*4.2. Hydration and Dehydration Mechanism 4.75H Crystal*

DIC-Na AH sorbs water molecules and directly transforms into 4.75H, which does not include the 3.5H form. In contrast, DIC-Na 4.75H loses water and transforms first into 3.5H and then into AH. The difference between the hydration and dehydration behaviors can be explained based on the similarity of the crystal structures.

According to the DVS isotherm sorption plot (Figure 12, red), the DIC-Na AH form was stable in a humid environment up to 50% RH. However, it rapidly absorbed water to form DIC-Na 4.75H at 65% RH. The DIC-Na 3.5H form did not appear in the absorption process. This stoichiometric absorption behavior may be due to the large difference in the crystal structures between DIC-Na AH and 4.75H (Figure 6). In fact, the alternating layered structure of hydrophilic and hydrophobic regions in 3.5H and 4.75H forms was not observed in the AH form. Usually, a large hysteresis in the DVS isotherm plot (Figure 12) indicates a large difference in the crystalline structure. The AH form may be kinetically stable owing to such a difference that it did not rapidly change into hydrate phases. The hydration critical RH of 65% RH in the AH form exceeded the stable region of the 3.5H form (30 to 60% RH), which prevented the formation of 3.5H during the hydration of the AH form.

In the case of dehydration, the DVS isotherm desorption plot (Figure 12, blue) reveals that DIC-Na 4.75H was stable down to 65% RH. Then, it gradually released water and transitioned to 3.5H, which was stable between 65% and 30% RH. Below 30% RH, the 3.5H form rapidly when transformed to the AH form. The smooth dehydration from 4.75H to 3.5H can be explained by their similar crystal structure, with analogous hydrophilic/hydrophobic alternating layers (Figure 6). In the TG-DTA curve (Figure 11), which was recorded under flowing dry N<sup>2</sup> gas, a partial stoichiometric weight loss (5.32%) confirmed the presence of 3.5H at approximately 50 ◦C. Similarly, the simultaneous PXRD-DSC measurements (Figure 10) showed the first dehydration step to generate 3.5H, and a few 2*θ* diffraction peaks revealing the presence of 3.5H were observed at 14◦ , 29◦ , and 32◦ (indicated by pink markers in Figure 10). Together, these results suggested a mechanistic aspect of this transition, namely that it was not until the crystal lattice of 4.75H could no longer accommodate the void structures formed during dehydration in which another lattice emerged, which corresponded to that of 3.5H. In this manner, the reported "tetrahydrate" structure with the same cell dimensions as 4.75H [35] might arise from the partial decrease in the occupancies of water molecules.

The change in the crystal structure from 4.75H to 3.5H is illustrated in Figure 14. Out of the 19 water molecules in the unit cell of 4.75H, the five that do not interact with Na<sup>+</sup> were released during dehydration to form 3.5H (i.e., the ratio of water/DIC reduced from 19:4 (4.75) to 14:4 (3.5)). Thus, water molecules bonded to their surrounding molecules only through classical OH · · · O hydrogen bonds were preferentially lost by dehydration. This mechanism is consistent with the previous conjecture by Bartolomei et al. that some water molecules were tightly bound and immobile, while the others were highly mobile [36].

The release of five water molecules during the dehydration changed the coordination environment around Na<sup>+</sup> . The number of Na<sup>+</sup> · · · O interactions is summarized in Table 2 with other crystallographic indices. During dehydration from 4.75H to 3.5H, the number of Na<sup>+</sup> · · · O(water) interactions decreased, but new Na<sup>+</sup> · · · O(carboxylate) interactions formed to compensate for this decrease, thereby maintaining either five or six Na<sup>+</sup> · · · O(all) interactions per one Na<sup>+</sup> . This change in the Na<sup>+</sup> coordination environment implies that the coordination of Na<sup>+</sup> with O is flexible, allowing a smooth change in the coordinating atom from O(water) to O(carboxylate). In addition, a coordination number of 5 or 6 around Na<sup>+</sup> in 4.75H is commonly observed, and more than 6-coordination is undesirable owing to steric hindrance [44].

**Figure 14.** Structural changes during the dehydration from 4.75H to 3.5H. Non-bonded water molecules are represented by blue spheres. Hydrogen atoms are omitted. Figures were drawn with crystallographic a, b, c-axis marks.

During dehydration, the orientation of the DIC molecules changed. Both the 4.75H and 3.5H forms have hydrophobic DIC layer structures, but the directions of these layers differ. Specifically, the alternating layers in the crystal structure of 4.75H are oriented in the opposite direction (orange and light-green in Figure 14), whereas the layers in 3.5H are in the same direction (orange only). This change is highlighted by the yellow and light-blue molecules in Figure 14. During dehydration, the yellow molecule retained the same orientation in both structures, but the light blue one rotated. This rotation may have facilitated the breaking and formation of Na<sup>+</sup> · · · O (water or carboxylate) interactions associated with structural reconstruction.

A large rearrangement in the crystal structure of the AH form was observed below 30% RH. During this change, the hydrophilic/hydrophobic alternating-layer structure disappeared, and a one-dimensional chain structure of hydrophilic (Na<sup>+</sup> and O) formed along the b-axis (Figure 7). Although this change was large, O(carboxylate) atoms almost maintained the Na<sup>+</sup> coordination number at five. The packing indices (Table 2) were calculated using the PLATON program [40]. The packing index of 4.75H is slightly lower than that of 3.5H, possibly due to a small void space (ca. 5.9 Å<sup>3</sup> <sup>×</sup> 2), which would explain why the slightly unstable 4.75H starts to dehydrate to 3.5H, even in the high RH region. Meanwhile, compared with AH, the 3.5H form is more efficiently packed, utilizes a greater number of H-bonds, and has more water molecules filling spaces.


**Table 2.** Number of Na+–O interactions and packing indices.
