Thermodynamics of Charge Regulation during Ion Transport through Silica Nanochannels

Ion–surface interactions can alter the properties of nanopores and dictate nanofluidic transport in engineered and biological systems central to the water–energy nexus. The ion adsorption process, known as “charge regulation”, is ion-specific and is dependent on the extent of confinement when the electric double layers (EDLs) between two charged surfaces overlap. A fundamental understanding of the mechanisms behind charge regulation remains lacking. Herein, we study the thermodynamics of charge regulation reactions in 20 nm SiO2 channels via conductance measurements at various concentrations and temperatures. The effective activation energies (Ea) for ion conductance at low concentrations (strong EDL overlap) are ∼2-fold higher than at high concentrations (no EDL overlap) for the electrolytes studied here: LiCl, NaCl, KCl, and CsCl. We find that Ea values measured at high concentrations result from the temperature dependence of viscosity and its influence on ion mobility, whereas Ea values measured at low concentrations result from the combined effects of ion mobility and the enthalpy of cation adsorption to the charged surface. Notably, the Ea for surface reactions increases from 7.03 kJ mol–1 for NaCl to 16.72 ± 0.48 kJ mol–1 for KCl, corresponding to a difference in surface charge of −8.2 to −0.8 mC m–2, respectively. We construct a charge regulation model to rationalize the cation-specific charge regulation behavior based on an adsorption equilibrium. Our findings show that temperature- and concentration-dependent conductance measurements can help indirectly probe the ion–surface interactions that govern transport and colloidal interactions at the nanoscale─representing a critical step forward in our understanding of charge regulation and adsorption phenomena under nanoconfinement.