## 4 Results and Discussion  
The presented research investigated what range of fibers size can be expected for the considered sets of parameters and the wide range of \(\chi\). The results are shown in Figure 1(a) (case 1) and Figure 1(b) (case 2). It can be seen that, in two instances, it was possible to produce fibers of 1000 nm in diameter (and less). In the next step, it was checked how the \(\chi\) changes may affect the fibers of 105 nm and 340 nm diameter (Figure 2(a),b, dashed line). As shown in Figure 2(a), the slight changes in the \(\chi\) values still led to fibers of \(\approx\)105 nm. However, as the \(\chi\) values decreased, the fiber sizes became larger. The results shown in Figure 2(b) indicated that small changes in the \(\chi\) values significantly influenced the size of the fibers; \(\chi=6.35\) led to the fibers of 340 nm diameter, while \(\chi=25\) led to fibers of \(\approx\)200 nm diameter. It can also be observed that, in both cases, the change in applied voltage had a crucial influence on the fiber size. The results of the simulations confirmed the rule that, the higher the voltage applied to the solution, the thinner the fibers obtained [19].  
The individual ranges of \(\chi\) values that lead to fibers with diameters of 500 nm, 200 nm, 150 nm, and 100 nm are shown in Figures 3-6. According to the results, it was possible to obtain fibers of F\({}_{\text{D}}=500\) nm, when \(\chi\in[4.7;\,5.5]\) (Figure 3(a)) and \(\chi\in[4.7;\,5.0]\) (Figure 3(b)) for all considered situations (\(\Delta\text{V}=\{12,\,16,\,22,\,25,\,27\}\) kV). With regard to Figure 4, it was possible to obtain fibers of 200 nm diameter, when \(\chi\in[8;\,100]\) (Figure 4(a)) and  
Figure 6: The fiber diameter and characteristic axial length scale dependence: (a) 8 wt% of the poly(acrylonitrile) (PAN) solution and (b) 11 wt% of the PAN solution.  
\(\chi\in[6;\ 25]\) (Figure 4b) (also for all considered situations, where \(\Delta\mathrm{V}=\{12,\ 16,\ 22,\ 25,\ 27\}\)). Further investigations are shown in Figure 5; it can be seen that, to obtain the fibers with \(\mathrm{F_{D}}=150\) nm, \(\chi\in[19.6;\ 272]\) (Figure 5a) and \(\chi\in[11;\ 267]\) (Figure 5b) had to be used. It is also worth noting that it was not possible to obtain fibers of \(\mathrm{F_{D}}=150\) nm when \(\Delta\mathrm{V}=12\) kV (Figure 5a). To obtain fibers of \(\mathrm{F_{D}}=100\) nm, \(\chi\in[587;\ 1283]\) (Figure 6a) and \(\chi\in[43;\ 239]\) (Figure 6b) were applied. Nevertheless, the production of fibers with this diameter and \(\chi\) range was possible only for higher applied voltages: \(\Delta\mathrm{V}=\{25,27\}\) (Figure 6a) and \(\Delta\mathrm{V}=\{22,25,27\}\) (Figure 6b).  
According to the studies carried out, it was possible to determine the poly(acrylonitrile) fiber size with respect to the \(\chi\) values and applied sets of parameters. The presented approach can be useful in terms of the filtration materials design. In general, the nonwovens of ultrathin fibers at \(\approx\)100 nm can be used to remove particles of aerodynamic diameter about 2500 nm or less. The nonwovens consisting of thick (\(\approx\)1000 nm) fibers can be used to remove bigger particles (aerodynamic diameter \(\approx\)10,000 nm). It is also possible to use hybrid solutions or constructions that can increase the packing density of the nonwovens (bead-on-string structures); the schematic view of fiber fabrication via electrospinninging as well as the PM\({}_{10}\) and PM\({}_{2.5}\) removing operations can be seen in Figures 7 and 8.