A more adequate extended Prandtl-Tomlinson model in two dimensions (2D) analysis is proposed in the aim to thoroughly investigate the interplay between kinetic friction, relative humidity (RH), normal load, and temperature in both contact and tapping mode atomic force microscopic (AFM). In contact mode operation, results firstly show that for various applied normal loads highly wetted surface in contrast to partially wetted surface exhibits lower friction at finite temperature range. This phenomenon is attributed to the film layer acting as a lubricant. Secondly, two different regimes when varying the relative humidity were further observed with increasing temperature. The first one shows the thermolubricity’s effect at low RH (RH 20%) while the second regime remarkably confirms an increase of friction with temperature at higher RH (RH60%) which is inconsistent with common observation. The latter regime is characterized by the thermally activated capillary bridge formation leading to an increase of the total adhesion force. Thirdly we demonstrated that both regimes also hold in ac mode operation and regardless to the humidity level, either low or high RH, friction force decreases with increasing amplitude modulation. Good agreement was found with measurement and analytical data reported previously. In the model treatment, however, only effects of capillary force which dominate in AFM measurement were considered.

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