Sotnikov_Vatolin

R = ρ	l	=	1		l	,	(4.4)
	S
			S
ρ − ".
& ,							" ρ ,

! ". !

! "

" "

L. % !

" -1 -1 / ( − ).

& "

" !

! , !

" : "

, .

* ! "

. ,

", ,

,

! .

& ( " )

" "

(i = I	S )
" ( E )
" ψ :
i = E = − dψ .	(4.5)
d x

&" "

! : Na+, Ca2+, Mg2+, SiO44- . ! j-

70

" :

ij = − j dψ , i = i j , (4.6)

d x	j

j − ",

" j- .

) j-

" !

	j- ( t j ):
	t j =	j	, = j .	(4.7)
			j

! , "

",

! .

', ! ( . ! 3),

, "

"

"!:

= 0e−	E	.
	RT		(4.8)
* E − " ". &			E / NA

! ! " ,

, "

" . # ! "

!

, ! ( ),

. # " 0 !! .

71

( ! ,

CaO, SiO2, MgO, Al2O3, FeO, 0,1 - 1 /

! , ! "

(106 - 107 / ). & E

40 - 200 ) / ! .

! ! ,

!

.

# ( 10 .%) !

(FeO, Fe2O3) (MnO, V2O3, Cr2O3) " !,

"

. '

" "

"!

	. .
" Me2+	- O2- - Me3+,

, !

" . (, !

! FeO - Fe2O3 102 / ,

! .

4.4.

( ! !,

" " (ψ )

. % ! " ! "

(ϕ ):

ϕ =ψ −ψ - .

72

'
! ϕ			, "

! ! " -

". 1 ! ,

, ", i - " ,

!	! (ε i )	ϕ i		"
, !
		εi = ϕi − ϕ . .
&	ε i !	"	i -	"

" . &

! ! ",

H2 =2H+ + 2e

aH+ = 1, pH2 = 1 ( " ).

& " ε i !

" , ,

( , ) :

	ε i =ε i0 + RT ln	∏ aiνi (Ox)		(4.9)
		i	.
		∏aiνi (Red )
	zF

i

* z − ", " ; ν i −

" i - ; ε i0 −

" , !

. & (4.9)

( Ox ) , ! −

( Red ) . , ,

73

", .%%

!,

ci , / 3. # "

. (, , "

2SO24- =S2O82- + 2e

"

ε ε 0 + RT ln	cS2O82-		.
2F	cSO2	42-
& , "
Me= Mez+ + ze ,		(4.10)

!

! ε i0 ( . 4.1). ) ,

, ! ε i0 . 4.2.

,, " , !

!. & ,

"	('))
( min) " !. + min	!
(ε ) (ε ):
min = ε -ε ,	(4.11)

" ! ! ')

", ! ! . &

(4.9), ! ε i0 !

. 4.1 4.2. # " !,

, ! ,

74

			( 4.1
"
'		%	0
			ε i , &
Li, Li+		Li=Li+ + e	+3,045
K, K+		K = K+ + e	+2,925
Ca ,Ca2+		Ca = Ca2+ + 2e	+2,87
Na, Na+		Na = Na+ +e	+2,713
Mg, Mg2+		Mg = Mg2+ + 2e	+2,38
Al, Al3+		Al = Al3+ + 3e	+1,66
Zn, Zn2+		Zn = Zn2+ + 2e	+0,763
Fe, Fe2+		Fe = Fe2+ + 2e	+0,44
Cd, Cd2+		Cd = Cd2+ +2e	+0,402
Co, Co2+		Co = Co2+ + 2e	+0,27
Ni, Ni2+		Ni = Ni2+ + 2e	+0,23
Sn, Sn2+		Sn = Sn2+ + 2e	+0,14
Pb, Pb2+		Pb = Pb2+ + 2e	+0,126
H2(Pt), H+		H2 = 2H+ +2e	± 0,000
Cu, Cu2+		Cu = Cu2+ + 2e	-0,337
Cu, Cu+		Cu = Cu+ + e	-0,52
Ag , Ag+		Ag = Ag+ + e	-0,799
Au, Au3+		Au = Au3+ + 3e	-1,42

75

( 4.2

"

'	%	0
		ε i , &
H+, O2, H2O (Pt)	2H2O = 4H+ + O2 +4e	+1,229
Cr2+, Cr3+ (Pt)	Cr2+ = Cr3+ + e	+0,41
V2+, V3+ (Pt)	V2+ = V3+ + e	+0,255
H2(Pt), H+	H2 = 2H+ +2e	± 0,000
OH-, O2 ( ) (Pt)	2OH- = 1/2O2 + H2O + 2e	-0,401
I-, I2 ( ) (Pt)	I- = 1/2I2 + e	-0,536
Br-, Br2 ( ) (Pt)	Br- = 1/2Br2 + e	-1,066
Cl-, Cl2 ( ) (Pt)	Cl- = 1/2Cl2 + e	-1,358
F-, F2 ( ) (Pt)	F- = 1/2F2 + e	-2,87

(4.9)

.

, !

,

! " .

4.5.

) , " ,

! . &

, ! . 4.1 "

, , ( ,

76

CO , Al2O3	),
(4.1) G < 0. 2	, G(4.1) = 0,

! !

" .				) ,
"	" .
+, !				G
! ') ( ). ! !					G
	E = −	G	,	(4.12)
		zF
	F − / ( F = eN A ).			# !	zF

! ", !

!

. #, ,

(4.12) ! " 3 !

( G , ) / Al). # " 1,5

CO , ! 3 eN A , . . 3F

", Al

! ". ,

z .

,! ! ') "

, ! "

4 !

	∂ E	=	S	,
	∂ T	P	z F

∂ E		= −	V	.	(4.13)
	∂ P T		z F

, ') "

, S > 0. S

" ,

77

“ E − T ”. & E

, "

4 V < 0.

,! ')		G (4.12)		S (4.13) "
, ":
	H =	G + T S .			(4.14)
(	!,	!		-	-

",

')

.

4.6.

% ",

i - " (4.10). & ,

(4.10) ,

" ! ε i . #

" ! !

ε i ε i .

# ε i >ε i

(4.10) ( ) ,

	Mez+ ,
".		+,		ε i <ε i		(4.10)
		( )	,
			Mez+	! "

, .

78

) " "

(i ), ! , ! ! ε i -ε i ,

! " ( ε i ):

ε i = ε i -ε i .

& ! i ε

, , . & ! ,

4,

! . 2 !

" ! !,

.
,!	!		,
				( ε A > 0),	–
(		ε < 0).	# "

" ! ') ( )

:

E = ε − ε = (ε +				ε ) − (ε + ε ) =
= Emin + εA +		εK		= Emin + E .

' ( E ) ! " !

" ". (

" ! ! Emin ≈ 1,06 &,

E 0,8 &,

" " ~70%.

& ! !.

#, , Zn2+

, . . 4.1,

" " ! !,

, ~(-0,76 &). # "

( H+ ): 79