Ion Association Effects In Partitioning and Transport of Salt In NF and RO

The present paradigm of salt transport in reverse osmosis (RO) and nanofiltration (NF) views ion exclusion as a combination of three effects, steric, dielectric and Donnan (electric), collectively referred to as the SDE mechanism. However, there has been significant evidence that the SDE-based models fail to explain a number of experimental results. Particularly striking are the data obtained by Rutherford back-scattering spectroscopy (RBS), which indicates that partitioning of both co- and counter-ions within the polyamide toplayer of RO and NF membranes exceeds theoretical estimates and values deduced from transport measurements by several orders of magnitude [1]. In addition, the variation of salt rejection with feed concentrations, especially for divalent counter-ions, markedly deviates from SDE predictions [2]. Finally, physical characteristics of the membrane fitted to measured rejections, such as dielectric constant and fixed charge density, are often much off directly measured values.

In order to explain the observed deviations it is proposed here to include in the SDE model a previously missing ingredient, the effect of ion association, which seems to reconcile SDE with most contradictory observations. Ion association is a consequence of the low dielectric constant of the membrane phase, just as dielectric exclusion, therefore the two may be viewed as related complementary phenomena within the same physical picture. Specifically, dielectric exclusion is related to self-energy of individual ions, while association arises from the electrostatic interaction betweenions. In both cases the involved electrostatic energies are of the same order of magnitude, however, association is accompanied by a loss of entropy and thus the concentration of associated species within the membrane differs in concentration dependence from that of individual ions.

As a result of association, salt partitions and passes the membrane as neutral species at a much smaller electrostatic cost. Notably, partitioning and permeability of such neutral species has a concentration dependence that resembles and thus may be mistaken for a Donnan-type exclusion. Fitting to the standard SDE model may then yield a reasonable agreement, but unreasonable values of dielectric constant and fixed charge content, as indeed observed. In addition, a large fixed charge may promote enhanced uptake of salt rather than its exclusion, i.e., produce an effect opposite to that expected based on the Donnan mechanism. Indeed, beyond a certain critical concentration, very low in a hydrophobic medium, fixed charges serve as centres of “condensation” of large ionic aggregates, resulting in a high partitioning of both co- and counter-ions, in good agreement with RBS data [1]. The ions within such aggregates may however be fairly immobile and contribute little to overall ion transport.

The presentation will also discuss in detail some other consequences of ion association, such as the effect of pH on ion transport and the transport of salts containing divalent ions, for which association successfully explains experimental observations as well. These examples suggest that the proposed physical picture may be a crucial step towards truly predictive physical modeling of RO and NF separations.

 

1. X. Zhang, D. G. Cahill, O. Coronell, and B J. Mariñas."Partitioning of salt ions in FT30 reverse osmosis membranes," Appl.Phys.Lett. 2007, 91, 181904
2. S. Bason, V. Freger, Phenomenological analysis of transport of mono- and divalent ions in nanofiltration, J. Membr. Sci., 2010, 360, 389