在40 Hz～10 MHz频率范围测量了纳滤膜在八种电解质溶液中的介电谱，发现了两个随电解质浓度而变化的弛豫，建立了由膜内支撑层和分离层以及溶液相构筑的三相体系介电模型，并利用严格的数值解析法计算了体系中各组成相的电参数。本文聚焦于103Hz左右因膜内层间界面极化而引起的低频弛豫，考察了两层电参数与电解质种类和浓度的关系，计算得到膜内各层的介电性质，并获得了关于不同电解质在膜内支撑层和分离层中的分布的信息。

Dielectric measurements were carried out on the systems composed of nanofiltration membrane and dilute solutions of eight electrolytes over the frequency range from 40Hz to 10MHz. Two relaxations were observed for each system. Three-phase dielectric model, which consist of  the supporting layer and separation layer of membrane and solution phase, was established. The the electrical parameters of each layer were obtained through strict mathematical calculation. This paper focused on low-frequency relaxation about 103Hz caused by interfacial polarization between the two layers. The variation of electrical parameters of the two layers with concentration and species of the electrolyte was discussed in detail. Further, dielectric properties of each layer were obtained and the distribution information of different electrolyte in supporting layer and separation layer of membrane were given.

[1] Mohammad A W, Hilal N, Al-Zoubi H, et al. Modelling the effects of nano- filtration membrane properties on system cost assessment for desalination applications[J]. Desalination, 2007, 206: 215–225.
[2] Richard Bowen W, Julian S Welfoot. Modelling the performance of membrane nanofiltration —critical assessment and model development[J]. Chem Eng Sci, 2002, 57: 1121–1137.
[3] Yaroshchuk A E, Makovetskiy A L, Boiko Y P, et al. Non-steady-state membrane potential: theory and measurements by a novel technique to determine the ion transport numbers in active layers of nanofiltration membranes[J]. J Membr Sci, 2000, 172: 203–221.
[4] Chaufer B, Baudry-Rabiller M, Guihard L, et al., Retention of ions in nanofiltration at various ionic strength, Desalination,1996, 104: 37–46.
[5] Schaep J, Van der Bruggen B, Vandecasteele C, et al., Influence of ion size and charge in nanofiltration, Separ. Purif. Technol, 1998, 14: 155–162.
[6] Peeters J M M, Mulder M H V, Strathmann H, Streaming potential measurements as a characterization method for nanofiltration membranes, Colloids Surf. A: Physicochem. Eng. Aspects, 1999, 150: 247–259.
[7] Khulbe K C, Hamad F, Feng C, et al. Study of the surface of the water treated cellulose acetate membrane by atomic force microscopy[J]. Desalination, 2004, 161: 259-262.
[8] Khayet M. Membrane surface modification and characterization by X-ray photoelectron spectroscopy, atomic force microscopy and contact angle measurements[J]. Appl Surf Sci, 2004, 238: 269-272.
[9] Anthony Szymczyk, Nicolas Fatin-Rouge, Patrick Fievet. Tangential streaming potential as a tool in modeling of ion transport through nanoporous membranes[J]. Colloid And Interface Sci, 2007, 309: 245–252.
[10] Shang W J, Wang X L, Yu Y X. Theoretical calculation on the membrane potential of charged porous membranes in 1-1, 1-2, 2-1 and 2-2 electrolyte solutions[J]. J Membr Sc, 2006, 285: 362–375.
[11] Xu T W, Fu Y Q, Wang X L. Membrane potential model for an asymmetrical nanofiltration membrane — consideration of noncontinuous concentration at the interface[J]. Desalination, 2004, 171: 155-165.
[12] Mathias Ernst, Alexander Bismarck, Jürgen Springer, et al. Zeta-potential and rejection rates of a polyethersulfone nanofiltration membrane in single salt solutions[J]. J Membr Sci, 2000, 165: 251–259.
[13] Asami Koji. Characterization of heterogeneous systems by dielectric spectroscopy[J]. Prog Polym Sci, 2002, 27: 1617-1659.
[14] 赵孔双. 介电谱方法及其应用[M]. 北京：化学工业出版社，2008: 59-101.
[15] Li Y H, Zhao K S. Dielectric analysis of nano?ltration membrane in electrolyte solutions: in?uences of electrolyte concentration and species on membrane permeation[J]. Colloid And Interface Sci, 2004, 276: 68-76.
[16] Zhao K S, Li Y H. Dielectric Characterization of a Nanofiltration Membrane in Electrolyte Solutions: Its Double-Layer Structure and Ion Permeation[J]. J Phy Chem B, 2006, 110: 2755-2763.
[17] Ni G Z, Zhao K S, Dielectric Analysis of Nano?ltration Membrane in Electrolyte Solutions: In?uences of Permittivity of Wet Membrane and Volume Charge Density on Ion Permeability[J]. submitted to Chem Eng Sci.
[18] Torben Smith Sørensen. Interfacial Electrodynamics of Membranes and Polymer Films[M], in: Torben Smith Sørensen (Eds), Surface Chemistry and Electrochemistry of Membranes, New York, pp.623-747.
[19] Hanai T, Zhang H Z, Sekine K, et al. The number of interfaces and the associated dielectric relaxations in heterogeneous systems[J]. Ferroelectrics, 1988, 86: 191–204.
[20] Kiyohara K, Zhao K S, Asaka K, et al. Determination of Capacitances and Conductances of the Constituent Phases from dielectric observations on terlamellar composite systems[J]. Japanese J Applied Physics, 1990, 29(9): 1751-1756.
[21] Asami K, Irimajiri A, Hanai T, et al. A method for Estimating Residual Inductance in High Frequency A.C. Measurements[J]. Bull Ist Chem Res Kyoto Univ, 1973, 51: 231-245.
[22] Alexander Yu. Zasetsky, Igor M. Svishchev. Dielectric Response of Concentrated NaCl Aqueous Solutions: Molecular Dynamics Simulations[J]. J. Chem. Phys., 2001, 115: 1448-1454.