## 3 Results and Discussion  
### Radius of Gyration  
Polymer molecular chains have multiple conformations due to the internal rotation of single bonds. Under the action of thermal motion, the molecular conformation changes constantly, and the molecular size and morphology change accordingly. The mean square radius of gyration can be used to characterize the size of the polymer molecular and the morphological distribution characteristics of molecular chains. It is defined as the mass average of the square of the distance from all atoms to their center of mass, which can be expressed as  
\[R(g)^{2}=\sum_{i=1}^{n}m_{i}r_{i}^{2}/\sum_{i=1}^{n}m_{i} \tag{1}\]  
Figure 1: Simulation models. (**a**) Initial model of composite system; (**b**) Initial conformation of composite system under static conditions; (**c**) Initial conformation of the composite system after shear; (**d**) Initial conformation of pure polyethylene (PE) system after shear.  
where \(R(g)\) is the radius of gyration, \(m_{i}\) is the mass of the \(i\)th atom, and \(r_{i}\) is the distance from the \(i\)th atom to the center of mass of the molecular chain.  
According to the distribution curve of the radius of gyration in Figure 2 and the evolution curve of the mean radius of gyration in Figure 3, the distribution interval (10.8 A, 27.46 A) of the radius of gyration of PE molecular chains in the static composite system is small, and the mean radius of gyration increases gently. This also shows that PE molecular morphology changes little and the adjustment induced by the CNT is limited in the static composite system, while the distribution range (53.84-74.86 A) of the radius of gyration of PE molecular chains in the sheared composite system is markedly increased. The mean radius of gyration decreases a little initially, and then increases gradually. This also indicates that elastic shrinkage occurs to some extent, due to the viscoelastic properties of the molecular chains at a higher melt temperature after the cessation of shear. Subsequently, the molecular chains further extend under the action of the CNT. In particular, the distribution curve of the radius of gyration of the sheared pure PE system moves to the left, relative to the sheared composite system, and the distribution range decreases significantly. Moreover, the mean radius of gyration decreases sharply within 100 ps. This shows that the atoms migrate closer to the center of mass of the molecular chain at a higher temperature after the cessation of shear, the size of molecular chains decreases considerably, and the degree of bending and winding of the molecular chains rises quickly. Then, the radius of gyration gradually stabilizes with the decreasing temperature.  
Figure 3: The evolution curve of the mean radius of gyration of PE molecular chains.  
Figure 2: The distribution curve of the radius of gyration of PE molecular chains after running for 500 ps.  
It can also be seen from Figure 3 that the mean radius of gyration (66.2 A) of the PE molecular chains in the sheared composite system is not only higher than the sheared pure PE system and the static composite system, but also higher than the sum of the static composite system (17.5 A) and the sheared pure PE system (39.9 A). Therefore, compared with the single effect of shear flow and the CNT, the combination of the two has a more obvious effect on the size of the molecular chains.