Dielectric spectroscopy of a nanofiltration membranes-electrolyte solution system: I. Low-frequency dielectric relaxation from the counterion polarization in pores and model development.

The dielectric spectra of nanofiltration membranes NF90, NF-, and NF270 in eight electrolytes, NaCl, KCl, CuCl(2), MgCl(2), Na(2)SO(4), K(2)SO(4), MgSO(4), and CuSO(4), were investigated as a function of the electrolyte concentration over a frequency range from 40 Hz to 11 MHz. Two relaxations were observed: the one at high frequency was caused by interfacial polarization between the membrane and electrolyte, and the low-frequency relaxation, on which we focus on in this work, was confirmed to be due to the counterion polarization effects in the pores of the membrane. A model of cylindrical pores which were dispersed in membrane base was developed to interpret the low-frequency relaxation. On the basis of this model, we amended the expression deduced by Takashima for describing the dielectric behavior of a cylinder particle suspension to fit our dielectric data from the low-frequency relaxation. The data fitting with this improved expression was suitable for all the systems measured in this work; structural and electrical parameters such as the radius of the pore in the membrane, the thickness of the active layer of the membrane, surface charged density, and zeta potential on the pore wall were obtained finally.