*3.4. Sweep Current*

Figure 9 presents the storage modulus of the MRE samples at various magnetic flux densities. All MRE samples showed an increasing trend in the storage modulus parallel with the increase of the magnetic field. The summary of the rheological properties of the samples is tabulated in Table 3. The initial storage modulus of MRE + A2 showed a higher value of 0.26 MPa than the control MRE, which was at 0.19 MPa, while, the MRE + A1 exhibited the lowest initial storage modulus of 0.07 MPa. Furthermore, the MRE + A2 depicted the highest storage modulus of 0.82 MPa, followed by the control MRE at 0.50 MPa and MRE + A1 at 0.47 MPa. Both of the MRE samples with A1 and A2 show a higher MR effect—264% and 40% higher, respectively—than the control MRE. It is well known that the enhancement of the rheological properties of MRE depended on the concentration of the magnetic particles, interaction between matrix–filler and also, that of filler–filler. Therefore, the finding in this study revealed that both MREs with nanosized Ni-Mg cobalt-ferrites indicated good compatibility, interaction and bonding between matrix–filler. Due to good adhesion and binding forces between matrix-CIPs and nanosized Ni-Mg cobalt-ferrites, the macromolecular chains are restricted, thus enhancing the storage modulus, which resulted in a higher MR effect. Moreover, the general behavior of the nanosized particles—in which they tend to orient and respond faster than the larger particles—subjected to the magnetic field is also contributed to the increase in the storage modulus and magnetic effect.

**Table 3.** The initial modulus, absolute (Δ), and relative magnetoresistance (MR) effect.


**Figure 9.** The storage modulus of all MRE samples as a function of magnetic flux density.

### *3.5. Electrical Resistance of the MRE Samples*

The electrical resistance of the MRE samples provides valuable information about the behavior of electric charge carriers, which leads to a good understanding and explanation of the conduction mechanism in MRE with nanosized Ni-Mg cobalt-ferrites. Figure 10 displays the behaviors of MRE with A1 and A2, correlated to different applied weights in the <sup>o</sup>ff- and on-state conditions.

**Figure 10.** Electrical resistance comparison of MRE samples at the <sup>o</sup>ff- (0 T) and the on-state (0.1 T) conditions.

The results obtained by changing the applied weight in the range of 50 to 600 g showed that the electrical resistance decreased at a higher applied weight, which proved that the MRE with nanosized Ni-Mg cobalt-ferrites is capable of exhibiting a significant change towards the electrical resistance of the MRE. Initially, in the <sup>o</sup>ff- and on-state conditions—(0 T) and (0.1 T)—the electrical resistances of MRE + A1 and MRE + A2 in the applied weight range from 50 to 600 g at increments of 50 g, showed an exponential decay. The summary of the electrical resistance of both MRE samples is tabulated in Table 4.


**Table 4.** The electrical resistance of MRE + A1 and MRE + A2 with an increment of weight at the off-state (0 T) and the on-state (0.1 T) conditions.

The results demonstrated that for both the <sup>o</sup>ff- and on-state conditions, MRE + A1 exhibited a low electrical resistance as compared to MRE + A2, which implied that MRE + A1 is more sensitive towards the changes in force. In general, in the presence of a magnetic field, the forces between the CIPs and nanosized Ni-Mg cobalt-ferrites increased as the particles tended to form a chain-like structure. In the meantime, due to the existence of the nanosized Ni-Mg cobalt-ferrites in the MRE, the strength of the materials increased. Therefore, the mobility of these particles was restricted and led to a reduction in the electrical resistance.

The mechanism of the particle interactions in the MRE samples in the absence and presence of magnetic and electric fields are shown in Figure 10. As shown in Figure 11a, during the absence of external magnetic and electric fields, the CIPs and the nanosized Ni-Mg cobalt-ferrites tend to disperse randomly in the MRE samples. However, in the presence of a magnetic field, the CIPs tend to form chain-like structures, which can be seen in Figure 11b. In addition, the nanosized Ni-Mg cobalt-ferrites fill the void between the CIPs, which enhanced the attraction force of these particles. Notably, in the presence of magnetic and electric fields (Figure 11c), the CIPs and nanosized Ni-Mg cobalt-ferrites tend to vibrate and form a chain-like structure according to the strength of the magnetic and electrical field applied. Due to the small size of the nanosized Ni-Mg cobalt-ferrites that formed in the magnetic field, the reaction is easier as compared to the CIPs. Hitherto, the CIPs and nanosized Ni-Mg cobalt-ferrites exhibit an increased magnetic moment and lead to an enhancement in the interparticle attraction force. The enhancement of this interparticle attraction force resulted in a decrease in the electrical resistance of the MRE samples, which was proven experimentally and is shown in Figure 10.

**Figure 11.** Mechanism of particles interaction in MRE with the absence and presence of magnetic and electric fields.
