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.

(wasq@elch.chem.msu.ru)

http://www.elch.chem.msu.ru/rus/prgfnm.htm



7 6 5

­ 10



4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10

«» -- 1 -- 1



2 zi2 e0 1. -Gs = N A 8 0 ri

1 1 -

1 = 100 1 100 - 1- 1-



2. =

= [Ci 2 / ] z+ + c z- - c [/3 /3] = 0 - (2b + bp 0 ) c [/] - H2O + - c0 = = 0 - (2b + bp 0 ) c0 0 = 0 + 0 0 i1000 5 0.01 cpp = 0.01 - ic = cpp 0.05

c=

-

H2O

i1000

H2O

0 = +
+ 0

- 0

= - (2b + bp ) c
0 0

= ic ze0 F 6ri


R=
0

l S i

H2O H2O 0

-

i0 = const =

b , bp -

=







3. G


= H ­ TS Pb G
2 1

G1 = ­nFE0 Pb
2+

G 2 = 2 G1 + G



n=4

E0



= E0 -

G

Au+2Pb2+ +4e­ = AuPb2 PbBr2 ­ ,

G nF





AuPb2 J

G lg f
i

N

zi2 h J - 1+ J

a

Pb

2+

=

( f Br - cBr - )

2

E = E0



+

E = E -

2.3RT lg a nF

Pb

2+

4. c(Zn2+) = x, c(Ox­) = 2x, c(ZnOx2) = c0 = 10­4 M

K=

f

Zn

2+

c0 x f

2 Ox

-

4x

2

x=

3

c0 K f
Zn
2+

f

2 Ox

-

4
Zn
2+

J

lg f

N i

zi2 h J - 1+ J

E = E0 +

2.3RT lg f nF

x



( ) ( )

(electron transfer)


: .., - . ., , 1959.



1 : = v

8.1-8.2


k

1 vk

= =





:


ck (t , x, y, z )



j

() k

=j

() k

+j

( ) k
)

+j

( ) k

ck =- div jk( t

i =± nFj

() k

i( E )



I

8.2

j =- Dk grad ck
II

c i =± nFDk k x d 2ck =0 dx 2

x =0

ck 2ck = Dk 2 0= t x

0 dck ck - cks = const = dx k


0 s cO - cO i = nFDO O 0 cR - c i =- nFDR R 0 s R 0 cO = nFDO O ( idO ) - c= bO ( id R ) - s cR = bR s O

i i

(O ) d

(R) d

c =- nFDR

0 R R

nFDO O i nFDR ; bR = R
; bO =

i

s RT cO ln s E=E + nF cR ( ( RT DR O RT idO ) - i RT idO ) - i ln ln ( ln ( E=E + + = E1/ 2 + nF DO R nF id R ) + i nF id R ) + i 0 ( ( idO ) - id R ) P ( E ) i= 1 + P( E )

nF ( E - E1/ P ( E ) = exp RT

2

)





8.4

i =±0.62nFDk2/ 31/ 2v

-1/ 6

0 (ck - cks )

(1943)
· · n · D · ( ) · ( )


.., .. (1959)
· (, ..)


Chanel microband (« »)
· (injection technology)





. (1922)
ck 2ck = Dk 2 t x
0 ck - cks i =± nFDk Dk t 0 0 ck ( x, 0) = ck ck (, t ) = ck

8.5

ck (0, t ) = cks = const ( E = const )



(1934)
1 0 I =±7.34 10-3 nFDk / 2 m 2 / 3t1/ 6 (ck - cks ) 1 0 I = ±6.29 10-3 nFDk / 2 m 2 / 31/ 6 (ck - cks )







E = E1/ 2 +

RT I d - I RT D ln ; E1/ 2 = E 0 + ln R nF I 2nF DO


I=

Id 1 + P( E )




8.5

I

d

­ .


(Electrochemical Impedance Spectroscopy, EIS)



8.6, 9.4


E = Ecp + V sin(t )



: (., 1899) W W RT 1 1 ZW = ; W= 2 2 -j +0 0 c D n F 2 O cR DR O RT : = i0 nF 1 W W (Nyquist diagram) = Rs = + Cs

. ... .., . ., , 1973.



E = E ± vt

8.6

~ 1 t


c 0 - c s (t ) i = nFD (t ) nF 0 i = nF DO v cO f ( ); RT (., .
1/ 2 1/ 2

nF nF vt ( E - E ) = RT RT , 1948) =
2

F 3 3/ 2 1/ 2 1/ i = 0.4463 n DO cO v RT

E = E1/ 2 - 1.109

RT nF

E - E = 2.3 i (i )0 = + i i

RT nF 0.485(i ) i

0

+ 0.086

(.)



(E v) (E v)

9.4

(E v)

RT E = E - F
0

1/ 2 1/ DO 2 Fv 0.780 + ln + ln ks RT



i = const

8.7

E = const

s 0 cO = cO -

2i nF

t DO

s cR =

2i nF

t DR

s s cO = const ; cR = const 0 ck - cks i =± nFDk Dk t

RT - t ln nF t ( ) E = E1/ 2 +

( )




8.7



i = 4nFDcr


(SECM)


· (, , ) · · ·

M.V.Mirkin, B.R.Horrocks, Electroanalytical measurements using the scanning electrochemical microscope, Analytica Chimica Acta 406(2000)119-146


«»
TCNQ2­ [Fe(CN)6]
4-

TCNQ

·­

TCNQ

[Fe(CN)6]

3-

t
40 s

1s

C. Amatore et al. / Electrochemistry Communications 2 (2000) 353­358




E. Ahlberg et al. / Journal of Electroanalytical Chemistry 548 (2003) 85/94 S. Valizadeh et al. / Electrochimica Acta 47 (2001) 865­874