# Modified Dual-Site Langmuir Adsorption Equilibrium Models from A GCMC Molecular Simulation
## 4 Results and Discussion
### Regression of Adsorption Equilibrium Data with the DSL Model and the M-DSL Model
Similarly, the adsorbates in these systems contained common organic gases such as CH\({}_{4}\) and C\({}_{2}\)H\({}_{4}\) and common inorganic gas CO\({}_{2}\). Therefore, it could be said that the adsorption systems studied in this paper were sufficiently comprehensive, and the conclusions could be applied to most systems in industry. Supplementary Figure S1 compares the correlation curves of the DSL model and the M-DSL model for different systems. Tables 7 and 8 show the corresponding parameter values that were obtained by the regression of the adsorption equilibrium data on each system by using the DSL and M-DSL models, respectively. As shown in Figure S1, for the C\({}_{2}\)H\({}_{4}\)-HHPAC system, the DSL model was able to relate the entire adsorption isotherm, and the regression effects were quite different under different temperatures and pressures. From Tables 7 and 8, when the temperature was 253.15, 273.15, and 293.15 K, the DSL model was able to correlate the adsorption equilibrium data, which verified the applicability of the DSL model in the normal temperature range. However, the M-DSL model can better describe the adsorption isotherms of the system at these temperatures. The value of R\({}^{2}\) was greater than 0.998, and the SSE value was less than 0.1. By calculating the change in the SSE, we can see that the regression accuracy of the data with the M-DSL model was approximately 30% higher than that with the DSL model. These results indicated that the M-DSL model inherited the advantages of the DSL model in the normal temperature range and had better applicability. describe adsorption isotherms in the low-temperature range. The regression accuracy of the M-DSL model to the adsorption equilibrium data was improved by more than 50%, the R\({}^{2}\) was greater than 0.995, and the SSE was less than 0.3. In addition, the M-DSL model had obvious advantages in the high-temperature range. When the temperature was 313.15 K, the correlation curve of the M-DSL model was smoother than that of the DSL model. The R\({}^{2}\) of the M-DSL model increased to 0.999, the SSE decreased to 0.03, and the regression accuracy increased by 94%. We drew similar conclusions for the CH\({}_{4}\)-BPL activated carbon and CO\({}_{2}\)-H-Mordenite systems. The regression accuracies of the M-DSL model and the DSL model were 22% and 8%, respectively. In conclusion, in ranges, in which large changes in adsorption capacity occur, such as high-temperature or low-temperature ranges, the adsorption energy cannot be simply assumed to be constant. The M-DSL model, which takes into account the linear relationship between adsorption energy and adsorption pressure, has a wider application range than the DSL model. It is also able to correlate adsorption equilibrium data well in the low-temperature range, the high-temperature range, and a relatively high-pressure range, where the DSL model is inapplicable. Regarding the MIL-101 (Cr)-CO\({}_{2}\) system, because the pore structure of the adsorbent was more complex than that of carbon materials and molecular sieves, the regression effect of the DSL model was poor. The value of R\({}^{2}\) was only 0.98, which cannot produce the expected effect. The regression effect of CO2-MIL-101 (Cr) was greatly improved when using the M-DSL model. The R\({}^{2}\) value was 0.9999, which is close to its upper limit (1), and the SSE was also very small (almost 0). The accuracy of the regression was 98% higher than that of the original DSL model. This result showed that the M-DSL model better correlated the adsorption equilibrium data on systems with a complex structure. Considering the linear relationship between the adsorption energy and pressure in an adsorption system with a complex pore structure can greatly improve the accuracy of the DSL model and improve the universality of the DSL model.