Three symmetric polymer melt blends have Flory-Huggins parameters that vary with…

PHYSICS · Subjective · 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

Three symmetric polymer melt blends have Flory-Huggins parameters that vary with absolute temperature

T

\chi(T) = A + B/T

, with

A

and

B

as given. Each blend is made of two chemically different chains of equal length

N

(so

\chi_c = 2/N

for each pair). (a) Pair 1:

N = 100

A = 0.0020

B = 1.0\,\mathrm{K}

. (b) Pair 2:

N = 500

A = 0.0020

B = 6.0\,\mathrm{K}

. (c) Pair 3:

N = 200

A = 0.0250

B = -4.0\,\mathrm{K}

. Each blend is prepared at equal volume fractions,

\phi = 0.5

. For each pair, decide whether that sample is a single mixed phase at

T = 400\,\mathrm{K}

. For any sample that is demixed at

400\,\mathrm{K}

, state whether raising or lowering the temperature would bring it into a single phase, and give the temperature at which it crosses into the mixed region (or explain why that temperature is not practically reachable).

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