Early-stage light scattering from a quenched polymer blend gives two measured growth rates

PHYSICS · Subjective · 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

Early-stage light scattering from a quenched polymer blend gives two measured growth rates, both from wavevectors known to lie inside the growing band: R=1.0×10−2 s−1 at q=1.0 μm−1,R=1.6×10−2 s−1 at q=2.0 μm−1.\begin{aligned} R &= 1.0\times10^{-2}\,\mathrm{s^{-1}} \text{ at } q = 1.0\,\mathrm{\mu m^{-1}}, \\ R &= 1.6\times10^{-2}\,\mathrm{s^{-1}} \text{ at } q = 2.0\,\mathrm{\mu m^{-1}}. \end{aligned} Using only these two points, estimate the mobility-curvature product Mf′′Mf'', the mobility-gradient product MκgM\kappa_g, and hence the fastest-growing wavevector qmq_m and wavelength λm\lambda_m.

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