On the optimal use of isotherm models for the characterization of biosorption of lead onto algae

For the first time we apply a new method based on the mathematical derivation of some known isotherm from the Burr function which describes many birth-death (sorption-desorption) phenomena in ecology and economy. Therefore, in this study the experimental isotherm data of biosorption of Pb(II) onto algae was modeled to Langmuir, Hill-Sips, Brouers-Sotolongo, Brouers-Gaspard, and Redlich-Peterson isotherm models. The parameters of each model were determined by nonlinear fitting algorithms using Mathematica program. The maximum Pb(II) removal rate increased with the increase of temperature and reached the maximum value (98%) at the temperature of 40 °C. The results showed that the Hill-Sips and the Brouers-Sotolongo isotherms were definitely the most suitable models to satisfactorily describe biosorption of Pb(II) on the algal biomass. In addition, as these two models gave very close results, the use of an intermediate one the Brouers-Gaspard isotherm model could also describe the sorption in most cases. High coefficient of determination values was obtained by using nonlinear methods and these findings are contrary to most works in this field that use linearization methods. Further, this study showed that a complete set of data is necessary to have a good representation of the isotherm and using only coefficient of determination is not always an adequate tool to compare the goodness of the nonlinear fit of an isotherm models.