## 3 Results
### Numerical Simulations and MWCNT/PDMS Magnetic Patterning  
To propose low electrical percolation threshold designs for the fabrication of sensors, MWCNT interaction with more than one magnet was simulated. Three different configurations of permanent magnets were studied. The first pattern consisted of the use of permanent magnets in an alternating configuration; the second pattern consisted of a Halbach array; and finally, the third pattern consisted of the utilisation of permanent magnets in a design where the surface of the magnets had the same polarity. The configurations were first simulated using ANSYS software and then replicated in the laboratory. The magnets were placed under MWCNT/PDMS nanocomposites with a concentration of 0.1 wt.% before the cure of the polymer. Figure 8 represents the simulation results for the magnetic field distribution and the magnetic flux lines for the three different configurations. Figure 9 shows the magnetic patterns achieved using the three magnetic configurations (Figure 8a-c), compared with a randomly distributed nanocomposite (Figure 9a). The top line of Figure 9 represents the 3D image obtained in the micrographs, while the bottom line shows optical micrographs of the nanocomposites prepared. The 3D images reinforce the location of the MWCNT agglomerates on the polymeric matrix. A comparison of the  
Figure 8: Magnet configuration to create linear and discontinuous patterns, using **(a)** alternated polarity, **(b)** Halbach array, and **(c)** same polarity configurations. simulation and experimental results shows the similarity between the MWCNT location and the simulation predictions, the latter showing the density of the magnetic field of permanent neodymium magnets in the air. As demonstrated in Figures 8 and 9, the MWCNT localisation replicates the magnetic pattern of the permanent magnets, accumulating in the regions of higher magnetic flux and following the magnetic field patterns of the interaction between multiple permanent magnets. Figure 9b illustrates the effect of using alternate polarity magnets, showing that it generates a continuous pattern, such as continuous lines. Using magnets aligned with the same polarity (Figure 9d) creates discontinuities due to the low magnetic field in the region between the magnets. Finally, the utilisation of Halbach arrays (Figure 9c) also creates discontinuities due to the non-uniform field at the surface of the magnets. Lastly, sensor electrodes were developed using MWCNT patterns in PDMS generated with permanent magnets. The first step consisted in simulating the patterns using ANSYS software and then replicating the patterns in the laboratory, as shown in Figure 10.  
Figure 10 illustrates that, as demonstrated before, the pattern generated by the simulation for the magnetic field intensity is replicated by the MWCNT localisation inside the PDMS matrix. While analysing the electrical resistivity of the nanocomposites prepared with different magnetic patterning, shown in Figure 11, it is observed that the random distribution nanocomposite with 0.5 wt.% MWCNTs has a high electrical resistivity due to a lack of contact between conductive particles. The nanocomposites prepared with magnetic patterning presented lower electrical resistivity compared with randomly distributed nanocomposites, either for 0.5 or 1 wt.% MWCNT concentration. The zig-zag pattern produced higher electrical resistivity nanocomposites than the other patterns, probably due to the increase in length of the electrically conductive path. This increase in resistivity may help to adjust the electrical resistance of a sensor if needed. Figure 9: Magnetic patterns and 3D reconstruction of the samples (**a**) randomly distributed, (**b**) magnetic pattern with alternate polarity, (**c**) magnetic pattern with Halbach array, and (**d**) magnetic pattern with the same polarity. Figure 11: Electrical resistivity of the nanocomposites fabricated with different magnetic patterns.