A symmetrical method to obtain shear moduli from microrheology

Kengo Nishi, Maria L. Kilfoil*, Christoph F. Schmidt, F. C. Mackintosh

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Passive microrheology typically deduces shear elastic loss and storage moduli from displacement time series or mean-squared displacements (MSD) of thermally fluctuating probe particles in equilibrium materials. Common data analysis methods use either Kramers-Kronig (KK) transformation 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 χ(ω) = χ′(ω) + iχ′′(ω) as direct integral transforms of the MSD of thermal particle motion. This procedure significantly improves the high-frequency fidelity of χ(ω) relative to the use of KK transformation, which has been shown to lead to artifacts in χ′(ω). We test our method on both model 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.

Original languageEnglish
Pages (from-to)3716-3723
Number of pages8
JournalSoft Matter
Issue number19
Publication statusPublished - 21 May 2018


M. L. K. was supported by NSF (OISE-1444209). F. C. M. was supported in part by NSF (PHY-1427654). The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Frame-work Programme (FP7/2007–2013)/ERC grant agreement no. 340528 (C. F. S and K. N.), and the DFG Collaborative Research Center SFB 937 (Project A2) (C. F. S.). M. L. K., C. F. S. and F. C. M. thank the Kavli Institute for Theoretical Physics, where a portion of this work was done.

FundersFunder number
European Union’s Seventh Frame-work Programme
National Science Foundation340528, OISE-1444209, PHY-1427654, 1427654, 1444209
European Research Council
Deutsche ForschungsgemeinschaftSFB 937


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