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

We have investigated the fractal characteristics and shape complexity of the fracture surfaces of swelled isotactic polypropylene Y1600 in supercritical carbon dioxide fluid through the consideration of the statistics of the regions embedded in the contours at different height of fracture landscapes (also called islands in the literature) of binary scanning electronic micrography images. The probability density functions of the areas A, perimeters L, and shape complexities C (defined by L/2 sqrt piA) of islands are shown to follow power laws p(A) approximately A-(muA+1), p(L) approximately L-(muL+1) and p(C) approximately C-(nu+1), with the scaling ranges spanning over two orders. The perimeter and shape complexity scale respectively as L approx. A(D/2)and C approx. A(q) in two scaling regions delimited by A approximately equal to 10(3). The fractal dimension and shape complexity increase when the temperature decreases. In addition, the relationships among different power-law scaling exponents muA, muB, nu, D, and q have been derived analytically, assuming that A, L, and C follow power-law distributions.