Hierarchical Structure of Glucosamine Hydrochloride Crystals in Antisolvent Crystallization

: The crystal morphology of glucosamine hydrochloride (GAH) during antisolvent crystallization was investigated in this work. Particles of different shapes, such as plate-like crystals, leaﬂike clusters, fan-like dendrites, ﬂower-like aggregates, and spherulites, were produced by tuning the type of antisolvents and crystallization operating conditions. The hierarchical structures of GAH crystals tended to be formed in a water + isopropanol mixture. The effects of operation parameters on the polycrystalline morphology were studied, including crystallization temperature, solute concentration, feeding rate of GAH aqueous solution, solvent-to-antisolvent mass ratio, and stirring rate. The evolution process of GAH spherulites was monitored using SEM, indicating a crystallographic branching mode. The crystal habit was predicted to identify the dominant faces. Molecular dynamics simulations were performed and the interaction energy of solute or solvent molecules on crystal surfaces was calculated. The experimental and simulation studies help to understand the branching mechanism and design a desired particle morphology.


Introduction
Hierarchical structures are common in the biomineralization process, which are organized by nanostructured building blocks [1,2]. Seashells, corals, nacre, and eggshells are typical examples that have three-dimensional complex structures consisting of highly ordered nanocrystals [3,4]. These materials possess enhanced mechanical properties [3]. Motivated by exploring unique properties, research from a wide range of fields has been focused on the synthesis of hierarchical structures [5][6][7]. For instance, by combusting inorganic powder mixtures, AIN three-dimensional structures with diverse morphology have been demonstrated: from wildflower-like patterned crystals to multilayer hierarchical structures [5]. The micro/nano-spherulitic hierarchical 2,2 ,4,4 ,6,6 -hexanitrostilbene has been fabricated, which is promising to solve the problems of nanoscale energetic materials in agglomeration and microscale bulk crystals in low activity [6]. Materials with hierarchical structures could find broad applications in batteries [8], ceramics [9,10], catalysis [11,12], sensors [13,14], the food industry [15], pharmaceutics [16], etc. For example, when the flower-like SnO 2 nanocrystal was used as the photoanode in dye-sensitized solar cells, the photoelectric conversion efficiency could be largely enhanced [8]. Flower-like MgO crystals growing in the face of the ceramics create photoluminescence of Mg-cBN ceramics [9]. Photonic crystals with biological hierarchical structures show tunable optical properties by external stimuli [17]. By controlling the crystal phase structure of WO 3 hierarchical spheres, the gas sensing performance is enhanced significantly [14]. There are also growing reports about hierarchical structures of organic or pharmaceutical crystals [18][19][20]. It has been reported that spherical calcium citrate could be prepared via controllable reactive

Antisolvent Crystallization Experiments
The raw GAH was dissolved in water to prepare GAH solution at a certain concentration. Antisolvent crystallization was carried out by introducing aqueous solution of GAH into organic solvent, which was preloaded in a 150 mL jacketed crystallizer. The solutions were kept at a constant temperature by using a water circulation bath (Ministat 230, Huber, Berching, Germany). The feeding rate of GAH solution was controlled by a peristaltic pump. After agitating for another 30 min, the suspensions were filtered, washed, and dried in a vacuum oven at 40 • C. The effects of solvent, temperature, solute concentration, feeding rate, of solvent (water)-to-antisolvent (organic solvent) mass ratio, and stirring rate on the morphology of GAH crystals were investigated. Details about the crystallization conditions are listed in Table 1.

Characterization
Polarized optical microscopy (POM, Olympus BX53M, Olympus Corporation, Tokyo, Japan) and scanning electron microscopy (SEM, SUPRA™ 55, Hitachi Ltd., Tokyo, Japan) were used to characterize the particle morphology. The evolution of GAH hierarchical structures during antisolvent crystallization (E16 Table 1) was also ex situ monitored, where time-controlled samples were observed using SEM. The crystal form was identified by powder X-ray diffraction (XRD, Miniflex 600, Rigaku Corporation, Tokyo, Japan) using Cu Kα radiation (λ = 0.1541 nm). It was operated at 40 kV and 30 mA. The PXRD patterns were collected in a 2θ range from 5 • to 50 • with a step size of 0.02 • at a scanning speed of 8 • min −1 .

Molecular Simulations
The GAH crystal has a space group of P2 1 and Z = 2 in the unit cell (a = 7.147 Å, b = 9.214 Å, c = 7.765 Å, and β = 112.88 • ) [39]. Materials Studio software was applied for molecular simulation using the COMPASS force field [40,41]. The crystal morphology of GAH in a vacuum was simulated using the Bravais-Friedel-Donnay-Harker (BFDH) model, which uses the crystal lattice and symmetry to generate a list of possible growth faces [42]. Molecular dynamics (MD) simulations were carried out to study the interactions between the crystalline plane of GAH and the solution layer. To build a crystal surface of GAH exposed to a solution, the unit cell was cleaved according to the Miller indices and then extended to a supercell. The bulk solution was constructed containing 200 water molecules, 300 isopropanol molecules, and a certain number of solutes. The supersaturation of the solution was set to be 20 and the solute concentration was calculated based on the solubility of GAH in water-isopropanol mixtures at 298.15 K [35]. The solution layer was added to the top of the crystal surface, and a 50 Å vacuum slab was also included in the simulation box. A motion constraint was applied to the crystal surface and the whole simulation system was geometrically optimized. MD simulations were performed for 1000 ps in the NVT ensemble at 298.15 K using a Nose thermostat. The electrostatic interactions were calculated using the Ewald summation method and the van der Waals forces were calculated using the atom-based method. The cutoff radius was set to be 15.5 Å and the time step was 1 fs. The interaction energies between the crystalline surface and solvent or solute in the equilibrium system were calculated using the following expressions: where E surface is the energy of the crystal face, E solvent is the energy of the mixed solvent of water and isopropanol, and E solute is the energy of the solute GAH. E total(surface-solvent) represents the total potential energy in the simulation box removed from solute. E total(surface-solute) represents the total potential energy in the simulation box removed from solvent molecules.

Crystal Form and Morphology of GAH in Different Solvents
Antisolvent crystallization is carried out in aqueous solution mixed with different organic solvents (Table 1 E1-E6). Microscope images of GAH crystals are shown in Figure 1. The crystals grown in water + methanol and water + ter-butanol mixed solvents present a hexagonal plate-like morphology. In water + ethanol mixtures, GAH crystals grow in a pentagonal shape, exhibiting asymmetric growth. Interestingly, dendritic spherulites form when isopropanol is used as the antisolvent. When n-propanol or butanol is used as the antisolvent, irregular aggregates are obtained.
XRD measurements are employed to identify the crystal form of GAH. Figure 2 displays XRD spectra of the GAH single crystal [39], raw materials, and crystals grown from antisolvent crystallization in three binary solvent mixtures. The XRD patterns nicely match with the calculated pattern based on the single crystal structure, indicating the same crystal form. But the peak intensities of GAH samples are different due to the differences in crystal shape and size. For example, in water + methanol, ethanol, isopropanol, or tert-butanol, the most intense band is located at 12.4 • , which is assigned to the (001) face of the GAH crystal. In water + ethanol and water + isopropanol systems, the peak intensity at 25.2 • becomes low, leaving the peak at 24.9 • more prominent. They are related to the  and (20-1) faces, respectively. The observed reduction in signals is possibly due to the crystal orientation effect [43]. XRD measurements are employed to identify the crystal form of GAH. Figure 2 plays XRD spectra of the GAH single crystal [39], raw materials, and crystals grown fr antisolvent crystallization in three binary solvent mixtures. The XRD patterns nic match with the calculated pattern based on the single crystal structure, indicating same crystal form. But the peak intensities of GAH samples are different due to the ferences in crystal shape and size. For example, in water + methanol, ethanol, isopropa or tert-butanol, the most intense band is located at 12.4°, which is assigned to the (0 face of the GAH crystal. In water + ethanol and water + isopropanol systems, the p intensity at 25.2° becomes low, leaving the peak at 24.9° more prominent. They are rela to the  and (20-1) faces, respectively. The observed reduction in signals is possi due to the crystal orientation effect [43]. Figure 2. (a) XRD patterns of GAH single crystal, raw material, and GAH crystallized in wat methanol, water+ ethanol and water + isopropanol; (b) GAH crystals obtained from water + npanol, water + butanol and water + tert-butanol.  XRD measurements are employed to identify the crystal form of GAH. Figure 2 d plays XRD spectra of the GAH single crystal [39], raw materials, and crystals grown fro antisolvent crystallization in three binary solvent mixtures. The XRD patterns nice match with the calculated pattern based on the single crystal structure, indicating t same crystal form. But the peak intensities of GAH samples are different due to the d ferences in crystal shape and size. For example, in water + methanol, ethanol, isopropan or tert-butanol, the most intense band is located at 12.4°, which is assigned to the (00 face of the GAH crystal. In water + ethanol and water + isopropanol systems, the pe intensity at 25.2° becomes low, leaving the peak at 24.9° more prominent. They are relat to the (11-2) and (20-1) faces, respectively. The observed reduction in signals is possib due to the crystal orientation effect [43]. (a) XRD patterns of GAH single crystal, raw material, and GAH crystallized in wate methanol, water+ ethanol and water + isopropanol; (b) GAH crystals obtained from water + n-p panol, water + butanol and water + tert-butanol.

Temperature
To explore the branching behavior of GAH crystals in the water + isopropanol sy tem, the effects of operation conditions are investigated. Crystallizations at different tem peratures varying from 278.15 K to 318.15 K containing saturated GAH in aqueous sol tions are firstly carried out (Table 1 E7-E10). The optical microscopy images show th Figure 2. (a) XRD patterns of GAH single crystal, raw material, and GAH crystallized in water + methanol, water+ ethanol and water + isopropanol; (b) GAH crystals obtained from water + n-propanol, water + butanol and water + tert-butanol.

Temperature
To explore the branching behavior of GAH crystals in the water + isopropanol system, the effects of operation conditions are investigated. Crystallizations at different temperatures varying from 278.15 K to 318.15 K containing saturated GAH in aqueous solutions are firstly carried out (Table 1 E7-E10). The optical microscopy images show that lower temperatures yield particles of flower-like morphology densely assembled by flaky crystals (Figure 3a,b). Spheres are formed at the initial stage of antisolvent crystallization, indicating that high supersaturation could promote the aggregation of nuclei. As the temperature increases, the size of subindividuals increases, but the number of branches reduces (Figure 3c). At 318.15 K, most particles are plate-like crystals ( Figure 3d). Hence, branching of the crystal subunits is more favored at low temperature. Increased temperature would decrease solution viscosity and then weaken the agglomeration of platelet crystals [44].
Moreover, the thermal motion of molecules and mass transfer would be accelerated [15]. Crystal growth becomes more dominated at higher temperature, leading to the formation of larger monodisperse crystals. perature increases, the size of subindividuals increases, but the number of branches duces (Figure 3c). At 318.15 K, most particles are plate-like crystals (Figure 3d). Hen branching of the crystal subunits is more favored at low temperature. Increased tempe ture would decrease solution viscosity and then weaken the agglomeration of plat crystals [44]. Moreover, the thermal motion of molecules and mass transfer would be celerated [15]. Crystal growth becomes more dominated at higher temperature, leading the formation of larger monodisperse crystals.

GAH Concentration
To investigate the effect of solute concentration in an aqueous solution on cry morphology, GAH concentrations from 0.07 to 0.40 g/g H2O are used at 278.15 K (Tab E11-E15). POM graphs of these crystals are presented in Figure 4. Upon the addition GAH aqueous solution at low concentration (0.07 g/g H2O), clusters of plates are observ which might be formed via surface nucleation and oriented crystal growth (Figure Subunits are nucleated on the most dominant face of the plate-like crystals and th growth direction is similar to the mother crystal. It is reported that the most domin crystal growth direction is also the most energetically favorable [43]. The orientation eff could be affected by the solution composition, polarity, and charge density of substra and the intermolecular interaction energy between the solute and surface [45][46][47]. At 0 g/g H2O, crystals present a dendritic morphology (Figure 4b). At larger GAH concen tions, the branches increase and the dendrites become more compact (Figure 4c,d). As GAH concentration increases to 0.40 g/g H2O, spherulites are produced (Figure 4e). A h crystallization driving force is a necessary condition for spherulites [48]. Therefore, wit the experimental concentration range, a more concentrated GAH solution that crea

GAH Concentration
To investigate the effect of solute concentration in an aqueous solution on crystal morphology, GAH concentrations from 0.07 to 0.40 g/g H 2 O are used at 278.15 K (Table 1 E11-E15). POM graphs of these crystals are presented in Figure 4. Upon the addition of GAH aqueous solution at low concentration (0.07 g/g H 2 O), clusters of plates are observed, which might be formed via surface nucleation and oriented crystal growth (Figure 4a). Subunits are nucleated on the most dominant face of the plate-like crystals and their growth direction is similar to the mother crystal. It is reported that the most dominant crystal growth direction is also the most energetically favorable [43]. The orientation effect could be affected by the solution composition, polarity, and charge density of substrates, and the intermolecular interaction energy between the solute and surface [45][46][47]. At 0.14 g/g H 2 O, crystals present a dendritic morphology (Figure 4b). At larger GAH concentrations, the branches increase and the dendrites become more compact (Figure 4c,d). As the GAH concentration increases to 0.40 g/g H 2 O, spherulites are produced (Figure 4e). A high crystallization driving force is a necessary condition for spherulites [48]. Therefore, within the experimental concentration range, a more concentrated GAH solution that creates larger supersaturation promotes heterogenous nucleation and facilitates the formation of spherulites [32].

Feeding Rate
The feeding rate of GAH aqueous solution varies from 0.05 g/min to 2.0 g/min, while other crystallization conditions are the same (Table 1 E16-E20). Figure 5 presents POM micrographs of GAH particles precipitated at different feeding rates. It can be seen that more developed spherulites are formed at lower feeding rates (Figure 5a,b). This condition provides a longer crystallization time for fabricating hierarchical structures. The lamellar bunches spread out, resulting in a curved structure as well as spherulites with hollow cores. When the feeding rate increases to 0.5 g/min, the spherulites become more open, which contain more free space between individual crystallites (Figure 5c). At faster feeding rates like 1.0 g/min and 2.0 g/min, most polycrystalline aggregates present a fan-like shape (Figure 5d,e). A possible reason is that rapid feeding results in a more extensive nucleation in bulk solution, leaving less supersaturation consumed by surface nucleation [44]. To study the influence of the solvent-to-antisolvent mass ratio on the hierarchical

Feeding Rate
The feeding rate of GAH aqueous solution varies from 0.05 g/min to 2.0 g/min, while other crystallization conditions are the same (Table 1 E16-E20). Figure 5 presents POM micrographs of GAH particles precipitated at different feeding rates. It can be seen that more developed spherulites are formed at lower feeding rates (Figure 5a,b). This condition provides a longer crystallization time for fabricating hierarchical structures. The lamellar bunches spread out, resulting in a curved structure as well as spherulites with hollow cores. When the feeding rate increases to 0.5 g/min, the spherulites become more open, which contain more free space between individual crystallites (Figure 5c). At faster feeding rates like 1.0 g/min and 2.0 g/min, most polycrystalline aggregates present a fan-like shape (Figure 5d,e). A possible reason is that rapid feeding results in a more extensive nucleation in bulk solution, leaving less supersaturation consumed by surface nucleation [44].

Feeding Rate
The feeding rate of GAH aqueous solution varies from 0.05 g/min to 2.0 g/min, while other crystallization conditions are the same (Table 1 E16-E20). Figure 5 presents POM micrographs of GAH particles precipitated at different feeding rates. It can be seen tha more developed spherulites are formed at lower feeding rates (Figure 5a,b). This condition provides a longer crystallization time for fabricating hierarchical structures. The lamellar bunches spread out, resulting in a curved structure as well as spherulites with hollow cores. When the feeding rate increases to 0.5 g/min, the spherulites become more open which contain more free space between individual crystallites (Figure 5c). At faster feed ing rates like 1.0 g/min and 2.0 g/min, most polycrystalline aggregates present a fan-like shape (Figure 5d,e). A possible reason is that rapid feeding results in a more extensive nucleation in bulk solution, leaving less supersaturation consumed by surface nucleation [44].

Solvent-to-Antisolvent Mass Ratio
To study the influence of the solvent-to-antisolvent mass ratio on the hierarchica structure, crystallization experiments E21-E25 (Table 1) are performed. At a mass ratio o 1:2, most particles are crystallized in a leaf-like morphology (Figure 6a). As the ratio

Solvent-to-Antisolvent Mass Ratio
To study the influence of the solvent-to-antisolvent mass ratio on the hierarchical structure, crystallization experiments E21-E25 (Table 1) are performed. At a mass ratio of 1:2, most particles are crystallized in a leaf-like morphology ( Figure 6a). As the ratio reduces to 1:3 or 1:7, branching is enhanced and the dendrites develop along multiple directions (Figure 6b,c). This might be the result of the higher supersaturation created by the increased mass fraction of the antisolvent, when the same amount of GAH aqueous solution is added. In this way, flowerlike and asterisk-like structures are formed. When the solvent-to-antisolvent mass ratio decreases to 1:20 and 1:50, the spherulites are still undeveloped and the subunits become smaller, exhibiting a needle-like shape (Figure 6d,e). Therefore, further increased supersaturation produces an excessive crystal nucleus, and the growth of subunits will slow. tals 2023, 13, x FOR PEER REVIEW 8 of reduces to 1:3 or 1:7, branching is enhanced and the dendrites develop along multi directions (Figure 6b,c). This might be the result of the higher supersaturation created the increased mass fraction of the antisolvent, when the same amount of GAH aqueo solution is added. In this way, flowerlike and asterisk-like structures are formed. Wh the solvent-to-antisolvent mass ratio decreases to 1:20 and 1:50, the spherulites are s undeveloped and the subunits become smaller, exhibiting a needle-like shape (Figu 6d,e). Therefore, further increased supersaturation produces an excessive crystal nucle and the growth of subunits will slow.

Stirring Rate
The stirring rate is one of the most important factors affecting solution mixing, n cleation, and collisions of particles [49]. Fast stirring creates a high shear rate and accel ates the movement of the fluid, increasing the possibility of collision among the crysta crystallizer, and mixing propeller [50]. In general, a higher stirring rate will induce crys breakage and inhibit the agglomeration of particles [51], whereas a dendritic morpholo tends to form in a static environment, where crystal growth is limited by diffusion a the growth condition is far from equilibrium [27]. It is essential to study the effect of s ring rate on the morphology of polycrystalline aggregates. Therefore, crystallizations different stirring rates are performed, changing from 100 rpm to 800 rpm (Table 1 E2 E31). Figure 7 illustrates the POM micrographs of these crystals. At a lower stirring r (100 rpm and 200 rpm), fan-like dendrites composed of diamond-shaped platelets are p duced (Figure 7a,b). As the stirring rate increases, the dendrites become more ramifi (Figure 7c,d). When the stirring rate rises to 600 rpm or 800 rpm, spherulites are dev oped, and the size of both spherulites and subindividuals becomes smaller (Figure 7e In this case, the branching mechanism of GAH crystals is not diffusion-limited aggreg tion [26,30]. Fast agitation that enhances particle collision might cause more crystal d fects, inducing more extensive surface nucleation. Under the experimental conditions higher stirring rate could facilitate heterogeneous nucleation and branching.

Stirring Rate
The stirring rate is one of the most important factors affecting solution mixing, nucleation, and collisions of particles [49]. Fast stirring creates a high shear rate and accelerates the movement of the fluid, increasing the possibility of collision among the crystals, crystallizer, and mixing propeller [50]. In general, a higher stirring rate will induce crystal breakage and inhibit the agglomeration of particles [51], whereas a dendritic morphology tends to form in a static environment, where crystal growth is limited by diffusion and the growth condition is far from equilibrium [27]. It is essential to study the effect of stirring rate on the morphology of polycrystalline aggregates. Therefore, crystallizations at different stirring rates are performed, changing from 100 rpm to 800 rpm (Table 1 E26-E31). Figure 7 illustrates the POM micrographs of these crystals. At a lower stirring rate (100 rpm and 200 rpm), fan-like dendrites composed of diamond-shaped platelets are produced (Figure 7a,b). As the stirring rate increases, the dendrites become more ramified (Figure 7c,d). When the stirring rate rises to 600 rpm or 800 rpm, spherulites are developed, and the size of both spherulites and subindividuals becomes smaller (Figure 7e,f). In this case, the branching mechanism of GAH crystals is not diffusion-limited aggregation [26,30]. Fast agitation that enhances particle collision might cause more crystal defects, inducing more extensive surface nucleation. Under the experimental conditions, a higher stirring rate could facilitate heterogeneous nucleation and branching.

Morphological Evolution of GAH Spherulites
To explore the formation mechanism of GAH spherulites, the evolution of polycr talline particles in the antisolvent crystallization process is ex situ monitored using SE (Figure 8). Originating from a hexagonal plate-like crystal, there are lamellae nucleati on the surface of the parent crystal and growing in similar directions (Figure 8a,b). T shape of the lamellae seems asymmetric and is similar to pentagonal. Two sides of trunk are nucleated, forming dendritic crystals (Figure 8c). Branching on the existing mellae with small misorientation angles generates a fan-like morphology (Figure 8d). the lamellae fan out, flower-like crystals with curved structure can be observed (Figu 8e). Intermittent branching of the fans leads to spherulites with holes, and complete sph ulites can be formed when the spaces are filled by lamellae (Figure 8f). This behavior small-angle branching matches the mode of noncrystallographic branching, which is d tinct from crystallographic branching in dendritic snow crystals or diffusion-limited gregation in fractal-like forms [48]. The subunits of polycrystalline aggregates often gr radially via noncrystallographic branching, resulting in three-dimensional spheres [5 In our case, the final evolved particles of GAH looks like a circular layer without bran ing along another axis. The reason might be that the largest face of the plate-like crys overwhelmingly dominates the crystallization, which imposes a strong orientation eff [45].

Morphological Evolution of GAH Spherulites
To explore the formation mechanism of GAH spherulites, the evolution of polycrystalline particles in the antisolvent crystallization process is ex situ monitored using SEM (Figure 8). Originating from a hexagonal plate-like crystal, there are lamellae nucleating on the surface of the parent crystal and growing in similar directions (Figure 8a,b). The shape of the lamellae seems asymmetric and is similar to pentagonal. Two sides of the trunk are nucleated, forming dendritic crystals (Figure 8c). Branching on the existing lamellae with small misorientation angles generates a fan-like morphology ( Figure 8d). As the lamellae fan out, flower-like crystals with curved structure can be observed (Figure 8e). Intermittent branching of the fans leads to spherulites with holes, and complete spherulites can be formed when the spaces are filled by lamellae (Figure 8f). This behavior of small-angle branching matches the mode of noncrystallographic branching, which is distinct from crystallographic branching in dendritic snow crystals or diffusion-limited aggregation in fractal-like forms [48]. The subunits of polycrystalline aggregates often grow radially via noncrystallographic branching, resulting in three-dimensional spheres [52]. In our case, the final evolved particles of GAH looks like a circular layer without branching along another axis. The reason might be that the largest face of the plate-like crystal overwhelmingly dominates the crystallization, which imposes a strong orientation effect [45].

Molecular Simulation Analysis
The predicted crystal shape of GAH by the BFDH model and molecular topology of four faces are shown in Figure 9. The prominent planes are (100), (020), and (001), and the surrounding faces are (10-1), (110), (011), and (11-1), as well as their symmetry-related equivalents. The most important surface is the (001) face, which occupies more than 49% of surface area. This is in agreement with the XRD patterns of the experimental crystals in which the strongest characteristic peak is assigned to the (001) face. The predicted crystal habit matches well with the experimental morphology of the plate-like crystal. During antisolvent crystallization in the water + isopropanol system, heterogeneous nucleation also occurs on the (001) surface. On this face, the molecules are oriented diagonally to the plane with NH 3+ and hydroxyl groups pointing out from the surface. This enables the formation of hydrogen bonding and electrostatic interactions with other molecules. The (100) face is less dominant and exposes hydroxyl groups. The (020) and (0-20) faces are symmetric with respect to the b-axis, but they show different structures on the surfaces.
small-angle branching matches the mode of noncrystallographic branching, which is d tinct from crystallographic branching in dendritic snow crystals or diffusion-limited a gregation in fractal-like forms [48]. The subunits of polycrystalline aggregates often gro radially via noncrystallographic branching, resulting in three-dimensional spheres [5 In our case, the final evolved particles of GAH looks like a circular layer without branc ing along another axis. The reason might be that the largest face of the plate-like crys overwhelmingly dominates the crystallization, which imposes a strong orientation eff [45].

Molecular Simulation Analysis
The predicted crystal shape of GAH by the BFDH model and molecular topology of four faces are shown in Figure 9. The prominent planes are (100), (020), and (001), and the surrounding faces are (10-1), (110), (011), and , as well as their symmetry-related equivalents. The most important surface is the (001) face, which occupies more than 49% of surface area. This is in agreement with the XRD patterns of the experimental crystals in which the strongest characteristic peak is assigned to the (001) face. The predicted crystal habit matches well with the experimental morphology of the plate-like crystal. During antisolvent crystallization in the water + isopropanol system, heterogeneous nucleation also occurs on the (001) surface. On this face, the molecules are oriented diagonally to the plane with NH 3+ and hydroxyl groups pointing out from the surface. This enables the formation of hydrogen bonding and electrostatic interactions with other molecules. The (100) face is less dominant and exposes hydroxyl groups. The (020) and (0-20) faces are symmetric with respect to the b-axis, but they show different structures on the surfaces. On the (020) face, NH 3+ , hydroxyl groups, and Cl − ions are exposed, whereas hydroxyl groups and methylene are protruded on the (0-20) surface.  Figure 10a shows that the (001) face has the strongest intermolecular interaction energy with the GAH solute, followed by (020) and (100) faces. The interaction energy of the solute on the (0-20) face is weakest. Solvent molecules also exhibit a much larger interaction energy with the (001) face than with the other three faces (Figure 10b). This suggests that solvent molecules tend to adsorb on the (001) face and the detachment of solvent molecules from the surface becomes more difficult. Consequently, the self-assembly of GAH on the (001) face is hindered and crystal facet growth would be inhibited. This is in agreement with the experimental morphology of plate-like shape. Since solute molecules and ions also prefer to adsorb on the (001) face, they would accumulate on this surface, resulting in a higher local supersaturation and inducing surface nucleation. Moreover, this  Figure 10a shows that the (001) face has the strongest intermolecular interaction energy with the GAH solute, followed by (020) and (100) faces. The interaction energy of the solute on the (0-20) face is weakest. Solvent molecules also exhibit a much larger interaction energy with the (001) face than with the other three faces (Figure 10b). This suggests that solvent molecules tend to adsorb on the (001) face and the detachment of solvent molecules from the surface becomes more difficult. Consequently, the self-assembly of GAH on the (001) face is hindered and crystal facet growth would be inhibited. This is in agreement with the experimental morphology of plate-like shape. Since solute molecules and ions also prefer to adsorb on the (001) face, they would accumulate on this surface, resulting in a higher local supersaturation and inducing surface nucleation. Moreover, this strong intermolecular interaction would facilitate oriented crystal growth of newly formed nuclei. On the other hand, the interaction energy of the solute on the (020) face is stronger than the interaction energy on the (0-20) face. This indicates that GAH has a higher tendency to adsorb on the (020) face than on the (0-20) face. Thus, crystal facet growth along the +b direction could be promoted and growth along the -b direction would be inhibited, resulting in the formation of asymmetric crystals. als 2023, 13, x FOR PEER REVIEW 11 of growth along the +b direction could be promoted and growth along the -b direction wou be inhibited, resulting in the formation of asymmetric crystals.

Concluding Remarks
Antisolvent crystallization was shown to be effective at inducing hierarchical stru tures of GAH particles when isopropanol was used as the antisolvent. The particle mo phology varied from fan-like dendrites to flower-like aggregates or spherulites dependin on different crystallization operation parameters. Branches could be increased at low temperature, larger GAH concentration, slower feeding rate, moderately higher solven to-antisolvent ratio, and faster stirring rate. The morphological evolution process of GA spherulites was monitored and indicated that the hierarchical structure was formed v noncrystallographic branching of lamellae. Combined with the predicted and exper mental crystal habit, the (001) face dominated the plate-like shape and heterogenous n cleation occurred on this surface. The intermolecular interaction energy of the solute solvent on crystal faces was calculated. They were both strongest on the (001) face, whic induced surface nucleation under high supersaturation and facilitated oriented cryst growth. The interaction energy of the solute on the (020) face was stronger than that o the (0-20) face, leading to asymmetric crystal growth. Overall, this work has provided a insight into the important roles of crystallization environment and operation condition on the morphological variations. The study on the branching behavior of polycrystallin aggregates and solute-surface interactions would also help design and tune hierarchic structures of organic crystals.

Concluding Remarks
Antisolvent crystallization was shown to be effective at inducing hierarchical structures of GAH particles when isopropanol was used as the antisolvent. The particle morphology varied from fan-like dendrites to flower-like aggregates or spherulites depending on different crystallization operation parameters. Branches could be increased at lower temperature, larger GAH concentration, slower feeding rate, moderately higher solventto-antisolvent ratio, and faster stirring rate. The morphological evolution process of GAH spherulites was monitored and indicated that the hierarchical structure was formed via noncrystallographic branching of lamellae. Combined with the predicted and experimental crystal habit, the (001) face dominated the plate-like shape and heterogenous nucleation occurred on this surface. The intermolecular interaction energy of the solute or solvent on crystal faces was calculated. They were both strongest on the (001) face, which induced surface nucleation under high supersaturation and facilitated oriented crystal growth. The interaction energy of the solute on the (020) face was stronger than that on the (0-20) face, leading to asymmetric crystal growth. Overall, this work has provided an insight into the important roles of crystallization environment and operation conditions on the morphological variations. The study on the branching behavior of polycrystalline aggregates and solute-surface interactions would also help design and tune hierarchical structures of organic crystals.

Data Availability Statement:
The data presented in this study are available on request from the author.

Conflicts of Interest:
The authors declare no conflict of interest.