## 3 Results and Discussion  
### Simulations Results of PCNT  
Figure 1 shows the entering of PCNT from the aqueous phase into the lipid bilayer. Generally, the process was composed of two stages: (1) fast adsorption of PCNT at the lipid-water interface in an orientation parallel to the membrane plane, followed by (2) spontaneous tilting of the tube to insert the membrane. In detail, we employed the center of mass (COM) distance in the \(z\)-direction (denoted as \(d_{z}\)) between PCNT and the membrane to depict this entry (Figure 1B). The orientation of PCNT out and in the membrane is monitored by the tilt angle (\(\alpha\)), which is defined as the included angle between the central axis of PCNT and the membrane plane (\(xy\)-plane). It is observed that PCNT initially diffuses quickly toward the bilayer. Correspondingly, \(d_{z}\) drops fast from 4 nm to 2.5 nm in the first 3 ns. Then PCNT lies flat (\(\alpha\) is close to 90\({}^{\circ}\)) at the hydrophilic interface until \(t=24\) ns. However, at \(t=25\) ns, one end of the PCNT begins to slant and insert the membrane (see snapshots at t = 25 ns), and then the whole PCNT is quickly pulled into the membrane in the following 2 ns in a tilted position (see snapshots at t = 26 and 27 ns). Accordingly, \(d_{z}\) plummets from 2.5 to 0.5 nm, and \(\alpha\) drops from 90\({}^{\circ}\) to 45\({}^{\circ}\). After entering the membrane, the CNT just floats therein with a tilted orientation (snapshot at t = 100 ns). And the membrane is kept intact without any rupture. Similar to the permeation of fullerene and graphene in the lipid membrane, the fast insertion of PCNT is driven by the strong dispersion interactions between PCNT and lipid tails. We, therefore, calculated the interaction energy of PCNT with the bilayer (Figure 1C). Here, the energy is defined as the vdW interaction between the CNT and membrane. The energy curve exhibited the same trend as that of \(d_{z}\) (see Figure 1b,c), implying that the translocation of PCNT from the water to the membrane is driven by this interaction. The energy difference of CNT in and out of the bilayer reached about 1200 kJ/mol. It is clear that the huge fall in the energy makes PCNT adsorb fast into the lipid bilayer. The location and orientation of PCNT in the membrane can be characterized by the horizontal COM distance between PCNT and membrane (marked as \(d_{xy}\)) and the tilt angle \(\alpha\). As shown in Figure 2A, the curves of \(d_{xy}\) fluctuate dramatically in both systems, indicating that PCNT can move freely in the membrane. Interestingly, it is found that PCNT exhibits different orientations at the end of each simulation, namely, vertical (Figure 1, snapshot at \(t\)=100 ns), horizontal (Figure S1A, snapshot at \(t=100\) ns) and tilted (Figure S1B, snapshot at \(t=100\) ns). We, therefore, compared the interaction energy between CNT and bilayer at different tilt angles (\(0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), and \(90^{\circ}\)), as shown in Figure 2C. The energy at each tilt angle shows little difference, which is less than 3% between the strongest interaction (-1573 kJ/mol at \(\alpha=0^{\circ}\)) and the weakest one (-1529 kJ/mol at \(\alpha=45^{\circ}\)), implyingthat PCNT resided in the bilayer with no specific orientations. We repeated the simulations with PCNT embedded in the bilayer center horizontally and vertically and obtained similar results, though PCNT may be confined at local minima (see Supplementary Material, Figure S1). To explore the effects of CNT length on its insertion into the lipid membrane, we performed three additional independent simulations, with different lengths of PCNTs, namely, 2.4 nm, 3.6 nm, and 4.8 nm, which are shorter or close to or longer than the bilayer thickness. As shown in Figure 3, the spontaneous insertion of PCNTs in the lipid bilayer was robust, independent of the lengths of PCNTs (see snapshots at \(t=100\) ns).