# Modified Dual-Site Langmuir Adsorption Equilibrium Models from A GCMC Molecular Simulation
## 5 Conclusions  
In this study, a GCMC molecular simulation was used to calculate the CO\({}_{2}\) adsorption equilibrium on MIL-101 (Cr) at 298 K, and the characteristics and distribution of adsorption energy with pressure were obtained. The calculated results showed that the adsorption energies with different adsorption pressures fitted a normal distribution and the relationship of average adsorption energies with pressures had a linear form. The linear relationship between the adsorption energies and pressure was used to modify the parameters of the DSL model, and the M-DSL model was used to correlate the adsorption equilibrium data on CO\({}_{2}\)-MIL-101 (Cr), C\({}_{2}\)H\({}_{4}\)-HHPAC, CH\({}_{4}\)-BPL, and CO\({}_{2}\)-H-Mordenite. The results showed that the accuracy and generality of the M-DSL model were significantly improved after the modification and the average regression accuracy of the correlation of adsorption equilibrium data on each system was increased by 38%. The M-DSL model can better correlate the adsorption equilibrium data in high- or low-temperature ranges, and its correlation effect in the normal temperature range was also better than that of the DSL model. In addition, the M-DSL model showed a better correlation for systems with a more complex pore structure, such as CO\({}_{2}\)-MIL-101 (Cr). Similar to the DSL model, the linear relationship between the adsorption energy and pressure was also used to modify the TDSL model. The obtained M-TDSL model was checked with the abovementioned adsorption equilibrium systems. The results also indicated that the M-TDSL model could be used to improve the correlation of adsorption equilibrium data obtained at different temperatures. The average accuracy of the correlation for each system was increased by 23%, and the physical meanings of the parameters in the M-DSL model were clear and definite. In the process of practical applications, the modified models would increase the number of required calculations due to their more complex form, which will become a limitation. However, their good accuracy and versatility can make up for this disadvantage. Finally, our conclusion that adsorption energy has a linear relationship with pressure provides a basis for modifying other types of adsorption equilibrium models. The linear relationship between the adsorption energy and pressure could be further tested in other adsorption equilibrium models to determine its universality.  
**Supplementary Materials:** The following are available online at [[http://www.mdpi.com/2076-3417/10/4/1311/s1](http://www.mdpi.com/2076-3417/10/4/1311/s1)]([http://www.mdpi.com/2076-3417/10/4/1311/s1](http://www.mdpi.com/2076-3417/10/4/1311/s1)), Figure S1: Comparison curves of the DSL model and the M-DSL model for different systems, Figure S2: Comparison curves of the TDSL model and the M-TDSL model for different systems.  
**Author Contributions:** Conceptualization, [PERSON] and [PERSON]; methodology, [PERSON]; software, [PERSON]; validation, [PERSON], [PERSON] and [PERSON]; formal analysis, [PERSON]; investigation, [PERSON] and [PERSON]; resources, [PERSON]; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON] and [PERSON]; visualization, [PERSON]; supervision, [PERSON]; project administration, [PERSON] All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China (grant No.: 20276029) and the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province, China (grant No.: 16 KBJB430036).  
**Acknowledgments:** The authors appreciate [PERSON] and [PERSON] for their helps in the process of molecular simulations.  
**Conflicts of Interest:** The authors declare no conflict of interest.