Equilibrium Modelling for Adsorption of Aqueous Cd(II) onto Turmeric: Linear versus Nonlinear Regression Analysis

Abstract

Adsorption parameters determined from equilibrium modelling provides a powerful tool to understand adsorbate-adsorbent interaction mechanism but there is an on-going debate about pros and cons of linearizing isotherm equations. Therefore, in the present study, linear and nonlinear regression forms of  Langmuir, Freundlich, D-R and Temkin equilibrium models were applied on experimental data obtained from batch adsorption of aqueous Cd(II) onto turmeric. Five error functions i.e. Marquardt’s PSD, Least Absolute Errors (LAE), Sum of Squared Residuals (SSR), Chi-square test (χ²), Average Percent Error (APE) for nonlinear optimization were also applied to determine best fit adsorption model. Linearized as well as nonlinearized Freundlich model provided better fit as compared to other applied equilibrium models. Nonlinear error analysis further validated Freundlich isotherm as best fit model for experimental data. Comparison of linear and nonlinear regression suggested that nonlinearized isotherm equations provided more reliable fit for the adsorption data but it is more appropriate to evaluate goodness of fit after comparison between linearized and nonlinearized modelling parameters.