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V

.. , , 20.04.2012



1. . 2. . -. 3. - -. 4. .

cor




e
E
F

K()= E A (0), E A ()
EA

Q( ) K ( ) = 2k BT s Q(0)


i Q( ) = 2

-



1 1 d - exp ( -i ) ( )
.
N mod

S. Mukamel et al.


N


( )


K ( ) = 2k BT s



i =1

N

i exp(- / )

* i


i =1

N

i = 1



i - i-
«» N .

example


. :

K ( ) = 2k BT S 1 exp(- ) + 2 exp(- ) 1 2
DMA:

1 = 2.6 ps;1 = 0.17
2 = 0.44 ps; 2 = 0.83
N-afes


N (q1, ... qN):

U i (q1 , ..., qN ) =



N

j =1

j

2 jq j



U f (q1 , ..., qN ) =



N

j =1

j j (q j - 1) + I

pers, exp

2


S2O822 2 - -EG S2O8 - + e = SO4 - + SO4
: current vs EG content

12 8 4 0 0 20

I /A

potentials (V) vs SCE -0.6 -0.7 -0.8 -0.9 -1.0 -1.1

40

60

80
delta

x(EG), mol %



3 2 1


0.8 0.6 0.4 0.2 0.0 0 20 40 60




80

100

x(EG), %


eqv


Master equation
P(q , ) =


i =1

3

2 1 U (q ) Di 2 + P(q , ) - kin (q ) P(q , ) qi k BT qi qi

...

!
equat


qi

qi 1 U (q; r ) i =- i i + Frand ( ) 2s L qi

si

- i-
q



i L

- ;
q
0

U (q; r )

- ;

1

2

i Frand ( ) -



r:

d 2r 1 U (q; r ) =- + Frand ( ) 2 d m r
section




E



q

r

results




11.8
=3.1 V

lg k

11.6 11.4 11.2 11.0 0 20 40
=3.0 V =2.9 V

xEG [%]

60

80

100

problems


: 1. «»

k

k

* *

k 1+ kD

Ea k = veff e exp - k BT
*

2. «» 3.
edta


lgk ( s )

[Cr(EDTA)]lgk ( s )
10.8
-1

[Co(EDTA)]
-1

-

6.0

10.4

5.5

10.0

5.0

9.6 -12.75 -12.00

4.5

lgs (s)

-11.25

-10.50

-12.75

-12.00

lgs (s)

-11.25

-10.50

log ks vs. logs,, [Cr(EDTA)]- [Co(EDTA)]s = 0.3 ; =0.1 V (solid); =0.2 V (dashed); =0.3 V (dotted). Co(EDTA)- ( )

k

eff

1-

[Cr ( EDTA)]- , 0.7; [Co( EDTA)]- , 0.2

1 L



ptcl4


0.8 0.6

0.6
1 3 2



0.4 0.2 0.0



0.4 0.2 0.0 0.4

1.0

1.1

1.2

-E, B

0.8 1.2 1.6 /V

2.0


I.V. Pobelov, G.A. Tsirlina, Z.V. Kuz'minova, O.A. Petrii. Russ. J. Electrochem. 39 (2003) 920

vs. , [PtCl3H2O]

L

d lg( k ) = d lg( L )

NA


-

E (q, qin ) = q + U i (qin ) + a ( )d
2 U
0

0

( ) a ( ) = ( - a - ( )) 2 + ( ) 1

2

a = 2s q + U f ( qin ) - U i (qin ) + e0
( ) =


k

Vak ( - k )

2

( ) =

1

+



-



( / ) d / -
Vif


H+ + e = H Au(111) Au
0.5

54

6

5

4

3

2

0.5

Vif ( )
NA

1.0


0,2

0,0

E(q)
-0,2 -0,4 0,0 0,2 0,4 0,6 0,8 1,0 1,2

q
, Au-H (0.3 ­ 0.475 ).

spin


- -

a = ... + y- U + ...

*
0



- a

= ... + y U * + ...

y =

U


0

a ( )d



y

-

=

U


0

0

- a ( )d

( ) a ( ) = ( - a - ( )) 2 + ( )


1

2

In


[In(H2O)6]3+ + e = [In(H2O)6]2+ + e = [In(H2O)6]+
3

2

E
1

0 1 2 0 .5 1 0 0

q

in

q

out

z= 6 е ( = 0)
+-


- :
1) . 2) (). 3) .

:
1) . 2) . 3) .

problems


- -
1) «» . 2) «» - . 3) (-, ). 4) ( , ; ). 5) ( , ).

pcm


(r) 1) E 2) r :
2
solv

PCM.

E

solv

q = (1 - 1 / st ) 2r


[Fe(CN)6]3-/4r = 0.41

[CoMo6O24H6]3- (ox) r = 0.476 4- (red) [CoMo6O24H6] r = 0.542

cu(i)




[Cu ( H 2O )14 ]

+

Cu(I)

: Cu(H2O)

2

+

Inoh


[In(H2O)5OH]2+ * 8 H2O ( )

[In(H2O)5OH]2+/+.
list ex



1) . 2) . 3) «» - ( (), ).

curves


?
120

1' 1 2' 2
1.2 1.4

j -2

80

40 0

,

1.6

1.8

2.0

(1, 2) (1', 2')

( ) ke

nano




r0

d

H

x


( )
-15.16

-15.18

[Fe(CN)6]

3-

ln j

-15.20

c = 0.01 M

-15.22

=1.6 V
-15.24 34 36 38 40

1/kT, eV

-1

,

temp2


()
-9,76

-9,80

ln j

-9,84

-9,88

[Fe(CN)6]

3-

,

-9,92 34

nanowire, a =0.2 nm c = 0.01 M
36 38

1/kT, eV

-1

40