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 (E_a) 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 E_a values measured at high concentrations result from the temperature dependence of viscosity and its influence on ion mobility, whereas E_a 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 E_a 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.