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Adsorption-based carbon capture is widely regarded as an effective strategy for CO2 mitigation due to its high efficiency, structural tunability, and energy-saving potential. However, most conventional adsorption models are built upon the assumption of independent site occupation, which inherently neglects cooperative interactions and limits their ability to consistently describe complex adsorption behavior across different materials and operating conditions. In such context, this work aims to develop a cluster-based description of adsorption that captures cooperative effects while maintaining thermodynamic consistency. Such a perspective complements conventional adsorption models by incorporating cooperative effects beyond the assumption of independent site occupation. This work presents the Cluster Adsorption Langmuir Model (CALM), which introduces clusters as an abstract representation of the minimum cooperative unit of an adsorption event. Within this framework, the CALM formulation is derived from a statistical thermodynamic partition function, linking cooperative adsorption behavior to equilibrium properties in a consistent manner. First, the theoretical formulation of CALM is established based on the concept of cooperative clusters and thermodynamic considerations. Then, adsorption behavior is interpreted in terms of ideal and non-ideal adsorption to provide a thermodynamic perspective for understanding model parameters. Finally, CALM is validated through isotherm fitting and heat analysis for representative systems, including MOFs, solid amines, and zeolites over a range of temperatures, showing improved fitting accuracy and better AIC/BIC performance compared with classical models. Overall, this work provides a physically interpretable and thermodynamically consistent description of adsorption behavior, offering a useful perspective for analyzing cooperative effects in adsorption systems.
Lan et al. (Sun,) studied this question.