Evaluation of the steric, electric, and dielectric exclusion model on the basis of salt rejection rate and membrane potential measurements

Abstract

The current work focuses on the application of the steric, electric, and dielectric exclusion (SEDE) model to the study of both the ion rejection rate and the membrane potential of a nanofiltration polyamide membrane. The aim of this study was to evaluate the performance of the SEDE model and to compare it with steric/electric exclusion theory. Experiments were conducted with CaCl 2 solutions at various concentrations. The SEDE model is a four-parameter model because the effective pore size ( r p ), the effective thickness-to-porosity ratio ( Δ x / A k ), the effective volume charge density of the membrane ( X), and the dielectric constant of the solution inside the pores ( ε p ) have to be known to predict the rejection rate and the membrane potential. The first parameter was estimated from membrane potential measurements performed at high salt concentrations and the second from water permeability. In the case of single salt solutions, experimental rejection rates and membrane potentials can be described by a number of couples of values ( X , ε p ) because both electric and dielectric exclusion contribute to reject ions. A set of couples ( X , ε p ) were first estimated by fitting membrane potentials. One of the couples was found to provide a good description of experimental rejection rates as well. Results showed that the polyamide membrane is negatively charged in CaCl 2 solutions at natural pH and that the membrane charge increases with the salt concentration. A decrease in the effective dielectric constant inside the pores with respect to its bulk value was found. This is indirect evidence that dielectric exclusion plays a major role in the transport phenomena of the studied NF membrane. The standard steric/electric theory was also used to fit experimental rejection rates and membrane potentials, the effective volume charge density being the single adjustable parameter in this case. Unlike the SEDE model, the steric/electric exclusion theory was unable to account simultaneously for both rejection rate and membrane potential data by using a unique choice for X and ε p . This highlights the global coherence of the SEDE model and the nonappropriateness of the description of transport in NF membranes by the classical steric/electric exclusion theory.