Direct Measurement of Interaction Forces between Colloidal Particles Using the Scanning Force Microscope

We have measured the interaction forces versus distance between pairs of 2-µm diameter polystyrene spheres immersed in electrolytes containing up to 1 M KCl. A reproducible long-range repulsion was observed for concentrations below 0.01 M. Adhesion varied considerably from measurement to measurement (values ranged from 3.5 to 140 nN) and showed no systematic trend as a function of electrolyte strength. Data for repulsion in 0.001 M KCl are well fitted by a simple result based on the Derjaguin approximation and the linearized Poisson-Boltzmann equation. This fit yields a surface potential (ψ₀) of 87 mV and a Debye length of 7.7 ±0.1 nm, in reasonable agreement with the expected Debye length (9.5 nm) and the measured ζ potential (83 ± 2 mV). A full numerical solution of the Poisson-Boltzmann equation shows that the simple theory works reasonably in these conditions, despite the fact that ψ₀/k_BT > 1. Measurements made in pure water and measurements of the interaction between a sphere and a mice surface gave results that varied from run to run, none of which agreed with theoretical calculations.