Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy

In this short paper we explore the use of higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy (AFM) for the small-indentation imaging of soft viscoelastic materials. In viscoelastic materials, whose response depends on the deformation rate, the tip–sample forces generated as a result of sample deformation increase as the tip velocity increases. Since the eigenfrequencies in a cantilever increase with eigenmode order, and since higher oscillation frequencies lead to higher tip velocities for a given amplitude (in viscoelastic materials), the sample indentation can in some cases be reduced by using higher eigenmodes of the cantilever. This effect competes with the lower sensitivity of higher eigenmodes, due to their larger force constant, which for elastic materials leads to greater indentation for similar amplitudes, compared with lower eigenmodes. We offer a short theoretical discussion of the key underlying concepts, along with numerical simulations and experiments to illustrate a simple recipe for imaging soft viscoelastic matter with reduced indentation.