Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Abstract

To investigate the relationship between histological properties and thermal conductivities of binary self-assembled/self-organized fractal materials fabricated by the mixed diffusion of filler particles, the particle group distribution of the filler particles was analyzed. Unlike conventional research on particle size distribution, we performed an analysis that focuses on interactions and connectivity between particles from the perspective of the Barabasi-Albert model. In three complex network systems of β-Si3N4 (SN)/austenitic stainless steel (SUS), SN/piezoelectric polyvinylidene fluoride (PVDF), and BaTiO3 (BT)/PVDF, the size distribution of secondary particles was a power-law distribution until the particle group grew relatively large. In the SN/SUS and SN/PVDF systems, a crossover phenomenon was observed in which the order distribution exhibited a power-law in the region where the particle group area was small, and as the particle group became larger, the order distribution became exponential distribution. On the other hand, the BT/PVDF system deviated from the power law distribution as the particle group area increased but did not exhibit an exponential distribution. The characteristics of the particle group distribution of these filler particles were closely related to thermal conductivity, indicating that the connection of particle groups was important. Furthermore, the relationship between the multifractal capacitance dimension, which is strongly correlated with the distance between the particle groups, and the total number of filler particle groups suggests that the texture of these composite material systems may have both small-world and scale-free properties. We also focused on the relationship between the multifractal and complex network properties of the three particle groups. As a result, a correlation was found between the slope γ, which reflects the characteristics of the power distribution, and the thermodynamic parameter α (corresponding to internal energy change) obtained from multifractals. In particular, the smaller the change in γ relative to the change in α, the more pronounced the bonding of particles and particle groups, while the larger change in γ suggested the dispersion of particle groups.