Modeling the Conductivity and Diffusion Permeability of a Track-Etched Membrane Taking into Account a Loose Layer

The microheterogeneous model makes it possible to describe the main transport properties of ion-exchange membranes using a single set of input parameters. This paper describes an adaptation of the microheterogeneous model for describing the electrical conductivity and diffusion permeability of a track-etched membrane (TEM). Usually, the transport parameters of TEMs are evaluated assuming that ion transfer occurs through the solution filling the membrane pores, which are cylindrical and oriented normally to the membrane surface. The version of the microheterogeneous model developed in this paper takes into account the presence of a loose layer, which forms as an intermediate layer between the pore solution and the membrane bulk material during track etching. It is assumed that this layer can be considered as a "gel phase" in the framework of the microheterogeneous model due to the fixed hydroxyl and carboxyl groups, which imparts ion exchange properties to the loose layer. The qualitative and quantitative agreement between the calculated and experimental concentration dependencies of the conductivity and diffusion permeability is discussed. The role of the model input parameters is described in relation to the structural features of the membrane. In particular, the inclination of the pores relative to the surface and their narrowing in the middle part of the membrane can be important for their properties.