Mode-Coupling Theory —
Supercooled Liquids
α and β relaxation in F(q,t) — two-step decay and dynamical arrest near T_c
Temperature ε = (T−T_c)/T_c
0.200
Coupling λ
0.70
Wave vector q
2.0
Show N curves
5
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Intermediate Scattering Function F(q,t)
T > T_c (liquid)
T ≈ T_c (critical)
T < T_c (glass)
β-regime: F(q,t) ≈ f_c + h_q·t^{-a}
α-regime: F ~ exp[−(t/τ_α)^β]
τ_α ~ |ε|^{−γ}, γ = 1/2a + 1/2b
Non-Ergodicity Parameter f(T) and Relaxation Time τ_α
Above T_c: f(q) = 0 (ergodic liquid). At T_c: discontinuous jump to f_c > 0. Below T_c: glass — density fluctuations frozen in.