Optimizing the Accuracy of Viscoelastic Characterization with AFM Force-Distance Experiments in the Time and Frequency Domains

TL;DR

This paper analyzes the limitations of AFM force-distance experiments for viscoelastic characterization, proposing information-theoretic and frequency domain approaches to improve sensitivity and experimental design accuracy.

Contribution

It introduces a novel framework combining information theory and frequency domain analysis to optimize AFM-based viscoelastic measurements.

Findings

Frequency domain analysis enhances sensitivity over time domain methods.

Restrictions on accessible timescales improve experimental reliability.

Guidelines for designing more accurate AFM experiments for polymers.

Abstract

We demonstrate that the method of characterizing viscoelastic materials with Atomic Force Microscopy (AFM) by fitting analytical models to force-distance (FD) curves often yields conflicting and physically unrealistic results. Because this method involves specifying a constitutive time-dependent viscoelastic model and then fitting said model to the experimental data, we show that the inconsistencies in this method are due to a lack of sensitivity of the model with respect to its parameters. Using approaches from information theory, this lack of sensitivity can be interpreted as a narrowed distribution of information which is obtained from the experiment. Furthermore, the equivalent representation of the problem in the frequency domain, achieved via modified Fourier transformation, offers an enhanced sensitivity through a widening of the information distribution. Using these distributions, we then define restrictions for the timescales which can be reliably accessed in both the time and frequency domains, which leads to the conclusion that the analysis of experiments in the time domain can frequently lead to inaccuracies. Finally, we provide an example where we use these restrictions as a guide to optimally design an experiment to characterize a polydimethylsiloxane (PDMS) polymer sample.