## 2 Experimental
### Experimental Methods  
Mechanical properties. In order to investigate the influence of Fe\({}_{3}\)O\({}_{4}\) nanoparticles contents on the mechanical properties of Fe\({}_{3}\)O\({}_{4}\)/SBS/LLDPE composites, tensile tests at room temperature were performed with a SANS tester (Shenzhen SANS Material Test Instrument Co. Ltd., Shenzhen, China) according to ASTM D412. The strain rate was 2 mm\(\cdot\)min\({}^{-1}\).  
DSC. To explore the influence of the Fe\({}_{3}\)O\({}_{4}\) nanoparticles contents on thermal properties, the thermal properties of the SMPs were analyzed by differential scanning calorimetry (DSC) conducted on a DSC Pyris 1(Perkin Elmer, Itham city, MA, USA). The samples of about 5.0 mg were heated from 0 to 130 \({}^{\circ}\)C at a constant rate of 10 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\) and then passed through a cooling cycle with the same rate, and \(T_{\rm m}\)s were determined by this step.  
DMA. A dynamic mechanical analyzer was used to obtain the storage modulus of the Fe\({}_{3}\)O\({}_{4}\)/SBS/LLDPE composites. Dynamic mechanical analysis (DMA) was carried out in tensile loading mode using a DMA Q800 (TA Instruments, New Castle, DE, USA) to determine the thermo-mechanical properties. The samples were cut to dimensions of 2 \(\times\) 12 \(\times\) 30 mm\({}^{3}\) and the edges of the samples were wet sanded with 600 grit sandpapers. And the single cantilever clamping fixture (TA Instruments, New Castle, DE, USA) was used with amplitude of 10 \(\upmu\)m, a frequency of 1 Hz. The temperature was ramped from \(-\)20 to 130 \({}^{\circ}\)C at a rate of 3 \({}^{\circ}\)C/min.  
TEM and SEM. The particle size and morphology were characterized by the Transmission electron microscopy (TEM, Hitachi, H-600, Tokyo, Japan) and scanning electron microscope (SEM, INCA X-ACT, Tescan, Brno, Czech Republic). The Fe\({}_{3}\)O\({}_{4}\)/SBS/LLDPE composites were frozen in liquid nitrogen for 30 min, and then fractured quickly. The broken surfaces were sputter coated with a gold layer and observed with SEM.  
Shape memory properties of Fe\({}_{3}\)O\({}_{4}\)/SBS/LLDPE composites. The shape memory properties of Fe\({}_{3}\)O\({}_{4}\)/SBS/LLDPE composites were investigated by a method called fold-deploy shape memory test [23]. According to this method, the shape memory properties could be obtained by recording the bending angle. The specimens of 50 \(\times\) 10 \(\times\) 2 mm\({}^{3}\) (length \(\times\) width \(\times\) thickness) were folded at 110 \({}^{\circ}\)C followed by quenching into an ice-water bath. The folded samples were reheated at 110 \({}^{\circ}\)C or placed into an alternating magnetic field (\(f\) = 60 kHz) (GP-25 ultra-audio frequency induction heating equipment, Shannxi, China) to recover its original shape. The shape memory test of all samples was repeated for three times. The shape recovery process was recorded by using a digital camera (Canon Corporation, Tokyo, Japan). The changed angles of specimens were recorded; \(\theta_{f}\) was the angle of the folded samples after being exposed to room temperature for 5 min, and \(\theta_{r}\) was the final angle after one shape recovery process. The shape retention rate (\(R_{f}\)) and shape recovery rate (\(R_{r}\)) were calculated using Equations (1) and (2).  
\[R_{f}(\%)=\frac{180^{\circ}-\theta_{f}}{180^{\circ}}\times 100 \tag{1}\]  
\[R_{r}(\%)=\frac{\theta_{r}}{180^{\circ}}\times 100 \tag{2}\]