Effect of tip mass on frequency response and sensitivity of AFM cantilever in liquid

• Tip mass effect is considered in AFM dynamics equations.
• Frequency response of AFM cantilever in liquid is calculated.
• Characteristics equation of AFM cantilever is derived.
• Sensitivity of AFM cantilever with tip mass effect is analyzed.

The effect of tip mass on the frequency response and sensitivity of atomic force microscope (AFM) cantilever in the liquid environment is investigated. For this purpose, using Euler–Bernoulli beam theory and considering tip mass and hydrodynamic functions in a liquid environment, an expression for the resonance frequencies of AFM cantilever in liquid is derived. Then, based on this expression, the effect of the surface contact stiffness on the flexural mode of a rectangular AFM cantilever in fluid is investigated and compared with the case where the AFM cantilever operates in the air. The results show that in contrast with an air environment, the tip mass has no significant impact on the resonance frequency and sensitivity of the AFM cantilever in the liquid. Hence, analysis of AFM behaviour in liquid environment by neglecting the tip mass is logical.