While polyamide reverse osmosis and nanofiltration membranes have been extensively utilized in water purification and desalination processes, the molecular details governing water and solute permeation in these membranes are not fully understood. In this study, we apply transition-state theory for transmembrane permeation to systematically break down the intrinsic permeabilities of water and small ions in loose and tight polyamide nanofiltration membranes into enthalpic and entropic components using an Eyring-type equation. We analyze trends in these components to elucidate molecular phenomena that induce water−salt, monovalent−divalent, and monovalent− monovalent selectivity at different pH values. Our results suggest that in pores that are either too small or contain an electrostatically repelling mouth, the thermal activation of ions in the form of ion dehydration is less likely, promoting entropically driven selectivity with steric exclusion of hydrated ions. Instead, larger uncharged pores enable ion dehydration, inducing enthalpic selectivity that is driven by differences in the ion hydration properties. We also demonstrate that electrostatic interactions between cations and intrapore carboxyl groups hinder salt permeability, increasing the enthalpic barrier of the transport. Last, permeation tests of monovalent cations in the loose and tight polyamide membranes expose opposite rejection trends that further support the phenomenon of ion dehydration in large subnanopores.
While the detrimental effect of concentration
polarization (CP)
on water flux and solute rejection in pressure-driven membrane processes
has been extensively explored, the impact of CP on the selectivity
between solutes in these processes has been somewhat overlooked. Considering
the growing interest in solute–solute selectivity, in this
study, we explored the effect of CP on ion–ion selectivity
in nanofiltration (NF) membranes. We first show and discuss the “reversed”
observed rejection trend of monovalent cations in NF, which is opposite
to the trend of the ions’ hydrated size and mobility in solution.
Next, we apply the film theory using three independent approaches
to evaluate the extent of CP in the boundary layer adjacent to the
membrane surface, from which the real rejection of the ions can be
calculated. Our calculated real rejections of monovalent cations,
which were in higher correspondence with the ions’ hydration
properties and mobility in solution, suggest that CP played a major
role in the “reversed” selectivity observed. Last, we
demonstrate how CP adversely affects the commonly pursued monovalent–divalent
ion separation in NF. Overall, our results highlight the necessity
to rigorously account for CP in future studies on NF and suggest minimizing
CP as a primary step to improve the selectivity between solutes.
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