## 3 Results and Discussion
### Molecular Chain Motion  
The motion of the molecular chains is closely related to the conformation evolution of the molecular chains. It is usually characterized by mean square displacement (_MSD_), which is the mean square value of the increment of the atomic position vector at different times. It can be used to characterize the migration behavior of PE chains, which can be expressed by  
\[MSD=\left\langle\left|r_{i}(t)-r_{i}(0)\right|^{2}\right\rangle \tag{2}\]  
where \(r_{i}(0)\) and \(r_{i}(t)\) are the positions of the \(i\)th atom at the initial time and time \(t\), respectively.  
According to the change in the trend of \(MSD\) with time, as shown in Figure 5, the \(MSD\) values of the three curves increase most in their respective 100 ps, and the slopes of the curves are highest. According to the [PERSON] equation, the atomic diffusion coefficient \(D\) is one-sixth of the slope of the \(MSD\) curve, as shown in Equation (3) [29]. When the temperature is high, the energy of the system is correspondingly high, and the molecular chains easily overcome the migration barrier and cross the region of high potential energy. Thus, the diffusion of molecular chains is promoted, with a high diffusion coefficient and \(MSD\) value. Especially for the sheared pure PE system after the cessation of shear, the diffusion coefficient is much larger than those of the composite systems. For a linear chain polymer with good flexibility, the viscous flow activation energy is low. The viscous flow activation energy is the minimum energy required for the molecular chain segments to overcome the barrier and jump from the original position to the adjacent \"hole\". Therefore, PE molecular chains can easily overcome the viscous flow activation energy, undergo a violent thermal movement, and shorten the relaxation time, which is the time required for the molecular chains to recover from the unstable orientation state to the low-energy winding state through molecular motion. Subsequently, the entanglement barrier is difficult to overcome with decreasing temperature, the relaxation speed decreases significantly, and the slope of the \(MSD\) curve decreases rapidly. Thus, the molecular chains migration weakens. However, the \(MSD\) of PE chains in the sheared composite system is markedly reduced. This occurs because the molecular chains movement slows down under the action of CNT adsorption, and the stretched state of PE chains is basically maintained. Thus, the molecular chain segments only need minor adjustments, and only migrate and diffuse within a small range. The slope of the \(MSD\) curve is very gradual. Compared with the sheared composite system, the molecular chain segments need to be adjusted slightly more under the induction of the CNT, due to the initial molecular chains of the static composite system, which are mainly in a random state. The migration and diffusion of the molecular chains are slightly stronger, and the \(MSD\) is slightly larger.  
\[D=\frac{1}{6}\lim_{t\rightarrow\infty}\frac{d}{dt}\left\langle\left|r_{i}(t)- r_{i}(0)\right|^{2}\right\rangle \tag{3}\]  
Figure 5: The change in the mean square displacement (\(MSD\)) of PE molecular chains over time.