Modeling viscoelasticity through spring-dashpot models in intermittent-contact atomic force microscopy

We examine different approaches to model viscoelasticity within atomic force microscopy (AFM) simulation. Our study ranges from very simple linear spring-dashpot models to more sophisticated nonlinear systems that are able to reproduce fundamental properties of viscoelastic surfaces, including creep, stress relaxation and the presence of multiple relaxation times. Some of the models examined have been previously used in AFM simulation, but their applicability to different situations has not yet been examined in detail. The behavior of each model is analyzed here in terms of force-distance curves, dissipated energy and any inherent unphysical artifacts. We focus in this paper on single-eigenmode tip-sample impacts, but the models and results can also be useful in the context of multifrequency AFM, in which the tip trajectories are very complex and there is a wider range of sample deformation frequencies (descriptions of tip-sample model behaviors in the context of multifrequency AFM require detailed studies and are beyond the scope of this work).