纳米复合材料分散相分散均匀性的分形表征

Fractal characterization of uniformity of discrete phase in nanocomposites

针对传统的纳米复合材料分散相分散均匀性评价方法的不足,提出了一种以分形理论为数学模型基础,以纳米复合材料的透射电镜(TEM,Transmission Electron Micro-scope)图像为评价对象的分散相分散均匀性的定量评价方法.运用离散对象构成的自然分形体的分形维数建立了分散相分散均匀性的数学模型.将纳米复合材料TEM图像进行图像处理,以纳米复合材料TEM图像的中心为圆心以不同的半径做圆,提取不同的圆内的粒子数与回转半径,并在双对数坐标中直线拟合.该直线的斜率的倒数即为分散均匀性参数,并以此作为评价分散相分散均匀性的指标.将该方法实际应用于聚合物基纳米填充复合材料分散相分散均匀性的描述,验证了该评价方法的可行性.

The traditional method to evaluate uniformity of discrete phase in polymer nanocomposite is deficient. A quantitative description method was proposed to evaluate uniformity of filling particles in polymer nanocomposite. The method is based on the mathematical model of fractals theory and takes the TEM （transmission electron microscope） image of polymer nanocomposite as the research object. An evenly distributed dispersed phase of the mathematical model was established by using a natural sub-fractal dimension formed by discrete objects. Then, the polymer nanocomposite TEM image was processed with image processing. Circles were drawn with different radius and with the TEM image＇s centroid as the circle center. The particle counts and gyration radius were extracted from the circles of the different radius and made coordinates of linear fitting in bi-logarithm. The reciprocal value of the linear slope just is uniformity parameter, which can be used as the evaluating indicator to evaluate the uniformity. The method was applied to describe the polymer-nano-particle composites, and the feasibility of the evaluating was verified.