Measurements of dynamic forces between drops with the AFM: novel considerations in comparisons between experiment and theory

Abstract

Dynamic forces between a deformable tetradecane oil drop (radius of curvature ≈ 25 μm) anchored on the cantilever of the Atomic Force Microscope (AFM) and similar oil drops (radii of curvature 80 to 500 μm) on the substrate in aqueous electrolyte with added sodium dodecyl sulfate surfactant have been studied. Measurements were made over a range of scan rates that span the range of Brownian velocities of such emulsion drops. The adsorbed anionic surfactants impart a stabilising electrical double layer repulsion between the drops so coalescence was not observed under present conditions. Force–displacement data follow reversible trajectories at low scan rates (<0.5 μm s⁻¹) but exhibit increasingly large hysteric effects for scan rates up to 30 μm s⁻¹. The coupling between deformations of the interacting drops and deflections of the AFM cantilever at high scan rates facilitates a self-consistent and independent estimate of the cantilever spring constant if one models variations of cantilever deflection with piezo displacement. In addition to giving excellent agreement between predicted and measured dynamic forces, our model also furnishes quantitative information about: variations of the force with interfacial separation, deformations and velocities of interfaces, pressure distributions in the aqueous film between the drops as well as the absolute separation between the interacting drops. A new dimpling phenomenon is inferred to occur when interacting drops are being separated after the formation of a flattened aqueous film. These new capabilities in the evaluation and interpretation of AFM force measurements overcome a major limitation in the use of the AFM for the absolute quantification of force–separation data.