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

Abstract

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.

Machine Learning Approach to Characterize the Adhesive and Mechanical Properties of Soft Polymers Using PeakForce Tapping AFM

“…We use EAM to calculate F ts in eq , and we model the surface viscoelasticity and tip–surface interaction by the standard linear solid (SLS) model and Lennard-Jones (LJ) equation, respectively. The creep compliance function, J ( t ), of an SLS viscoelastic element is where, τ, E ∞ , and E 0 are retardation (creep) time and long- and short-term moduli of the surface, respectively.…”

“…The continuum mechanics-based contact model proposed by Attard , is arguably the most comprehensive and rigorous model to capture the physics of interaction on adhesive viscoelastic samples. In prior work, we implemented three key enabling strategies on Attard’s model to enhance its computational part and make it faster and more robust . These strategies are (a) using a set of optimized orthogonal basis functions instead of the computationally expensive radial discretization technique of the original Attard’s model; (b) solving the model’s governing ordinary differential equations (ODEs) using multistep Adams–Bashforth methods, and (c) facilitating the explicit solution of the ODEs of the model by rearranging the original formalism.…”

“…In this work, we first develop an algorithm to predict PFT force curves with a known set of operating conditions, microcantilever parameters, and material viscoelastic and adhesive properties. The algorithm adopts EAM to model the tip–surface interactions when performing PFT AFM on viscoelastic adhesive surfaces . The algorithm is then employed to conduct a parametric study to predict variations in force–distance curves due to changes in PFT AFM operational parameters, microcantilever parameters, and surface properties.…”

“…In prior work, we implemented three key enabling strategies on Attard's model to enhance its computational part and make it faster and more robust. 21 (a) Schematic of an interacting AFM microcantilever tip and a surface in FVM-like AFM operational modes is illustrated, and the relevant parameters are specified: the tip−surface distance Z(t), tip deflection q(t), surface deformation u(r, t), and axisymmetric tip profile f tip (r). The other parameters shown in the figure can be defined based on Z(t), q(t), u(r, t), and f tip (r) as follows: surface forces.…”

“…The algorithm adopts EAM to model the tip−surface interactions when performing PFT AFM on viscoelastic adhesive surfaces. 21 The algorithm is then employed to conduct a parametric study to predict variations in force−distance curves due to changes in PFT AFM operational parameters, microcantilever parameters, and surface properties. In the second part of this work, we examine using a machine learning (ML) algorithm to estimate the viscoelastic and adhesive properties of the sample based on observed PFT AFM force curves.…”