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.