Simple isotherm equations to fit type I adsorption data

TL;DR

This paper introduces simple, multiparametric isotherm models based on statistical mechanics to accurately fit type I adsorption data, enabling better estimation of thermodynamic properties with minimal parameters.

Contribution

The authors propose a new multiparametric isotherm model derived from grand canonical ensemble statistics, simplifying the fitting process for type I adsorption data.

Findings

High accuracy in fitting experimental adsorption data

Parameters have statistical significance and interpretability

Models effectively estimate thermodynamic properties

Abstract

A simple model to fit experimental data of adsorption of gases and vapours on microporous adsorbents (type I isotherms) is proposed. The main assumption is that the adsorbate phase can be divided into identical and non-interacting effective subsystems. This gives rise to a simple multiparametric isotherm based on the grand canonical ensemble statistics, whose functional form is a ratio of two polynomial functions. The parameters are interpreted as effective equilibrium constants. A simplified isotherm that reduces the number of adjustable parameters with respect to the general isotherm is also proposed. We show how to use these isotherms to fit the adsorption data in such way that the parameters have statistical significance. Due to their high accuracy, both isotherms can be used to estimate thermodynamic properties like isosteric and differential heats of adsorption. A simple method is presented for systems that show an apparent variation in the coverage limit with temperature. This method avoids overparametrization and improves fitting deviations. Finally, several applications to fitting data, taken from literature, of adsorption of some gases on activated carbon, molecular sieving carbon, silica gel, and pillared clays are presented.