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# Perspective of Research for Healing Processes

## Applications of Healing Properties

Applications of the healing process are emerging in many fields. Here we discuss the possible direction of the healing mechanism related to the porous lithium silicate systems. Recently, lithium disilicate and related materials have been used as dental ceramics. Due to its hardness, stability, and high thermal shock resistance, it is expected to play roles as the dental materials [28]. For example, IPS Empress® glass-ceramics (Ivoclar Vivadent) consists of 70% of needle-like lithium disilicate crystals embedded in a glassy matrix [29] and appear to have a good quality to fulfill the dental standard for abrasion behavior, chemical durability, and optical properties such as translucency of all glass-ceramics. As shown in the previous section, self-healing property of Li rich composition such as in lithium metasilicate can have a better self-healing ability. In this kind of application, a self-healing ability is one of the desirable properties, although it may have a trade-off relation with some of the other ones such as hardness.

## Multifractal Nature and Possible Scale Gaps in the Problems of Healing and Nanofractures

Molecular dynamics simulations in these systems and related ones are useful for examining the mechanisms self-healing as well as mechanical properties such as nanoductility, nanofractures in nanostructured materials. For a measure of the roughness, multifractal analyses are often used after the pioneer works by Mandelbrot and collaborators [30]. For example, Vernede and collaborators [31] have examined a surface roughness of three systems, that is, an aluminum alloy, a mortar, and a sintered glass beads ceramic. The roughness of the fractured specimen is measured using a mechanical stylus profilometer. They have introduced the quantity (x):

where s = |dx| and dh[x, dx| = h(x + dx) - h(x) is the local slope of the surface in the direction of dx. The value Q is chosen so that the average of f(x) over all x becomes 0. In Fig. 7.17, the distribution of height fluctuations P{dhdr) at various scales dr for the three samples considered is shown. The distribution found in Fig. 7.17 having a tail part and a truncation seems to be comparable to the Levy distribution discussed in Chapter 5. In Fig. 7.18, spatial correlations represented for a>e computed at different scales e for three materials are shown. The cut-off length £ is represented for each case. They have reported that the length scale £ can separate the two regions of the surface as shown in this figure. Above this value, slope amplitudes are uncorrelated, and the fracture surface is mono-affine, while below £, long-range spatial correlations lead to a multifractal behavior of the surface, which is reminiscent of turbulent flows. The size of £ was reported to be 50 ± 9 pm for ceramic in that work.

As found in this example, nanoscopic mechanical properties are not necessarily directly connected to the macroscopic behavior of the system.

Figure 7.17 Distribution of height fluctuations P(d/i|dr) at various scales dr for the three samples considered. Reprinted with permission from Vernede, S., Ponson, L., Bouchaud, J.-P. (2015), Turbulent fracture surfaces: A footprint of damage percolation? Phys. Rev. Lett., 114, 215501 (1-5). Copyright (2015) by the American Physical Society.

Even though multifractality is commonly found in experiments and MD simulations, one needs to be careful to connect the result of MD simulations of nanostructured systems to the macroscopic realistic systems directly. Time and length scale regions examined are not necessarily comparable. Furthermore, mechanical properties of the system related to the healing processes might depend on factors not only roughness of the surface but also defects, mixing of ordered and disordered phases in experimental conditions. Similar problems will be found for the study of fractures. The length scale of pm order mentioned above cannot be immediately applicable to the nanostructured materials. Therefore, it seems to be necessary to examine the problem of the scale-gaps and to clarify such characteristic length scales in nanostructured materials.

Figure 7.18 Spatial correlations of a>£ for the three materials considered. The correlations are represented for are computed at different scales e. The cut-off length £ is represented for each case. Reprinted with permission from Vernede, S., Ponson, L., Bouchaud, J.-P. (2015). Turbulent fracture surfaces: A footprint of damage percolation? Phys. Rev. Lett., 114, 215501(1-5). Copyright (2015) by the American Physical Society.

Further systematic research for the relation between the self- healing ability and other mechanical properties is required. A comparison of details with experiments including size-dependent behaviors will be also useful. Again, multifractal analyses can be a common tool, which can give a connection between the structures and processes including the power law behaviors found in healing processes.

There is a possibility that through such analyses, healing processes and fractures can be understandable on the same basis, although one may also find some differences between them.

# Conclusion

Two topics have been discussed in this chapter. One is concerned with the heterogeneous dynamics in porous systems in NVE conditions and the other is concerned with the formation of larger voids and a self-healing process of the porous systems in the subsequent runs in the NPT conditions.

In Chapter 6, enhancement of the dynamics of Li ions with the maximum is shown and the diffusive motion of Li ions is found to start from an early time (NCL) region of MSD corresponding to caged ion dynamics. The results demonstrate that the loosening of the cage in porous glass contributes to the enhancement.

As shown in the first part of this chapter, enhanced dynamics in porous lithium disilicate are heterogeneous dynamics with a non-Gaussian character as clearly proved by MD simulations. Changes in the characteristic times are more closely examined as the function of the density (porosity) and it was corroborated that the maximum of the inverse of the characteristic times is already found in the NCL region. From both changes of the characteristic time of MSD and changes in the power law exponent, it is shown that the changes in the motion in a longer length scale also contribute to the enhancement of the dynamics in porous systems, differently. In conclusion, dynamic heterogeneity of the system is affected by introducing pores in a complex manner in porous systems. Since the systems are sensitive to modifications, porous materials can be a useful platform to examine the complex behaviors of heterogeneous dynamics and the mechanism of glass transition related to such behaviors.

In the second part of this chapter, mechanisms of the selforganization of large voids in NVE runs and the self-healing process in NPT runs have been also examined. There are several time regions in healing processes and differences in these processes are discussed. In the healing process, it is found that the stress relaxation of the system plays an important role. The perspective of MD simulations in this field has also been discussed.

# Summary of MD Simulations and Modeling of Porous Silicates

The lithium silicate systems examined here have been explained in the appendix in Chapter 6. Here we briefly summarize them for the reader of this chapter. The system examined is lithium disilicate, which is located in the silica-rich region of Li20-Si02 systems, and pores are introduced by the scaling of volume and positions. Each original and porous lithium disilicate (Li2Si205) system examined contains 3456 atoms in the basic MD box with a periodic boundary condition. The following model function was used:

The model potential consists of the Coulombic term, the pair potential function of the Gilbert-Ida type [32, 33] with the r~6 for correction of the softness of the oxygen atom. The value r is the distance between atoms and a,- is the effective radius and bt is the softness parameters of the atom i with a constant /0 (=1 kcal A"1 mol"1 = 4.184 kj A'1 mol'1). Potential parameters were derived based on the ab initio molecular orbital calculations [3, 34]. The Ewald method was used for the calculation of the Coulombic force. A cut-off distance was chosen to be 12 A for the calculation of both the repulsive force and that for the real space term of the Coulombic force. The procedure for preparing porous systems is as follows. First, lithium disilicate in the glassy state was obtained by the rapid cooling (~1 К ps"1) from the melt at 3000 К with the combination of constant pressure condition and temperature scaling to the target temperatures (2000, 1700, 1400, 1200, 1000, 800, 700, and 600 K). Systems were quasi-equilibrated at each temperature in the NPT condition and then following runs in the NVE condition were done. Then porous systems were prepared by the scaling of the volume and position of particles at 600 K. Similar methods had been previously used to prepare the porous silica [35, 36]. After the expansion of the system, each system was equilibrated during 300,000 steps run in the NVT condition and the following NVE runs are used for analyses. The time step used in the MD run was 1 fs for almost of porous systems. The densities p examined are 2.47 (original), 2.30, 2.13, 1.98, 1.84 and 1.58. As the porosity, P0, was found to be proportional to -p, the results are shown as a function of density.

That is, P0 = -17.57(p) + 100.08, where P0 is given in percent and density is in g cm"3.

Simulations of porous metasilicate are also done to examine the enhanced diffusion and the self-healing process. Some results of the latter are shown in [27] and this chapter and details will be shown elsewhere. Some results of the self-healing process in porous lithium disilicate and metasilicate have been reported in several meetings [37, 38].

Recently, Zhang and coworkers pointed out that our potential model for sodium silicate is rather ductile in the NPT condition, while the behavior in the NVT condition is reasonable [39].

They concluded that one should obtain the stress-strain behavior in the NPT conditions and therefore our potential model for sodium silicate is not suitable for studying fractures.

Of course, in general, potential parameters are not necessarily optimized to study fractures of systems and therefore, some cautions are required for research of them. However, here we note that the nano-ductility and nano-fracture discussed in MD in certain conditions are not necessarily directly comparable to the real experiments under the atmospheric condition. These processes also show time-dependent properties. Further study for the condition of "determination of the stress-strain curve under the constant pressure” will be required before concluding the validity of the potential parameters. This is because in such a case, the behavior of the system is determined by the competition between the stress relaxation to form fractured structure and the self-healing process under the fluctuating pressure, where both processes have different time constants.

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