Capillary liquid bridges in atomic force microscopy: formation, rupture, and hysteresis.

Atomic force microscopy (AFM) can work in a variety of environment with different humidities. When the tip of AFM approaches a sample, the measured adhesion force would be significantly affected by the presence of nanometer-sized liquid bridge. The formation and rupture of liquid bridges can occur either through equilibrium or nonequilibrium process. In this work, the liquid bridges are assumed to be in thermodynamic equilibrium with the surrounding vapor medium. To study theoretically the stability of liquid bridge, a constraint is added into the lattice density functional theory to stabilize a series of bridges with different radii at a given tip-substrate distance. With the help of the constraint, we can identify not only stable and metastable states but also transition states for the formation and rupture of liquid bridges. Using this constrained method we calculate the energy barriers involved in the formation and rupture of the liquid bridges, respectively, and then discuss their stability as well as the origin of the hysteresis behavior observed with atomic force microscope measurements. On the whole, the calculated force-distance curves are found to be qualitatively in agreement with experimental observations. The energy barriers for the formation and rupture of liquid bridges are also analyzed as a function of tip-sample distance, humidity, and tip-fluid interaction.