## 3 Results and Discussion
### Mechanical Property of Coatings  
Scratch resistance is an important property of coatings, especially the ones for optical applications. The hardness of the coatings was assessed by a pencil hardness test on the basis of the ASTM D3363 standard [46], using pencils ranging from 6B (the softest) to 9H (the hardest). As shown in Figure 3f, with MTES as the silane coupling agent, the TM coating had the softest pencil hardness < 6B, due to its low refractive index and high porosity. In fact, the hydrogen bonds among the methyl-embedded particles are weakened and the extent of cross-link is greatly reduced, leading to a high porosity [33]. The NH\({}_{3}\)-OSER coating, using GPTES as the silane coupling agent, was also soft, which showed a pencil hardness < 3B, as Figure 3e. That means the single Si-O-Si cross-link is not strong enough to achieve ultra-scratch resistance. However, as shown in Figure 3a, there were only minor scratches on DETA-OSER, caused by an 8H pencil, yet it suffered evident scratch damage by 9H in Figure 3b. What is more, MXDA-OSER was also ultra-scratch resistant, absolutely none scratches on its surface as Figure 3c showed. In summary, owing to the double cross-links, the hardness of coatings is greatly enhanced to 8H. GPTES achieved the cross-link structure of Si-O-Si through hydrolysis and condensation because of ammonia, but this single cross-link was not very strong. The extent of the cross-link between the molecular chains is relatively weak, and there are still the possibility of slippage and dislocation under external force tearing. When introducing the curing agent, molecular chains are double cross-linked to each other, which strengthens the stability and robustness of the network and increases the relative molecular mass. Macroscopically, these make the polymer coatings rather hard, up to 8H. In fact, the extension of the double cross-link decides the hardness of the coating. As mentioned, each mole of active hydrogen in the amines react with one mole of epoxy group (H:epoxy = 1:1), theoretically. However, there is always a dynamic equilibrium in organic reaction, that is, not every epoxy group goes through a ring-opening reaction. In order to improve the conversion of epoxy groups, excessive curing agent is supposed to be added to the solution. According to Table 1, when  
Figure 2: FTIR spectra of NH\({}_{3}\)-OSER, MXDA-OSER, DETA-OSER and GPTES.  
the proportion of hydrogen increased, the pencil hardness of both coatings also increased, proving that the excessive curing agent made the ring-opening reaction more thorough, and then the double cross-link network was strengthened. In detail, when the curing agent was less (\(\leq\)1:1), the curing efficiency of DETA was higher, and the hardness reached to 5H. In other words, most GPTES was cured by DETA with a low concentration. As for MXDA, its small amount had a small increase in hardness. When H:epoxy = 2:1, the hardness of two coatings increased to 8H. However, the sol soon becomes a gel because of excessive curing in about 8 days. This is because the size of the cross-linked networks continues to expand as the aging time increases. Macroscopically, the fluidity of the sol is continuously weakened, and finally becomes a gel, making it impossible to go through the dip-coating process. So, the sol (epoxy:H = 1:2) needs to be diluted to slow down the growth of the cross-linked networks to prolong its life. According to experiments, when the concentration of sol was diluted to half, the sol was kept in a fluidized condition after 180 days.