Isotherms for the adsorption of Cu(II) onto lignin -comparison of linear and non-linear methods

Abstract

Abstract Equilibrium studies were carried out for the adsorption of Cu(II) onto Kraft lignin as an adsorbent. The experimental data were fitted to the Freundlich, Langmuir and Redlich-Peterson isotherms by linear and non-linear methods. Comparison of linear and non-linear regression methods was given in selecting the optimum isotherm for the experimental data. The coefficient of correlation r 2 and chi-square test χ 2 were used to select the best linear theoretical isotherm. The best linear model is Redlich-Peterson isotherm model, where r 2 = 0.985 and χ 2 = 0.02. In order to predict the error ERRSQ, HYBRD, MPSD, ARE and EABS were used. Moreover, by minimizing these error functions the optimal values of parameters and also the optimum isotherm was found. The Redlich-Peterson isotherm was found to be the best representative for adsorption of Cu(II) on the adsorbent in the cases when ERRSQ, HYBRD and MPSD functions were used. Their coefficients of determination were 0.986, 0.985 and 0.984, respectively and chi-square was 0.02 in all cases. Freundlich isotherms obtained by minimization of the ERRSQ, HYBRD, MPSD, ARE and EABS function showed very good agreement with experimental data. In all cases the coefficients of determination were greater than 0.91. Besides, it was observed that non-linear isotherm models were better for representation of equilibrium data than linearized models. There is increasing interest in the development of economically viable new applications of lignin, which can be found as waste from cellulose and paper industry. This is evidenced by the existence of the International Lignin Institute, which promotes new technologies with lignin as the main component. Among others, the possibility of using lignin as an adsorbent for different pollutants from water has been considered Equilibrium relationships between adsorbent and adsorbate are described by adsorption isotherms and characterized by certain constants, the values of which provide information on adsorbent capacity and affinity for some kind of adsorbate. In addition, the quality of the fit of experimental results indicates whether ad- sorption is monolayer or multilayer, on a homogeneous or heterogeneous surface. Isotherm equations do not consider which adsorption mechanisms, such as external mass transfer of solute, intraparticle diffusion or adsorption at sites, are decisive in the adsorption process, but can be used for design of batch adsorption systems. Some of the isotherm equations that can explain solid-liquid adsorption systems are: Langmuir, Freundlcih, Temkin, Sips, Toth, Redlich-Peterson isotherm equations Linear regression has been frequently used to determine the most fitted models and the method of least squares has been frequently used for finding the parameters of the models In this study, binding characteristics of Cu(II) on Kraft lignin were investigated and feasible application of different adsorption models for description of its adsorption on this low-cost and environment-friendly adsorbent was described. For that purpose, linear and non-linear equations of Freundlich, Langmuir and Red