Insights into mathematical characteristics of developed adsorption model using a sigmoid model

Abstract In this work, a developed adsorption model was brought forward based on the sigmoid model. Under certain conditions, the model is mathematically equivalent to the hyperbolic model, and it has the ability to predict the adsorption equilibrium time and the adsorption mass of the adsorbent per unit mass of adsorbent in equilibrium. The proposed model can be deduced to the empirical model and other forms under certain conditions. The aim of this study is to obtain a mathematically simplified model, provide a probability to predict related parameters and offer mathematical sights into the Langmuir kinetics. The proposed model is verified through experimental study and the results show that it has a prominent agreement with the experimental data. The model can be dedicated to driving the process of dynamic analysis from fitting to prediction.