An unentangled polymer melt chain is modelled by the Rouse model with Kuhn segments…

PHYSICS · Subjective · 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 unentangled polymer melt chain is modelled by the Rouse model with N=150N = 150 Kuhn segments of length b=0.50 nmb = 0.50\,\mathrm{nm}, a monomeric friction coefficient ζ=6.0×10−11 kg s−1\zeta = 6.0\times10^{-11}\,\mathrm{kg\,s^{-1}} per segment, at T=298 KT = 298\,\mathrm{K} (take kBT=4.11×10−21 Jk_BT = 4.11\times10^{-21}\,\mathrm{J}). Using the Rouse relaxation time τR=ζb2N26π2kBT,\tau_{\rm R} = \frac{\zeta b^2 N^2}{6\pi^2 k_BT}, calculate τR\tau_{\rm R} for this chain.

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