Comparative study of Box–Behnken, central composite, and Doehlert matrix for multivariate optimization of Pb (II) adsorption onto Robinia tree leaves


Correspondence to: Javad Zolgharnein, Department of Chemistry, Faculty of Science, Arak University, Arak, 38156–876, Iran.



A comparative study of Box–Behnken, central composite, and Doehlert matrix was performed on the adsorption of Pb (II) by Robinia tree leaves in a batch system. As a case study, uptake capacity (q) and removal efficiency (R) of Pb (II) biosorption have been evaluated with all theses approaches. The advantages and limitations of these different response surface techniques have been experimentally considered. The results show the different statistical predictability of Doehlert matrix and Box–Behnken design at 95% confidence level comparable with some extent with that of central composite design at some extreme conditions. An environmental and economical comparison was also carried out between individual and simultaneous optimization of removal efficiency (R) and uptake capacity (q) using desirability function. Optimization of q proves only to have advantages over R or simultaneous optimization of R and q in this particular biosorption process. Copyright © 2013 John Wiley & Sons, Ltd.