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Charge and mass transfer across the metal-solution interface
E. Gileadi School of Chemistry Tel-Aviv University, ISRAEL gileadi@post.tau.ac.il

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Time-Resolved Kinetics
· The idea of different time scales for electron transfer and solvent reorganization is inherent in the Marcus theory · The characteristic time for different processes is: Electron transfer Solvent reorganization 1 fs 1 ps (103 fs)

Diffusion across the interface 0.1 ns (105 fs)

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The Marcus Theory of Charge Transfer
· Symmetrical electron transfer

[Fe(

H 2O

)n ]

3+

+ e - [Fe(H 2O

)m ]

2+

· The energy of the system as a whole does not change BUT: immediately following electron transfer, both ions find themselves in an unstable position, hence the total energy of the system will increase:

[Fe(

H 2O

)n ]

2+

and

[Fe(

H 2O

)m ]3
3+

+

Fe2+ with a solvation shell of Fe

and vice versa
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Time-Resolved Kinetics
· Common wisdom: An unstable intermediate can be
stabilized by adsorption

· Example: Fe2+ + e Fe+ads · Problem: There are two processes taking place ­Fe ­Fe
2+ +

+ e Fe+ Fe+ads soln

soln

1 fs 105 fs

· Problem: Although Fe+ may be stabilized by
adsorption, it must first be formed in solution, where it is highly unstable
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Formation of Adsorbed Intermediate

2.0

Fe e

+

soln

Go/eV

1.0 ~1 fs 0.0 ~105 fs

Fe

2+

soln

-1.0

Fe

+

ads

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2+ Fesoln + Fesoln

+ + ecrys Fesoln 1 fs + Feads 105 fs

Metal surface

OHP

+ +

+

+

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Charge Transfer in Metal Deposition-Dissolution
· The common wisdom: Charge is carried across
the interface by electrons

· Two problems:
­ Highly unstable neutral atoms would be formed on the solution side of the interface ­ There is no driving force for neutral atoms to cross the interface

· Conclusion:

Charge is carried across the interface by ions
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Proof for ion transfer mechanism
Reductio Ad Absurdum
Assume that electron transfer does occur:

[Ag(

H 2O

)n ]

+ soln

+e

crys

[Ag(H 2O

)n ]

0 soln

1 fs 103 fs 105 fs

[Ag[H 2O]n ]
Ag
0 soln

0 soln

0 Ag soln + n (H 2 O

)

Ag

0 crys

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The Fate of the Neutral Species Formed by Electron Transfer
The neutral atoms could: 1. 2. 3. Be incorporated in the metal Diffuse away into the solution Interact with the solvent to form H
2

The last two processes would decrease the Faradaic efficiency

Ag

0 soln

+ H 2O Ag

+ soln

+

1

2

H 2 + (OH

)

-

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Ag Ag
Metal surface

+ soln 0 soln

1fs + ecrys Ag

0 soln

Ag

105 fs

0 crys

OHP

+ +

+

+

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The Energy of a Neutral Atom in Solution
(Ag Ag
+ soln

+e

crys

G ) =0 Ag

0 crys G
subl



G G

subl



0 soln

- - - - - Ag

G 0

0 gas

The difference between the Gibbs energies of a neutral atom and a hydrated ion in solution is roughly equal to the energy of sublimation.

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Silver as an Example
For silver one finds G For the reaction:
subl

= 2.55 eV.

Ag

+ soln

+e

crys

Ag

0 soln

E0 = - 2.55 V vs. Ag+/Ag = - 1.75 V vs. SHE
This reaction could not occur at or near the Ag+/Ag reversible potential.

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A sobering thought
· "In metal deposition charge is carried across the interface by ions, not by electrons" · · · · D.C. Graham K. Vetter V.V Losev N. Sato 1955 1967 1972 2002

.

· Non of these scientist took the next obvious step of realizing that the mechanism of ion transfer can be radically different from that of electron transfer.
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The Marcus theory of electron transfer (ii)
The Gibbs energy of activation is given by Replacing the Gibbs energy by the electrochemical Gibbs energy yields
G
0#

G

0#

=

(

+G
4

02

)

= G - F =
0#

(

+G - F
0

)

2

4

G 0 F = 05 + . - 2 4
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The quantities involved in determining the energy of activation
Vertical electron transfer leads to an increase of the total energy of the system
Energy

G
o#

G

o

Total Reaction Coordinate

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Calculated reversible potentials
· METAL: Fe
· · · G/n E0(1) E0(2) -1.92 -0.41 -2.33

Ni

Cu

Zn

Sn

Ag

-1.99 -1.55 -0.50 -1.39 -2.55 eV -0.23 +0.34 -0.76 -0.14 +0.80 V/SHE -2.22 -1.21 -1.26 -1.53 -1.75 V/SHE

(1) Mz++ ze- M0

crys

(tables) (hypothetical)

(2) Mz++ ze- M0

soln

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Metal deposition is too fast!
· The rate constants for metal deposition are comparable to those for outer-sphere charge transfer. · They should not be! · For a divalent metal G0 20 eV and for outer-sphere charge transfer = 1-2 eV.

17


Comparison between rates of outer sphere charge transfer and metal deposition on Hg
Reaction Pb2+/Pb [Cr(CN)6]-3/-4 Tl+/Tl [Fe(CN)6]-3/-4 Cd2+/Cd Fe3+/Fe2+ Bi3+/Bi V+4/V+3 k (cm/s) 2.0 0.9 1.8 0.09 1.0 5x10-3 3x10-4 1x10-3 j0 (A/cm2) (1 mM) 0.38 0.18 0.34 0.018 0.19 1.0x10-3 6x10-5 2x10-4
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What is the mechanism of charge transfer for metal deposition?
· It cannot be electron transfer because
· (a) It would form an unstable intermediate

· (b) Some of the neutral atom would diffuse into the
solution, never reaching the electrode

· (c) It is too fast · Conclusion:
· Charge must be transferred by the cations

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Field-induced ion transfer
· It is proposed that the high electrostatic field in the double layer is the driving force. Example:

E = = 0.3 V 0.6 nm = 5x108 V cm
But what about the field at = 0?

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The gradient of is proportional to that of the electrochemical potential
= + zF
But when an overpotential is applied, the chemical potential is not changed, hence

= nF ,

x

()

= nF x

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Variation of the electrochemical potential with the reaction coordinate
Electrochemical Gibbs energy / eV

OHP
0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2

Fig. 1

Metal surface

0.3

0.4

0.5

0.6

Distance from the solvated cation in the OHP / nm

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Influence of the overpotential
The barrier is lowered by the gradient of
Electrochemical Gibbs energy / eV

Fig. 2
0.5 0.4
0#

0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 0.0 0.1 0.2 0.3

G a b c d
a b c d
0.4 0.5 0.6

Distance from the solvated cation in the OHP / nm

Overpotential / V

0.3

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Comparison with experiment
· For the deposition of a divalent metal, one often finds bc = 0.12V; ba = 0.04V, (c = 0.5; a = 1.5) · For ion transfer, the rate equation is

j= j0 exp ( - nF RT

)

In Fig.2, c = 0.25, hence c = 0.5 · Also, a = 0.75, hence a = 1.5
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How can we explain the high rate constants?
· The solvation shell is removed in many small steps, each requiring a very small solvent rearrangement energy. · The effective charge also changes in small increments. Transfer of a full electron is not assumed along the reaction coordinate. · There is a break-before-make mechanism. Interaction with the surface starts well before there is physical contact

25


Conclusions
· In metal deposition charge is carried across the interface by the positive ions, not the electrons · In outer-sphere charge transfer, charge is carried across by electrons · The above two processes are physically different and cannot be treated by the same formalism · A mechanism of ion transfer assisted by the electrostatic field is proposed · A full theory of ion transfer is yet to be developed.

26


References
E. Gileadi, J. Electroanal. Chem, 532 (2002) 181 E. Gileadi, Chem. Phys Lett, 392 (2004) 421 E. Gileadi, Proc. Symp. Electrochem. Processing in ULSI and MEMS, H. Deligianni et-al, Eds. Vol. 17, (2004) 3 E. Gileadi and E. Kirowa-Eisner, Corr. Sci. 47 (2005) 3068 E. Gileadi, Electrochem. Soc. Trans: 5th Symposium on Proton-Exchange Membrane Fuel Cells. T. Fuller et-al Eds. 1 (6) (2005) 3 E. Gileadi, Isr. J. Chem, (2008) in press
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Final Conclusion

IN ORDER TO CREATE ONE MUST FIRST QUESTION THAT WHICH EXISTS

28


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The New Challenge: are all interpretations of Electrode Kinetics Wrong?
· There are some types of electrode kinetic where the notion of adsorbed intermediates seems to fit the experimental results: The hydrogen evolution reaction Oxygen evolution Oxidation of large anions Organic oxidation or reduction (e.g. Kolbe)
31

1. 2. 3. 4.


Application to Hydrogen Evolution
· Common wisdom:
Formation of Hads as an intermediate is assumed. H3O+ + e Hads + H2O

· This may be correct, since:
­ The surface is solvated. ­ The ion is solvated (as [H3O(H2O)n]+ ) ­ There are initially hydrogen atoms in contact with the surface ­ Electron transfer may lead to formation of H redistribution of charges, without significant movement of atoms
ads

by
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Details of formation of Hads

H 2Oads + e H
- +

-

ads

+ OH

-

OH + H 3O 2 H 2O
An electron is added to an adsorbed species, not one in the OHP
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Application to Oxygen Evolution
· Common wisdom:
Formation of OH
ads

as

intermediate is assumed

OH- OHads + e

crys
ads

· This may be correct, for the same reasons as for H

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Details of formation of OHads

H 2Oads H H
+ 2Oads

+ 2Oads

+e

-

+ OH HOads + H 2O

-

An electron is removed from an adsorbed species, not one in the OHP
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Discharge of Large Anions
Consider the reaction Br-



Brads + e

· This is an intermediate case
­ If the anion is "contact adsorbed" (having replaced water from the surface), the above equation is correct ­ If there is a layer of water on the surface, it may be necessary to write the above equation in two steps, since the Br- ion will have to move after electron transfer

36


Details of formation of Brads
- Brads

Brads + e
- Brads

-

Brads +

Br2 + e

-

An electron is removed from an adsorbed species, not one in the OHP
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IHP H2 O Br
-

OHP

Oxidation of Anions

Ag

+

38


Conclusions (1)
· Metal deposition and dissolution occur by ion transfer, not by electron transfer · A reaction in which both electrons and ions are transferred across the interface cannot be considered as a single step · The formation of unstable intermediate following electron transfer cannot be justified by adsorption. · Exceptions may be where the species is already adsorbed, before electron transfer has occurred

39


Conclusions (2)
· Steps in electrode kinetics may involve
­ Electron transfer ­ Proton transfer ­ Heavy ion transfer

· Such steps occur on widely different time scales · Changes in the Gibbs energy must be regarded for each step individually · New ways of analyzing electrode kinetics must be found.
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