**3. Microstructure observation**

To see microstructure of Gr-MREs, LV-SEM (JSM 6490LV SEM) is used. Figures 1- 3 show the surface imaging for MRE microstructures. Specifically, Fig. 1 shows the microstructure of isotropic and anisotropic Gr-MREs without graphite. The carbonyl iron particles are arranged in chains in the anisotropic sample, where they are dispersed randomly in the isotropic sample. According to Fig. 2 (a) and Fig. 3 (a), in the anisotropic Gr-MREs, the carbonyl iron particles are arranged in chains, whereas the graphite powders dispersed randomly in the matrix. The reason of this phenomenon is that the magnetic field only affects the carbonyl iron particles, but not the graphite. So upon magnetisation, the carbonyl iron particle chains tend to orient along the same direction as the magnetic field in the matrix.

By comparing Fig. 1 (a), Fig. 2 (a) and Fig. 3 (ba), we can see that the carbonyl iron chains in the sample without graphite have the best alignment performance. Further, the carbonyl iron chains in Fig. 2 (a) are aligned better than those in Fig. 3 (a). The reason is that when the mixture of carbonyl iron, silicone rubber, silicone oil and graphite is curing under the magnetic field, the graphite powders in Gr-MREs affect the carbonyl iron particles' movement. The more graphite in the mixture, the more effects are applied on to the carbonyl iron chains, which influence the magnetorheology of MREs.


**Table 1.** Components of Gr MRE samples
