4.4.2. Roughness of Surfaces

To quantitatively describe the surface properties, a parameter *S* was introduced to evaluate the roughness of crystal surfaces:

$$S = \frac{A\_{\text{acc}}}{A\_{\text{box}}} \tag{7}$$

where *A*acc and *A*hkl represent the solvent-accessible area and surface area for the (h k l) crystal surface in the unit cell, respectively. A larger *S* means a rougher surface with larger adsorption areas for the solute and solvent molecules to interact with crystal surfaces. With the accessible areas of solvents calculated by the Connolly surface model (showed in blue in Figure 7), Table 4 lists the calculated *S* values of the crystal faces. Although the shapes of the solvent-accessible areas varied on each crystal face, they all had periodic fluctuations which could form grooves of more contact area with solute and solvent molecules. As shown in Table 4, the order of the roughness values for the six crystal faces was as follows: (1 0 1) > (0 1 1) > (0 0 2) > (1 1 0) > (1 1 −1) > (1 0 −1). The (1 0 −1) face with the smallest *S* value (1.23) provided the minimum areas for molecule incorporation, which meant it was probably difficult for solute and solvent molecules to adsorb on this face compared with the other faces. This was consistent with the relatively slow growth rate of the (1 0 −1) face, which led to a larger face area. Similarly, the (1 1 0) face grew more slowly than the (1 0 1) face and had a larger area proportion in methyl acetate. It is worth noting that the (0 0 2) faces with a moderate *S* value disappeared in all kinds of crystals grown from solvent systems, while the (1 0 1) faces with the largest *S* value remain at last. As can be seen from Table 3, the |*E*s| values of the (1 0 1) faces were larger than those of the (0 0 2) faces in all three solvents, which meant that the solvent molecules were more likely to adsorb on the (1 0 1) face compared to the (0 0 2) face, leading to a stronger solvent inhibition on the growth of the (1 0 1) face. As for the (0 0 2) face, less adsorbed solvent molecules provided possibilities for the continuous adsorption of the solute molecules, which indicated a fast growth rate.

**Figure 7.** Solvent-accessible areas (the blue grid) of the six important faces of the catechol crystal represented by the Connolly surface.


**Table 4.** The roughness values (S) of the dominant crystal faces of the catechol crystal.
