## 3 Results and Analysis
### Analysis of Critical Infiltration Pressure  
Critical infiltration pressure \(P_{\rm in}\) is defined as the initial pressure for liquid molecules invade nanoporous medium. NEAS with cascade characteristics have second-order critical infiltration pressure. Figure 7 shows the critical infiltration pressure of both large/bottom tube and small/top tube in a certain NEAS at different system temperatures. It can be seen from the figures, the critical infiltration pressure of the small tube (in DNEAS) and the top tube (in SNEAS) decreases with the increase in system temperature. The smaller the pore size, the faster the critical infiltration pressure decreases.  
To further illuminate the influence of pore configuration on infiltration process, we calculated the process of water molecules invading into a single tube, namely single tube NEAS, the diameter of which corresponds to the CNTs in DNEAS/SNEAS. Fixing the type of the large/bottom tube (in DNEAS/SNEAS, respectively) as CNT(22,22), the critical infiltration pressure of small/top tube (in DNEAS/SNEAS, respectively) is compared with that of the corresponding single tube NEAS at different temperatures, as shown in Figure 8.  
Figure 6: Critical pore difference varying with the larger tube at different temperatures. (**a**) DNEAS; (**b**) SNEAS.  
As can be seen from Figure 8a, the critical infiltration pressure of the small tube in DNEAS and the critical infiltration pressure of the corresponding single tube basically coincided. In our previous study, infiltration of water molecules into the large tube and the small tube in DNEAS were independent to each other [62]. Thus, the influence of system temperature on the critical infiltration pressure of DNEAS is a superposition of the corresponding single tubes NEAS.  
Yet, things were a little different in SNEAS. As can be seen from Figure 8b, the critical infiltration pressure of the top tube in SNEAS was lower than that of the corresponding single tube, and the smaller the pore size, the greater the difference. In SNEAS, the critical infiltration pressure of the top tube decreased with the increase in the diameter of the bottom tube, at a certain temperature [62]. Thus, the critical infiltration pressure of the top tube in SNEAS was lower than that of the corresponding single tube.  
The number of hydrogen bond in water determines the density, surface tension, boiling point, and other key properties of water [63]. The change of surface tension will directly lead to the change of critical infiltration pressure. To further analyze mechanism of temperature effect on the cascade characteristics of SNEAS, the number of hydrogen bonds at the entrance of the top CNTs of SNEASs is extracted for comparative analysis  
Figure 8: Comparison of critical infiltration pressure of small/top tube in different NEASs at different temperatures. (**a**) DNEAS; (**b**) SNEAS.  
Figure 7: Critical infiltration pressure of NEASs at different temperatures. (**a**) DNEAS; (**b**) SNEAS.  
in Figure 9, as well as the number of hydrogen bonds of the corresponding single tube NEAS. SNEASs composed of CNT(16,16)+CNT(8,8) and CNT(16,16)+CNT(12,12) were taken as examples. It can be seen from the figure that the number of hydrogen bonds at the entrance of CNT(16,16) in all the three studied systems were consistent at different system temperatures. Consequently, the critical infiltration pressure of water molecules invading into CNT(16,16) were the same, which coincided with the rule found in Figure 7b. With the decrease in pore size, the sensitivity of all system parameters to system temperature increased. With the lift of system temperature, the free energy of the system increased, the intermolecular forces decreased [64], and it was easier to lose hydrogen bonds for water molecules during invading. For the top tube CNT(8,8)/CNT(12,12) in SNEAS, the number of hydrogen bonds at their entrance was less than that of the corresponding single tube NEAS, and decreased significantly with the increase in system temperature.