Forces between a rigid probe particle and a liquid interface. III. Extraction of the planar half-space interaction...

The deformation of a liquid drop (radius R0) under the probe particle (radius a) greatly complicates the interpretation by atomic force microscopy. For rigid interfaces, F(DeltaX) can be directly related to the interaction energy E(D) per unit area between planar half-spaces of probe material and drop material across a thickness D of the liquid medium by the Derjaguin approximation, [formula in text], where D(0) is the intersurface separation distance on the line of the centers of the bodies and DeltaX0 is a constant set by the somewhat arbitrary choice of origin for the separation distance DeltaX between the stage on which the drop rests and the lowest point on the probe particle. The problem of absolute intersurface separation distance is common to all surface force measurement techniques. For rigid interfaces, DeltaX0 may be established by bringing the surfaces into close (essentially hard) contact and making measurements in the constant compliance regime. For deformable interfaces, this is not possible and a general method of extracting the absolute separation distance has yet to be devised. In this paper we discuss a general algorithm for extracting E(D+DeltaX0) from F(DeltaX) data. We apply the method to constructed data to investigate the effect of data noise and to a set of real data for a sessile tetradecane droplet in water with an anionic surfactant and a bare silica probe.