An Application of Percolation Theory to the Electrolyte Penetration through Porous Water-Swollen Cellulose Triacetate Membrane

Permeability coefficients P of KCl through porous cellulose triacetate (CTA) membranes were measured as a function of the water volume fraction V_W and diffusion coefficients D were determined using solubility parameters K and a membrane thickness d from the relationship of P = KD/d. D increased with an increase in V_W. D especially increases abruptly around V_W = 0.5, which corresponds to 2% triethylene glycol (TEG) content. The percolation theory was applied to the experimental results under the conditions D_A = D (V_W = 1) = 1.8 × 10⁻⁵ cm² s⁻¹, D_B = D(V_W = 0) = 1.8 × 10⁻⁸ cm² s⁻¹, coordination number (Z) = 2.5, 3, 3.5, and 4, and packing fraction f = 1.0. A good fit was obtained at Z = 3.5 because the experimental and calculated results also shifted at the same V_W below V_W = 0.5. It is suggested that a phase inversion, that is, change of a discontinuous water phase to a continuous water phase, occurs around V_W = 0.5. Above V_W = 0.5, the experimental results agree well with the calculated line for Z = 3 or Z = 2.5 which means that the coordination numbers decrease with an increase in water content. It is thought that V_W is overestimated because it is hard to completely wipe off the excess water quickly from the membrane surface. Z = 3.5 means that a pore can connect in 3.5 directions.