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.