Thermodynamics and kinetics of multi- electron transfer Marc Koper Leiden University
Jan 14, 2016
Thermodynamics and kinetics of multi-electron transfer
Marc Koper
Leiden University
Redox reactions of water
E (vs.RHE)
currentdensity
0 1.23
2 H+ + 2 e- → H2
H2 → 2 H+ + 2 e-
diffusion-limitedcurrent
2 H2O → O2 + 4 H+ + 4 e-
O2 + 4 H+ + 4 e- → 2 H2O
diffusion-limitedcurrent
PtNilaccase
RuO2
PSIIplatinumhydrogenase
overpotential
Catalysis of multi-step reactions
Practically every (interesting) chemical reaction happens in a series of steps; catalysis is often about optimizing that
sequence
1 e- / 1 step / 0 intermediate
2 e- / 2 steps / 1 intermediate
>2 e- / >2 steps / >1 intermediate
Single electron transfer
• Marcus Theory
• Activation energy determined by solvent reorganization energy λ (very difficult quantity to calculate accurately!)
Movie of electron transfer
Cl-Cl0
Cl0 + e- Cl-
C.Hartnig, M.T.M.Koper, J.Am.Chem.Soc. 125 (2003) 9840
Nonlinear solvent reorganization
Orientation of water depends on charge: strongest change in electrostriction from 0 to -1
Effective radius gets smaller with higher charge
C.Hartnig, M.T.M.Koper, J.Chem.Phys. 115 (2001) 8540
What Marcus does not account for
• Proton transfer
• Bond making and bond breaking
• Catalysis
Two electron transfer
2 H+ + 2 e- H2
H+ + e- Hads (Volmer)
Hads + H+ + e- H2 (Heyrovsky)
H+ + e- Hads H2 freeenergy
Thermodynamics
2 H+ + 2 e- H2 E0 = 0 V
H+ + e- Hads E10 = - ΔGads(H)/e0
Hads + H+ + e- H2 E20 = ΔGads(H)/e0
Thermodynamic restriction: (E10 + E2
0)/2 = E0
Potential-determining step
The potential-determining step
is the step with
the least favorable equilibrium potential
The difference in the equilibrium potential of the potential-determining step and the
overall equilibrium potential we will call the thermodynamic overpotential ηT
Thermodynamic volcano plot
zero thermodynamic overpotential
descriptor
M.T.M.Koper, H.A.Heering, in pressM.T.M.Koper, E.Bouwman, Angew.Chem.Int.Ed. (2010)
R.Parsons,Trans.Faraday Soc. (1958); H.Gerischer (1958)J.K.Nørskov et al., J.Electrochem.Soc. (2004)
Generalization
H+ + e- Hads plus 2 Hads H2 (e-chem)
H+ + 2e- H- plus H- + H+ H2 (hydrogenase)
The optimal electrocatalyst is achieved if each step is thermodynamically neutral.
The H intermediate must bind to the catalyst with a bond strength equal to ½ E(H-H).
What about activation barriers?
• Can in principle be estimated with a more sophisticated model
• Contribution of water is constant (to a first approximation) as we vary the catalyst
• Activation barrier follows variations in the thermodynamics because of the Bronsted-Evans-Polanyi (BEP) relationship
δEact = αδEreact
“Marcus” model for HER/HOR
• Combines a Hückel-type model for a diatomic molecule with a coupling to the metal electronic levels and a Marcus-type coupling to the solvent
• Calculates approxi- mate activation
barriers
E.Santos, M.T.M.Koper, W.Schmickler, Chem.Phys. 344 (2008) 195
Experimental volcano for H2 evolution
J.Greeley, J.K.Nørskov, L.A.Kibler, A.M.El-Aziz, D.M.Kolb, ChemPhysChem 7 (2006) 1032
Good catalysts for HOR exist
• Platinum• Hydrogenases (FeFe, FeNi)
• They optimize for the binding of H*/Hads
More than 2 electron transfers
O2 + 4 H+ + 4 e- 2 H2O E0 = 1.23 V
O2 + H+ + e- OOHads E10
OOHads + H+ + e- 2 OHads E20
2 OHads + 2 H+ + e- 2 H2O E30
Thermodynamic restriction:
(E10 + E2
0 + 2 E30)/4 = E0
Lining up energy levels
O2 OOHads OHads H2Ofreeenergy
Thermodynamic overpotential now dependson the ability of the catalyst to bind oxygenGold: weak oxygen bindingPlatinum: stronger oxygen binding
Scaling relationships
F.Abild-Petersen, J.Greeley, F.Studt, P.G.Moses, J.Rossmeisl, T.Munter, T.Bligaard, J.K. Nørskov,
Phys.Rev.Lett. 99 (2007) 016105
Thermodynamic volcano plot
Bad news : because of the scaling relationships, we cannot line up the E0’s.
non-zero thermodynamic overpotential
Experiment volcano plot ORR
J.Greeley et al. Nature Chem. 1 (2009) 552
Pt3Ni and Fe-based catalyst
V.Stamenkovic et al., Science (2007)
M.Lefevre et al. Science (2009)
ORR is a difficult case
Man and nature have the same problem:Pt and laccase are good but not perfect
catalysts for the ORR
We need to beat the scaling relationships
Fundamental problem with catalyzing reactions with more than 2 steps and more than 1 intermediate.
Mechanism for OER
O2 + 4 H+ + 4 e- 2 H2O E0 = 1.23 V
H2O OHads + H+ + e- E01
OHads Oads + H+ + e- E02
2 Oads O2 Keq
Oads + H2O OOHads + H+ + e- E03
OOHads O2 + H+ + e- E04
Volcano plot
non-zero thermodynamic overpotential
J.Rossmeisl et al. J.Electroanal.Chem (2007)
Comparsion RuO2 and OEC
J.Rossmeisl, K.Dimitrevskii, P.Siegbahn, J.K.Norskov, J.Phys.Chem.C 111 (2007) 18821
Oads + H2O OOHads + H+ + e- PDS on RuO2 (ηT=0.37 V) and on Loll et al. (ηT=0.32 V)
OOHads O2 + H+ + e- PDS on Ferreira et al. (ηT=0.21 V)
Ni-doped RuO2
P.Krtil et al., Electrochim. Acta (2007)
Why chlorine electrolysis works
2 Cl- Cl2 + 2 e- E0 =1.36 V
2 H2O O2 + 4 H+ + 4 e- E0 = 1.23 V
Both are catalyzed by RuO2/TiO2
Chlorine electrolysis works thanks to the scaling relationships.
ηT = 0 V
ηT > 0 V
Electrocatalytic CO2 reduction
CO2
CO
HCOOH
C2O42-
2e-
2e-
2e-
CH4, C2H4, CxHy
Cu
highoverpotential
aldehyde Calvin cycle
alcohol
fuel?
difficult
Conclusions
• Optimizing the binding of key intermediates is the key to a good catalyst
• This is inherently more difficult for 2 or more intermediates than for 1 intermediate (scaling relationships)
• DFT is a useful tool in understanding and screening catalysts
• Can we efficiently and selectively reduce CO2 to something useful?
Acknowledgments
• Dirk Heering (Leiden)
• Jan Rossmeisl, Jens Nørskov (Lyngby)
• ELCAT Marie Curie Initial Training Network, http://www.elcat.org.gu.se/
• NWO, NRSC-C