Fractal Characteristics of Porosity of Electrospun Nanofiber Membranes

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 · · ·). e porosity distribution of nanofiber membranes was studied by VC++ and Matlab based on the image obtained by using a scanning electron microscope. e porosity distribution calculated by using a computer is magnified by e α 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. e correlation fractal dimension calculated from the relative porosity distribution series was between 1 and 2, consistent with geometric characteristics of coincidence samples. e 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.

Fractal Properties of Pore Distribution of Electrospun Nanofiber Membrane

“…The fractal dimension of the average pore width obtained is consistent with the fractal dimension of porosity obtained by Ting Wang etc. [13] under the meaning of the relative error less than 10%, this shows that it is reasonable to discuss the correlation fractal dimension.…”

“…In this paper, the correlation fractal dimension was selected as a tool to analyze the chaotic and disordered pore distribution of electrospun nanofiber membrane. The relationship between the correlation fractal dimension of the average pore width of samples and its resistance [13,14] is shown in Table 3. Matlab was used to fit Table 3, and the correlation fractal dimension of the average pore width of the sample has a quadratic function relation with its resistance, that is, y=-0.000762226660605591x^2+0.0288271256410095x+1.3232485018709.…”

“…Taking sample 2 as an example, the BMP images of nanofibers were grayed successively, and the gray-value matrix was obtained by Matlab. We adopted the idea of Ting Wang and Ying Chen [13], and use 85% of the average gray value as the threshold value to transform the gray matrix into a 0-1 matrix, the number of 1 or -1 obtained by subtracting adjacent elements in each row of the 0-1 matrix , namely the number of pore or fibers in the row. Then, divide by the total length of the fiber pore (the sum of all zeroes for each row in the 0-1 matrix)to get the width of the average pore, or the average pore for short.…”

“…After obtaining the average pore data, multiply it by e . α , where α= 2.5029078750... (Feigenbaum's constant [13]):…”

“…In this paper, We used the average pore width value as the basis to calculate the fractal.However, the results obtained were surprisingly consistent with the results of Ting Wang, Ying Chen etc. [13]under the meaning of the relative error less than 10%, as shown in Table 5.…”