A synthetic rubber is measured to have shear modulus at and at .

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

Condensed Matter Physics, Ch Soft matter: when entropy, not bonding, sets the structure

Problem

A synthetic rubber is measured to have shear modulus

G=0.62\,\mathrm{MPa}

293\,\mathrm{K}

and

G=0.68\,\mathrm{MPa}

320\,\mathrm{K}

. ((a)) Check whether these two measurements are consistent with

G\propto T

. ((b)) Use the

293\,\mathrm{K}

measurement to find the cross-link density

n_x

, and the mean spacing between cross-links,

n_x^{-1/3}