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Multifractal analysis of the fracture surfaces of foamed polypropylene/polyethylene blends |
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| Authors: | Chuang Liu Xiu-Lei Jiang Ling Zhao Wei-Kang Yuan |
| Institution: | a State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China b Engineering Research Center of Process Systems Engineering (Ministry of Education), East China University of Science and Technology, Shanghai 200237, China c School of Business, East China University of Science and Technology, Shanghai 200237, China d School of Science, East China University of Science and Technology, Shanghai 200237, China e Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China |
| Abstract: | The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene (PP/PE) blends at different temperatures. Nice power-law scaling relationship between the detrended fluctuation function Fq and the scale s is observed for different orders q and the scaling exponent h(q) is found to be a nonlinear function of q, confirming the presence of multifractality in the fracture surfaces. The multifractal spectra f(α) are obtained numerically through Legendre transform. The shape of the multifractal spectrum of singularities can be well captured by the width of spectrum  and the difference of dimension  . With the increase of the PE content, the fracture surface becomes more irregular and complex, as is manifested by the facts that  increases and  decreases from positive to negative. A qualitative interpretation is provided based on the foaming process. |
| Keywords: | Fracture surface Batch foaming Multifractal detrended fluctuation analysis Singularity spectrum Complexity |
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