A physical gel shows a loss tangent that is independent of frequency over three…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Condensed Matter, Materials & Soft Matter · Solid continuum mechanics and complex fluids

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

Problem

A physical gel shows a loss tangent tan⁡δ=G′′/G′=1.73\tan\delta = G''/G' = 1.73 that is independent of frequency over three decades of angular frequency, consistent with a power-law relaxation modulus G(t)∝t−nG(t) \propto t^{-n} near its gel point. ((a)) Using G′/G′′=cot⁡(nπ/2)G'/G'' = \cot(n\pi/2), find the exponent nn. ((b)) State whether this gel is more solid-like or more liquid-like than the stoichiometric critical gel of Winter and Chambon, for which n=1/2n=1/2.

Browse the problem library