TY - JOUR

T1 - Equilibrium of ion-exchange polymeric membrane with aqueous salt solution and its thermodynamic modeling

AU - Shiryaeva, Irina M.

AU - Victorov, Alexey I.

PY - 2001/4/15

Y1 - 2001/4/15

N2 - A thermodynamic model is proposed to describe distribution of the components between a liquid solution and a swollen membrane undergoing structural transformations. Free energy contributions related to formation of solution-filled micro-cavities in the membrane interior are estimated. Formation of the cavities of different shape is accounted for by using the Helfrich expressions for the bending energy of a curved interface. Three adjustable parameters of the model are related to the hydrophobic polymer matrix of the membrane, while the electrostatic contribution is estimated explicitly. Structural changes in the membrane are described as a transition from spherical to cylindrical cavities. Predominance of cavities having definite shape (spheres, cylinders) results in a specific shift of the Donnan equilibrium, which thus, becomes dependent on the structure of the membrane on the mesoscale. The results of model calculations are compared with the experimental data on the distribution of ions (H+, Li+, Cs+, K+, Na+, Ca2+, Mg2+) between the aqueous solution and the membrane. Different types of predicted thermodynamic behavior of the membrane in the liquid solution, including the hysteresis of ion-exchange equilibrium curves, are discussed. The model takes into account the effect of micro-inhomogeneties and helps to establish a link between molecular characteristics of the perfluoropolymer membrane and its macroscopic behavior in the liquid solution.

AB - A thermodynamic model is proposed to describe distribution of the components between a liquid solution and a swollen membrane undergoing structural transformations. Free energy contributions related to formation of solution-filled micro-cavities in the membrane interior are estimated. Formation of the cavities of different shape is accounted for by using the Helfrich expressions for the bending energy of a curved interface. Three adjustable parameters of the model are related to the hydrophobic polymer matrix of the membrane, while the electrostatic contribution is estimated explicitly. Structural changes in the membrane are described as a transition from spherical to cylindrical cavities. Predominance of cavities having definite shape (spheres, cylinders) results in a specific shift of the Donnan equilibrium, which thus, becomes dependent on the structure of the membrane on the mesoscale. The results of model calculations are compared with the experimental data on the distribution of ions (H+, Li+, Cs+, K+, Na+, Ca2+, Mg2+) between the aqueous solution and the membrane. Different types of predicted thermodynamic behavior of the membrane in the liquid solution, including the hysteresis of ion-exchange equilibrium curves, are discussed. The model takes into account the effect of micro-inhomogeneties and helps to establish a link between molecular characteristics of the perfluoropolymer membrane and its macroscopic behavior in the liquid solution.

KW - Ion-exchange equilibrium

KW - Method of calculation

KW - Non-uniformity on mesoscale

KW - Perfluorosulfonate membrane

KW - Swelling polyelectrolyte

KW - Thermodynamic model

UR - http://www.scopus.com/inward/record.url?scp=0035870923&partnerID=8YFLogxK

U2 - 10.1016/S0378-3812(00)00516-1

DO - 10.1016/S0378-3812(00)00516-1

M3 - Article

AN - SCOPUS:0035870923

VL - 180

SP - 115

EP - 138

JO - Fluid Phase Equilibria

JF - Fluid Phase Equilibria

SN - 0378-3812

IS - 1-2

ER -