以平均首度穿越時間研究膠體穩定性
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(3) Colloid Stability Studied by Mean First Passage Times NSC 87-2113-M-009-001 86 8
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(6) mean first passage time, Tr ! stability ratioW"#$ % DLVO &'
(7) () Abstract. Overbeek 4 ¯ ° ± * ² ³ ´ µ turbidity E L AgI Ag2S *+3 ¶/ E ·¸V ¹D (dE / dt )t →0 ! W Wº" »:P± Fuchs &'$¼½ ¾¿ÀÁÂè$ ÄÅ_3¶ÆÇ%ÈK ÉÊB,-Ë4}ÌÍÎÏ]Ð ÑÒ>Ó, -;<ÔÕÖinduction timeÐ $ ×W·ØÔÙ Ú>
(8) 5-7$ Û:>Ü{ÝÞ
(9) ßàÄÅ0 ,-4`á>ºâreflective »0,4=}ã;ä4åæ Û:;ä4`á> çèabsorbing »0ÄÅéêz£*`ë ìÒ;ä`í±$ . The task of this project is to study the colloidal stability under the context of the DLVO theory by the concept of mean first passage time and compare with the results obtained from the usually used stability ratio.. Keywords: Colloid Stability, DLVO Theory, Mean First Passage Times `|}Fîï.
(10) 25 F^|# Ú ψ < mv 2| z *+,-./0123 4 56 } VR ðFîW 8,9 ñ κ a > 10 789-:;< =>?@A:B$CD VR = 2πε aψ 2 ln {1 + exp( −κ Ho )} ( 2a ) EFDGHIJKL%MNOPQRSTUV WXNOYZ[\]UK^_`abRcYdef ñ κ a ≥ 5 !gfhijklm_nopKqgrst 2 a 4πε aψ (d − a ) VR = ln 1 + exp( −κH o ) uv 1$ d (d − a ) wx DLVO Derjaguin, Landau, Verwey and 2 Overbeek&' y_z{|}~ `0 (2b) van der Waals } `0pa C d 0zòóô a 0§¨ô 2|} : 2|}!.//+ H o = d − 2 a ô ε 0f.Hô ψ 0 .dF^|_$:y F^|ô κ 0 Debye − H&u&ckel H õ *,+9->|}y$ 9-&' > =ö÷øù+ú z : z ²³$:F 3 Fuchs 0 49-on 25 mv ñ κ a > 3 :¡¢`£ "stability ratio, ^|#n Ú ψ > z W, ¤ 2|} VR ðFîW 8 ∞ exp[V ( r) / kT] T dr (1) W = 2a a 2a r2 VR = 2 L( Z , κH o ) ( 2c ) z 0* ¥¦ C a 0§¨ . ∫. VT (r ) 0|} k 0©ª«H T 0¬. C Z. ®$ 1. =. ze ψ Lû|0 10−7 ergs/cm$3¶ Z kT.
(11) . κ Ho. ! L ÄÅ ^üý. ý 0±å `Î3 =ö÷þ. ï. `9-0 » 9-Ó 2 1$é. ñZ = 2. ê
(12) ,- ó0 R Ä. L = exp[ 2.02681 − 0.881944 × κ H o. Å A B z0` éê A /o. − 0.0257656 × (κH o ) ] 2. òÎ x 0 | A B zi½Aó. ñZ = 3. 0 2a | 0Kq Ó u Fîô . L = exp[2.76729 − 0.979338 × κ Ho. B x R | | 0q Ó d F. + 0.00455125 × (κH o ) ] 2. î$ñ B 9-Kq "K! A <#. ñZ = 4. `í ð°0 B x 2a | 0 0 . L = exp[ 3.25795 − 1.12159 × κH o. | 0çè ÝÞÂ$absorbing boundaryô. + 0.0392934 × (κ Ho ) ] þ`å^ 2|} VA 0 8 2. »ÄÅ=ö÷ A B z9-0 ñ B q| =}æ% 3}æ& » x 2. A 2 2 s −4 [ 2 + 2 + ln( 2 )] ( 3) 6 s −4 s s C A 0 Hamaker Hô s = d / a $» |} VT 0 VT = V A + VR ( 4) VA = −. 25oC 1 κ 2 = (2000 F2 / εRT)I. ( 5). C F 0 Faraday’s H I 0 ionic strength . κ. R | 0ºâ ÝÞÂ$reflective boundary $ ÄÅ Siegel. `/0ð°0
(13) /²³ K i S hi !. T ( i) ( s) ýï0 sinh(qhi ) cosh(qh ) − ~ i T (s ) = DqK i ~ − DqKi sinh( qhi ) cosh( qhi ) ( i). ( 1/ nm ). (6). (10). ~ C K i = Ki r2 ô q = s / D $»ÄÅ=ö÷`. 9-åÔï. * B ý 4ð B °0 Dirac. 0ð 9-åÔï C. delta-function ýï . åÔï0 10. ∂ 1 ∂ ∂ ρ ( r, t ) ρ ( r, t ) = 2 D(r )K (r) r2 ∂t r ∂r ∂r K ( r). aˆ d (s) aˆ u (s ) 1 00 Jˆ ( s) = T (s) Jˆ ( s) + 0 11 d u T11( s) T12 ( s) aˆu ( s) 0 = + T21(s) T22( s) Jˆ u (s ) 1. ð Stokes’s law éê9-3·| V
(14) D(r) D C0. 11. kT 6π aη. ( 8). (11). C aˆ x ( s) Jˆx ( s) 0J ax (t ) o J x (t ) y Laplace V×ï x u 5FKq x d. 0 25o C f0 8.937 poise. ô, K(r) !|} VT (r ) 0 10. 11. K ( r) = exp( −VT (r ) / kT). ! B \3 n. /0 9-Ô'()*Fî0 13. (7). C D(r) 09- K(r) 0,$9-. η. T ( i) ( s) ,2. 03 £ i /0,Sód)*'($. C M 0/mol/L$. D=. '()*B9-.
(15) /9-$ÄÅ9--.,W n £/0 1. 1. κ = 3.288 × z × M. 12. 0 », K ·| V +ÓÁ>`,. . ðW. ! . 5 F q $ T(s) > 6 £ - . ) * ' (. ( 9). T (s) = T ( n) (s )T ( n−1) ( s) LT (1) ( s)ô Tij (s ) > T(s). k
(16) . '(78$»KqJ . ÄÅÓ/oò. aˆu ( s) = 0 qo. Jˆd (s) = 0 zÂ$59 (11) ï ð 2.
(17) Jˆu ( s) = −. 1 T22( s). 160 102.4m V. ( 12). 140. ¹ Ï ¤ @. 120 100. ;Ôy;Û<,= »
(18) :; t >. 76.8mV. 80. log W. B 9-Kqo ð°0 A ! B z:. 60 40. 0
(19) mean first passage time5-7 . 51.2mV. 20. C0. 25 .6mV. 0 -2 0 -3. d ˆ J u ( s) − t J u ( t )dt ∫ 0 ds = − lim t = ∞ s→0 Jˆ u (s ) − J ( t ) dt ∫ u. -2.5. -2. -1.5. -1 lo gM. ∞. 0.5. 1. 51.2mV 20. ¹ Ï ¤ G. 38.4mV 15. log W. 812!13zï ð . d T22( s) d t = lim ds = lim T22( s) s→0 T ( s) s→0 ds 22. 10 2 5.6mV 5 12.8mV. ( 14). 0. -5 -3 .5. T22 (0) = 1 » B 9-Ô ?_@ºÉ. -3. -2.5. -2. -1 .5. -1. -0.5. 0. lo gM 9. A$0±! W "# _|}~y
(20) . 34.1m V. 8. t f Fî B|}y
(21) . 7. ts Fî ts ñ¤ö Tr 0C. 5. 25.6mV. ¹ Ï ¤ T. 6. log W. Ó. 0. 25. ( 13). 0. Ó. -0.5.
(22) C0. 4. 17mV. 3 2. t Tr = f ts. 1. ( 15). 8.53mV. 0 -1. -5. -4.5. -4. -3.5. -3. - 2.5 lo gM. -2. -1.5. -1. -0.5. D " 2. KD0 z = 1 A ,20 2 × 10−20 J . 8,-ó0 R ,BEF ». 5 × 10 −20 J 10 × 10−20 J 3¶F^|y. 1ï¸GW 1,9. exp(−VT / kT) dr ∫ 2a 2 r W= R 1 ∫ 2a r 2 dr R. =. ∫. R. 1 dr K (r) r 2 R 1 ∫ 2a r 2 dr. logWMNFî ! logTrONFî. 2a. logM K$ ÄÅðÆ¢ F^|# C¶ logM y logW ! logTr #` T$þ`å^ A ) ) $. (16) HI'!<'. 10. D ÄÅI' a = 100 nm T = 298K R =. H o < 1000 nm ý "#8. 15!16ï+ <J 1. K`LKk0 A =. ¹ Ï ¥ |. 6. log W. 1200 nm Ú 0 <. 8. 2 × 10 −20 J z ,. A=10. 4. A=5. A=2. 2. 0. 20 1, 2, 3 y 3¶F^| logW. -2. MNFî! logTrONFî logM . -4. -3.5. -3. -2.5. -2. -1.5. -1. -0.5. Y± z = 1 QF^|> 75 mv/ ccc (critical coagulation concentration) Z½[\ K` "d
(23) o lo gM. K$ÄÅð¹D PÛ#QF^| C¶ logM y logW ! logTr _`R3¶ Sn T: zUVWXi½$þ`å^ ÄÅð Æ¢ F^|)Q) $ 3.
(24) ]Cñi½$ 1. R. J. Hunter, Foundations of Colloid Science (Clarenden Press, Oxford, Vol. 1, 1989). 2. E. Verwey and J. Th. G. Overbeek, Therory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948). 3. N. A. Fuchs, Z. Physik. 89, 736 (1934). 4. H. Reerink and J. Th. G. Overbeek, Trans. Faraday Soc. 18, 74 (1954). 5. G. H. Weiss, Adv. Chem. Phys. 13, l (1967). 6. N. G. von Kampen, Stochastic Processes in Physics and chemistry (North-Holland, Amsterdam, 1981). 7. A. Szabo, K. Schulten and Z. Schulten, J. Chem. Phys. 72, 4350 (1980). 8. J. Th. G. Overbeek, in Colloid Science, ed. by H. R. Kruyt, (Elsevier, Amsterdam, Vol. 1, p. 270, 1952). 9. L. N. MaCartney and S. Levine, J. Colloid Interface Sci. 30, 345 (1969) 10. J. M. Deutch, J. Chem. Phys. 73, 4700 (1980). 11. J. H. Noggle, Physical Chemistry (Scott, Boston, 1989). 12. R. A. Siegel, J. Phys. Chem. 95, 2556 (1991). 13. J. S. Chen and W. Y. Chang, J. Chem. Phys. 106, 8022 (1997). 14. R. M. Barrer, Diffusion in and through Solids (Cambridge Univ. Press, 1951). 15. J. Crank, The Mathematics of Diffusion (Clerendon Press, Oxford, 1975). 16. J. S. Chen, J. Chem. Soc. Faraday Trans. 90, 2765 (1994). 17. W. G. Shi and J. S. Chen, J. Chem. Soc. Faraday Trans. 91, 469 (1994).. 4.
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