Determination of structural, selective, electrokinetic and percolation characteristics of ion-exchange membranes from conductive data

The structural, selective and electrokinetic characteristics and percolation parameters were determined for different ion-exchange polymer membranes from their conductivity data using the two-phase model of membrane conductivity and percolation theory. The two different combinations of micro-phases in IEM, used in the two-phase conductivity model and percolation theory are presented and discussed. Based on this two-phase model and concentration dependences of membrane conductivity, the structural membrane heterogeneity was determined for 14 commercial IEMs. The diffusion coefficient, molar conductivity of counter-ions and hydration capacity of the gelphase were calculated and analyzed for cross-linked and linear ion-exchange polymers. The ion-exchange equilibrium constants for MK-40 were estimated from values of membrane conductivity at the iso-conductance point in individual electrolyte solutions and their mixtures. The percolation theory was used to describe the conductivity of different membrane compositions with various volume fraction of the conducting phase. The estimation of φcr and γ percolation parameters showed that the obtained values of critical index γ agree with the theory for investigated materials, and the value of the threshold parameter φcr depends on the preparation method and structural heterogeneity of a given composition.

Using conductometry method and theoretical approaches of two-phase model of membrane conductivity we have investigated the degree of heterogeneity of 14 commercial ion-exchange membranes. The hydration capacity, and diffusion coefficient and molar conductivity of the gelphase were estimated and compared for membranes MK-40, CM-1, CMX, MF-4SC. It was shown that diffusion coefficient and molar conductivity of counter ions in the membrane gelphase depends on hydration capacity of the gel-phase as well as on the structure of polymer matrix and degree of networking water. The apparent ion-exchange equilibrium constants of K+/H+, Na+/H+, Li+/H+ for membrane MK-40 were calculated from the values of membrane conductivity at the iso-conductance point in individual electrolyte solutions and their mixtures. The ion-exchange constants determined conductometrically are in agreement with those determined by independent analytical method. The conductivity of different membrane compositions with various volume fraction of conducting phase were described using percolation theory. The estimation of φcr and γ percolation parameters showed that the obtained values of critical index γ agree with the theory for the investigated materials, and the value of the threshold parameter φcr depends on the preparation method. Nomenclature κm κ κ f1, f2 α Ciso D t membrane conductivity conductivity of equilibrium solution and inter-gel phase in membrane conductivity of membrane gelphase volume fraction of the gel-phase and inter-gel phase corresponding parameter characterizing the spatial arrangement of membrane phases equilibrium electrolyte solution concentration at the iso-conductance point diffusion coefficient of counter ion in membrane gel-phase counter-ion transport number in membrane gel-phase R T Q dm F λ n dH2O, MH2O K κ H , κ Me, κ Σ gas constant temperature ion-exchange capacity of membrane membrane density Faraday constant molar conductivity of counter ion in membrane gel-phase hydrate capacity of gel-phase, number of water molecules per one ionexchange group water density and water molar mass ion-exchange equilibrium constant specific conductivity at iso-conductance point for membrane in H+-, Me+- and hetero-ionic forms corresponding Greek symbols αMe φ φcr γ equivalent fraction of metal ion in equilibrium electrolyte mixture volume fraction of the conducting phase critical volume fraction of conducting phase critical exponent of conductivity