Nonlinear two-phase equilibrium model for the binding of arsenic anions to cationic micelles

The binding of arsenic ions to cationic cetylpyridinium chloride (CPC) micelles has been investigated using the semiequilibrium dialysis (SED) technique. In SED experiments, it has been shown that CPC micelles are very effective in binding arsenic ions in the retentate. At the studied pH (pH 8), the unbound and bound arsenic exists primarily as divalent anions (HAsO42−) while CPC molecules exist as monovalent cations. Therefore, arsenic ions are bound electrostatically to the cationic micelle. The resultant colloid is large enough not to pass through the dialysis membrane, producing a rejection greater than 99.59%. The concentration of the unbound arsenic anions passing through the dialysis membrane is practically the same as the permeate concentration of these species in the analogous micellar-enhanced ultrafiltration (MEUF) experiments. Therefore, a nonlinear equilibrium model which combines thermodynamic relations, charge balance equations, and material balance equations with the Oosawa two-phase polyelectrolyte theory has been developed to correlate the binding of arsenic to CPC micelles in SED and MEUF. It was shown that the equilibrium model successfully accounts for the experimental data in both SED and MEUF in the absence and presence of monovalent (HCO31−) and divalent co-ions (HPO42−). Because of their small sizes (less than 10 nm), micelles should retain their equilibrium shapes in the presence of hydrodynamic shear typically attained in most dynamic processes. Therefore, the equilibrium model can be used to predict separation efficiencies in other ultrafiltration units such as in crossflow ultrafiltration processes.