A good-solvent polymer solution well above the overlap concentration has measured…

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 solutions and blends

Problem

A good-solvent polymer solution well above the overlap concentration has measured osmotic pressure Π1=1.20 kPa\Pi_1 = 1.20\,\mathrm{kPa} at volume fraction ϕ1=0.050\phi_1 = 0.050. Someone argues: "In the semidilute regime the second virial (Flory-Huggins) term dominates and Π∝ϕ2\Pi \propto \phi^2, so doubling the volume fraction to ϕ2=0.100\phi_2 = 0.100 should quadruple the osmotic pressure, giving Π2=4×1.20=4.80 kPa\Pi_2 = 4 \times 1.20 = 4.80\,\mathrm{kPa}." ((a)) Explain why this reasoning uses the wrong power law for a semidilute solution. ((b)) Using the correct scaling law for the semidilute regime, calculate Π2\Pi_2 at ϕ2=0.100\phi_2 = 0.100.

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