PSI - Issue 83

Alla V. Balueva et al. / Procedia Structural Integrity 83 (2026) 196–207

206

4.3. Adhesion Strength between Ti (II) and Ca 3 (SiO 3 ) 2

The same calculation is conducted for the critical surface energy of the reaction of tricalcium silicon trioxide Ca 3 (SiO 3 ) 2 with titanium Ti 2+ . To calculate the critical surface energy of the reaction, we decided to use the density of rankinite (Ca 3 Si 2 O 7 ) as the density of tricalcium silicon trioxide, for it most resembled tricalcium silicon trioxide. Density of rankinite (Ca 3 Si 2 O 7 ) is 3.00 g/cm3 (https://handbookofmineralogy.org/pdfs/rankinite.pdf ). The molar mass of tricalcium silicon trioxide was calculated to be M ≈ 272.4014 g/mol, calculation can be seen below.

Molar Mass (M) of Ca3(SiO3)2 = 3 (40.078 g/mol) + 2 (28.086 g/mol)) + 6 (15.999 g/mol) = 272.400 g/mmol

Then, we assume that one Ti atom is bound to each molecule of tricalcium silicon trioxide, and according to the above calculations, their binding energy is E = 0.94 a.u. This way, the total surface energy released from all atoms on the unit surface, or the adhesive strength (specific surface energy of adhesive destruction) γ can be obtained from (4.1) as: ൌ ሺ0.94 x 4.36 ൉ 10ି ଵ଼ Jሻൈ ൬3.01 ௖௠ ௚ య ൈ ሺ଺ൈଵ଴ మయ ௠௢௟ షభ ଶ଻ଶ.ସ଴଴ ೘ ೒ ೚೗ ൰ మ య ൎ 0.00014464 ௖௠ ௃ య ൎ14.431 ௠ ௃ మ (4.4) Calculations show that adhesion strength between Ti and Ca 3 (SiO 3 ) 2 was greater than the adhesion strength between Ti and Ca 3 (PO 4 ) 2 . It is recommended to that Ca 3 (PO 4 ) 2 coating be doped with the Ca 3 (SiO 3 ) 2 coating. Meaning that the structure of Ca 3 (PO 4 ) 2 coating will remain the same expect the most upper layers of the coating will be replaced with Ca 3 (SiO 3 ) 2 . This allows the titanium to bind to the Ca 3 (SiO 3 ) 2 while keeping the general structure of the coating similar to the bone structure. 5. Conclusions Based on the results of the binding energies between the TiCa 3 (PO 4 ) 2 (Figure 6a) and TiCa 3 (SiO 3 ) 2 (Figure 6b), it would indict that the additive of the TiCa 3 (SiO 3 ) 2 was improved coatings for dental implants. Additionally, after further analysis and calculating the critical surface energy of both TiCa 3 (PO 4 ) 2 (Figure 6a) and TiCa 3 (SiO 3 ) 2 (Figure 6b), which determined TiCa 3 (SiO 3 ) 2 to have a higher adhesion strength. The critical surface energy of TiCa 3 (SiO 3 ) 2 was calculated to an average of 14.60 J/m 2 while the critical surface of TiCa 3 (PO 4 ) 2 was calculated to be 6.927 J/m 2 . Furthermore, the structures of TiCa 3 (PO 4 ) 2 (Figure 6a) and TiCa 3 (SiO 3 ) 2 (Fig. 6b) was analysed to support the claim that the use of Ca 3 (SiO 3 ) 2 would be beneficial in dental implants. The structure of TiCa 3 (SiO 3 ) 2 (Fig, 6b) revealed a tight pore structure which would enhance the packing density and allow for the coating to act as a cement between the implant and the jawbone to create a stronger bond. Note that the structure of the Ca 3 (PO 4 ) 2 is meant to mimic the natural structure of bone; by implementing this, the bone is more receptive of the implants as it increases the biocompatibility between the implant and the bone. Therefore, it was also concluded that the use of Ca 3 (SiO 3 ) 2 and Ca 3 (PO 4 ) 2 could be combined to further improve dental implants, as the combined use of Ca 3 (SiO 3 ) 2 and Ca 3 (PO 4 ) 2 coating would enhance the bonding of the implant to the jawbone and promote osteogenesis.