Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc15791/doc.pdf Дата изменения: Mon Oct 29 13:18:40 2007 Дата индексирования: Mon Oct 1 20:43:09 2012 Кодировка:

.. () ­ . , , , , . Theory of Liesegang Patterns Polezhaev A.A. (Moscow) Liesegang patterns are a striking example of pattern formation phenomena in chemical systems. In the present paper physical mechanisms, causing their formation, as well as the existing theoretical approaches are considered and the model explaining besides simple patterns also complex and rarely observed ones is suggested. 1. , , , ­ , . , [1], . , , , . : HCl + AgNO3 AgCl + ; 2KI + Pb(NO3)2 PbI2 + ; MgSO4 + 2NH3OH Mg(OH)2 + . ,
307


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. . . . , , , , (. 1A). , , . , [1] (. 1B). , , , « » [2-4]. , , 1987 [5]. . «» ("Ostwald ripening") ­ (.,.,[6]). . , . : · , , [7,8].
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· . , , , , [9-11]. · / [12-13]. · , [8]. , , . , , , . 2. . , , . , : "post-nucleation" "pre-nucleation theories". [14-20] , , - [21], .. : , . , (Ortoleva) [14-18]. , f, 309


3. (II)

(f(R,x)drdx ­ R R+dR dx). : f = - (v ( c, R ) f ) , (1) t R v(c,R) ­ ( ) R c. :

v = ( c, R )[c - ccr ( R )],


ccr ( R) = c [1 + b(c, R) / R].

(2)

(1) (2) . , (postnucleation) , , , , . (prenucleation), , , [21-29]. , 1897 . [5], , . , A+BC. a b c :

a = D1a - kab, t

b = D2 b - kab, t
310

(3)


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u ­ , . . ­ , . Dee [23]. :

c = D3c + kab - u. t

f = ( 4 / 3v ) J ( x, t ' ) r ( x, t , t ' ) dt '.
0

t

(4)

:

u=

f t = ( 4 / 3v ) J ( x, t ) r 3 ( x, t , t )
t

s=(c-c)/ c. J(s)=G(s)N(s), N ­ , G ­ , . [23], , :

r + ( 4 / v ) J ( x, t ' ) r 2 ( x, t , t ' ) ( x, t , t ' )dt '. 0 t * J, r r r(x,t,t)

(5)

N ( s ) = c (1 + s ) exp( -4r * / 3k B T ), G ( s ) = ( D3 / d 2 )[4r *dc (1 + s )], r * ( s ) = w / ln(1 + s ), r = s. t
,
311

(6)


3. (II)

- "pre-nucleation" , , (. (6)). [30] , (6) "post-nucleation" , (2). , ( - ) . . , , , [22,26,29]. , , , , . , , . [31,32], "post-nucleation" , . 3. f fi. - : . ( ) , c c3, .. . , , c c2, ( ). c < c2, .
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, c > c1. c1 c2 ­ , (c3>c2>c1c). f1 , ( ). f2 ­ . (2) :

u=

f1 = v1 ( c ) + v2 ( c )f1 - v3 ( c )f1, t f 2 = v3 ( c )f1 + v4 ( c )f 2 , t


f1 f 2 , + t t

(7)

v1 = ( c - c3 ) ( c - c3 ), v 2 = ( c - c2 ), v3 = ( c - c2 ) ( c - c2 ), v 4 = ( c - c1 ) ( c - c1 ).
(2), (7) , , [31-32], .

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. 1. () 1%- , . : [KI] = 0,17 M, [Pb(NO3)2] = 0,009 M. () 5%- . : [AgNO3] = 0,9 M, [K2Cr2O7] = 0,007 M. ( ..)

. 2. . () - f2=. () . : L = 100 mm (400 ); A = 50; B = 10; c1 = 1,1; c2 = c3 = 1,5; = 2·10-2; = = 10-2; = 2·10-3; Da = 9·10-6; Db = Dc = 6·10-6; k = 10-4.

. , , , . , . [11], , , , . , . .1. , ,
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. , : ; a A 0 ­ , b 0 B ; A >> B. . .2. .2 - , .2. , , , .. , , . , , [11]. . , [1], , . , ( .1). .3. 200·200 . b B, a A , 1% . .

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. 3. . r (x,y). : L·L = 50·50 mm; A = 200; B = 5; c1 = 1,1; c2 = c3 = 2; = = = 10-2; = 3·10-3; Da = Db = Dc = 10-5; k = 10-4.

. 4. , x, - () .

. , . - , . ­ , .1. , . .4. , ( ). , , . , .4, , , , . , , ,
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, , . 4. , ( ), , - , . , . , , , , (. [31,32]. , , , . [8], [12], , [12]. ? , , , , . , , , , . , , , . ­ , ,
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