3.1 Description of PBAs

PBAs are coordination polymers obtained in aqueous solution from the substitution of the water molecules in [M(OH₂)₆]^k+ complexes by the isocyanide ligands from [M′(CN)₆]^j− complexes (where M and M′ are transition metal ions). The resulting MN≡CM′ linkages form a face-centered cubic lattice [17] that may exhibit vacancies in M′(CN)₆ units (Fig. 1). In the vicinity of these vacancies, water molecules are coordinated to the M cations. Additional alkali cations and zeolite water molecules can be inserted into the structure. The general formula of PBAs is A_xM₄[M′(CN)₆]_α□4−α·nH₂O (where A⁺ is an alkali cation and □ is a M′(CN)₆ vacancy; α = 4(k + (x/4))/j), called A_xMM′ in the following. Depending on the nature of the A, M and M′ cations, the formers are known to interact with the bimetallic network in some PBAs [13].

The assignment of the IR vibration bands of PBAs has been performed thanks to a series of cobalt–iron PBAs (A_xCoFe) where k = 2 and j = 3. The general formula of A_xCoFe is therefore given by A_xCo₄[Fe(CN)₆]_{(8+x)/4□(4−x)/3}·nH₂O. Thus, the stoichiometry of A_xCoFe is completely defined by the amount x of alkali cations inserted in the structure. The A_xCoFe PBAs can exhibit two different Co^II(HS)Fe^III(LS) and Co^III(LS)Fe^II(LS) (HS: high spin; LS: low spin) electronic states [18] (called Co^IIFe^III and Co^IIIFe^II in the following). However, as the amounts of cobalt and iron cations per unit cell are not the same, part of cobalt cations cannot undergo the Co^IIFe^III ↔ Co^IIIFe^II electronic transition. Consequently, the chemical formula of A_xCoFe PBAs can be rephrased as A_xCo^II₄[Fe^III(CN)₆]_{(8+x)/3□(4−x)/3}·nH₂O (in the Co^IIFe^III state) and A_xCo^III_(8+x)/3Co^II_(4−x)/3[Fe^II(CN)₆]_{(8+x)/3□(4−x)/3}·nH₂O (in the Co^IIIFe^II state), taking into account the small amount of residual Co^II cations in the Co^IIIFe^II state.

According to the chemical composition and the structure of PBAs, their IR spectrum is expected to exhibit the following vibration bands:

• • the ν{C≡N} vibration band, related to the cyanide bridges;
• • the ν{MN}, ν{MO} and ν{M′C} vibration bands, related to the metal-to-ligand bonds;
• • the ν{OH} vibration band, related to the water molecules of the system (both zeolite water molecules and water molecules bound to the M cations at the M′(CN)₆ vacancies).

3.2 Assignment of the ν{C≡N} vibration band

The ν{C≡N} vibration band is located in the 2100–2200-cm⁻¹ spectral range. As the cyanide bridge is extremely sensitive to its environment, including the oxidation state and the spin state of the M and M′ cations, the ν{C≡N} band has already been extensively used to characterize the electronic state of switchable PBAs [19]. In the case of the A_xCoFe PBAs, the ν{C≡N} vibration band exhibits a maximum located at 2120 cm⁻¹ in the Co^IIIFe^II state, characteristic of the cyanide bridge in the Co^IIIN≡CFe^II linkages [19,20]. In the Co^IIFe^III state, the maximum, located at 2160 cm⁻¹, is characteristic of the cyanide bridge in the Co^IIN≡CFe^III linkages [19,20]. The several minor contributions located between 2100 and 2120 cm⁻¹ have been assigned to residual Co^IIN≡CFe^II linkages, surface non-bridging cyanides or residual Co^IIIN≡CFe^II linkages [21]. The IR spectrum of the thermally switchable Na₂CoFe PBA [19,22] in both the Co^IIFe^III and Co^IIIFe^II states is shown in Fig. 2. While the ν{C≡N} band shall contain a tremendous amount of information concerning PBAs (presence of minority species, interaction between the alkali cations and the bimetallic network, etc.), hardly obtainable through other techniques, the superimposition of several contributions for this vibration band over a very small spectral range results in a mutual hindering of this information. Consequently, the metal-to-ligand vibrations bands were investigated in order to unravel these various contributions to the electronic properties of PBAs.

3.3 Assignment of the ν{ML} vibration bands

The assignment of the ν{ML} vibration bands has been performed based on the Co^IIFe^III ↔ Co^IIIFe^II thermally activated transition of Na₂CoFe [19,22] (Fig. 3). The IR spectrum of Na₂CoFe measured at different temperatures (200 K and 300 K) exhibits two pairs of vibration bands, coupled during the electronic transition, located respectively in the 150–350-cm⁻¹ and 400–600-cm⁻¹ spectral ranges. According to the literature dealing with the [M(NH₃)₆]^k+ (resp. [M′(CN)₆]^j−) complexes [23], the vibration bands in the 150–350-cm⁻¹ (resp. 400–600 cm⁻¹) spectral range have been assigned to the CoN (resp. FeC) bonds.

Based on the Co^IIFe^III electronic state of Na₂CoFe at T = 300 K, the band located at 220 cm⁻¹ has been assigned to the Co^IIN bonds and the one located at 430 cm⁻¹ has been assigned to the Fe^IIIC bonds. Similarly, based on the Co^IIIFe^II electronic state of Na₂CoFe at T = 200 K, the band located at 270 cm⁻¹ has been assigned to the Co^IIIN bond and the band located at 540 cm⁻¹ has been assigned to the Fe^IIC bond. Finally, the broad bands located in the 250–400 cm⁻¹ spectral range have been assigned to the Co^II/IIIO bonds, according to the literature dealing with the [M(OH₂)₆]^k+ complexes [23].

These assignments are in agreement with the vibration bands observed for the free [M′(CN)₆]^j− complex [23]; for instance, the displacement of the ν{Fe^IIC} vibration band from 585 cm⁻¹ in [Fe(CN)₆]⁴⁻ to 540 cm⁻¹ in the Co^IIIFe^II state of Na₂CoFe is consistent with the depletion of the electronic density on the Fe(CN)₆ entity due to the coordination of the isocyanide ligands to the cobalt cations [23].

3.4 Assignment of the ν{OH} vibration bands

The spectral range associated with the ν{OH} vibration band in PBAs comprises two distinct regions:

• • from 3000 to 3500 cm⁻¹, the IR spectrum exhibits very broad bands associated with water molecules involved in a hydrogen-bonded network;
• • from 3550 to 3700 cm⁻¹, the IR spectrum exhibits one or several very sharp bands associated with water molecules that are not involved in a hydrogen-bonded network.

The number of the sharp bands in the 3550–3700-cm⁻¹ spectral range may vary depending on the nature of the PBA (supplementary data). According to their position in energy, comprised between 3590 cm⁻¹ (water dimers [24]) and 3755 cm⁻¹ (isolated water molecules [25]), the bands located in the 3600–3700 cm⁻¹ range have been assigned to water molecules bound to metallic cations (either transition metal cations M or alkali cations A). This assignment can be further refined when considering the electronic transition of the Na₂CoFe PBA (Fig. 4).

Amongst the three vibration bands located in the 3600–3700-cm⁻¹ range in Na₂CoFe, the two located at a lower energy are evolving through the Co^IIFe^III ↔ Co^IIIFe^II electronic transition. Consequently, these two bands have been assigned to water molecules bound to the cobalt cations at the Fe(CN)₆ vacancies. Based on the Co^IIFe^III electronic state of Na₂CoFe at T = 300 K, the band located at 3645 cm⁻¹ has been assigned to the ν{OH} vibration of water molecules bound to Co^II cations; similarly, based on the Co^IIIFe^II electronic state of Na₂CoFe at T = 200 K, the band located at 3620 cm⁻¹ has been assigned to the ν{OH} vibration of water molecules bound to Co^III cations. This assignment is consistent with the water-to-bimetallic network partial charge transfer relying on the mostly σ character of the water-to-metal bond: in the Co^IIFe^III electronic state, the depletion of the electronic density on a water molecule bound to the Co^II cation is rather small, which results in a rather strong OH bond (ν{OH} = 3645 cm⁻¹); in the Co^IIIFe^II electronic state, the depletion of the electronic density on a water molecule bound to the Co^III cation is much more important, which results in a weaker OH bond (ν{OH} = 3620 cm⁻¹).

The higher energy band has been assigned to water molecules bound to alkali cations. The appearance and the intensity of this latter vibration band are highly sensitive to the nature and the amount of alkali cations per unit cell (supplementary data).

This assignment of the IR spectrum of PBAs over the whole 100–4000-cm⁻¹ spectral range allows the fine investigation of the structure of PBAs (presence of vacancies, position of the alkali cation in the lattice, etc.) and the alkali-cyanide interaction [13]. The following sections aim at demonstrating the relevance of the IR spectroscopy in the study of such properties of PBAs, which cannot be probed by other techniques.

3.5 Signatures of the M′(CN)₆ vacancies

In the Co^IIFe^III electronic state, the chemical formula of A_xCoFe PBAs can be rephrased as A_xCo^II₄[Fe^III(CN)₆]_{(8+x)/3□(4−x)/3}·nH₂O. Consequently, the mean composition of the coordination sphere of the Fe^III cations is always given by Fe^III(C≡NCo^II)₆, whatever the amount x of alkali cations inserted in the structure. A single type of ν{Fe^IIIC} vibration band, associated with the Co^IIN≡CFe^III linkages, is therefore expected for the A_xCoFe PBAs in the Co^IIFe^III electronic state.

The IR spectrum of the A_xCoFe PBAs in the Co^IIFe^III electronic state in the spectral range associated with the ν{Fe^IIIC} vibration band shows a single contribution, whichever the nature and the amount x of inserted alkali cations (Fig. 5). This observation is consistent with the expected single contribution to this band for the A_xCoFe PBAs in the Co^IIFe^III electronic state.

The situation is however very different for the Co^IIIFe^II electronic state: according to the A_xCo^III_(8+x)/3Co^II_(4−x)/3[Fe^II (CN)₆]_{(8+x)/3□(4−x)/3}·nH₂O chemical formula of the A_xCoFe PBAs in the Co^IIIFe^II state, each octahedral Fe^II cation exhibits a mean Fe^II(C≡NCo^III)_(8+x)/2(C≡NCo^II)_(4−x)/2 coordination sphere. While the presence of residual Co^II cations can be monitored by magnetic measurements, the subsequent Co^IIN≡CFe^II linkages are hardly measurable by IR spectroscopy in the ν{C≡N} spectral range due to:

• • the small amount of these Co^IIN≡CFe^II linkages in Co^IIIFe^II PBAs;
• • the superimposition of numerous contributions to the IR spectrum in the ν{C≡N} region.

In Na₂CoFe (x = 2), the mean coordination sphere of the iron cations depends on the electronic state of the system: in the Co^IIFe^III state, the mean coordination sphere of Fe^III is Fe^III(C≡NCo^II)₆, while in the Co^IIIFe^II state, the mean coordination sphere of Fe^II is Fe^II(C≡NCo^III)₅(C≡NCo^II)₁. In the Co^IIFe^III state, the IR spectrum of Na₂CoFe (Fig. 6a) exhibits a single symmetrical band (ν{Fe^IIIC} = 433 cm⁻¹); in the Co^IIIFe^II state, the IR spectrum of Na₂CoFe (Fig. 6b) exhibits a well-defined main contribution (ν{Fe^IIC} = 539 cm⁻¹) and a broad shoulder at higher energy. These observations are consistent with the anticipated coordination spheres for the iron cations: the single contribution to the ν{Fe^IIIC} vibration band can be assigned to the Fe^IIIC bond in Co^IIN≡CFe^III linkages; the two contributions to the ν{Fe^IIC} vibration band can be assigned to the Fe^IIC bonds in Co^IIIN≡CFe^II and Co^IIN≡CFe^II linkages. According to:

• • the relative intensity of the two contributions to the ν{Fe^IIC} vibration band;
• • the broadness of the contribution at higher energy, the main contribution has been assigned to the Fe^IIC in the majority Co^IIIN≡CFe^II linkages, while the higher energy contribution has been assigned to the Fe^IIC in the minority Co^IIN≡CFe^II linkages.

The broad width of the higher energy shoulder is consistent with the mismatch between the Co^IIN≡CFe^II linkage and the surrounding mostly Co^IIIFe^II environment, resulting in some structural disorder.

This study highlights the relevance of the IR spectroscopy in the investigation of the different CoN≡CFe linkages in A_xCoFe PBAs.

3.6 Study of the alkali–cyanide interaction

The existence of an interaction between the alkali cations and the bimetallic network has already been evidenced in some A_xCoFe PBAs [13]. This interaction, whose nature is still debated, may result in the modulation of the relative stability of the Co^IIFe^III and Co^IIIFe^II electronic states, as evidenced, for instance, in the A₂CoFe series: while the Rb₂CoFe and Cs₂CoFe PBAs always exhibit a Co^IIIFe^II ground state [26], Na₂CoFe shows a thermal transition between the Co^IIFe^III and Co^IIIFe^II states around T = 250 K [19,22]. According to the nucleophilic nature of the cyanide bridge, the interaction between the alkali cations and the bimetallic network is expected to involve the electron-rich bridging cyanide ligands. However, no direct signature of this interaction has been, to date, proposed in the literature.

In the A₂CoFe series of PBAs, all the compounds exhibit the same {Co₄[Fe(CN)₆]_3.3□0.7(OH₂)₄} bimetallic network. In the Co^IIIFe^II state, the cobalt cations of these PBAs share a common Co^III(N≡CFe^II)₅(OH₂)₁ mean coordination sphere. The IR spectra of Rb₂CoFe and Cs₂CoFe in the Co^IIIFe^II state (Fig. 7) exhibit a single contribution to the ν{Co^IIIN} vibration band, which has therefore been assigned to the Co^IIIN in the Co^IIIN≡CFe^II linkages. However, the IR spectrum of Na₂CoFe in the Co^IIIFe^II state (Fig. 7) shows two distinct contributions for the ν{Co^IIIN} vibration band. The nature of the alkali cation being the sole difference between these A₂CoFe PBAs, this splitting of the ν{Co^IIIN} vibration band is therefore due to the different interactions between the alkali cations and the bimetallic network.

The presence of two contributions for the ν{Co^IIIN} vibration band in Na₂CoFe reveals two chemically non-equivalent Co^IIIN bonds, which have been assigned to Co^IIIN≡CFe^II linkages interacting and non-interacting with an alkali cation [11]. Thus, the difference in energy between these two contributions is a probe of the strength of the alkali–cyanide interaction.

This assignment can be further confirmed by considering the Cs_xCoFe series of PBAs. In the case of large alkali cations standing at the center of the octants of the lattice (Fig. 1), each alkali cation can interact with a maximum of 12 cyanide bridges. In a given A_xCoFe series, each unit cell comprises 2 × (8 + x) cyanide bridges; therefore a maximum of 2x × (8 + x) cyanide bridges per unit cell are interacting with an alkali cation. Consequently, if x ≥ 1, each cyanide bridge is interacting with an alkali cation, and the resulting ν{CoN} vibration band should exhibit a single contribution. On the contrary, in the case of A_xCoFe PBAs with low amounts of alkali cations per unit cell (x < 1), two contributions are expected for the ν{CoN} vibration band, one corresponding to the CoN in CoN≡CFe linkages that are not interacting with an alkali cation, and the other corresponding to CoN≡CFe linkages interacting with an alkali cation. Such assumption can be confirmed in the Cs_xCoFe series: while the Cs_0.7CoFe PBA (x < 1) shows a splitting of the ν{Co^IIN} vibration band in the Co^IIFe^III electronic state (Fig. 8), no splitting of the ν{Co^IIIN} vibration band is observed in the Co^IIIFe^II electronic state of Cs₂CoFe (x ≥ 1) (Fig. 7). Furthermore, no splitting of the ν{Co^IIN} vibration band is observed in the case of the alkali-free K₀CoFe PBA (Fig. 8).

3.7 Positioning of the alkali cation

IR study of the alkali-cyanide interaction taking place in A_xCoFe PBAs can also bring some insight into the much debated question of the position of the alkali cation in the lattice. While the initial description of PBAs locates the alkali cations at the center of the octants of the lattice [17], recent studies tend to question this positioning [11,27]. Indeed, according to the distance between the center of the octants and the cyanide bridges, this positioning seems unsuitable for smaller alkali cations. Consequently, in the case of small alkali cations, a splitting of the ν{CoN} vibration band is anticipated even for A_xCoFe PBAs with an important amount of alkali cations per unit cell. Experimentally, two distinct contributions to the ν{CoN} vibration band are observed for the Na₂CoFe PBA, for which both the ν{Co^IIN} vibration band (in the Co^IIFe^III electronic state; Fig. 8) and the ν{Co^IIIN} vibration band (in the Co^IIIFe^II electronic state; Fig. 7), corresponding to the CoN bonds implied either in the CoN≡CFe linkages interacting with an alkali cation, or in the CoN≡CFe linkages that are not interacting with an alkali cation. This splitting of the ν{CoN} vibration band in Na₂CoFe indicates that the sodium cation does not stand at the center of the octants of the lattice. Such results demonstrate that IR spectroscopy can bring new insights into the intimate structure of PBAs, as such information cannot be inferred from standard X-ray diffraction studies of PBAs containing small, disordered alkali cations. Further refinement of the position(s) of the alkali cations in the unit cell of PBAs and highlighting of possible displacements of the alkali cations in the unit cell are in progress.

Finally, the impact of the interaction between the alkali cation and the bimetallic network on the metal–ligand bonds can also be pointed out in the Cs₂CoFe PBA: while no splitting of the ν{Co^IIIN} vibration band is observed for this system in the Co^IIIFe^II state (Fig. 7), a broadening of the contributions to the ν{Fe^IIC} vibration band is evidenced. This broadening reveals a perturbation of the Fe(CN)₆ units due to the presence of the large cesium cations, with respect to smaller ones (as rubidium cations; Fig. 9).

This last series of examples highlights the suitability of IR spectroscopy to the fine investigation of the weak interactions between the alkali cation and the bimetallic network in PBAs, hardly detectable at the macroscopic scale, taking place in PBAs.