Anisotropy in Stable Conformations of Hydroxylate Ions between the {001} and {110} Planes of TiO₂ Rutile Crystals for Glycolate, Lactate, and 2-Hydroxybutyrate Ions Studied by Metadynamics Method

Control over TiO₂ rutile crystal growth and morphology using additives is essential for the development of functional materials. Computer simulation studies on the thermodynamically stable conformations of additives at the surfaces of rutile crystals contribute to understanding the mechanisms underlying this control. In this study, a metadynamics method was combined with molecular dynamics simulations to investigate the thermodynamically stable conformations of glycolate, lactate, and 2-hydroxybutyrate ions at the {001} and {110} planes of rutile crystals. Two simple atom-atom distances were selected as collective variables for the metadynamics method. At the {001} plane, a conformation in which the COO^- group was oriented toward the surface was found to be the most stable for the lactate and 2-hydroxybutyrate ions, whereas a conformation in which the COO^- group was oriented toward water was the most stable for the glycolate ion. At the {110} plane, a conformation in which the COO^- group was oriented toward the surface was the most stable for all three hydroxylate ions, and a second most stable conformation was also observed for the lactate ion at positions close to the {110} plane. For all three hydroxylate ions (α-hydroxycarboxylate ions), the stability of the most stable conformation was higher for the {110} plane than for the {001} plane. At both planes, the stability of the most stable conformation was highest for the 2-hydroxybutyrate ion and lowest for the glycolate ion. Supposing that all three hydroxylate ions serve to decrease the surface free energy at the rutile surface and that a more stable conformation at the rutile surface leads to a greater decrease in the surface free energy, the present results partially explain experimentally observed differences in the changes in growth rate and morphology of rutile crystals in the presence of glycolic, lactic, and 2-hydroxybutyric acids.