A Statistical Approach to Determine Optimal Models for IUPAC-Classified Adsorption Isotherms

Adsorption heat transformation (AHT) systems can play a major role in protecting our environment by decreasing the usage of fossil fuels and utilizing natural and alternative working fluids. The adsorption isotherm is the most important feature in characterizing an AHT system. There are eight types of International Union of Pure and Applied Chemistry (IUPAC) classified adsorption isotherms for different “adsorbent-adsorbate” pairs with numerous empirical or semi-empirical mathematical models to fit them. Researchers face difficulties in choosing the best isotherm model to describe their experimental findings as there are several models for a single type of adsorption isotherm. This study presents the optimal models for all eight types of isotherms employing several useful statistical approaches such as average error; confidence interval (CI), information criterion (ICs), and proportion tests using bootstrap sampling. Isotherm data of 13 working pairs (which include all eight types of IUPAC isotherms) for AHT applications are extracted from literature and fitted with appropriate models using two error functions. It was found that modified Brunauer–Emmet–Teller (BET) for Type-I(a) and Type-II; Tóth for Type-I(b); GAB for Type-III; Ng et al. model for Type-IV(a) and Type-IV(b); Sun and Chakraborty model for Type-V; and Yahia et al. model for Type-VI are the most appropriate as they ensure less information loss compared to other models. Moreover; the findings are affirmed using selection probability; overall; and pairwise proportion tests. The present findings are important in the rigorous analysis of isotherm data.