### An Adsorption Equilibria Model for Steady State Analysis

*Azhar Bin Ismail, Karan M. Sabnani, Li Ang, Kim Choon Ng*

**Abstract**:

The investigation of

adsorption isotherms is a prime factor in the ongoing development of adsorption

cycles for a spectrum of advanced, thermally-driven engineering applications,

including refrigeration, natural gas storage, and desalination processes. In

this work, a novel semi-empirical mathematical model has been derived that

significantly enhances the prediction of the steady state uptake in adsorbent

surfaces. This model, a combination of classical Langmuir and a novel modern

adsorption isotherm equation, allows for a higher degree of regression of both

energetically homogenous and heterogeneous adsorbent surfaces compared to

several isolated classical and modern isotherm models, and has the ability to

regress isotherms for all six types under the IUPAC classification. Using a unified

thermodynamic framework, a single asymmetrical energy distribution function

(EDF) has also been proposed that directly relates the mathematical model to

the adsorption isotherm types. This fits well with the statistical rate theory

approach and offers mechanistic insights into adsorption isotherms.

**Keywords**: Adsorption; Energy distribution function; Statistical rate theory; Universal isotherm model

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