Ion Exchange Selectivity as a Surrogate Indicator of Relative Permeability of Ions in Reverse Osmosis Processes

Abstract

The existing body of experimental data in the open literature clearly indicate that reverse osmosis (RO) processes reject ions of identical valence (i.e., homovalent ions) to different degrees. For example, rejections (or relative permeations) of monovalent anions (such as Cl-, NO3-, Br-, CH2ClCOO-, ClO4-, etc.) during RO processes are different under otherwise identical conditions. The same is true for divalent anions (namely, SO42-, HPO42-, SeO42-) or monovalent cations (namely, Li+, Na+, K+, and NH4+). The solution diffusion model with the Nernst−Planck equation is unable to predict the differential permeation behaviors of homovalent ions. It is recognized that hydrated ionic radii data, if available, could be used to compute interdiffusion coefficients (or salt permeability coefficients) of permeating electrolytes. However, a careful scrutiny of the existing body of hydrated ionic radii data in the open literature provide clear evidence that they are unreliable for polyatomic ions such as nitrate, nitrite, selenate, phosphate, chloroacetate, sulfate, etc. Also, ionic diffusivities computed from equivalent conductance data fail to predict the hierarchy of relative permeations of homovalent ions in RO processes. Central to this study is the underlying scientific premise that ion-exchange selectivity can be used as an effective parameter to predict the relative permeability of homovalent ions in a multicomponent system. For two ions of identical valence, ion-exchange selectivity based on Coulombic interaction is dependent only on their relative hydrated ionic radii, which in turn govern the interdiffusion coefficients of permeating electrolytes. The higher the ion-exchange selectivity of a specific ion, the lower is its hydrated ionic radius and, hence, more permeable is the ion. The theoretical relationship between ion-exchange selectivity and permeability can be well explained with the aid of the Stokes−Einstein equation. Experimental results presented in this study with both monovalent and divalent ions show a strong characteristic correlation between ion-exchange selectivity and relative permeation, i.e., a higher ion-exchange selectivity always leads to a greater permeability. One major advantage of this approach is the ease with which ion-exchange selectivity can be determined by ion chromatography and/or batch isotherm technique. A large body of existing experimental data for RO and nanofiltration processes in the open literature, when carefully reviewed, also validate this scientific premise. Type of membrane, solvent dielectric constant, and pH influence the overall solvent and salt permeation fluxes, but the relative permeation of homovalent ions still follows the ion-exchange selectivity sequence.