Some Critical Remarks about Mathematical Model Used for the Description of Transport Kinetics in Polymer Inclusion Membrane Systems

Comparison of Kinetic Models Applied for Transport Description in Polymer Inclusion Membranes

Five mathematical models for transport description in polymer inclusion membranes (PIMs) were presented and compared via regression analysis. The applicability of the models was estimated through the examination of experimental data of Zn(II), Cd(II), Pb(II), and Cu(II) ions transported by typical carriers. In four kinetic models, a change in the feed and stripping solution volume was taken into account. The goodness of fit was compared using the standard error of the regression, Akaike information criterion (AIC), Bayesian (Schwarz) information criterion (BIC), and Hannan-Quinn information criterion (HQC). The randomness distribution in the data was confirmed via a nonparametric runs test. Based on these quantities, appropriate models were selected.

Calixresorcin[4]arene-Mediated Transport of Pb(II) Ions through Polymer Inclusion Membrane

A facilitated transport of Pb(II) through polymer inclusion membrane (PIM) containing 1,8,15,22-tetra(1-heptyl)-calixresorcin[4]arene and its tetra- and octasubstituted derivatives containing phosphoryl, thiophosphoryl or ester groups as an ion carrier was investigated. The efficiency of Pb(II) removal from aqueous nitrate solutions was considered as a function of the composition of membrane (effect of polymer, plasticizer, and carrier), feed (effect of initial metal concentration and presence of other metal ions) and stripping phases, and temperature of the process conducting. Two kinetic models were applied for the transport description. The highest Pb(II) ions removal efficiency was obtained for the membrane with tetrathiophosphorylated heptyl-calixresorcin[4]arene as an ion carrier. The activation energy value, found from Eyring plot to be equal 38.7 ± 1.3 kJ/mol, suggests that the transport process is controllable both by diffusion and chemical reaction. The competitive transport of Pb(II) over Zn(II), Cd(II), and Cr(III) ions across PIMs under the optimal conditions was also performed. It was found that the Cr(III) ions’ presence in the feed phase disturb effective re-extraction of Pb(II) ions from membrane to stripping phase. Better stability of PIM-type than SLM-type membrane was found.