## 2 Materials and Methods  
Samples for AFM investigations were prepared by electrospinningning with a wire-based electrospinning machine Nanospider Lab (Elmarco Ltd., Liberec, Czech Republic), using the following spinning parameters: voltage 80 kV, nozzle diameter 0.9 mm, carriage speed 100 mm/s, distance between bottom electrode and substrate 240 mm, distance between ground electrode and substrate 50 mm, temperature in the spinning chamber 22 \({}^{\circ}\)C and a relative humidity of 32-33%. To prepare the spinning solution, 16% polyacrylonitrile (PAN) (X-Pan, copolymer with 6% methyl methacrylate, from Dralon, Dormagen, Germany) were dissolved in dimethyl sulfoxide (DMSO, min 99.9%, S3 Chemicals, Bad Oeynhausen, Germany) by vigorously stirring at room temperature for 2 h.  
The nanofiber mats were detached from the polypropylene substrate after electrospinning and glued on glass slides for AFM investigations. The surfaces of the electrospun nanofiber mats were investigated by a FlexAFM (Nanosurf, Liestal, Switzerland) with an SHR300 cantilever (tip diameter 1 nm) in the dynamic mode. The sharp tip is supportive to avoid moving the nanofibers erroneously. Images sizes covered areas of 25 um \(\times\) 25 um, the lateral resolution is \(\sim\)100 nm. Approach parameters were optimized according to these surfaces (setpoint 60%, P-gain 750, I-gain 1200-1300 and D-gain 100, where the setpoint describes the oscillation amplitude of the cantilever, while P, I and D describe the proportional, integral and differential part of a common PID controller, respectively). Post-processing was performed in Gwyddion 2.51 software, using the following steps: polynomial background subtraction (3 rd degree horizontally and vertically), aligning rows (method: median of differences), deleting horizontal errors and sharpening (5 pixels) once or twice, in this order. In this way, five post-processed images were obtained in addition, to the original one. It should be mentioned that these steps are not always performed in exactly the same way, but the choice of parameters depends on the respective images. However, since the aim of these methods is always to gain the best possible images, there cannot be many variations between the post-processed images and so the influence on the Hurst exponent calculations must also be small. Calculation of the Hurst exponent followed procedures described in [28; 29; 30; 31]. In brief, a digital image for which the Hurst exponent is calculated is (in the simplest case) a black-and-white image, typically with the black area denoting the material (here, the nanofibers) and the white areas defining the pores between. On the black area of such an image, a random walking is performed, meaning that starting from an arbitrary pixel, a step in an arbitrary direction (up, down, left, or right) is done, followed by the next step in an arbitrary direction, etc. After a defined number of steps, the distance between starting and ending point is measured. If this displacement \(\Delta r\) is squared and averaged over several repetitions, a relation between \(\langle\Delta r^{2}\rangle\) and the number of steps \(n\) can be found:  
\[\langle\Delta r^{2}\rangle=Cn^{2h}\]  
with the Hurst exponent \(h\) and a constant \(C\) that has no relevance for our investigation. For a completely black square, \(h\) is \(\frac{1}{2}\), while for images with fine features, the value becomes smaller since the possible ways for the random walks are limited on these fine structures. The Hurst exponent is, thus, a good measure for hairiness of textiles or similar features [28; 29; 30]. For statistical examinations, the procedure is performed more than once, e.g., for 100-1000 randomly chosen starting points per image. For practical reasons, we usually use random walks with numbers of steps \(n\) in the range of 100-1,000,000 to test different possible scenarios of obtained distances.