Universal Scaling Laws for Surface Ionization: Influence of Salt, Confinement, and pH

The ionization of surfaces and macromolecules stands as a pivotal topic in the realms of nanofluidics, soft matter, and biology. In this work, we present quasi-geometry-independent scaling laws for the degree of ionization of charged surfaces, derived from the classical Poisson-Boltzmann equation and Langmuir adsorption isotherm, to elucidate the influence of salt, confinement, and pH on surface ionization. We identify new scaling regimes beyond the co-ion-exclusion approximation and provide new insights into the critical role of surface ionizable group density in determining various transitions of scaling regimes with added salt or separation distance using a diagram. Our theoretical predictions for surface charge density align well with experimental characterizations for carbon nanotubes, Si₃N₄ nanopores, and SiO₂ nanoparticles, demonstrating the broad applicability of our theoretical framework and rationalizing the observed power laws. This work paves the way for future investigations on polyelectrolytes, bubbles, and broad electrokinetic phenomena.