http://www.tagen.tohoku.ac.jp/labo/muramatsu/mura/main.html E-mail: mura@tagen.tohoku.ac.jp 1
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1 mol/l KCl 3
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Derjaguin Landau Verway Overbeek B.V.Derjaguin and L.Landau;Acta Physicochim.,URSS, 14, 633 1941. E.J.W.Verwey and J.Th G Overbeek; Theory of the Stability of Lyophobic Colloids, 193 1948. 5
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-Si-O-H -Si-O + H + 15
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0 Helmholtz 0 20
0 Gouy-Chapman 0 21
0 Stern Stern Stern 0 Slip 22
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0=Stern d 0 24
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z+ eψ n+ = n + exp (1) 0 kt z eψ n = n0 exp kt n: n 0 : z: k: T: ψ: +,-: 26
ψ0 c RT c ψ 0 = ln zf c (2) R: c 0 : c at ψ 0 = 0 0 27
Poisson 2 2 2 ψ ψ ψ ρ Δ ψ = div (grad ψ ) = + + = 2 2 2 x y z ε ε ε r : ε 0 : ρ: r 0 (3) 28
29 ρ: n n n z z z = = = = + + 0 0, = = = + kt ze nze kt ze kt ze nze n n ze ψ ψ ψ ρ sinh 2 exp exp ) ( (4)
Poisson-Boltzmann (3),(4) x 2 d ψ 2nze zeψ = sinh (5) 2 dx ε ε kt r 0 (5) zeψ zeψ 0 tanh = tanh exp( κx) 4kT 4kT (6) 30
zeψ kt <<1 (5) d dx 2 ψ 2 2 = κ ψ κ = 2 2 2 2 nz e ε ε kt r 0 25 9 κ = 3.3 10 z c (7) ψ = ψ exp( κ ) 0 x (7) (8) (9) (10) Debye-Huckel 31
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: h P P = P E + P O P P E O = = ( n ε + r ε 2 + 0 n 2 dψ dx ) kt 2nkT (15) (16) 33
P O P E ψ 0 P E (1) (16) P O P R (h) P R zeψ h / 2 ( h) = 2nkT cosh 1 kt ψ 2/h : (17) 34
ψ h/2 ψ s(h/2) zeψ / 4kT << 1 then tanh( zeψ / 4kT) zeψ / 4kT (6) ψ<20 mv ψ γ ( h / 2) = 8kT h = γ exp κ ze 2 zeψ 0 tanh 4kT (18) (19) 35
(17) ze ψ 2 h / 2 / kt << 1 then PR ( h) nkt{ zeψ h / 2 / kt} (18) κh>1 h cosh y 1 + y 2 P R 2 ( h) = 64nkTγ exp( κh) (20) 36
V R ( h) h = P R ( h) dh = 64nkT κ γ 2 exp( κ h) (21) 37
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Derjaguin Derjaguin : a 1 a 2 H H<<a 1,a 2 P R ( H ) = 2π a a 1 2 V ( a H 1 a R + 2 (21) (22) a 1 =a 2 =a P R ( H ) = 64 π ankt κ γ 2 exp( ) κ h) (22) (23) 39
a V R ( H H ) = PR ( H ) dh 64πankT 2 = γ exp( κh) (24) 2 κ 40
zeψ 0 / 4kT << 1 then tanh( zeψ 0 / 4kT) zeψ 0 / 4kT (23),(24) zeψ 0 =4kT 1:1 25 ψ 0 =103 mv ψ 0 =20 mv zeψ 0 /4kT tanh{ zeψ 0 /4kT} 1% P V R R 20mV ( H ( H ) ) = = 2 2 π π a a ε ε r r ε ε (13) 2 0κψ 0 exp( κh) 2 0ψ 0 exp( κh) (25) (26) 41
42 ) exp( 2 ) ( 2 0 0 h a H P r R κ κψ ε ε π = ) exp( 2 ) ( 2 0 0 h a H V r R κ ψ ε ε π = (13) ) exp( 2 ) ( 0 2 H a H P r R κ ε κε σ π = ) exp( 2 ) ( 0 2 2 H a H V r R κ ε ε κ σ π = (25) (26) (27) (28) 0 0 0 κψ ε ε σ r = (13)
van der Waals aa P A ( H ) = 12H aa V A ( H ) = 12H A Hamaker 2 (29) (30) 43
44 2 0 2 12 ) exp( 2 ) ( H aa H a H P r T = κ ε κε σ π H aa H a H V r T 12 ) exp( 2 ) ( 0 2 2 = κ ε ε κ σ π H aa h a H V r T 12 ) exp( 2 ) ( 2 0 0 = κ ψ ε ε π (31) (32) (33)
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V T ( H ) = 2 π a ε r ε ψ 2 0 κ 0 exp( H ) aa 12 H ε r, ε 0, ψ 0, A a κ 46
2 2 κ = ε nz r ε 0 2 e 2 kt e ε r ε 0 k n z T 47
n z T κ 48
V T ( H ) 2 a r 0 0 exp( H ) = π ε ε ψ κ 2 aa 12 H 49
van der Waals 50
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van der Waals 52
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KCl 1 mol/l KCl 69
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2,3,7,8- ppm O- n- cm/day ppb 2 96
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5.22 12.20 4.31 11.57 0.14 1.78 7.18 16.05 7.33 7.40 No data 2-1 100
10 10 587 (8.01%) 49 (16.67%) 242 (3.62%) 59 (0.81%) 1 (0.34%) 2 (0.03%) 54 (0.74%) 11 (3.74%) 26 (0.39%) 914 (12.47%) - 311 (4.65%) 81 (1.11%) 16 (5.44%) 29 (0.43%) 1614 (22.03%) 61 (20.75%) 581 (8.68%) 7327 294 6690 2-2 101
(A) [%] (B) [%] B/A 1.20 2.80 2.3 0.61 2.01 3.3 9.04 14.42 1.6 0.21 3.14 15.0 102
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gteq/ 4300 547 707 250 20 16 3 0.2 0.07 ( ) (5140 5300) 0.78 0.06 5140 5300 106
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( C) (ng-teq/nm 3 ) 700 700 750 750 800 800 850 850 900 900 950 950 1000 1000 36 81 77 26 25 17 30 14 13 33 11 11 7.8 7.8 7 7 390 500 1800 600 590 210 480 83 0.2 0.57 0.22 0 0 0 0.01 0 ( 1111) 79 34 43 206 380 234 85 50 110
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