds between the water molecules and the rigid framework of 3. In the system above 300 K, the mobilities of the water molecules were uniformly high, regardless of the distance from the surface (Fig. 3c). This is likely because hydrogen bonds and interactions between water molecules and the pore surface are not strong enough to limit the mobility of water molecules at higher temperatures. It should be noted that these MD simulations employed the TIP4P-Ew water model, which reproduces the qualitative spatial trends in water mobility but does not account for effects such as interfacial polarization, absolute diffusion coefficients, and hydrogen-bond lifetimes. Thus, a more sophisticated computational model would be required to investigate these properties in detail. Nevertheless, the diffusion coefficients of water molecules obtained in this present approach, which are dependent on temperature and distance from the pore surface, provide a rationale for the inhomogeneity of interfacial water (Supplementary Fig. 28).

Fig. 3. MD simulations and statistical analyses of water molecules in 3.

a–c The diffusion coefficients (D) of water molecules are dependent on the distances from the central points of the pores at a 133, b 233, and c 333 K, respectively. d, e The statistical plots of tetrahedrality (d) and hydrogen bonding numbers (e) of the water molecules located at pore centers (333 K).

Furthermore, to understand the dynamics of the water molecules in the central pore region, statistical analyses of the hydrogen-bonded tetrahedral structure and coordination numbers of the water molecules were performed (Fig. 3d and e). The results reveal a deviation from the ideal tetrahedral structure and an average of three hydrogen bonds per water molecule at 333 K. This distribution differs from that of bulk water, further supporting the highly dynamic and mobile nature of the water molecules in the pore center (Supplementary Fig. 29). The results of the MD simulations are consistent with those obtained from the VT-SCXRD measurements (Fig. 2).

Infrared absorption and X-ray emission spectroscopy measurements of water molecules in the pore channel

Biocompatible organic polymers containing water have a range of structures at the water–polymer interfaces. These structures can be investigated using infrared (IR) spectroscopy⁵⁰. The characteristics and binding modes of water at the interfaces have attracted attention as indicators of bio/blood compatibility (bio-inertness)⁵¹. However, the molecular mechanism of water at interfaces has not been fully demonstrated, despite extensive theoretical and experimental efforts⁵². This is because of the limited information about the surface structure of polymer materials. However, 3 contained numerous interfacial water molecules on its pore surfaces. SCXRD analysis and MD simulation of 3•H₂O enabled assessment of the dynamic characteristics of water at the interface and structurally resolved water clusters with specific hydrogen-bonding patterns in the pore channel. This feature of 3•H₂O enabled us to unveil a clear relationship between the characteristics of the interfacial water and spectroscopic information at atomic resolution.

Microscopic FT-IR spectroscopy of a crystal of 3•H₂O was conducted to identify and quantify water at the interfaces in the pores of 3. By monitoring the dehydration of 3•H₂O at 298 K and 50% RH, characteristic spectroscopic features of the water molecules removed from the channels of 3 were identified, revealing distinct differences from those of bulk water (Fig. 4a)⁵³. The IR spectrum of 3 showed no significant change in the band at 2900 cm^–1 but a gradual decrease in the –OH bands around 3100–3700 cm^–1, suggesting that the dehydration of 3•H₂O proceeded without the collapse of the porous structure, as supported by powder XRD studies (Supplementary Figs. 15 and 30). Notably, at 50% RH, the formation of the first hydration layer at the surface was maintained, providing spectroscopic information about water molecules at the secondary and tertiary hydration layers. The difference FT-IR spectrum revealed broad bands having a maximum at 3520 cm^–1 and a small shoulder at 3260 cm^–1, ascribed to water in the secondary hydration shell (Fig. 4b). The OH stretching frequency can be used to assess hydrogen-bond strength^52,53, and the obtained spectrum suggests the presence of high-entropy, weakly hydrogen-bonded water molecules with low tetrahedrality in the second hydration layer during the dehydration of 3•H₂O. The lower frequency band around 3260 cm^–1 can be assigned to H₂O molecules interacting strongly with the pore surface of 3, resulting in a large shift to a lower frequency compared to that of the flexible molecules at around 3520 cm^–1. Time-dependent measurements of the dehydration of 3•H₂O showed that the intensity of the shoulder band at 3260 cm^–1 decreased more rapidly than that of the main band at 3520 cm^–1 (Supplementary Fig. 31). This is because the elimination of water molecules from the second hydration layer reduces the water density in the pores and weakens the hydrogen-bond network on the pore surface. These FT-IR results explain the dynamic characteristics of water molecules in the second hydration layer in the 1D water channel of 3, as well as the inhomogeneous nature of water at the interface, as clarified by SCXRD analyses.

Fig. 4. Infrared and X-ray emission spectroscopy (XES) analyses of 3•H₂O.

a, b Infrared spectra following the dehydration of 3•H₂O (298 K, 50% RH); enlarged (a), and the difference spectra (b) in the OH and CH stretching region (3800–2800 cm^–1). c O1s XES of liquid H₂O (blue line) and H₂O molecules in the pore of 3 (black line).

To unveil the electronic structure of the water in the second hydration on the pore surface of 3•H₂O, we performed X-ray emission spectroscopy (XES) measurements. XES probes the electronic transitions between the core and valence orbitals of oxygen atoms, providing information about the hydrogen-bonding states of water molecules because the timescale of the excitation process and O1s core–hole lifetime (femtoseconds) is much shorter than that of the rearrangement of the hydrogen-bonding network⁹. For example, the XES spectrum of bulk H₂O consists of four peaks corresponding to oxygen 2p orbitals: 1b₁’, 1b₁”, 3a₁, and 1b₂, obtained from the emitted X-rays associated with the electronic transition from the valence state to the core level (Fig. 4c). The relative intensities of the double 1b₁ peak depend on measurement conditions, associating spectral features with two distinct structural motifs in liquid water: 1b₁’ at 525.8 eV and 1b₁” at 526.7 eV, corresponding to fourfold ice-like hydrogen bonds and less distorted tetrahedral hydrogen bonds, respectively^54,55. The high-entropy and temperature-sensitive behavior of water molecules contained in the pore channels of 3 was elucidated through SCXRD. The combined XES and SCXRD analysis of 3·H₂O provides deeper insights into the inhomogeneous nature of these confined water molecules. XES measurements during the dehydration of 3·H₂O at 305 K revealed distinctive spectroscopic features, consistent with the IR results. The XES spectrum displayed four peaks for H₂O, assigned to 1b₁″, 1b₁′, 3a₁, and 1b₂ (Fig. 4c). Notably, the intensity of the 1b₁″ peak at 526.7 eV exceeded that of 1b₁′ at 525.8 eV, and a pronounced shoulder at 524.5 eV was observed in the 3a₁ region. The IR measurements of 3·H₂O during dehydration provided structural insights into the second hydration layer in the pores. Similarly, the XES results suggest that water molecules in the central regions of the pore channel form fewer than four hydrogen bonds in a distorted pattern, deviating from the tetrahedral, ice-like hydrogen bonds observed under ambient conditions. This supports the dynamic nature of the second hydration layer. Although the experimental conditions posed challenges for directly correlating temperature with water dynamics, theoretical XES simulations clarified this relationship. The simulated spectra showed an intense 1b₁′ peak at 173 K and a dominant 1b₁″ peak at 333 K (Supplementary Fig. 36). These simulations reflected the hydrogen-bonding characteristics of the second hydration layer. Additionally, the experimental XES spectrum was reproduced as a linear combination of the simulated spectra of the water molecules in the pore center and the dehydrated form of the supramolecular framework (Supplementary Fig. 39).

The combined IR and XES results suggest that the hydrogen-bond network of the second hydration layer in 3·H₂O collapses easily, indicating its highly dynamic structure. In contrast, the first hydration layer forms stable clusters because of strong interactions with the surface components. These findings highlight the inhomogeneous nature of interfacial water. Although spectroscopic studies of interfacial water in polymeric materials often yield ambiguous results because of the high-entropy characteristics (low periodicity and limited structural information) about these surfaces, the supramolecular crystal 3·H₂O offers a robust model system. Crucially, its well-defined, low-entropy surface structure enables a precise relationship between the water structure and interfacial properties to be established, offering atomic-resolution insights. This study demonstrates the potential to explore the behavior of secondary hydration layers on organic surfaces, advancing our understanding of water at interfaces.

Discussion

Porous crystalline materials typically have symmetric frameworks, creating confined spaces capable of capturing various small molecules through interactions with their large surface areas. Here, we have reported the formation of a supramolecular porous crystal comprising a concave organic host and an octahedral coordination complex. This assembly produces an anisotropic, information-rich surface structure. VT-SCXRD studies revealed the unique cluster motifs of the first hydration layer of water molecules and the dynamic characteristics of the second hydration layer, enabled by the information-rich pore channels in the crystal. These atomic-resolution structural insights into interfacial water provide stronger correlations with the interpretations from previous spectroscopic studies and advance the understanding of their inhomogeneity. MD calculations based on the SCXRD structures offered additional perspectives on the system. This combined approach demonstrates how low-entropy materials can establish a clear relationship between hydrogen-bonded structures and the temperature-dependent behavior of interfacial water. Although the binding forces between the components in this study are weaker than those typically found in conventional porous crystalline materials, their synergistic effects impart additional functionality to the system. Furthermore, the properties of these supramolecular frameworks can be readily tuned by optimizing the molecular components and binding modes. This methodology offers significant potential for designing novel supramolecular crystalline materials based on noncovalent interactions, opening new avenues in materials science and surface chemistry. Although low-entropy porous materials are still difficult to obtain owing to the large entropic penalty in the self-assembly process, theoretical applications combined with machine learning, judging from information entropy of the material, might provide a hint for producing a rational molecular design of low-entropy materials, similar to the approaches for understanding protein folding⁵⁶.

Methods

Apparatus and reagents

All diffraction data were collected with a temperature-controlled cold nitrogen stream on the X-ray diffractometer (Rigaku Varimax Saturn/1200S). The powder X-ray diffraction data were obtained with the Dectris MYTHEN detector on the beamline BL02B2 (298 K, 2θ = 1.2–75°, λ = 0.79987 Å) at the SPring-8 synchrotron facility. The TG-DTA measurements were performed with a SHIMADZU DTG-60. The Impedance measurements were carried out with a Solartron SI 1260 impedance/gain-phase analyser and 1296 dielectric interface. The IR spectra were measured on the IR beamline BL43IR at the SPring-8 synchrotron facility. An FT-IR microspectrometer (BRUKER model HYPERION IR microscope with model VERTEX70 FTIR spectrometer) was used with the IR synchrotron radiation. The XES measurement was performed using the SPring-8 BL07LSU ultra-high-resolution soft X-ray emission spectrometer HORNET. All commercially available compounds were used as received without further purification.

Computational studies

All-atom MD simulations in this study were performed using the MD program GROMACS 2020.5. The initial structure of the porous framework was built up based on the crystal structure. The TIP4P-Ew model was used for water molecules. The simulated XES spectra were obtained within the framework of the density functional theory. The semiclassical Kramers–Heisenberg (SCKH) formula was applied to mimic the experimental XES spectra. The detailed parameters of the computational methods were provided in the Supplementary Information.

Author contributions

S.H. designed the study, analyzed the single-crystal X-ray structures, and prepared the draft of the paper. S.O. prepared the supramolecular crystals for measurements. K.O. performed the powder X-ray diffraction and proton conductivity studies. Y.S., H.T., and G.W. performed MD simulations. Y.I. supported the synchrotron IR measurements. H.K. and Y.H. conducted the synchrotron soft X-ray emission spectroscopies. O.T. performed the theoretical calculations of the XES spectra. The manuscript was co-written by S.H., K.O., Y.I., G.W., O.T., M.H., E.S., Y.A., K.U., and Y.H. All the authors discussed the results and commented on the paper.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

The authors declare that the data supporting the findings of this study are available within this article and Supplementary Information files as well as from the corresponding authors upon request. The crystallographic data for the structure reported in this study were deposited at the Cambridge Crystallographic Data Center at www.ccdc.cam.ac.uk/data_request/cif under accession numbers 2404956–2404959. The experimental data are available in the Supplementary Information.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-025-62578-0.