Forces between a rigid probe particle and a liquid interface - I. The repulsive case

The effect of disjoining pressure between a rigid spherical probe particle (attached to an AFM cantilever) and a liquid interface (e.g., oil/water or air/water) is treated in an analytic manner to describe the total force F exerted on the probe as a function of the distance X of the probe from the rigid substrate (AFM stage) on which the liquid interface resides. Two cases (i) a hat interface under gravity and (ii) a drop whose size is sufficiently small that gravity can be neglected have been examined. A simple numerical algorithm is given for computing F(X) (the AFM observable) from a given form for the disjoining pressure. Numerical results are displayed for electrostatic probe/interface interactions which reveal the linear compliance regime experimentally observed in AFM experiments on these systems. The slope of the linear compliance regime is shown to be a function of the properties of the interface (capillary length, particle radius, drop size, contact angle of drop on rigid substrate etc.). (C) 2001 Academic Press.