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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.

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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

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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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