Lattice Gas Monte Carlo Simulation of Capillary Forces in Atomic Force Microscopy

We review recent work concerned with lattice gas (LG) Monte Carlo (MC) simulations of the water meniscus formed between an atomic force microscope (AFM) tip and the surface in contact with the tip. Grand canonical MC simulations were performed to study the meniscus structure and capillary force, and this work allowed us to examine the mechanism of meniscus formation as a function of the tip–surface distance and humidity. It is found that the meniscus becomes unstable when it is narrower than the diameter of the tip–surface contact area. The calculations suggest that the ultimate size limit for a stable meniscus is five molecular diameters. We developed thermodynamic integration and perturbation methods to calculate the capillary force. The magnitude and humidity dependence of capillary force are significantly affected by the hydrophilicity of both the tip and surface. A mean field density functional theory (DFT) closely approximates the capillary forces calculated from the MC simulation. Changing the atomic scale roughness of the tip and surface drastically changes the capillary force. In particular, at low humidity, a slight roughening of the tip or surface leads to a drastic change in the force. The roughness effect persists even at 80% relative humidity. The capillary force is governed by the degree of confinement of the water and, therefore, increases as the free volume between the tip and surface decreases. The humidity dependence of the capillary force depends on the susceptibility of the meniscus width to tip retraction. For strongly hydrophilic tips at high humidity, the susceptibility is small so that the capillary force decreases as the humidity rises.