Reversal in mobility and interfacial ionic layering for electrophoresis of a pH-regulated nanoparticle in multivalent...

Strong coupling in ion distribution and hence, short-range coulombic interactions manifest in a multivalent electrolyte. The surface charge density arising through protonation/deprotonation reactions is also influenced by the presence of the multivalent counterions. Thus, the electrophoresis of a charge-regulated nanoparticle (NP) in electrolytes with multivalent counterions will be substantially different from that predicted by existing theories based on the mean-field approach, which neglects the correlations among ions. This type of study is lacking in the literature. We develop a continuum-based model that incorporates the short-range hydrodynamic steric interactions and ion-ion correlations of finite-sized ions to analyze the electrophoresis of a pH-regulated NP in a multivalent electrolyte. The governing equations are solved numerically, supplemented by a thin-layer analysis. We have established an excellent agreement with existing experimental results for NPs with constant surface charge density in multivalent electrolytes, as well as for mobility of a charge-regulated NP in monovalent and trivalent electrolytes. Our study shows that the SiO₂ NP can undergo a reversal in mobility at a higher pH level and an ionic layered structure develops near the NP. This reversal in mobility is suppressed and the condensed-layer counterion diffuses with further increase in the pH level. Through theoretical analysis corroborated by numerical results, we find that the ion-ion correlations remain significant even for the lower ionic volume fraction, for which steric interaction is negligible.