Dielectric Spectroscopy of a Nanofiltration Membranes−Electrolyte Solution System: I. Low-Frequency Dielectric Relaxation from the Counterion Polarization in Pores and Model Development

Abstract

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.

Estimation of electrical parameters inside nanofiltration membranes in various electrolyte solutions by dielectric spectroscopy analysis

“…The low-frequency relaxation around at 10 2 Hz caused by the counterion polarization in the membrane pores had been discussed thoroughly in Part 1. 1 This paper focuses solely on the analysis and discussion of high-frequency relaxation. From Fig.…”

“…In our previous paper, 1 we have calculated thickness and pore diameter of the three membranes. The average values of the thickness in different concentrations are 0.2335 mm, 0.2337 mm and 0.2334 mm, and the average values of pore diameter are 0.2838, 0.3250, 0.3582 nm for NF90, NF-and NF270 membrane, respectively.…”

“…29,34 The membrane (herein-aer, the term membrane refer to the effective layer of NF membrane)/electrolyte solution systems were measured in the same way and conditions described in Part 1. 1 In this paper, we take NF90 membranes-K 2 SO 4 solution as an example to illustrate the dielectric analysis processes. But, the analysis results for all three membranes (NF90, NF-and NF270 membrane) are discussed.…”

“…All the raw data were subjected to certain corrections for the errors arising from residual inductance due to the cell assembly, 35 and the detail is also described in the Part 1. 1 The relative permittivity 3 and conductivity k were determined by following equations 3 ¼ C s /C l and k ¼ G s 3 0 /C l (3 0 is the permittivity of vacuum).…”

“…Dielectric spectroscopy is a particularly insightful method because it can monitor relaxation processes of various systems in a non-invasive way, especially heterogeneous systems including membrane-solution. In our previous paper 1 (to be referred to as Part 1 hereinaer) of this series, the low-frequency dielectric behavior of nanoltration (NF) membranes have been studied. In Part 1, we proposed an expression for describing low-frequency relaxation by which the structural and electrical parameters such as the pore radius, thickness of the active layer of the NF membrane, surface charged density and zeta potential on the pore wall were obtained.…”