*4.1. Process of Rapid Formation of Thin and Uniform HA Film Consisting of Fine Spherical Particles on Ti-AT-SPT*

With SPT in the calcium phosphate solution, HA spherical particles were precipitated on the Polished-Ti surface, but the size of the spherical particles was 5–20 μm in diameter. The density of the HA crystals was too low to form an HA film (Figure 3a). However, it was demonstrated that a thin and uniform HA film consisting of fine spherical HA particles with a diameter of 5 μm formed on Ti-AT-SPT (Figure 3b). This rapid formation of the uniform HA film was attributed to the synergistic effect obtained by combining an alkaline treatment with SPT in a calcium phosphate solution.

The driving force for the formation of the HA film from a supersaturated solution was the change in Gibbs free energy, Δ*G*, for transfer from a supersaturated solution to an equilibrium solution with HA crystals:

$$
\Delta G = -RT\ln S \tag{1}
$$

where *R* is the gas constant; *T* is the absolute temperature; and *S* is the degree of supersaturation, which is expressed as:

$$S = I P / \mathcal{K}\_{\text{sp}} \tag{2}$$

where *IP* is the ionic activity and *K*sp is the thermodynamic solubility product. Since the solubility product of HA, *K*sp, decreases with increasing temperature, it is apparent that an increase in the degree of supersaturation, *S*, together with a decrease in the *K*sp value as a result of SPT was responsible for the precipitation of HA crystals on Polished-Ti. SPT for 30 min without alkaline treatment, however, was insufficient for the formation of a dense and uniform HA film. This probably arose from the fact that the SPT was not sufficient to lower the activation energy to enhance the formation of HA crystals (Figure 11a) and a few critical and supercritical HA nuclei were induced by SPT, as shown in Figure 12a.

**Figure 11.** Energy profile in the hydroxyapatite formation. Activation energy of hydroxyapatite formation was lowered by (**a**) SPT and (**b**) alkaline treatment, and was notably lowered by (**c**) SPT and alkaline treatment and SPT.

**Figure 12.** Schematic illustration of HA nucleation and HA crystal growth on the titanium surfaces. The appearance of particles formed on the Ti surface was quite different among (**a**) Ti-SPT, (**b**) Ti-AT-IT, and (**c**) Ti-AT-SPT.

With 5 M NaOH treatment, a sodium titanate hydrogel layer formed on the polished titanium [5]. It was also found that the hydrogel layer quickly released sodium ions with the uptake of calcium ions when alkaline-treated Ti was soaked in calcium phosphate solution. This ion exchange reaction was proposed to take place very quickly to maintain the electrical neutrality of the hydrogel and increased the calcium ion concentration at the hydrogel surface. Increase in *IP*, as a result of a higher calcium ion concentration, also increased the degree of supersaturation with respect to HA, which enhanced the apatite nucleation in a mineralizing solution [13]. In this case, the activation energy required for HA nucleation was also insufficiently lowered by the increased concentration of Ca ions (Figure 11b) to induce a few nuclei (Figure 12b). The HA crystals grew larger with an increase in soaking time in a calcium phosphate solution, and a thick HA film consisting of coarse HA spherical particles was formed after soaking for 1 day at 60 ◦C (Figure 11b).

With the combination of alkaline treatment and SPT, the degree of supersaturation, *S*, was markedly increased with both an increase in *IP* and a decrease in *K*sp. The activation energy required for HA nucleation was probably lowered sufficiently (Figure 11c) to induce a large number of HA nuclei as shown in Figure 12c. As a result, a thin and uniform HA film consisting of fine spherical particles could be obtained (Figure 12c). As it is a uniform precipitation with fine and round HA particles, the height of the precipitation is equal to the height of HA crystal, which is 1 μm.
