Direct conversion of rheological compliance measurements into storage and loss moduli

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 [$G^{\prime }\left(\omega \right)$ and $G^{″}\left(\omega \right)$, 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.