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.

(wasq@elch.chem.msu.ru)

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



( ) ( )

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

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


(Electrochemical Impedance Spectroscopy, EIS) E = Ecp + V sin(t )




8.6, 9.4


: (., 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 (., . F 3 3/ 2 1/ 2 1/ i = 0.4463 n DO cO v RT
1/ 2

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

2

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



( ) ( )

(electron transfer)





(, -, 1930)


9.1

O + ne­ R; zO ­ n = z

R


G v = kc exp RT : G = G = F

-

nF i = nFkcO exp - RT nF i = nFkcR exp RT

a=

(1905)

E = a + b log i



2.3RT ln i0 F

b=

2.3RT nF

:

:

i = i = i0


i =i -i





nF (1 - ) nF - exp - i = i0 exp RT RT - cO RT k RT (Butler-Volmer Equation) = ln + ln (+ )nF k (+ )nF cR = - = E - E + = 1 E0
i0 = nFk
1- 1 k cO- c R




(.., 1933)
G = G = F ( - 1 )

9.1, 9.6

1.

2. (- , 1) (g)
g - z F cO = cO exp O O 1 c RT
R

g - z F = cR exp R R 1 RT

g (n - zO ) F 1 nFE i = nFkcO exp O exp exp - RT RT RT

:
zO F 1 nF = const - ( E - 1 ) RT RT ( )

ln i +

1 i,E- .

M2S2O8/MCl



=0 0,9

9.2, 9.6

(n - zO ) F 1 < 0 ( ) RT
(gO, gR, 1)

0,001

=0


0,1

K2S2O8/KCl

0,002


-
( ) .
. (1931 .): .

9.7

(~10-15 c) , (~10-13 ).

­


(1956)
/ 1 0 U / (Q ) = (Q - Q / ) 2 + U / 2 1 = + = (Q2 - Q1 ) 2 0 0 G = U - U 1 G = (Q* - Q1 ) 2 2 (G + ) 2 G = 4


2

G = + G 4


=

d (G ) 1 G =+ d (G ) 2 2





- F - W + W =

e = NA 40 2 e0 = NA 40

2 0

1 1

1 1 1 1 j ( ) - + - 2a1 2a2 R 1 1 1 ( ) - - ( ) 2a 4 R
f j ( Q j )
2

1 2

fj =

2 fO f R fO + f R

( -)



WO = FzO 1 + g
W O = c exp - O RT
(0 ) O
O

9.7
R

WR = Fz R 1 + g

G = F - WO + WR

i = nFcO k



G k = A exp - RT A =


( G + ) G = WO + 4


2

2

x

v2 + v 2 = 2

1/ 2

2 4 2 = H h

2 DA

1 4 kT

1/ 2





9.8




F
+ ( + G - ) 2 1 WO i = const exp - exp () d RT - 4 RT 1 + exp RT (, , , )


(in situ )

I

peak

= 910U

tun

exp(-9.73( +U tun ))

Au Utun=const

E

peak

= E0 +

(0.5 -)U

tun

Es=const

I.V.Pobelov, Z.Li, T.Wandlowski, Electrolyte Gating in Redox-Active Tunneling Junctions - An Electrochemical STM Approach, J.Am.Chem.Soc. 130(2008)16045-16054



Au(111) / [Ru(NH3)6]
3+

Au(210) / [Ru(NH3)6]

3+

bare

9

16

L.V. Protsailo, W.R. Fawcett : Electrochimica Acta 45 (2000) 3497­3505




N.J.Tao, Nature Nanotechnology 1(2006)173