A quenched blend has free-energy curvature per site

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 quenched blend has free-energy curvature

f''(\tfrac12) = -0.006\,k_BT

per site, gradient coefficient

\kappa_g = 0.12\,k_BT\,\mathrm{nm^2}

per site, and mobility

M = 0.02\,\mathrm{nm^2}\,(k_BT\,\mathrm{s})^{-1}

. ((a)) Find the fastest-growing wavevector

q_m

and wavelength

\lambda_m

. ((b)) Find the maximum growth rate

R_{\max} = Mf''^2/(4\kappa_g)

and the characteristic time

1/R_{\max}

for the amplitude of that mode to grow by a factor

e

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