Thermal properties of composite materials with a complex fractal structure

Abstract

In this work, we report the thermal characterization of platelike composite samples made of polyester resin and magnetite inclusions. By means of photoacoustic spectroscopy and thermal relaxation, the thermal diffusivity, conductivity and volumetric heat capacity of the samples were experimentally measured. The volume fraction of inclusions was systematically varied in order to study the changes in the effective thermal conductivity of the composites. In some samples, a static magnetic field was applied during the polymerization process resulting in anisotropic inclusion distributions. Our results show a decrease in the thermal conductivity of some of the anisotropic samples compared to the isotropic randomly distributed ones. Our analysis indicates that the development of elongated inclusion structures leads to the formation of magnetite and resin domains causing this effect. We correlate the complexity of the inclusion structure with the observed thermal response by a multifractal and lacunarity analysis. All the experimental data are contrasted with the well known Maxwell-Garnett's effective media approximation for composite materials.

Order-fractal transitions in abstract paintings

“…This measure of complexity has been employed to characterize the structural transition of rheological fluids [23,25,33], granular materials [26,34], magnetic wall domains in boracite [27] and other complex systems [35,36].…”

“…However the maximum value of the multi-fractal spectrums presented above, can be associated with different degree of order [23,25,26,27]. We obtained for an specific array of paintings listed in table (1), the evolution of the maximum value on the multi-fractal spectrum for each paint, corresponding to the HausdorfBesicovich dimension when Q = 0. mension increases, approaching to a dimension close to two, and it happens in all the groups of paintings.…”

Thermal properties of composite two-layer systems with a fractal inclusion structure

“…Figure 3 shows micrographs taken from CSLs with a thickness of ∼ 400 µm. The kind of inclusion structure formed by the arrangement of magnetite particles exhibits multifractal properties as discussed in [7], with the magnetite particles forming chain-like aggregates that grow with the concentration of inclusions as shown in the figure.…”

“…On the other hand, controlling thermal conduction of composite materials by means of changes in their structure and composition is an area of current research for its potential applications [2,3,4,5,6]. In particular, controlling the inclusion structure seems to be promising in this regard, as it allows to tune the thermal properties of the composite without having to change the component materials themselves [7]. These kinds of studies may eventually lead to the development of intelligent materials with a real-time controllable thermal response, as it has happened with some other properties like elastic, optical and electrical to mention a few.…”

“…Regarding experimental approaches, the photoacoustic (PA) technique in combination with the thermal relaxation method (TRM) have proven to be reliable and useful non-destructive techniques to measure thermal properties of different kinds of materials [7,13,14,15]. About the first, there has been an ongoing effort to extend the photoacoustic technique for the characterization of multilayered systems, with the purpose to determine their effective thermal diffusivity from the knowledge of the thermal properties of the layers themselves [16,17,18,19,20].…”