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

Abstract

Two kinetic models which are applied for the description of metal ion transport in polymer inclusion membrane (PIM) systems are presented and compared. The models were fitted to the real experimental data of Zn(II), Cd(II), Cu(II), and Pb(II) simultaneous transport through PIM with di-(2-ethylhexyl)phosphoric acid (D2EHPA) as a carrier, o-nitrophenyl octyl ether (NPOE) as a plasticizer, and cellulose triacetate (CTA) as a polymer matrix. The selected membrane was composed of 43 wt. % D2EHPA, 19 wt. % NPOE, and 38 wt. % CTA. The results indicated that the calculated initial fluxes (from 2 × 10−11 up to 9 × 10−10 mol/cm2s) are similar to the values observed by other authors in systems operating under similar conditions. It was found that one of the most frequently applied models based on an equation similar to the first-order chemical reaction equation leads to abnormal distribution of residuals. It was also found that application of this model causes some problems with curve fitting and leads to the underestimation of permeability coefficients and initial maximum fluxes. Therefore, a new model has been proposed to describe the transport kinetics in PIM systems. This new model, based on an equation similar to the first-order chemical reaction equation with equilibrium, was successfully applied. The fit of this model to the experimental data is much better and makes it possible to determine more precisely the initial maximum flux as the parameter describing the transport efficiency.

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

“…The usefulness of two kinetic models, proposed by Danesi [ 27 ] and Szczepanski [ 28 ], in the metal transport description was evaluated. According to the Danesi model, the ion transport can be described with a first-order kinetic reaction (Equation (1)) [ 27 ].…”

“…Model proposed by Szczepanski (Equation (2)) takes into account the volume of the feed phase and the membrane area and assumes reaching the equilibrium state of the system. Such an approach made it possible to estimate more accurately, compared to the Danesi model, the values of the initial fluxes of selected metal ions in transport through the PIM with a commercial carrier di-(2-ethylhexyl)phosphoric acid [ 28 ].…”

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

“…It was previously shown that the transport of Cd(II), Zn(II), Pb(II), and Cu(II) ions through PIMs containing reactive ionic liquids or D2EHPA (di-(2-ethylhexyl)phosphoric acid) as a carrier obeys the kinetic laws of a reversible first-order reaction [ 18 , 19 ]: …”

A Polymer Inclusion Membrane for Sensing Metal Complexation in Natural Waters

“…Various studies have used the carrier di-(2-ethylhexyl) phosphoric acid (D2EHPA) incorporated in PIMs for the transport of divalent metals, such as Zn and Cu. Szczepanski evaluated the simultaneous transport of Zn, Cd, Cu, and Pb through a PIM consisting of 38% CTA, 43% D2EHPA, and 19% of the plasticizer 2-nitrophenyloctyl ether (NPOE) using a 0.5 M HNO 3 solution as a receiving phase [14]. A PIM made of 60% PVC and 40% D2EHPA was also the basis of a new passive sampler developed to measure Zn ion in urban waters [15].…”