Determining the Forces between Polystyrene Latex Spheres Using Differential Electrophoresis

Abstract

The attractive force holding two polystyrene latex spheres in a doublet was measured by the method of differential electrophoresis. The two spheres of each doublet had different surface chemistries (e.g., sulfate and carboxylate) and different ζ potentials ζ1 and ζ2. The doublet acted as a dipole, and an applied electric field (E∞) caused the doublet to rotate such that the less negative sphere pointed in the direction of the field. Once the doublet was aligned, the tendency of the spheres to translate at different velocities produced a tension, the “electrophoretic displacement force”. This force, proportional to ζ2 − ζ1 and the applied electric field E∞, is calculated from solutions to the electrostatic and hydrodynamic equations. For our systems (5 μm diameter spheres, ζ2 − ζ1 ≈ 40 mV, E∞ ≈ 200 V/cm) the electrophoretic displacement force was 20−50 pN, which is more than a factor of 10 greater than the maximum attractive force predicted by DLVO theory for doublets in a secondary minimum. In no case could we break the doublets with the electrophoretic displacement force. We conclude that DLVO theory is inadequate for our colloidal system, either because the doublets were in a primary minimum (even though DLVO theory predicted an insurmountable energy barrier) or because the depth of the secondary minimum was more than a factor of 10 greater than predicted.