Nano-quantitative ion character–activity relationships of adsorption of rare earth ions on multi-walled carbon nanotubes

Abstract

ABSTRACTIn this study, the maximum adsorption capacities (qmax) of multi-walled carbon nanotubes (MWCNTs) for 16 rare earth ions were estimated from the experimental data using Langmuir isotherm model. The Langmuir model fitted the experimental data very well, with R2 > 0.98. To explore the impact of ion properties of their adsorption onto MWCNTs, Quantitative Ion Character–Activity Relationships (QICAR) method was applied. The experimental values of qmax were used as dependent variable and the rare earth ions properties were considered as independent variables. Based on covalent index, a new variable was defined which is highly correlated to qmax (correlation coefficient of 0.776). Different variable selection techniques and wrapper models were applied to choose the best subset of variable. Among all developed linear and non-linear models constructed using support vector machine regression (SVR), neural networks, random forest and multiple linear regression, the SVR model presents the best statistical performance. The result of the Wrapper-SVR developed model, with R2c = 0.993 and R2p = 0.794, was excellent than those of other models. The importance of some thermodynamic parameters, Gibbs free energy (ΔG0f) and enthalpy of formation (ΔH0f) of the trivalent lanthanide ions (M+3) at 25°C, indicated the role of thermodynamic aspects on adsorption mechanism. Atomic radius, ionisation energy and electronegativity of rare earth ions should also be considered.