( ) 1 1.1?
( ) ( ) ( ) 1.1(a) T m ( ) 1.1(a) T g ( ) T g T g
500 74% ( ) T K ( 1.1(b) 15 T g T g 10 13 T g
T g T g [ ] A ( ) exp (1.1) T T 0 Vogel-Fulcher T 0 T 0 T K T K Ortho-Terphenil (OTP) SiO 2 (1.1) T 0 = 0 exp[a/t ] exp [ E/k B T ] 1.2?? T K
exp [A/T ] (1.1) [2] [2] [3]
( ) Soft Glassy Materials RNA [4] [5] ( ) [6] ( )
[7] [8, 9] ( ) 2 τ exp[a/t ] T = T c
E = σr 2 G (2.2) R ( ) σ G = G crystal G liq (Gibbs) G R 3 R R 2 R 3 R 2.1(a) ρ(r) ( S(k) ) S(k) 20 2.1(b) [11] (dynamic heterogeneneities)
[11,12] 3 3.1 Adam-Gibbs [13] (mode-coupling theory, MCT)
T = 0 1.1 T = 0 exp[b/t 2 ] 4 (RFOT) (MCT) RFOT MCT (MCT) MCT MCT 1950 [17] MCT
MCT [18] 1980 Kirkpatrick MCT MCT [19] MCT ρ m v ρ m = (ρ m v) t ρ m v t + (ρ m vv) = p + η 2 v + (ζ + 13 η ) v (4.1) p η ζ ρ m ρ m v ρ = ρ m /m δρ (4.1) 2 δρ k t 2 = c 2 k 2 δρ k Γk 2 δρ k t (4.2) ρ 0 Γ = (ζ + 4η/3)/ρ m c = 1/ ρ 0 χ χ = V 1 ( V/ p) T δρ k e zt (4.2) z = ± c 2 k 2 + Γ 2 k 4 /4 Γk 2 /2 (4.3)
k k 2 z ±ick 1 2 Γk2 k (4.3) k (4.2) δρ k t = c2 k 2 Γk 2 δρ k (4.4) ( k 2 ) Γ Γ(k) Γ(k) k 2 Γk 2 Γk 2 = ζ c c(k) k c(k) χ 12 [10] N 1 N 2 = ρ 0 k B T χ N (2.1) N ρ 0 k B T χ = dr δρ(r)δρ(0) (4.5) 2.1(a) S(k) (4.5) c 2 ρ 0 k B T χ = lim k 0 S(k) (4.6) c 2 k BT S(k) (4.4) (4.7) δρ k t = Dk2 S(k) δρ k (4.8) D = k B T/ζ (4.8) S(k) S(k) 2.1(a)
de Genne Narrowing (4.8) (4.8) δρ k t = Dk2 S(k) δρ k D dq k qc(k q)δρ k q δρ q (4.9) c(k) [20] dx dt = µx + 1 2 Vx2 (4.10) C(t) = x(t)x(0) x(0) C(t) = µc(t) + 1 t 2 VC 2,1(t) (4.11) C 2,1 (t) x 2 (t)x(0) 3 x(t) C 2,1 (t) = C 1,2 (t) x(t)x 2 (0) C 1,2 (t) C 1,2 (t) t = µc 1,2 (t) + 1 2 VC 2,2(t) (4.12) C 2,2 (t) = x 2 (t)x 2 (0) 4 (4.12) C 2,1 (t) = t 0 dt e µ(t t ) 1 2 VC 2,2(t ) = t 0 dt 1 2 VC 2,2(t t )C (0) (t ) (4.13) C (0) (t) = e µt 0 C(t) (4.11) C(t) t = µc(t) + 1 4 t 0 dt V 2 C 2,2 (t t )C (0) (t ) (4.14)
5.1 3 3 p = 3 [21] H = N J ijk S i S j S k (5.1) ijk S i (i = 1,, N) J ijk S i N Si 2 = N (5.2) i N 1 i S i q = 1 S i 2 (5.3) N (overlap) J ijk ( ) i F = k B T ln Z (5.4) Z J ijk ln x = lim n 0 x n 1 n (5.5) n n 0 J ijk n q = 0 q q 0 = 0 q 1 ( 0)
T K S c S c 1 1.1(a) S c 3 ( [22] 4 ) 5.2 3 3 S i t = µs i H S i + f i (5.6) f i f i (t)f i (t ) = 2k B T δ(t t ) [21] µ (5.2) (5.1) S i t = µs i jk J ijk S j S k + f i (5.7) (4.10) C(t) = N 1 i S i(t)s i (0) dc(t) dt = µc(t) + 3J 2 2k B T t 0 dt C 2 (t t ) dc(t ) dt (5.8) (4.16) 4.1 T d T d
(2.2) E = σr θ s c R 3 (5.9) s c S c /N θ E R R = (σ/s c ) 1/(d θ) R E τ exp [ E /T ] E [ ] s c R s θ/(d θ) c τ exp s c T = T K As θ/(d θ) c s c a(t T K ) θ = d/2 [ ] A τ exp T T K (1.1) (5.10) 4 T d ( ) T d ( T K ( ) R
6? 4 5 5 3 3 ( ) ( ) 64% [23]
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