Bridging the Adsorption Data and Adsorption Process by Introducing a Polynomial Structure To Accurately Describe IUPAC Isotherms, Stepwise Isotherms, and Stepwise Breakthrough Curves

Porous heterogeneous adsorbents, those composed of multiple pore structures and surface chemical adsorption sites, can result in various gas or vapor adsorption isotherms, including five types of IUPAC adsorption isotherms and stepwise adsorption isotherms that have been difficult to model using a single adsorption equilibrium model. The limitation of the above equilibrium model further restricts the calculations of complex stepwise breakthrough curves. To bridge the adsorption data and adsorption process, it is important to first develop a simple model or method to describe these isotherms of various complex adsorption systems. In this work, assuming that the effect of the diffusion rate can be neglected under the static condition and the adsorption process is discontinuous, the number of adsorption isotherm inflection points can be used to represent the changed number of adsorption interactions. With the introduction of the polynomial structure, a series of empirical or semi-empirical polynomial adsorption models were developed. The N-site polynomial Langmuir–Freundlich equation could accurately fit common type I, II, III, IV, and V adsorption isotherms and complex stepwise adsorption isotherms covering various adsorbates, such as volatile organic compounds (VOCs), toxic industrial chemicals (TICs), water vapor, and carbon dioxide, as well as different adsorbents, such as metal/covalent organic frameworks (MOFs/COFs), zeolites, and porous carbons. Similarly, the introduction of a polynomial structure, such as the N-site polynomial Yoon–Nelson equation, was also successful in the description of interesting stepwise breakthrough curves. This work provides a more accurate adsorption equilibrium model to characterize all types of isotherms. As a foundation model, it is expected to be used to simulate the gas–solid adsorption process inside the fixed and fluidized beds packed with porous adsorbents.