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In this study, the maximum adsorption capacities (q max ) 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 R 2  &gt; 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 q max  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 q max  (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 R 2c  = 0.993 and R 2p  = 0.794, was excellent than those of other models. The importance of some thermodynamic parameters, Gibbs free energy (ΔG 0f ) and enthalpy of formation (ΔH 0f ) 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.

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