Importance of estimation of optimum isotherm model parameters for adsorption of methylene blue onto biomass derived activated carbons: Comparison between linear and non-linear methods

A comparison of the linear and non-linear methods for the selection of optimum equilibrium isotherm for the adsorption of methylene blue onto the banana root ( Musa acuminata ) derived activated carbons was carried out. The adsorption equilibrium data were fitted to three isotherm models: Langmuir, Freundlich, and Temkin. The prediction of optimum isotherm was based on six error functions: the coefficient of determination ( R 2 ), the sum of the squares of the errors (SSE), the sum of the absolute errors (SAE), the average relative error (ARE), the hybrid fractional error function (HYBRID), and the Marquardt’s percent standard deviation (MPSD). The optimum isotherm achieved was the Temkin isotherm in non-linear and linear form followed by Freundlich and Langmuir based on the error functions. Non-linear pseudo-first-order and pseudo-second-order kinetic models analyzed the adsorption data. The present work demonstrated that the non-linear method is a more suitable method to estimate the isotherm parameters than the linear method, and the pseudo-first-order model best fitted the corresponding experimental data.