Shape complexity and fractality of fracture surfaces of swelled isotactic polypropylene with supercritical carbon dioxide

摘要

We have investigated the fractal characteristics and shape complexity of thefracture surfaces of swelled isotactic polypropylene Y1600 in supercriticalcarbon dioxide fluid through the consideration of the statistics of the islandsin binary SEM images. The distributions of area $A$, perimeter $L$, and shapecomplexity $C$ follow power laws $p(A)\sim A^{-(\mu_A+1)}$, $p(L)\simL^{-(\mu_L+1)}$, and $p(C)\sim C^{-(\nu+1)}$, with the scaling ranges spanningover two decades. The perimeter and shape complexity scale respectively as$L\sim A^{D/2}$ and $C\sim A^q$ in two scaling regions delimited by $A\approx10^3$. The fractal dimension and shape complexity increase when the temperaturedecreases. In addition, the relationships among different power-law scalingexponents $\mu_A$, $\mu_B$, $\nu$, $D$, and $q$ have been derived analytically,assuming that $A$, $L$, and $C$ follow power-law distributions.