A chain of Kuhn segments of length is dissolved in a solvent whose excluded volume…

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

A chain of N=2000N=2000 Kuhn segments of length b=0.70 nmb=0.70\,\mathrm{nm} is dissolved in a solvent whose excluded volume parameter varies linearly near a theta temperature Θ=300 K\Theta = 300\,\mathrm{K} as v(T)=v0 T−ΘΘ,v0=3.0 nm3v(T) = v_0\,\frac{T-\Theta}{\Theta}, \qquad v_0 = 3.0\,\mathrm{nm^3} ((a)) Find the chain size at T=310 KT=310\,\mathrm{K} using the Flory radius RF≈b(v/b3)1/5N3/5R_F \approx b(v/b^3)^{1/5}N^{3/5}. ((b)) Find the chain size exactly at T=ΘT=\Theta, where the chain is ideal. ((c)) Find the globule size at T=290 KT=290\,\mathrm{K} using Rgl≈b2N1/3/∣v∣1/3R_{\rm gl} \approx b^2N^{1/3}/|v|^{1/3}. ((d)) State in words how and why the chain's size changes as TT is lowered through Θ\Theta.

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