A fast first-principles approach to model atomic force microscopy on soft, adhesive, and viscoelastic surfaces

Quantitative atomic force microscopy (AFM) on soft polymers remains challenging due to the lack of easy-to-use computational models that accurately capture the physics of the interaction between the tip and sticky, viscoelastic samples. In this work, we enhance Attard’s continuum mechanics-based model, arguably the most rigorous contact model for adhesive viscoelastic samples, via three key enabling strategies. First, the original model’s formalism is rearranged to enable a fast and explicit solution of the model’s ordinary differential equations (ODEs). Second, the deformed surface is reconstructed using a complete set of optimized orthogonal basis functions as opposed to Attard’s original, computationally expensive radial discretization. Third, the model’s governing ODEs are solved using a multi-step numerical method to further stabilize the solution when using for soft and sticky samples. Implementing these enhancements, enhanced Attard’s model (EAM) is more stable, 3+ orders of magnitude faster, and equally accurate when compared to the original model. These facilitate EAM’s inclusion into simulations of various AFM operating modes. We demonstrate EAM based simulations of quasi-static force spectroscopy and amplitude modulation AFM approach curves on soft sticky polymer surfaces. On a typical desktop computer, simulation of an amplitude modulation approach curve with EAM takes less than a minute as compared to ≈15 h by the original Attard’s model. We expect EAM to be of interest to the AFM community because it facilitates the inclusion of rigorous models of tip-sample contact in simulations on polymer samples. EAM is available as part of the VEDA set of simulation tools deployed on nanoHUB.org cyber-infrastructure.