Probing power laws in multifrequency AFM

Quantification of conservative forces in multifrequency atomic force microscopy requires solving the general equations of the theory expressed in terms of the virials of interaction. Power law expressions are commonly utilized when dealing with electrostatic, ferroelectric, magnetic, or long range (van der Waals) forces. Here, we discuss long range forces modeled in terms of power laws (n), where the exponent n covers the range n = 2-5, and employ the multifrequency theory to explore the relevant parameter space. Numerical integration of the equations of motion suggest that only a narrow range of operational parameters are available when imaging where the approximations are valid. Albeit these conditions exist, and the corresponding errors can be as low as 10% throughout for all exponents explored.

Automated summary

Quantifying conservative forces in multifrequency atomic force microscopy involves solving the general equations expressed in terms of interaction energies. Power law expressions are commonly used for electrostatic, ferroelectric, magnetic, or long range forces. This study discusses long range forces modeled using power laws with exponent values ranging from 2-5, and applies multifrequency theory to explore the relevant parameter space. Numerical integration of motion equations shows a narrow range of operational parameters for valid approximations during imaging, with errors as low as 10% for all explored exponents.