Sensitivity of viscoelastic characterization in multi-harmonic atomic force microscopy

Abstract

This study discusses the sensitivity of viscoelastic characterization to multi-frequency atomic force microscopy observables.

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

“…In a mathematically simpler power-law viscoelastic model, it was recently demonstrated that the structure of the l 2 norm contained many local minima which resulted in frequent misidentifications of θ . 82 In Fig. 5a and b, we show the surfaces of the norm for both the time l t 2 and frequency l ω 2 domain models for a wide range of parameter space around the true minimum ( G̃ 1obs = 0.5, 1obs = 0.5).…”

“…Furthermore, if the surface of the l 2 norm encompasses regions of h for which the values of the norm are below the machine precision level, the computer will not be able to reliably distinguish between h's in these areas and the algorithm will also be unable to continue advancing towards the minimum. 86 In a mathematically simpler power-law viscoelastic model, it was recently demonstrated that the structure of the l 2 norm contained many local minima which resulted in frequent misidentifications of h. 82 In Fig. 5a and b, we show the surfaces of the norm for both the time l t 2 and frequency l o 2 domain models for a wide range of parameter space around the true minimum (G ˜1obs = 0.5, t1obs = 0.5).…”

“…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. 83 Despite these inconsistencies in the model parameters, the fitted FD curves in the time domain often are in close agreement with the data and require detailed inspection to validate their physical sensibility.…”

Tailored Microcantilever Optimization for Multifrequency Force Microscopy

“…[17] Due to the dynamic nature of advanced AFM techniques, during the nonlinear interaction between the cantilever-tip ensemble and specimen, higher harmonics of the fundamental frequency of the vibrating cantilever emerge. [18][19][20] The main source of these harmonics' responses is short-range attractive and repulsive forces as well as contact time. As a consequence, these harmonics carry plentiful information on the mechanical, physical, and chemical properties of the specimen.…”

“…As a consequence, these harmonics carry plentiful information on the mechanical, physical, and chemical properties of the specimen. [18,20] Recent studies demonstrated the harmonics of microcantilever signal are highly sensitive to the local elasticity of the materials, [18,21] and higher contrast with detailed imaging were achieved from the higher harmonics of the microcantilever signal rather than its fundamental frequency. [22,23] Hence, using harmonic amplitude images with higher spatial resolution can open a path for fast, robust, and non-invasive mapping of mechanical, physical, and chemical properties of advanced materials at the nanoscale.…”