## 3 Results and Discussion
At 100 ns of simulation, the structural peaks related to the ion\(-\)ion correlation are visible, indicating the growth of NaCl crystals. When the function \(r^{2}h_{+-}(r)\) becomes negative, a rough indication of the \"crystal magnitude\" is obtained: the positive region reflects the increase in the ion density in the crystal, and the negative region is the corresponding decrease in the ion density in the surrounding solution [30; 33]. This effect is evident in the bulk NaCl solution. For the bulk NaCl solution, a larger order is visible up to 2 nm, whereas for NaCl in contact with the hydrophobic membranes, it is up to 1.5 nm. Figure 5: NaCl crystals after 100 ns of simulation obtained in (**a**) bulk solution NaCl, (**b**) PVDF, and (**c**) PP system. Figure 6: _Cont._  
The presence of PP and PVDF membranes modified the shape of the r\({}^{2}\)h\({}_{+-}\)(r) function. Only positive regions are present in both Figure 6b,c, indicating the augmented ion density in the crystal. However, the disorder in the figure visible at larger separations could be related to the distinct crystal distribution in the PP (PVDF) systems, with a higher number of small crystals, and to the presence of water molecules (discussed below). Snapshots referring to specific simulation times, i.e., 5 ns (Figure 7a), 20 ns (Figure 7b), and 100 ns (Figure 5c) of PP model were related to the radial distribution function g(r) (Figure 7c) of the interaction of Na\({}^{+}\) and Cl\({}^{-}\) (the PP model was used as a reference, showing similar behavior to PVDF). Figure 6: r2h(r) function of NaCl (**a**) in bulk solution, (**b**) in PVDF system, and (**c**) in PP system. Here, both water molecules and polymeric membranes are not shown. After 5 ns of simulation, several crystals with small dimensions were distinguishable. So, a distinct order among the ions existed (Figure 7a), although the nuclei were immersed in amorphous NaCl agglomerates (disorder),  
Figure 7: Snapshot of NaCl in PP system at (**a**) 5 and (**b**) 20 ns of simulation; (**c**) g(r) function at 5, 20, and 100 ns of simulation. showing that the crystal structures were not completely stable yet. After 20 ns, larger crystals were found and the central part of the system appeared to be stable (Figure 7b). This reveals how rapidly the crystals grow over time, such as to form significant aggregates even at 20 ns. At 100 ns of simulations, stable crystals are made with few free ions available in the solution (Figure 5c). The analysis of the dimension is reflected by the analysis of the g(r). At 5 ns of simulations, one sharp peak and a second peak, less resolved at larger interionic distances referring to the increased spatial ordering of the ions, are visible. The evolution of the g(r) at 20 ns indicated well-defined peaks demonstrating nucleation and spatial ordering of the ions as reported also for the NaCl bulk solution at different concentrations [62; 63]. A similar g(r) plot appears at 100 ns as indicated by the crystal dimension at 20 ns (Figure 7b) and at 100 ns (Figure 5c). The contribution of water molecules to the formation of crystals is reflected by analyzing the Na\({}^{+}\) ion\(-\)water interaction (Figure 8). The peaks of the g(r) plot refer to the area corresponding to the growth of the crystal that decreased with time. At 5 ns, the peaks referring to the ion-water interaction are high and at a value corresponding to the first shell of solvation of Na\({}^{+}\) (0.23 and 0.25 nm) and in agreement with ab initio MD [64], neutron diffraction data [65], and with large-angle X-ray scattering (LAXS) data [66]. After 20 and 100 ns of simulation, the corresponding peaks are smaller and smaller but present, indicating that some residual water remained within the crystals both in the bulk solution and in the presence of the membrane surfaces. The place where crystals nucleate and grow is an important parameter to consider in the entire process because it is dependent on the strong repulsion between water and ions approaching the hydrophobic PVDF and PP surfaces.