On modeling and measuring viscoelasticity with dynamic Atomic Force Microscopy

TL;DR

This paper develops a simple analytical and numerical model for viscoelasticity in soft materials using dynamic Atomic Force Microscopy, capturing impact dynamics and providing a universal quantitative surface characterization.

Contribution

It introduces a minimal moving surface model that combines elastic and viscous forces, deriving characteristic time constants and a dimensionless impact-rheology factor for viscoelastic surfaces.

Findings

Excellent fit of the model to experimental data across various samples

Identification of characteristic time constants explaining hysteresis

Introduction of a universal impact-rheology factor for surface characterization

Abstract

The interaction between a rapidly oscillating atomic force microscope tip and a soft material surface is described using both elastic and viscous forces with a moving surface model. We derive the simplest form of this model, motivating it as a way to capture the impact dynamics of the tip and sample with an interaction consisting of two components: interfacial or surface force, and bulk or volumetric force. Analytic solutions to the piece-wise linear model identify characteristic time constants, providing a physical explanation of the hysteresis observed in the measured dynamic force quadrature curves. Numerical simulation is used to fit the model to experimental data and excellent agreement is found with a variety of different samples. The model parameters form a dimensionless impact-rheology factor, giving a quantitative physical number to characterize a viscoelastic surface that does not depend on the tip shape or cantilever frequency.