Direct conversion of rheological compliance measurements into storage and loss moduli

TL;DR

This paper introduces a direct mathematical method to derive frequency-dependent storage and loss moduli from time-dependent rheological measurements, simplifying data analysis and reducing noise interference.

Contribution

It provides a novel, straightforward formula to convert experimental rheological data into moduli without complex inverse Laplace transforms or fitting procedures.

Findings

Eliminates need for inverse Laplace transforms

Applicable to various rheological measurement techniques

Reduces data smoothing and fitting artifacts

Abstract

We remove the need for Laplace/inverse-Laplace transformations of experimental data, by presenting a direct and straightforward mathematical procedure for obtaining frequency-dependent storage and loss moduli ($G'(\omega)$ and $G"(\omega)$ respectively), from time-dependent experimental measurements. The procedure is applicable to ordinary rheological creep (stress-step) measurements, as well as all microrheological techniques, whether they access a Brownian mean-square displacement, or a forced compliance. Data can be substituted directly into our simple formula, thus eliminating traditional fitting and smoothing procedures that disguise relevant experimental noise.