The Quantitative Ion Character–Activity Relationship (QICAR) method was used for correlating metal ionic characteristics with the maximum adsorption capacity (q_max) of multi-walled carbon for heavy metals. The experimental values of q_max for 25 heavy metal ions, estimated by the Langmuir isotherm model, were used to construct a QICAR model. The genetic algorithm, enhanced replacement method and successive projection algorithm procedures were applied as variable selection algorithms to choose the optimal subsets of descriptors. The selected variables were correlated with q_max values by using partial least squares (PLS) regression. Orthogonal signal correction was applied as a pre-processing technique. Among of different variable selection methods, the enhanced replacement method displayed noticeable statistical parameters of the final model. The results of the enhancement replacement method–orthogonal correction signal–PLS model, with RMSEC = 0.733, r²_c = 0.999 and r²_p = 0.946, were excellent and dramatically better than those of other models. The developed QICAR model satisfied the internal and external validation criteria. The importance of electronegativity, ionic radius and atomic number of the heavy metal ions indicated the impact of the tendency to accept electrons and the size of ions in adsorption on carbon nanotubes.

定量离子特征-活度关系（QICAR）方法用于将金属离子特征与多壁碳对重金属的最大吸附容量（q _max）相关联。用Langmuir等温线模型估算的25种重金属离子的q _max实验值用于构建QICAR模型。遗传算法，增强替换方法和连续投影算法程序被用作变量选择算法，以选择描述符的最佳子集。选择的变量与q _max相关通过使用偏最小二乘（PLS）回归得到的值。正交信号校正被用作一种预处理技术。在不同的变量选择方法中，增强的替换方法显示了最终模型的引人注目的统计参数。增强替换方法-正交校正信号-PLS模型的结果，RMSEC = 0.733，r ² _c = 0.999和r ² _p= 0.946，非常好，远胜于其他模型。所开发的QICAR模型满足了内部和外部验证标准。重金属离子的电负性，离子半径和原子序数的重要性表明了碳纳米管上吸附电子的趋势和离子尺寸的影响。