Abstract
In this paper, the method of measuring the porosity of electrostatic nanofiber membrane by VC++ and Matlab is introduced. It is found that the ratio of the calculated porosity to the porosity measured by the mercury intrusion method accords with the famous Feigenbaum constant (α=2.5029078750957⋯). The porosity distribution of nanofiber membranes was studied by VC++ and Matlab based on the image obtained by using a scanning electron microscope. The porosity distribution calculated by using a computer is magnified by eα times which was named as relative porosity distribution. According to the relative porosity distribution, we use the algorithm proposed by Grassberger and Procaccia (briefly referred to as the G-P algorithm) to calculate the correlation fractal dimension. The correlation fractal dimension calculated from the relative porosity distribution series was between 1 and 2, consistent with geometric characteristics of coincidence samples. The fractal meaning of the Feigenbaum constant was verified again. In the end, we obtained the relationship between the associated fractal dimension and the filtration resistance by fitting in accordance with the secondary function relationship and reached the maximum correlation fractal dimension when the filtration resistance was 15–20 pa.
Highlights
Electrospinning is a technology of drawing polymer solution with high viscosity into fibers by electrostatic force
We believe that the measurement of porosity by the mercury intrusion method and the calculation of porosity by the image processing method should satisfy a certain relationship. e experimental results confirm that the ratio of the two is a Feigenbaum constant, which should be derived from the intrinsic structure of the electrospinning nanofibers with fractal properties, making their ratio more directly related to the chaotic constants
The correlation fractal dimension of the electrospun nanofibrous membrane treated with the Feigenbaum constant is between 1 and 2
Summary
Electrospinning is a technology of drawing polymer solution with high viscosity into fibers by electrostatic force. The box counting method is simple and effective, it is very difficult to study the pore characteristics of electrospun nanofiber because of their obvious distribution. According to the characteristics of electrospun nanofibers, we choose the correlation fractal dimension method to study. With the proper selection of M, we can find the correlation fractal dimension: Select the appropriate value of M; when the double log curve ln CM(r) − ln r has a linear interval long enough, the sample is considered to have a fractal structure. Is feature, in a sense, reflects the fractal characteristics of the porosity distribution of the electrospun nanofiber membrane. When calculating the porosity of the electrospun nanofiber membrane, the porosity distribution is expanded to eα multiple at first, and the correlation fractal dimension of the porosity distribution is calculated by using the G-P algorithm. It is found that the dimension is between 1 and 2, which is more in line with the geometric characteristics
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