A polybutadiene series has an entanglement crossover at

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 polybutadiene series has an entanglement crossover at Mc=4.0×103 g mol−1M_c = 4.0\times10^{3}\,\mathrm{g\,mol^{-1}}. Sample P has MP=1.0×103 g mol−1M_{\rm P}=1.0\times10^{3}\,\mathrm{g\,mol^{-1}} (below McM_c, unentangled) and sample Q has MQ=1.0×105 g mol−1M_{\rm Q}=1.0\times10^{5}\,\mathrm{g\,mol^{-1}} (above McM_c, entangled). Suppose each sample's molar mass is doubled while temperature and chemistry are unchanged, using η0∝M1.0\eta_0\propto M^{1.0} below McM_c (Rouse) and the measured η0∝M3.4\eta_0\propto M^{3.4} above McM_c (reptation). ((a)) Predict the factor by which η0\eta_0 increases for sample P. ((b)) Predict the factor by which η0\eta_0 increases for sample Q.

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