Linear Viscoelasticity: Review of Theory and Applications in Atomic Force Microscopy

Abstract

Recently, much research has been performed involving the mechanical analysis of biological and polymeric samples with the use of Atomic Force Microscopy (AFM). Such materials require careful treatments which consider the rate-dependence of their viscoelastic response. Here, we review the fundamental theories of linear viscoelasticity, as well as their application to the analysis of AFM spectroscopy data. An outline of general viscoelastic mechanical phenomena is initially given, followed by a brief outline of AFM techniques. Then, an extensive outline of linear viscoelastic material models, as well as contact mechanics descriptions of AFM systems, are presented.

Characterizing viscoelastic properties of human melanoma tissue using Prony series

“…However, the viscoelastic properties of viscoelastic materials are known to be highly dependent on frequency. For instance, viscoelastic materials tend to have higher stiffness at high frequencies than low frequencies ( McCraw et al, 2021 ). These harmonic quantities include the storage modulus, representing the elastic portion and loss modulus representing the viscous portion.…”

Optimizing the accuracy of viscoelastic characterization with AFM force–distance experiments in the time and frequency domains

“…While these methods offer straightforward solutions for obtaining parameterized descriptions of viscoelastic materials, their accuracy and reliability has recently been questioned. 78,81 Specifically, the time domain approach often yields unphysical or even conflicting values of the model parameters which depend on the initialization of the fitting algorithm. 82 Furthermore, a recent work by Vemaganti et al demonstrates that relaxation times can only be reliably obtained from stress relaxation experiments if they are less than 20% of the total experiment length.…”

Analysis of the Electroconsolidation Process of Fine-Dispersed Structures Out of Hot Pressed Al2O3–WC Nanopowders

“…From the collected theoretical and experimental data, it is possible to predict the appearance and generation of dislocations during the sintering process. Under load, the atomic structure of the bulk material responds through deformation along the direction of the applied force [32]. In any sort of pressure-assisted sintering, the stress state during densification affects particle sliding and dimensional change due to the pore shrinkage [33].…”