A symmetrical method to obtain shear moduli from microrheology

TL;DR

This paper introduces a new symmetric integral transform method for passive microrheology that enhances the accuracy of shear moduli measurements at high frequencies by avoiding artifacts associated with traditional Kramers-Kronig transformations.

Contribution

The authors develop a novel integral transform approach to directly compute complex response functions from MSD data, improving high-frequency fidelity in microrheology analysis.

Findings

Improved high-frequency response measurement accuracy.

Better agreement with established methods at low frequencies.

Significant reduction of artifacts in shear moduli at high frequencies.

Abstract

Passive microrheology typically deduces shear elastic loss and storage moduli from displacement time series or mean-squared displacement (MSD) of thermally fluctuating probe particles in equilibrium materials. Common data analysis methods use either Kramers-Kronig (KK) transformations or functional fitting to calculate frequency-dependent loss and storage moduli. We propose a new analysis method for passive microrheology that avoids the limitations of both of these approaches. In this method, we determine both real and imaginary components of the complex, frequency-dependent response function $\chi(\omega) = \chi^{\prime}(\omega)+i\chi^{\prime\prime}(\omega)$ as direct integral transforms of the MSD of thermal particle motion. This procedure significantly improves the high-frequency fidelity of $\chi(\omega)$ relative to the use of KK transformation, which has been shown to lead to artifacts in $\chi^{\prime}(\omega)$. We test our method on both model data and experimental data. Experiments were performed on solutions of worm-like micelles and dilute collagen solutions. While the present method agrees well with established KK-based methods at low frequencies, we demonstrate significant improvement at high frequencies using our symmetric analysis method, up to almost the fundamental Nyquist limit.