A symmetric polymer blend has segments per chain

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Non-equilibrium statistical mechanics and stochastic thermodynamics

Soft Matter at the Thermal Scale, Ch Spinodal decomposition and coarsening

Problem

A symmetric polymer blend has N=800N=800 segments per chain, so the critical interaction parameter is χc=2/N\chi_c = 2/N, and a radius of gyration Rg=12 nmR_g = 12\,\mathrm{nm}. It is quenched to χ=0.0045\chi = 0.0045. ((a)) Find χ/χc\chi/\chi_c. ((b)) Use qmRg=32(χ/χc−1)q_mR_g = \sqrt{\tfrac32(\chi/\chi_c - 1)} to find qmq_m. ((c)) Find the dominant early-stage wavelength λm=2π/qm\lambda_m = 2\pi/q_m.

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