Guidelines for the use and interpretation of adsorption isotherm models: A review

[Display omitted] •Adsorption data modelling is an essential way of predicting adsorption mechanisms.•It discusses the guidelines of using mono/multi-parametric isotherm models.•It establishes criteria for choosing the optimum isotherm model.•Ten multi-parameter isotherm models and their applications were reviewed.•Linear and nonlinear regression equations were used to determine best-fit model. Adsorption process is considered as one of the most used separation and purification processes, in which adsorption occurs by the formation of the physical or chemical bonds between a porous solid medium and a mixture of liquid or gas multi-component fluid. By taking into consideration the equilibrium data and the adsorption properties of both the adsorbent and the adsorbate, adsorption isotherm models can describe the interaction mechanisms between the adsorbent and the adsorbate at constant temperature. Therefore, understanding modelling of the equilibrium data is a very essential way of predicting the adsorption mechanisms of various adsorption systems. Furthermore, adsorption isotherms in batch experiments can be used for the determination of the solid-water distribution coefficient (Kid). This review paper discusses the guidelines of using mono/multi-parametric isotherm models with different applications. The aim of this paper is to establish criteria for choosing the optimum isotherm model through a critical review of different adsorption models and the use of various mathematically error functions such as linear regression analysis, nonlinear regression analysis, and error functions for adsorption data optimization. In this paper, 15 mono-parametric adsorption isotherm models having one, two, three, four and five parameters were investigated. In addition, 10 multi-parameter isotherm models were reviewed as well as addressing their applications.