## 3 Results and Analysis
### Analysis of Critical Pore Difference  
According to the pressure-volume characteristic curve of the system, we can identify whether the system display cascade characteristics under quasi-static loading procedure. Figure 5 shows the pore distribution diagram of cascade characteristics of NEASs at different system temperatures, applying red dots and black dots to distinguish whether the NEAS displays cascade characteristics. Extracting the critical pore difference of cascade NEASs at different system temperatures, the relationships between the critical pore difference of cascade NEASs at different temperatures were drawn in Figure 6. In Figures 5a and 6a, Figures 5b and 6b correspond to DNEAS and SNEAS, respectively.  
As can be seen from Figure 5, with the increase in temperature, systems displaying cascade characteristics transform into a single-stage system without cascade characteristics. The critical pore difference increases with the lift of system temperature. The smaller the pore size is, the more sensitive the critical infiltration pressure is to temperature. Thus, the changing degree of the critical infiltration pressure of CNT with small pore size is greater than that of CNT with larger pore size under the same temperature gradient. That is, the critical pore difference increases with the increase in the pore size when the system temperature remains unchanged, as shown in Figure 6.  
Figure 4: Variation curves of pressure—volume characteristics of NEASs at different temperatures (CNT17,17+CNT13,13). (**a**) DNEAS; (**b**) SNEAS.  
Figure 5: Pore size distribution of NEASs at different system temperature. (**a**) DNEAS; (**b**) SNEAS.  
Define the pore difference \(\Delta d^{D}\) as the difference between pore size of the large tube and the small tube in DNEAS, \(\Delta d^{\rm D}=d_{\rm large}-d_{\rm small}\), where \(d_{\rm large}\) is pore size of the large tube, and \(d_{\rm small}\) is pore size of the small tube. Define the pore difference \(\Delta d^{S}\) as the difference between pore size of the top tube and the bottom tube in SNEAS, \(\Delta d^{S}=d_{\rm bottom}-d_{\rm top}\), where, \(d_{\rm bottom}\) is pore size of the bottom tube, and \(d_{\rm top}\) is pore size of the top tube. The minimum pore difference between large and small tubes which enables NEAS to display cascade characteristics is defined as the critical pore difference, written as \(\Delta d^{D}_{\rm cr}\) for DNEAS and \(\Delta d^{S}_{\rm cr}\) for SNEAS. Fitting the dots in Figure 6, the correlation between the critical pore difference and system temperature of DNEAS and SNEAS can be obtained.  
In DNEAS:  
\[\Delta d^{\rm D}_{\rm cr}=\frac{18.317-0.08T}{1+e^{(d_{\rm large}+0.014T-25.352)/( 0.025T-6.182)}}+0.067T-13.259\left(\rm\AA\right) \tag{3}\]  
where the pore of the large is \(d_{\rm large}\) = 8.14-29.83 A, temperature is \(T\) = 280-360 K, the fitting error is 2.81%.  
In SNEAS:  
\[\Delta d^{\rm S}_{\rm cr}=\frac{0.073T-16.409}{1+e^{(d_{\rm bottom}+0.02T-27.28 )/(0.015T-3.484)}}+0.07T-14.287\left(\rm\AA\right) \tag{4}\]  
where the pore of the bottom tube is \(d_{\rm bottom}\) = 8.14-29.83 A, temperature is \(T\) = 280-360 K, the fitting error is 3.07%.