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The diffuse layer properties of modified gold electrodes under potentiostatic control have been determined by direct force measurements. These measurements have been performed with a colloidal probe consisting of a silica particle attached to the cantilever of an atomic force microscope. The gold electrodes were modified by self-assembled monolayers (SAMs) of different thickness. Additionally, the terminating functional groups of the monolayer have been varied. The interaction force profiles have been fit to the full solutions of the nonlinear Poisson-Boltzmann equation. An accurate quantitative description of the force profiles has been obtained by taking charge regulation between the surfaces into account. The diffuse layer potentials obtained from these fits were studied in dependence of the potential applied to the gold electrode. The capacitance of the SAM and the potential of zero charge (pzc) have been determined for various SAMs of different thickness and surface termination. The values obtained by our direct force measurements are in agreement with the ones reported by classical electrochemical techniques. The capacitance of the SAM depends primarily on the thickness of the monolayer and its crystalline structure. Pronounced differences in the pzc for the different functional groups have been found. These changes are related to the dipole moment of the functional group terminating the SAM. Our data are in agreement with ion adsorption, but this effect seems to be less pronounced than for bare gold electrodes.

The Derjaguin approximation states that the interaction force between two curved surfaces is proportional to their effective radius, whereby the inverse effective radius is the arithmetic mean of the inverse curvature radii of the surfaces involved. The present study investigates the validity of this approximation with an atomic force microscope (AFM) by measuring interaction forces between colloidal particles of different sizes, but of identical composition. Forces were measured between silica particles of 2.0, 4.8 and 6.8 mm in diameter in KCl electrolyte solution with and without adsorbed poly(amido amine) (PAMAM) dendrimers. The Derjaguin approximation could be confirmed at all distances investigated, including those comparable with the characteristic length scales of the surface roughness or the surface charge heterogeneities. For the conditions investigated, the Derjaguin approximation turns out to be surprisingly robust.

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