Early-stage light scattering from a quenched blend gives the growth rate at two…

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

Early-stage light scattering from a quenched blend gives the growth rate R(q)R(q) at two wavevectors, plotted as R/q2R/q^2 against q2q^2 (a Cahn plot), since R/q2=−Mf′′−Mκgq2R/q^2 = -Mf'' - M\kappa_gq^2. Data: at q2=0.001 nm−2q^2 = 0.001\,\mathrm{nm^{-2}}, R/q2=8.0×10−4 nm2 s−1R/q^2 = 8.0\times10^{-4}\,\mathrm{nm^2\,s^{-1}}; at q2=0.004 nm−2q^2 = 0.004\,\mathrm{nm^{-2}}, R/q2=2.0×10−4 nm2 s−1R/q^2 = 2.0\times10^{-4}\,\mathrm{nm^2\,s^{-1}}. ((a)) Find Mf′′Mf'' and MκgM\kappa_g from the intercept and slope. ((b)) Find qmq_m and λm\lambda_m from these two quantities.

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