Fractal texture and dielectric properties of BaTiO3/poly-vinylidene fluoride composites

Abstract

The effects of the dispersion state of BaTiO3 ceramic fillers, which significantly improve the dielectric constant of BaTiO3/polyvinylidene fluoride composites, were investigated. To understand the microscopic and macroscopic features of the obtained composite textures, we have attempted a multifractal analysis of the microstructure of composite materials. The fractal nature of the composite material texture was investigated using multifractal parameters (the qth-moment dimension D(q) and scaling exponent τq) in the formation of fractal aggregates of BaTiO3 (BT) particles in polyvinylidene fluoride (PVDF) composites. In the plots of D(q) and τ(q) vs q, the obtained results confirmed that q > 0 could be quantitatively evaluated as local characteristics (morphology, arrangement, and dispersion), whereas q < 0 could be quantitatively evaluated as global characteristics (aggregate network structure formation). As a result of evaluating the internal energies and entropies of the micro- and macro-regions from the plot of τq vs q, the aggregate formation energy (E1), aggregate network formation energy (E2), and interaction energy between the aggregates (Eint) had a relationship of E2 = E1 + Eint. The configuration entropy for the aggregate network formation (S2), particle arrangement entropy (S1), and aggregate configuration entropy (Sint) had a relationship of S2 = S1 + Sint. At q > 0, the increase in the aggregate formation energy with the amount of additive indicates the formation of particle groups. At q < 0, the generation of the interaction energy between the aggregates (Eint) suggests that the particle groups interact to form an aggregate network. Similarly, at q > 0, the increase in the arrangement entropy with the amount of additive is related to the arrangement of particles, while at q < 0, the generation of the configuration entropy (Sint) is related to the formation of the particle group network. It was clarified from the multifractal analysis that the formation of particle groups and their network structure are strongly related to the piezoelectric characteristics in this BT/PVDF system. It was revealed that the Eint and Sint obtained from the plots of D(q) and τ(q) vs q of the multifractal analysis could be related to the formation of particle groups (local interaction) and occurrence of network structure (global interaction). Therefore, the plots of D(q) and τ(q) vs q are effective means of characterizing self-organization from the fractal nature and are expected to be applied in more general research fields other than material and condensed matter.

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

“…This is similar to the agglomeration/aggregation and growth of fillers in a matrix. As previously reported for fractal material texture organization, [6][7][8][9][10][11][12][13][14][15] the construction of this self-assembly/self-organization consists of the following two processes:…”

“…That is, as the slope of γ increases, the deviation in particle diameter increases, and it is difficult to form a gentle network. On the other hand, in the PVDF system [8,10] shown in Fig. 7(b), it has been revealed that SN addition can form percolation, but BT particle groups are isolated.…”

“…In particular, the interaction of the filler particles in the matrix and the resulting network formation are important for expressing specific functionality. In fact, in β-Si 3 N 4 (SN)/austenitic stainless steel (SUS) [6,7] and BaTiO 3 (BT)/piezoelectric polyvinylidene fluoride (PVDF) [8][9][10][11][12][13][14][15] systems, the characteristics of the material structure constructed by the process of self-assembly or self-organization have been mapped to material performance such as dielectric properties and thermal conductivity.…”

“…In fact, in the self-assembled/self-organized material texture that we have been dealing with, the particle size distribution of the filler in the matrix exhibits a power law distribution. Therefore, in this study, we discuss the fractal material texture and complex network properties such as scale-free property and small-world property of the highly fractal composite systems of SN/SUS, 6 BT/PVDF, 8 and SN/ PVDF 10 with improved thermal conductivity.…”

“…On the other hand, multifractal analysis [1-5], which is widely used in physics, chemistry, medicine, and engineering involving morphology and shape, is being applied to the field of materials science. Recently, this analysis has been used to reveal the particle morphology, arrangement, dispersion, and statistical thermodynamic properties during chemical reaction processes, and has been shown to be effective in clarifying the dissipation state of particles due to self-organized or self-assembled processes in real binary systems (metal/ceramics and polymer/ceramics) [6][7][8][9][10]. In particular, the general dimension D q (multiple fractal dimension for q-th order moment) and scaling exponent τ q obtained from the microstructural morphologies of self-organized or self-assembled materials serve as material design indices for designing composite materials with Fumio Munakata…”