MCT Glass Transition
Mode coupling theory (Götze 1984) describes dynamic arrest near T_c. The intermediate scattering function F(q,t) shows two-step relaxation: fast β-relaxation (cage rattling) then slow α-relaxation (cage escape). At T_c, F(q,t)→f_q>0 — structural arrest.
F(q,t) ≈ f_q + (1-f_q)Φ(t)
β-regime: F ≈ f_q + h_q·t^{-a}
α-regime: F ≈ f_q·exp(-(t/τ_α)^β_KWW)
τ_α ~ |T-T_c|^{-γ} → ∞ at T_c
β-regime: F ≈ f_q + h_q·t^{-a}
α-regime: F ≈ f_q·exp(-(t/τ_α)^β_KWW)
τ_α ~ |T-T_c|^{-γ} → ∞ at T_c
Temperature
Liquid Phase (T > T_c)
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τ_α
0.00
f_q (plateau)
—
Viscosity η
—
Diffusivity D