Proton enrichment and surface charge dynamics in pH-responsive nanopipettes

Comprehensive finite element models can be crucial for Scanning Ion Conductance Microscopy-based (SICM) applications, such as surface charge mapping, where the fitting of experimental curves to models is used to quantify substrate surface charge density. In the nanopipettes utilized for SICM, the acid-dissociation of surface groups on the nanopipette walls generate the surface charges that drive fundamental nanoscale transport behaviors such as ion current rectification. While nearly all existing finite element models of ion transport in conical nanopores assume a fixed and uniform surface charge, the dissociation of surface groups is in fact influenced by the local H+ and OH- concentrations, which themselves deplete or accumulate within the conical nanopore when the voltage across it is changed. As such, localized pH and hence surface charges should vary substantially from bulk values. To study the dynamic interplay between the magnitudes and distributions of ion concentrations, pH distributions and the localized surface charge, and the overarching effect of these parameters on the ion-current rectification as a function of electrolyte concentration, a new finite element model, that dynamically calculates the surface charge based on surface-site density, surface-site acid dissociation constant, and localized pH values, has been developed. This model additionally includes the water auto-ionization reaction. The surface charge density is revealed to be non-linear across the nanopore and highly asymmetric at different applied potentials, as well as highly influenced by the bulk pH and electrolyte concentrations. Our model qualitatively predicts experimental measurements of ion current rectification for different bulk pH values even in the regime of low electrolyte, and the potential implications of our results are discussed in the context of both fundamental nanopore transport studies and SICM charge mapping studies.