Analytical model of atomic-force-microscopy force curves in viscoelastic materials exhibiting power law relaxation

TL;DR

This paper introduces an analytical model for AFM force curves in viscoelastic materials with power law relaxation, validated through nanoindentation experiments on polyacrylamide gels, capturing their dynamic properties.

Contribution

It presents a novel analytical model for viscoelastic force curves with power law relaxation, validated with experimental AFM data on gels.

Findings

Exponents n < 1 depend on bisacrylamide concentration.

Model fits AFM force curves across different load speeds.

Reproduces dynamic viscoelastic properties of gels.

Abstract

We propose an analytical model for the force-indentation relationship in viscoelastic materials exhibiting a power law relaxation described by an exponent n, where n = 1 represents the standard viscoelastic solid (SLS) model, and n < 1 represents a fractional SLS model. To validate the model, we perform nanoindentation measurements of poylacrylamide gels with atomic force microscopy (AFM) force curves. We found exponents n < 1 that depends on the bysacrylamide concentration. We also demonstrate that the fitting of AFM force curves for varying load speeds can reproduce the dynamic viscoelastic properties of those gels measured with dynamic force modulation methods.