Deviations from Electroneutrality in Membrane Barrier Layers: A Possible Mechanism Underlying High Salt Rejections

Abstract

Reverse osmosis and nanofiltration (NF) employ composite membranes whose ultrathin barrier layers are significantly more permeable to water than to salts. Although solution-diffusion models of salt transport through barrier layers typically assume ubiquitous electroneutrality, in the case of ultrathin selective skins and low ion partition coefficients, space-charge regions may occupy a significant fraction of the membrane barrier layer. This work investigates the implications of these deviations from electroneutrality on salt transport. Both immobile external surface charge and unequal cation and anion solvation energies in the barrier layer lead to regions with excess mobile charge, and the size of these regions increases with decreasing values of either feed concentrations or ion partition coefficients. Moreover, the low concentration of the more excluded ion in the space-charge region can greatly increase resistance to salt transport to enhance salt rejection during NF. These effects are especially pronounced for membranes with a fixed external surface charge density whose sign is the same as that of the more excluded ion in a salt. Because of the space-charge regions, the barrier-layer resistance to salt transport initially rises rapidly with increasing barrier thickness and then plateaus or even declines within a certain thickness range. This trend in resistance implies that thin, defect-free barrier layers will exhibit higher salt rejections than thicker layers during NF at a fixed transmembrane pressure. Deviations from electroneutrality are consistent with both changes in NF salt rejections that occur upon changing the sign of the membrane fixed external surface charge, and CaCl2 rejections that in some cases may first decrease, then increase and then decrease again with increasing CaCl2 concentrations in NF feed solutions.

Ion and Water Transport in Ion-Exchange Membranes for Power Generation Systems: Guidelines for Modeling

“…Deviation from electroneutrality should be taken into account when describing transients and impedance spectra at small time scales or at high frequencies, when the double layer is charging and discharging, as well as when modeling length scales about the Debye length (on the order of nanometers) near the membrane surface. For these cases, Poisson's equation enables a correct description of the distribution and space charge density and electric potential/field strength [68].…”

An analytical solution of the solution-diffusion-electromigration equations reproduces trends in ion rejections during nanofiltration of mixed electrolytes

“…We recently developed a model where unequal anion and cation partitioning into ultra-thin membrane barrier layers leads to significant space-charge regions in the barrier. [58] This model postulates that due to differences among ions in their excess solvation energies, selective ion dissolution in the barrier leads to charge separation and electrical potential gradients that tend to equalize partition coefficients. For example, if due to excess solvation energies a barrier layer excludes doubly charged anions more than monovalent cations (this assumption agrees with lower permeances to doubly charged anions), the inter-phase electrostatic potential will attract anions to and repel cations from the barrier layer.…”

“…Additionally, virtual solutions are electrically neutral, whereas solutions in a membrane may deviate from electroneutrality, especially if the membrane contains immobile charge or is ultrathin. [58] For two salts with a common ion, Eq(1) is a system of three equations (one equation for each ion). At steady state is constant, and we assume constant values of throughout the membrane.…”