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The Laplace approach in microrheology

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Abstract

When coupled with the generalized Stokes–Einstein (GSE) equation, it is often reported that micro-rheology probes the dynamic properties differently than do macroscopic rheological measurements, especially in relatively condensed systems. In the present work, we empirically examine the GSE in its widely used form: following an analytical continuation, the Fourier transformed particle mean-square displacement (MSD) is used to determine the dynamic moduli [G′(ω) and G′′(ω)] and we compare the results with those obtained by direct inverse Laplace transform calculation of the relevant viscoelastic functions (either relaxation modulus or creep compliance) from the MSD. The results show that the inverse Laplace approaches can differ from the Fourier approach and give better agreement with macroscopic rheological measurements when this is the case. Some instances of agreement between the Fourier approach and the direct Laplace transform approaches are also shown. It is recommended that micro-rheology MSD data be interpreted using one of the direct Laplace transform based approaches.

Graphical abstract: The Laplace approach in microrheology

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Article information


Submitted
11 Nov 2019
Accepted
13 Mar 2020
First published
16 Mar 2020

Soft Matter, 2020, Advance Article
Article type
Communication

The Laplace approach in microrheology

Q. Li, X. Peng, D. Chen and G. B. McKenna, Soft Matter, 2020, Advance Article , DOI: 10.1039/C9SM02242B

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