Wavelet-Fractal Based Morphologies Research On Supported Polyethylene Catalysts Surface

A study was conducted to investigate the surface morphologies of supported polyethylene catalysts by characterizing the details on the catalyst surfaces with an approach combining fractal with wavelet.Firstly, the catalysts BCG and MSPC were researched by wavelet multi-resolution analysis method which can decompose a surface image into approximation components and details components at different scales. The fractal dimension and square root roughness R_s of these components were computed after they were reconstructed. The results reveal that the characterization of details parts at smaller scales and approximation components with fractal dimension calculated by fractal brown model is reasonable. Furthermore, it is concluded that the connotations of fractal dimension and R_s of an image are different, and the fractal dimension mainly describes the self-similarity feature of surface morphology. More importantly, we can have a conclusion that the key of the characterization of catalyst surface morphology is to characterize the image details at smaller scales.Secondly, the multiscale edge images of catalyst BCG and MSPC surfaces are extracted by wavelet transform modulus maxima (WTMM) method. And the distribution of edge points and their singularity intensity distribution at every scale are studied by multifractal method. Meanwhile, the catalysts surface morphologies are analyzed by multifractal spectrum based on WTMM. It suggested that the change of catalyst surface morphology could be reflected by edge points on catalyst surface reasonably, and the edge points could be characterized by box-counting dimension and multifractal spectrum of edge image. The results show that the characteristics of details on BCG and MSPC catalysts surfaces can be described by this method, and have a good relationship with the activity of catalyst after considering the distribution of activity center in the whole catalyst(surface and inside). It is proposed that the activity of catalyst surface will be higher on the catalyst surface having more details. In addition, it is implied that the surfaces of catalyst BCG and MSPC have the statistical self-similar and scale-invariant properties by the research on probability density function of edge points on the catalysts surface.The research on catalyst surface details with hybrid fractal and wavelet method exerts the superiorities of wavelet and fractal, and offers a thought for studying solid surfaces morphologies.