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The role of lattice vibration in the terahertz region for proton conduction in 2D metal–organic frameworks

Tomoya Itakuraa, Hiroshi Matsui*b, Tomofumi Tadac, Susumu Kitagawad, Aude Demessencee and Satoshi Horike*dfgh
aDENSO Corporation, 1-1, Showa-cho, Kariya, Aichi 448-8661, Japan
bDepartment of Physics, Graduate School of Science, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan
cMaterials Research Center for Element Strategy, Tokyo Institute of Technology, Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8501, Japan
dInstitute for Integrated Cell-Material Sciences, Institute for Advanced Study, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan. E-mail:
eUniversité Claude Bernard Lyon 1, Institut de Recherches sur la Catalyse et l'Environnement de Lyon (IRCELYON), UMR 5256 CNRS, Villeurbanne, France
fAIST-Kyoto University Chemical Energy Materials Open Innovation Laboratory (ChEM-OIL), National Institute of Advanced Industrial Science and Technology (AIST), Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
gDepartment of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo-ku, Kyoto 615-8510, Japan
hDepartment of Materials Science and Engineering, School of Molecular Science and Engineering, Vidyasirimedhi Institute of Science and Technology, Rayong 21210, Thailand

Received 13th November 2019 , Accepted 15th December 2019

First published on 16th December 2019

We studied the relationship between proton conductivity and the terahertz-regime vibrations of two-dimensional MOFs. The results of spectroscopy studies clarified the essential role played by the collective motions in the terahertz region in 2D layers for efficient H+ conduction. Ab initio calculations suggested the collective motion to be predominantly determined by the valence electronic structure, depending on the identity of the metal ion.

Solid state ion conductors are in wide demand for batteries, fuel cells, electrochemical sensors and electrochemical catalysis. The design and elucidation of ionically conductive paths in solid structures have, however, been significant challenges in relation to these applications.1 Ion conduction generally proceeds as a result of ions hopping to neighboring coordination sites, followed by local structural relaxation. These processes are often predominantly determined by lattice vibrations below 10 THz (333 cm−1).2,3 Indeed, ion conductivity in some representative inorganic materials correlates with the terahertz vibration. For α-AgI, for example, Ag+ behaves as a liquid and conducts as a consequence of sub-lattice melting with corresponding sub-lattice vibration modes of about 5–30 cm−1.4 For the typical proton (H+) conductors CsHSO4 and BaCeO3, the collective vibration modes of protonic species (i.e., HSO4 and lattice OH, respectively) have been observed at 58–170 cm−1 and 320–378 cm−1.2

Studies of ion conductivity for molecular-based crystals have been recently showing rapid progress.5 Of such crystals, metal–organic frameworks (MOFs) are a promising class of materials for obtaining different ion conductivities.6 Researchers have shown the ability to control the ion conductivity by making use of guests in the channels, redox activity in metal centers, and ligand dynamics or acidity/basicity in the frameworks. Although there are many reports on the synthesis of ion-conductive MOFs, there are few about observations of any relationship between ion conductivity and lattice vibration. Several reports have described the unique lattice dynamics and functions of MOFs in the terahertz region,7 but it is also important to elucidate using spectroscopy the relationship between lattice dynamics and ion conductivity in MOFs. For this purpose, we employed three isostructural MOFs having two-dimensional (2D) H+-conductive pathways, and characterized their lattice vibrations in the terahertz region to describe their mechanism of H+ conductivity. We also carried out ab initio calculations to analyze vibrational mode characteristics and to study the contribution of metal ions to the lattice vibration.

We prepared three 2D MOFs having different metal ions as shown in Fig. 1. Each of the compounds may be described using the formula [M(H2PO4)2(TrH)2], where M = Zn2+, Co2+, or Mn2+, and TrH = 1,2,4-triazole, and we denote the compounds as ZnTr, CoTr, MnTr, respectively.8 The crystal structure of ZnTr is shown in Fig. 1A and B, and the parameters of the crystal structures of CoTr and MnTr are summarized in Table S1. All three compounds crystallized in the same crystal system and space group (orthorhombic-Pbcn). H2PO4 was observed to be coordinated to the metal ion axially to form a hydrogen bond network in the ab plane, with the extended H-bonds with H2PO4 motion providing for the long-range hopping of H+ through the layer. The O(H)–O hydrogen bond distances between PO4 groups were measured to vary by less than 0.046 and 0.073 Å along the a and b directions, respectively. The X-ray results indicated negligible differences between the crystal structures of the three compounds.

image file: c9sc05757a-f1.tif
Fig. 1 (A) The crystal structure of ZnTr along the bc plane. (B) The hydrogen-bond network formed by PO4 tetrahedra in ZnTr in the ab plane. Zn2+ and TrH are omitted for clarity. Zn: gray, P: yellow, O: red, C: black, N: blue, H: pink. (C) Plots of the H+ conductivity of ZnTr (circle), CoTr (triangle), and MnTr (square) under dry N2 gas from 30 to 150 °C. The dashed lines represent the fittings of the linear expression to the data. (D) Infrared spectra at 27 °C, with regions I and III attributed to intramolecular modes of TrH and PO4 tetrahedra, region II attributed to the O–H modes, band A to the O–H stretching mode, and bands B and C to the Fermi resonance with combinations involving O–H bending modes.

The ratio of the amount of H2PO4 to that of metal ion was determined using ICP-AES for each of ZnTr, CoTr, and MnTr and found to be 1.58, 1.63, and 1.55. The lower value of the measured relative amount of H2PO4 compared with the stoichiometric amount in the crystal structure was attributed to H2PO4 site defects as described previously.9 These results also indicated the quantities of structural defects for the three compounds to be comparable. Therefore, the H+ conductivities for these structures were attributed to the mobility levels of the H2PO4 groups in the layers.

Fig. 1C shows the plots of anhydrous H+ conductivity under an N2 atmosphere. The conductivity of ZnTr was found to be the highest: the values at 150 °C were measured to be 4.6 × 10−4 (ZnTr), 1.9 × 10−6 (CoTr) and 9.1 × 10−8 S cm−1 (MnTr). The total activation energy of ZnTr was determined to be 0.50 eV, about half of those of CoTr and MnTr (1.06 and 1.17 eV). The considerable differences between the H+ conductivities of these MOFs were found despite the near identities of their crystal structures and compositions, implying the predominant influence of other factors on the conductivity.

Infrared (IR) spectroscopy measurements at 27 °C were taken to investigate the characteristics of the hydrogen bonds (Fig. 1D). Regions I and III were attributed to intramolecular modes of TrH and PO4 tetrahedra, and region II to O–H modes. We assigned three broad bands, known as ABC bands and observed here from 1600 to 3100 cm−1 to the O–H modes, specifically to O–H stretching modes in Fermi resonance with combinations involving O–H bending mode, and are typically seen in strong hydrogen-bonding systems such as metal dihydrogenphosphates.10 Although two kinds of hydrogen bonds in MTr were in theory identified from the crystal structure, we could not distinguish between them due to small difference between their O–O distances. These O–H modes were indicated to be identical in their band shapes and frequencies, consistent with the results of their similar O–O distances from single crystal XRD (Table S1). The IR spectroscopy results did not provide information about any distinct H+ conductivity.

To investigate the lattice vibration, we performed terahertz time-domain spectroscopy (THz-TDS) at 27 °C (Fig. 2A–C). We also computed the theoretical spectra using ab initio quantum mechanical calculations to identify the vibration modes (dotted lines and bars in Fig. 2A–C). The calculations were performed within the framework of density functional theory (DFT) using the VASP package.11 Vibrational properties were calculated using the linear response method of density functional perturbation theory (DFPT).12 For each normal mode, displacements of each of the ions and frequencies were calculated at the Brillouin zone center in a harmonic approximation. The theoretical spectra matched well with the experimental ones, although the frequencies were ca. 10 cm−1 higher.

image file: c9sc05757a-f2.tif
Fig. 2 (A–C) THz-TDS spectra of (A) ZnTr, (B) CoTr, and (C) MnTr at 27 °C. The dotted lines are spectra obtained using DFT, applied to a 5 cm−1 FWHM Lorentzian-shaped line. The colors of the bars represent the types of motions of the PO4 tetrahedra: R mode (red), Ta and Tb mode (blue), and Tc mode (green). (D) A schematic illustration of each collective vibrational mode for the PO4 tetrahedra. The calculated eigenvectors of each normal mode for ZnTr are indicated by arrows. Shown are the PO4 translational mode along the a axis (upper left, Ta mode; 86.6 cm−1), PO4 translational mode along the b axis (upper right, Tb mode; 82.3 cm−1), PO4 translational mode along the c axis (lower left, Tc mode; 73.8 cm−1), and PO4 rotational mode (lower right, R mode; 68.5 cm−1). The color scheme is zinc = gray, phosphorous = yellow, oxygen = red, carbon = black, and nitrogen = blue. Hydrogens are omitted for clarity. (E) A schematic illustration of the Tb mode for the ZnTr periodic structure.

The optimized cell constants, which were used for DFPT, were found to be a few percent larger than the experimental ones (Table S2), and this overestimate was attributed to the anharmonicity of the lattice vibrations of the MOFs or the limits of the exchange-correlation treatment in DFT.13 The increase of the baseline in the experimental spectra indicated the occurrence of considerable absorption at higher frequencies. In contrast to the IR results, the shapes of the THz-TDS spectra differed for the different samples tested, which suggested different lattice vibrations or intermolecular vibrations. We assigned the motions of each of the peaks by analyzing the eigenvector of each of the normal modes. With regards to the motions of the PO4 tetrahedron in H2PO4, related to structural dynamics of the hydrogen bond network and H+ conduction, we found three types of such motions. The typical modes are illustrated in Fig. 2D. They are collective rotational (R; red bar), a- or b-directing translational (Ta or Tb; blue bar) and c-directing translational (Tc; green bar) modes, shown in Fig. 2A–C. The rotational mode represents each ion forming a PO4 tetrahedron moving in a rotating direction, and the translational mode represents each ion moving in the same direction parallel to the hydrogen-bond network for Ta,b, but perpendicular for Tc. In the ZnTr spectra, a large absorption band was observed at 70 to 80 cm−1 and consisted of two vibrational modes, which were assigned to Ta and Tb. The other bands were assigned to Tc and R. In the cases of CoTr and MnTr, vibrational modes of PO4 were composed of Tc and R, and importantly, Ta and Tb modes were not observed in this frequency region. Thus, ZnTr, which exhibited the highest H+ conductivity, showed all PO4 modes in the terahertz region where we measured, with this feature increasing the degrees of freedom for PO4, resulting in the formation of an imperfect hydrogen-bond network and enhancing the mobility of H+. We also acquired THz-TDS spectra at various temperatures (27 to 107 °C, Fig. S2) in order to investigate the dynamic disorder of the H2PO4 in the lattice. The dependence of full width at half-maximum (FWMH) with temperature is shown in the figure. The bands corresponding to PO4 modes of ZnTr broadened and became more sensitive to temperature than did those of CoTr, which indicated that the dynamic disorder of PO4 increased in ZnTr upon heating. This behavior was reported for other inorganic H+ conductors such as solid acids, CsHSeO4 and CsH2PO4, which undergo a phase transition to that displaying superionic conductivity.14 The bands of collective XO4 modes (X = Se, P) including those of translational and rotational motions have been reported to broaden considerably as a result of the transition into the superionic phase. The lattice modes Ta and Tb in ZnTr, not observed in CoTr and MnTr, were indicated to be accompanied by a large displacement of Zn2+ in the ab plane, and also by a large distortion of the O–Zn2+–O bond angle—leading to oscillations of hydrogen-bonded network layers composed of H2PO4 and Zn2+-TrH layers in opposite direction as shown in Fig. 2E.

To reveal the origin of the different lattice vibrations of the different MTr samples, we evaluated their metal–O bond characteristics using crystal-orbital Hamiltonian population (COHP) analysis.15 The COHP is a bond-weighted density of states between two adjacent atoms, and is calculated based on the corresponding Hamiltonian elements. It shows the number of states with which electrons participate in a covalent bond. Negative and positive COHP signs indicate, respectively, bonding and an anti-bonding states, and the absolute value of integrated COHP (ICOHP) indicates the covalent bond strength. Here, we determined the COHP absolute value of the single metal–O pair in each of the three samples to evaluate the covalency (Fig. 3A–C). In the Zn2+–O bond of ZnTr, the valence state was found to be significantly lower than the Fermi level. And the absolute value of ICOHP was calculated to be 3.19 × 10−4 eV, quite a bit lower than those of Co2+–O (2.46 eV) and Mn2+–O (9.43 × 10−1 eV) and hence indicating the highly ionic nature of the Zn2+–O interaction but covalent nature of the Co2+–O and Mn2+–O interactions. The valence states for CoTr and MnTr were determined to originate from the s, p and d orbitals of metal ions, with the states near the Fermi level in particular having strong d-character and being partially occupied.

image file: c9sc05757a-f3.tif
Fig. 3 Bond characteristics from ab initio calculations. The absolute values of COHP of single metal–O pairs for (A) ZnTr, (B) CoTr, and (C) MnTr. The Fermi level (EF) was set at zero energy. Total density (black) is shown together with the contributions from the s (red), p (blue), and d orbitals (green) of the metal ion.

These states were attributed to molecular orbitals with eg and t2g symmetries formed from interactions between d orbitals of Co2+ and Mn2+ split in octahedral crystal fields and π-donating H2PO4 ligand orbitals of the same symmetry. Thus, the covalent natures of the Co2+–O and Mn2+–O bonds were expected to suppress random mobility of the H2PO4 ligands. On the other hand, the energy levels of the fully occupied d orbitals of Zn2+ were indicated to be localized at about −3.5 eV and to not interact with ligand orbitals of neighboring oxygen atoms in H2PO4 (Fig. S3). The valence state of Zn2+ consisting mainly of s-orbital character with a1g symmetry indicated little orbital interaction between Zn2+ and H2PO4 and hence the Zn–O bond to be ionic. Owing to the isotropic nature of the ionic bond, Zn2+ could easily change its coordination geometry, and hence allow the large distortions in O–Zn2+–O bond angle as seen in Ta and Tb modes. In other words, the limited lattice vibrations in CoTr and MnTr in the terahertz energy region were expected to prevent the free hopping of H+ attributed to the structural relaxation, resulting in the high activation energies (over 1.0 eV). The combination of THz-TDS and COHP analyses revealed the unique and preferential H+ conductivity of ZnTr compared with those of CoTr and MnTr.


We applied terahertz time-domain spectroscopy (THz-TDS) to elucidate the origin of H+ conductivity in 2D MOFs in relation to their intrinsic lattice dynamics. H+ conductivity was concluded to be exclusively determined by the terahertz vibration modes in the 2D structures, and the vibration behaviors were concluded to depend on the connectivity of the coordination bonds of metal ions and ligands. COHP analysis suggested the ionic bonding character in the Zn2+-based framework to be key for achieving high H+ conduction, due to the ionic nature allowing the display of more isotropic vibration modes in the framework and hence facilitating efficient H+ hopping. This result, for the first time to the best of our knowledge, showed the lattice vibration of MOFs in the terahertz region to be strongly correlated with H+ conductivity. This result was also complementary with other characterizations including AC impedance spectroscopy in accounting for the origin of H+ conductivity in MOFs. Since we could modulate the unique vibration modes of MOFs, we expect the work described here to encourage the pursuit of further discoveries or structural optimizations of ion-conductive MOFs and other molecular framework materials.

Conflicts of interest

There are no conflicts to declare.


The work was supported by the Japan Society of the Promotion of Science (JSPS) for a Grant-in-Aid for Scientific Research (B) (JP18H02032) Challenging Research Exploratory (JP19K22200) from the Ministry of Education, Culture, Sports, Science and Technology, Japan, and Strategic International Collaborative Research Program (SICORP) and Adaptable and Seamless Technology Transfer Program through Target-driven R&D (A-STEP) from the Japan Science and Technology, Japan.

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Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc05757a

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