An uncrosslinked polymer melt (no network at all) is well described by a single…

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

An uncrosslinked polymer melt (no network at all) is well described by a single Maxwell mode with

G_0 = 50\,\mathrm{kPa}

and

\tau = 0.5\,\mathrm{s}

. Someone measures

G'(\omega)

and

G''(\omega)

, finds that they cross at

\omega\tau=1

(i.e.

\omega = 2\,\mathrm{rad\,s^{-1}}

), and concludes: "

G'=G''

, so this is the gel point of the sample." ((a)) Compute

G'

and

G''

\omega\tau = 0.1,\ 1,\ 10

. ((b)) Say whether the crossing is evidence of gelation, and give the correct criterion.