4.4.4. Solvent Effects on Crystal Aspect Ratios

Discussions on energies and surface structures on solvent–crystal interfaces have pointed out some reasons for changes in crystal morphology. Apart from these factors, interaction types, especially hydrogen bonds, are worth discussing in our case since catechol and the three kinds of solvent molecules possess hydrogen and oxygen atoms to form hydrogen bonds.

The existence of hydrogen bonds is a significant factor affecting the types and the strength of the interactions on solvent–crystal interfaces, which play a vital role in crystal morphology [49]. Therefore, the radial distribution function (RDF), *g(r)*, was applied to explore the interactions on the

solvent–crystal interfaces, which described how atom density varied as a function of the distance from the specified hydrogen or oxygen atom [50].

In general, hydrogen bonds and van der Waals interactions belong to short-range interactions whose effective intermolecular range is under 5.0 Å. The effective range of hydrogen bonds is usually defined to be within 3.1 Å, while the range for van der Waals interaction is between 3.1 Å to 5.0 Å [51]. Interactions that are effective above 5.0 Å are called long-range interactions and usually refer to electrostatic interactions [37]. As mentioned above, the aspect ratio was defined as the length along the (1 0 −1) face divided by the width along the (1 0 1) face. From Figure 4 we can conclude that the crystal length along the (1 0 −1) face was decided by the growth of the (1 0 1) face, while the crystal width along the (1 0 1) face is mainly related to the growth of the (1 1 −1) face. So here we took the examples of the RDF on the (1 0 1) face and the (1 1 −1) face in all three solvents in order to find the solvent effects on crystal aspect ratios, with the outermost layer of each face analyzed because of its proximity to solvent molecules. As shown in Figure 8, the positions of the first sharp peaks in red were all in the range of 1.70–2.00 Å, indicating that the oxygen atoms of the solvent molecules formed a strong hydrogen bond with the hydrogen atoms of the catechol molecules on the (1 0 1) face and the (1 1 −1) face. Therefore, the crystal face growth was inhibited by the solvent molecules adsorbed around the crystal surface. With different positions and strengths of the peaks, the inhibition resulted in diverse effects on the crystal face growth, which could be analyzed by the aspect ratios and face areas in final crystal habits. In particular, as shown in Figure 8a, with larger numbers of sharper peaks (*r* = 1.71, 2.49 and 2.87 Å), the (1 0 1) face grew at a slower rate due to the stronger solvent inhibition in isopropanol compared to those in methyl acetate and ethyl acetate, leading to a shorter crystal length compared with those in the other two solvents. In other words, compared to that in isopropanol, the crystal morphology turns longer as a hexagonal tabular shape in ethyl acetate with the relatively weaker hydrogen bonds on the (1 0 1) face. The results were consistent with the *R'*hkl values of (1 0 1) faces in Table 3 which indicated the relative growth rates (1.40 and 19.65 in isopropanol and ethyl acetate, respectively). In addition, the crystal in methyl acetate had a fusiform-like morphology with the existence of the (1 1 0) face (the RDF curve shown in Supplementary Materials Figure S2). It is remarkable that the RDF curves of the (1 1 0) face and the (1 0 1) face showed great similarity in methyl acetate, but the (1 1 0)face was larger than the (1 0 1) face in the final morphology. Thus, the catechol crystal habit in methyl acetate was mainly related to the surface structure and the attachment energy of the crystal faces.

The similar RDF curves of the (1 1 −1) faces in methyl acetate and ethyl acetate showed the same numbers of peaks, but the peaks (*r* = 1.81 Å) in ethyl acetate appeared earlier compared to those in methyl acetate, which indicates the stronger inhibition of the (1 1 −1) face in ethyl acetate. The results corresponded with the *R'*hkl values of the (1 1 −1) faces in Table 3 (3.42 and 3.75 in ethyl acetate and methyl acetate, respectively). The relatively slow growth of the (1 1 −1) face led to a shorter crystal width in the final morphology, increasing the aspect ratio of catechol crystal in ethyl acetate indirectly. Therefore, the crystals tended to be longer in ethyl acetate than those in methyl acetate, which supports the conclusion that the crystal aspect ratio was mainly dependent on the growth of the (1 0 1) and (1 1 −1) faces. Apart from the peaks within 3.1 Å, several peaks appeared in the range of 3.1–5.0 Å and above 5.0 Å in all the RDF curves, indicating the existence of strong van der Waals and electrostatic interactions between the selected atoms.

Above all, it can be concluded that the differences in the aspect ratio of the catechol crystals were attributed to distinct growth inhibition effects of the three solvents mainly on the (1 0 1) and (1 1 −1) faces. Strong hydrogen bonds exist between the hydrogen atoms of catechol and the oxygen atoms of solvents in the three solvents, which becomes a non-negligible factor in catechol morphology, especially the crystal aspect ratio.

**Figure 8.** The radial distribution function (RDF) analysis between catechol and (**a**) isopropanol, (**b**) methyl acetate, (**c**) ethyl acetate molecules on the (1 0 1) face (left) and the (1 1 −1) face (right).
