A symmetric polymer blend has sites per chain for both components and (so )

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

A symmetric polymer blend has N=800N = 800 sites per chain for both components and χ=0.00625\chi = 0.00625 (so χN=5.0\chi N = 5.0). The binodal compositions satisfy ln⁡ ⁣[ϕ1−ϕ]=χN(2ϕ−1).\ln\!\left[\frac{\phi}{1-\phi}\right] = \chi N(2\phi-1). Using bisection (or any equivalent root-finder) to a tolerance of 10−610^{-6} in ϕ\phi, find the two binodal compositions, giving each to three significant figures.

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