DOI:
10.1039/D5SC05793K
(Edge Article)
Chem. Sci., 2026, Advance Article
Making room for reactivity in topochemical transformations under pressure
Received
31st July 2025
, Accepted 24th January 2026
First published on 26th January 2026
Abstract
The orderly arrangement of molecules in crystals provides a unique platform for the control of reactivity, where spatial vicinity and orientation of the molecules determine the course of the reaction. Common wisdom assumes that the densest crystal packings of the reactant molecules are most favorable for pressure-induced topochemical reactions. Based on thermodynamic and spatial arguments, here we show that the densest crystal packing may not be the most optimal platform for chemical synthesis. Instead, introducing void space within the crystal lattice significantly improves and even enables chemical reactions. In the case of sorbic acid confined between brucite-type layers, this reactivity is used to modify the optical, spectroscopic and magnetic properties of 2D layers and to synthesize a retrievable polymeric product.
Introduction
In topochemical reactions the spatial arrangement of molecules within a crystal lattice dictates the reaction pathway.1 These reactions have emerged as synthetic routes towards polymers with unprecedented regio- and stereoselectivity2–20 and as a means to control the physical properties of the crystal.21–35 Light, heat, and pressure are common stimuli, and densely packed structures, where reactants are in closest proximity, are intuitively regarded as the most favorable platforms for chemical reactivity. Based on fundamental thermodynamic considerations, we hypothesize that, perhaps contra-intuitively, providing ample space within the crystal packing can lower the energy barriers for pressure-induced transformations, hinder reversible reactions upon decompression, and enable permanent change in the physical properties of the crystal and retrievable polymeric product.
Derived from the fundamental equation for internal energy, the pressure-induced energization of solids is governed by
where

is the isothermal compressibility. From this equation, it follows that

increases with
β, and thus the energization effect of pressure is greater on systems with larger compressibility. Compression also decreases the system's entropy, that is,

, further driving the reaction forward. In solid-state reaction systems, this is manifested as reduced conformational space of the reactant, leading to enhanced selectivity. In fact, the simultaneous increase in energy and selectivity in pressure-driven systems is distinct from thermally driven systems, where heat increases both the energy and entropy, generally leading to decreased selectivity. Finally, a large volumetric reduction thermodynamically favors pressure-driven reactions, based on the fundamental equation for the Gibbs energy:
where a large and negative Δ
rV corresponds to a negative reaction Gibbs energy (Δ
rG) and spontaneity.
Based on these thermodynamic considerations, it follows that large β and large and negative ΔrV contribute to lowering the energy barriers and facilitating, even enabling, topochemical reactions. Consequently, instead of densely packed structures, packings capable of undergoing large volume changes emerge as favorable platforms for topochemical reactivity. Ample space within the crystal packing also facilitates reactivity due to spatial considerations. For example, topochemical polymerizations of unsaturated hydrocarbons change the carbon atom hybridization (sp/sp2 to sp2/sp3), which requires structural reorganization that can be more easily accommodated in packings with larger free volume around the reactive centers.
Experimental realization of ordered structures with larger free volume is challenging, as molecules have a natural tendency to adopt the densest crystal packing. However, there are viable strategies to achieve lower packing density.36–49 For example, carboxylic acids can be grafted onto brucite-type layers replacing hydroxide anions.50,51 The spacing between molecules in such hybrids is, to a large extent, controlled by the spacing between the metal ions in the robust inorganic layer, and it can often lead to a decrease in the packing density of the carboxylate anions. Furthermore, in a subset of these structures, only half of the hydroxides get replaced leading to a substantial amount of added space. We have shown that sorbic acid replaces half of the OH− anions in brucite-type Co(OH)2, forming Co(OH)(sorb) (Fig. 1a).52 Considering that OH− occupies significantly less space than sorbate anions, the interlayer in Co(OH)(sorb) has lower local crystal density compared to layered structures containing only sorbate anions, such as Mn(sorb)2 (Fig. 1b). The markedly different crystal density of their interlayers, with additional ample space caused by the presence of OH− in Co(OH)(sorb), presents an ideal opportunity to test the thermodynamic and spatial considerations for adding ample volume in pressure-induced reactions in order to enable chemical reactivity (Fig. 1c).
 |
| | Fig. 1 Crystal packing of (a) Co(OH)(sorb) and (b) Mn(sorb)2. (c) Schematic representation of pressure-induced reactivity. (Oxygen: red, carbon: gray, hydrogen: off-white, cobalt: blue, and manganese: green). | |
Results and discussion
First, we tested the pressure-induced reactivity of Co(OH)(sorb). Synchrotron X-ray powder diffraction (XRPD) patterns collected as a function of pressure (Fig. S1) show 2θ shift to higher angles, indicating compression of the lattice. Fig. 2a shows the response of the (001) peak to pressure corresponding to the inter-layer distance (Fig. S2). The lattice spacing, d001, decreases by 1.8 Å from ambient pressure to 10 GPa (Fig. 2b), reflecting the compression of the interlayer occupied by sorbates. Notably, the (001) peak shifts slightly to the left from 10.5 to 13.5 GPa, indicating a negative linear compressibility in this pressure range and suggesting non-mechanical effects. Upon decompression, the d001 distance shows an irreversible decrease, with a hysteresis in the d001 distance–pressure plot. This observation indicates an irreversible change in the organic interlayer. In situ compression of the sample led to a reduction in crystallinity, particularly evident from the diminishing intensity of the high-angle reflections, which prevented detailed structural analysis. Powder diffraction data collected after decompression confirmed an irreversible loss of crystallinity.
 |
| | Fig. 2 (a) Synchrotron XRD patterns (wavelength: 0.496 Å) and (b) d001 versus pressure for Co(OH)(sorb). (c) Optical spectra and (d) photographs before and after compression (bar = 50 µm). (e) Raman spectra in the C C stretching region and (f) Raman shift and full width at half maximum (FWHM) for Co(OH)(sorb). (g) Low-frequency Raman spectra. | |
Optical spectra of the compressed sample (Fig. 2c) show the emergence of absorption at 550 nm, resulting in a color change from orange to purple (Fig. 2d). These experimental observations indicate irreversible changes in the local environment of the Co2+ cations, caused by changes in the interlayer.
In situ Raman spectra (Fig. 2e) reveal an increase in the full-width-at-half-maximum (FWHM) of the C
C stretching modes53 at ∼1656 cm−1 during compression (Fig. 2f). The increase in FWHM is prominent and abrupt around 10 GPa, indicating major changes in the structure and environment of the C
C stretching modes. Density-functional theory (DFT) simulations confirmed that the number of non-degenerate normal modes associated with C
C stretching increases with the degree of oligomerization (Fig. S3). We attribute this broadening to chemical reactivity and the formation of extended molecules in the organic interlayer. The polymerization likely initiates simultaneously at multiple sites and propagates at variable rates, resulting in randomly distributed domains with variable chain lengths. The disruption of in-plane order may also contribute to the broadening of the Raman peaks. The broadening persists after decompression indicating that the polymeric product can be retrieved.
In the low-frequency region of the Raman spectrum (Fig. 2g), three peaks at 30, 80 and 110 cm−1 are present at ambient pressure, corresponding to lattice vibrations in ordered 2D materials.54 These peaks vanish at 8.4 GPa and are not recovered upon releasing the pressure.
Our previous studies have shown that anisotropic deformation is key to reactivity under isotropic compression.55,56 In Co(OH)(sorb), the structure is bound by van der Waals interactions in the (001) direction, making it more compressible than the in-plane directions bound by ionic and/or coordination bonds. This environment, together with the presence of reactive unsaturated carbon atoms in close proximity, leads to pressure-induced polymerization. The structural and chemical changes were explained using density functional theory (DFT) calculations (Fig. 3a). Theoretical modeling shows irreversible reduction of both the d001 and the unit cell volume upon compression (Fig. 3b, S4 and S5), consistent with the experimental XPRD data (Fig. 2a). The unit cell contraction is anisotropic, with a larger decrease in the (001) direction than in the other axes, leading to a large contraction of the interlayer spacing. The presence of OH− groups in the Co–O inorganic plane creates gaps between the adjacent sorbates, thereby sterically allowing for tilting motion of the sorbates (Fig. 3c), bringing the reactive atoms closer together (Fig. 3d) and allowing for an overlap of frontier orbitals (Fig. 3e). This environment eventually leads to chemical reactivity and formation of a polymer (Fig. 3f). The calculated bond formation pressure, 35 GPa, is higher than the experimental value (∼10 GPa), due to multiple factors including the omission of thermal fluctuations and limited phase space searched by the local optimization algorithm. We note that the DFT results do not capture the experimentally observed negative compressibility of d001 from XRPD measurements, likely due to limitations in the description of dispersive forces that dominate interlayer interactions.
 |
| | Fig. 3 (a) DFT simulated Co(OH)(sorb) structures at 0, 15, and 35 and back to 0 GPa. Blue, red, grey and white represent Co, O, C and H, respectively. (b) Unit cell volume and d001. (c) Sorbate tilting angle. (d) Average C5a–C2b distance as a function of pressure. (e) Schematic reaction mechanism. (f) Polymeric structure of the product. | |
To retrieve macroscopic amounts of the product, we used a six-ram Hall-type large volume press. The compressed product, HP-Co(OH)(sorb), had purple color (Fig. S6), consistent with optical spectroscopy measurements (Fig. 2c and d). This observation confirms that this topochemical reaction can be scaled-up and the product can be successfully retrieved.
Part of the sample was dissolved in a DCl/D2O/CD3OD solvent, suitable for measuring nuclear magnetic resonance (NMR) spectra. The dissolution resulted in the release of the Co2+ and OH− ions and unreacted sorbates, leaving an insoluble, swollen, white colored organic material (Fig. S7). We note that pristine, unreacted Co(OH)(sorb) is soluble in the solvent and does not leave a residue. This outcome is expected for the presence of an organic polymer in the interlayer. Proton nuclear magnetic resonance (1H NMR) spectra of HP-Co(OH)(sorb) show new peaks at 0.97 and 1.67 ppm (Fig. S8), indicative of hydrogen atoms bonded to sp3-hybridized carbon, as observed in the theoretical calculations (Fig. 3). Simulation of the 1H NMR spectra of oligomeric products (Fig. S9) further confirms the occurrence of irreversible, pressure-induced chemical reactions in the organic interlayer.
The diffraction and spectroscopic observation indicate irreversible changes and potential disorder in the 2D layer caused by the chemical reaction in the interlayer. It follows that structural changes in the organic structure can be used as a direct strategy to modify the properties of the inorganic layers. One notable physical property of the brucite-type 2D layers in Co(OH)(sorb) is their magnetic behavior, as we have previously shown that the material exhibits canted antiferromagnetism.52
The temperature dependent magnetic susceptibility of HP-Co(OH)(sorb) initially shows paramagnetic behavior upon cooling (Fig. 4a), followed by a sudden decrease of magnetization, similar to Co(OH)(sorb) (Fig. 4b). The zero-field-cooled (ZFC) data indicate that the antiferromagnetic Néel temperature occurs at TN = 38 K (3.7 K lower than TN = 41.7 K for Co(OH)(sorb)). The material shows bifurcation between the ZFC and field-cooled data, confirming that there are net ferromagnetic moments arising from canted antiferromagnetic (AFM) states. The susceptibility follows the Curie Weiss law χ = C/(T − Θ) quite nicely (Fig. 4a), with a θCW = −17 K (similar to θCW = −20 K for Co(OH)(sorb)). The negative θCW further confirms antiferromagnetic coupling. The effective magnetic moment, µeff, calculated from the Curie constant is 4.49 µB/CoII for HP-Co(OH)(sorb). In contrast, for Co(OH)(sorb), µeff is estimated to be 3.79 µeff/CoII, which is very close to the value of free Co(II) ions of 3.87 µeff/CoII.
 |
| | Fig. 4 Temperature dependent magnetic susceptibility data of (a) HP-Co(OH)(sorb) and (b) Co(OH)(sorb). The insets in (a) and (b) show inverse magnetization, and the red dashed line indicates Curie Weiss fitting. Magnetization hysteresis of (c) HP-Co(OH)(sorb) and (d) Co(OH)(sorb). | |
The field dependence measurements of the magnetization from −5 to 5T were carried out to further explore the nature of magnetic order of the material before and after high pressure treatment. The magnetization of HP-Co(OH)(sorb) does not saturate at high magnetic fields but instead shows a quasi-linear relation with the external magnetic field, H (Fig. 4c). Similar behavior was observed for Co(OH)(sorb) (Fig. 4d). The linear relation of M–H and the existence of magnetic hysteresis further indicate canted antiferromagnetism of the sample. To extract the saturation moment from the net ferromagnetism where the ferromagnetic order is provided by the small component canted by the magnetic moment of Co, the M–H curves were fitted using
For HP-Co(OH)(sorb), the saturation field is estimated to be 0.004 µB/CoII, smaller than 0.13 µB/CoII in Co(OH)(sorb). All the saturation magnetic moments of the samples before and after high pressure treatment are much smaller than the effective moment estimated from the Curie–Weiss law, further indicating the scenario of canted AFM in Co(OH)(sorb). Moreover, after high pressure treatment, the saturation moment is reduced, which can be attributed to a pressure modified canting angle, resulting in diminished net ferromagnetism.
The sample before and after applying pressure shows canted antiferromagnetism and overall similar magnetic properties, which can be attributed to the retainment of the layered structure after decompression. However, the irreversible chemical changes in the organic intralayer affect the electronic structure and local geometry of Co2+ cations, thus modifying the magnetic properties, evidenced in a larger effective magnetic moment, reduction of the saturation field and modification of the Néel temperature.
It has been reported that compressing crystals of sorbic acid (H(sorb))57 does not lead to reactivity. However, the crystal packing of H(sorb) is markedly different from that of Co(OH)(sorb) and direct comparison cannot be easily drawn. Instead, as a control study, we studied the high-pressure behavior of Mn(sorb)2. A hydrothermal reaction of 1
:
2 ratio of Mn2+ and sorb− provided yellow crystalline powder, whose structure was solved ab initio from high-resolution PXRD data (Fig. S10). The crystal structure features densely packed layers of sorbates, packed between inorganic Mn–O layers (Fig. 1b). The in situ Raman spectra show fully recovered C
C stretching mode after compression (Fig. 5a), indicating the absence of irreversible, pressure-driven polymerization. The low-frequency vibrational modes are recovered after release of pressure (Fig. 5b), further supporting their structural inertness under pressure. These modes are initially found at 34 and 50 cm−1 and become red-shifted to 31 and 48 cm−1 after recovery, suggesting only subtle structural changes.
 |
| | Fig. 5 Raman spectra in (a) the C C stretching region and (b) low frequency for Mn(sorb)2. (c) Raman shift and full width at half maximum (FWHM). (d) XRPD showing the (100) diffraction peak (wavelength: 0.496 Å). (e) d100 versus pressure. (f) DFT-simulated structures of Mn(sorb)2 from ambient pressure to 65 GPa. The rightmost panel shows the schematic strain in the crystal. (g) d100 and unit cell volume versus pressure. (h) Sorbate tilting versus pressure. (i) Changes of total energy (ΔU) versus pressure for Co(OH)(sorb) and Mn(sorb)2. (j) Average C1–C4 distance versus pressure upon compression. | |
High-pressure synchrotron XRPD further confirms the inertness of Mn(sorb)2. The (100) reflection shifts from 2θ of 1.51° at ambient pressure to 1.63° at 15.9 GPa (Fig. 5d and S11), corresponding to 1.5 Å contraction of d100 and showing lower compressibility than Co(OH)(sorb). No apparent hysteresis is observed in the distance–pressure plot (Fig. 5e). The sample pressure remained at 0.9 GPa after fully releasing the external pressure due to remnant stress, and d100 arrives at 18.1 Å, slightly lower than the initial value.
DFT studies of the high-pressure structures of Mn(sorb)2 (Fig. 5f) show that d100 and the unit cell volume decrease by 4 Å and 175 Å3, respectively, from 0 to 40 GPa (Fig. 5g). Closely packed sorbates sterically hinder the tilting motion: the tilt angle decreases by 13.4° from 0 to 40 GPa (Fig. 5h) (cf. 21.4° in Co(OH)(sorb) in the same pressure range). The distance between the reactive carbons monotonously decreases (Fig. 5j) without indication of chemical reactivity. The absence of irreversible changes in the simulation is consistent with the experimental findings (Fig. 5a–e).
Finally, we calculated the pressure-induced change of total energy per unit cell, ΔU, for both structures (Fig. 5i). ΔU was found to be 2.5 eV lower in Mn(sorb)2 than Co(OH)(sorb) in the same pressure range, from 0 to 40 GPa. This finding is consistent with our analysis that
depends positively on compressibility. The experimental data (Fig. 2 and 5) and the DFT calculated changes of the unit cell parameters for both systems (Fig. S4 and S5) show that the Co(OH)(sorb) system exhibits hysteresis compared to Mn(sorb)2 with respect to lattice parameters, beta angle and total energy during compression and decompression, indicative of irreversible chemical reactivity enabled by the introduced void space within the crystal lattice.
Additionally, it is worth mentioning that sorbic acid crystals are not readily polymerizable by light or heat.58–60 The same holds true for salts such as Co(OH)(sorb) and Mn(sorb)2. Prolonged UV-irradiation of both salts did not lead to formation of the product.
Conclusions
In summary, the topochemical reaction in Co(OH)(sorb) together with the absence of chemical reactivity in Mn(sorb)2 and H(sorb) indicates that additional free volume between sorbates facilitates reactivity and stabilization of the product. This rather counter-intuitive conclusion is supported by thermodynamic and spatial considerations. Larger free volume leads to a large isothermal compressibility which increases pressure-induced energization and enables the reactant to overcome the activation barriers. Reducing the free volume following the chemical reaction leads to a negative reaction volume corresponding to a negative reaction Gibbs energy and driving the reaction forward. Finally, the presence of voids allows for conformational reorganization required by changes in hybridization.
While further studies are necessary to generalize these conclusions, this design strategy is a valuable new addition to the solid-state chemistry toolbox. It is applicable to a wide range of systems prone to engineering added void space. These include 2D hybrids,49–51,61 hydrogen-bonded,36,37,46 metal–organic38,48 and covalent organic39 frameworks, molecular cages,40,41,62 porous crystals,42–45 and other classes of materials. This approach facilitates or even enables reactivity that can be used to fine-tune the physical properties of the crystal, and it allows for the synthesis of atomically precise polymers with unprecedented stereoselectivity. Further developments and generalization of this design strategy can open exciting new directions in crystal chemistry.
Author contributions
Conceptualization: TR and HY. Formal analysis and investigation: TL, JBL, ME, SB, WL, BL, LJK, HY, and TR. Funding acquisition: TR and BL. Project administration: TR and HY. Supervision: TR, HY, and BL. Writing – original draft: TR and HY. Writing – review & editing: TL, JBL, ME, SB, WL, BL, LJK, HY, and TR.
Conflicts of interest
There are no conflicts to declare.
Data availability
The data supporting this article have been included as part of the supplementary information (SI) or data is available by request. Supplementary information: includes material preparation and, experimental procedures, computational and crystallographic details, images and spctroscopic data. CCDC 2526627 contains supplementary crystallographic data for this paper.63 See DOI: https://doi.org/10.1039/d5sc05793k.
Acknowledgements
This material is partly based upon work supported by the National Science Foundation under grant no. DMR-2143581. We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III beamlines P02.1 and P61B. Beamtime was allocated by an in-house contingent. TR acknowledges DESY's Stephenson Distinguished Visitor Programme. The work at UT Dallas was supported by US Air Force Office of Scientific Research grant no. FA9550-19-1-0037, National Science Foundation-DMREF-2324033, and Office of Naval Research grant no. N00014-23-1-2020 and N00014-22-1-2755. This research used resources of the Advanced Light Source, a U.S. DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. This work used CRUNTCH, the high-performance computational facility at University of North Texas supported by the National Science Foundation under grant no, CHE-1531468 and OAC-2117247.
Notes and references
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Footnote |
| † These authors contributed equally. |
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| This journal is © The Royal Society of Chemistry 2026 |
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