Someone argues: "In a polystyrene melt

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

Soft Matter at the Thermal Scale, Ch The size and shape of a polymer chain

Problem

Someone argues: "In a polystyrene melt, every chain of N=1000N=1000 Kuhn segments (b=1.8 nmb=1.8\,\mathrm{nm}) is surrounded on all sides by other identical chains, so excluded-volume interactions are everywhere present, just as they are for a chain in a good solvent. The chain must therefore be swollen with the same Flory exponent as in dilute good solvent, giving R≈bN3/5≈113 nmR \approx bN^{3/5} \approx 113\,\mathrm{nm} rather than the smaller ideal value bN1/2bN^{1/2}." ((a)) Find the error in this reasoning. ((b)) Give the correct size of the chain in the melt.

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