A rheology report on a Maxwell liquid with and

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Polymer dynamics and viscoelasticity

Problem

A rheology report on a Maxwell liquid with

G_0 = 10.0\,\mathrm{kPa}

and

\tau = 0.20\,\mathrm{s}

, tested at

\omega = 2.0\,\mathrm{rad\,s^{-1}}

, states: "Since

G' = \dfrac{G_0\,\omega\tau}{1+\omega^2\tau^2}

is the storage modulus and

G'' = \dfrac{G_0(\omega\tau)^2}{1+\omega^2\tau^2}

is the loss modulus, we find

G' = 3.45\,\mathrm{kPa}

and

G'' = 1.38\,\mathrm{kPa}

, so the sample is predominantly elastic at this frequency." ((a)) Find the error in this working. ((b)) Give the correct values of

G'

and

G''

\omega = 2.0\,\mathrm{rad\,s^{-1}}

, and state whether the sample is predominantly elastic or viscous there.