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 VW 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 VW. D especially increases abruptly around VW = 0.5, which corresponds to 2% triethylene glycol (TEG) content. The percolation theory was applied to the experimental results under the conditions DA = D (VW = 1) = 1.8 × 10−5 cm2 s−1, DB = D(VW = 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 VW below VW = 0.5. It is suggested that a phase inversion, that is, change of a discontinuous water phase to a continuous water phase, occurs around VW = 0.5. Above VW = 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 VW 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.