Method to Quantify Nanoscale Surface Charge in Liquid with Atomic Force Microscopy

A theory is presented to obtain surface charge density on nanoscale objects from data in the snap-to-contact portion of an atomic force microscope force-separation curve. The mathematical model takes into account the tip's dielectric constant using the Self-Consistent Sum of Dipoles theory which includes the charge-charge interaction and the charge-dipole interaction with electrolyte-induced exponentially decaying screening, Debye and London dipolar force, and fluid viscosity including confined fluid layers to account for energy dissipation. Using previously published experimental data, the mathematical model is applied to measure the surface charge density on an individual nanoscale amine-modified polystyrene bead immobilized on the basal plane of highly oriented pyrolytic graphite in buffered aqueous solution. Within the experimental uncertainty, the magnitude of the charge density on a single bead obtained using the new method falls within the distribution of values determined by the manufacturer using titration and electron microscopy.