Optimization of the Ba+2 uptake in the formation process of hydrogels using central composite design: Kinetics and thermodynamic studies of malachite green removal by Ba-alginate particles

Document Type : Research Article


Department of Chemical Engineering, Faculty of Engineering, Kermanshah University of Technology, Kermanshah, Iran


Biocompatible materials, as efficient sorbent, are used for the removal of dyes and heavy metals ions from water and industrial wastewater. In this work, the optimal conditions for the maximum barium uptake in the formation process of Ba-alginate beads (Ba-ALG) were determined using the central composite design (CCD). The operational factors were evaluated for polymer/barium ratios of 1:3, 1:2, 1:1, 2:1, and 3:1 and residence times of 20, 30, 75, 120, and 180 minutes. The optimal ratio of sodium alginate to barium concentration for cations uptake was obtained at 3:1. Ba-ALG could not form a spherical and stable structure at higher polymer/cross-linker ratios. Validation tests illustrated the high accuracy of the selected model to determine the optimal experimental conditions in the barium uptake process. The maximum barium uptake is 88.61%, which was achieved at XAB =1.5 (optimal ratio of polymer to Ba+2) and Xt =1.5 (180 min). The ability of Ba-ALG to adsorb dye was also evaluated. Kinetics, equilibrium, and thermodynamic studies for adsorption of malachite green (MG) by Ba-ALG were statistically described. The adsorption results match the pseudo-second-order kinetics, suggesting that there was MG dye uptake to the adsorbent in monolayers due to its chemical affinity. The thermodynamic parameters were also determined by the Gibbs free energy function, confirming that the adsorption process was spontaneous and accompanied by an endothermic reaction.

Graphical Abstract

Optimization of the Ba+2 uptake in the formation process of hydrogels using central composite design: Kinetics and thermodynamic studies of malachite green removal by Ba-alginate particles


  • The optimal conditions for the barium uptake in the ionotropic gelation process were successfully evaluated using RSM based on the CCD model.
  • The biosorption rate of MG dye using Ba-ALG was followed by the pseudo-second-order kinetics model.
  • The thermodynamic study confirmed that the adsorption process was spontaneous by endothermic behavior.


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