Fractal Geometry Characterization of Fracture Profiles of Polymeric Materials

Abstract

The concept of fractals was used in the analysis of the fracture surfaces of two different polymeric materials. Polymer networks obtained from three popular dental dimethacrylate monomers: Bis-GMA, TEGDMA and UDMA as well as two copolymers of these monomers were analysed. Dense polymer membranes with dispersed magnetic powder (magnetic membranes) for air separation were also investigated. In both cases, profiles of fractures were described by a modified fractal dimension. It is based on scaling the length of a profile with the size of a measuring step. The modified fractal dimension is considered a diagnostic tool for structure-morphology analysis of fracture path and roughness parameter. A quantitative description of fracture surface is an important link in the investigation of the properties of materials and mechanisms of their decohesion.

A Guide through the Dental Dimethacrylate Polymer Network Structural Characterization and Interpretation of Physico-Mechanical Properties

“…The detailed analysis of the relationships between the chemical structure and fractal parameters led to the following conclusions [159,160]. The TEGDMA homopolymer morphology was characterized by the highest D F as well as D β and the lowest ∆D, indicating the highest structural homogeneity of this polymer network.…”

Characterization of the Structure and Transport Properties of Alginate/Chitosan Microparticle Membranes Utilized in the Pervaporative Dehydration of Ethanol

“…On the basis of the binarized membrane images obtained from the microscope, a fractal analysis concentrating on the fractal dimension D F and generalized fractal dimension D q were completed. These parameters allow one to quantify the structure and morphology of self-similar objects and is commonly used [16][17][18][19][20][21][22].…”

“…where N(ε) is the number of covering elements (boxes); ε is the size of the covering element (length of the edge); q is a real number (dimension index); and P i is the probability to find mass in the ith element (for example the number of mass pixels in an element divided by the total number of pixels in the element). The Box Counting Method (BCM) allows calculation of both the fractal dimension D F and its extension D q , termed the generalized fractal dimension [18][19][20][21][22]. For q = 0, the generalized fractal dimension D q is independent of the P i distributions (any nonzero P i raised to power 0 gives 1) and, therefore, equals D F .…”