Electrochemistry with DFT

Transcription

1 Department of Chemistry Electrochemistry with DFT Jan Rossmeisl. Department of Chemistry University of Copenhagen 1

2 Electrochemical Energy Conversion H 2 O ½O 2 +H 2 ½O 2 + H 2 H 2 O Electric energy Chemical energy H 2 Electric energy

3 Catalysis Without Catalyst Energy With Catalyst

4 H + H + O Electrocatalysis e e Energy H + H + O e e H 2 O H + e H + e O

5 Enhedens navn Electrochemical cell Sted og dato Dias 5

6 Why use DFT 0 U RHE /V 1 <A>= i A i P i P i =e - Ei(pH,φ)/kT /Z Z= s e - Es(pH,φ)/kT /Z

7 Enhedens navn Electrochemical interfaces Sted og dato Dias 7

8 Department of Chemistry Electrochemical cell Dias 8

9 µ(h + +e - ) ½H 2 H + +e - H + E F = 0 eu E F = µ(h + +e - )

10 µ(h + +e - ) ½H 2 H + +e - E F = 0 H + eu E F = µ(h + +e - )

11 Computational Hydrogen Electrode G ½H 2 H* H + +e - -eu Nørskov, Rossmeisl, Logadottir, Lindqvist, Kitchin, Bligaard Jónsson, J. Phys. Chem. B, 108, (2004)

12 Field effects Rossmeisl, Nørskov, Taylor, Janik, Neurock. J. Phys. Chem. B 110, (2006), Karlberg, Rossmeisl, Nørskov, PCCP, 9 (2007) 5158

13 Evaluate Surface energy depends of the surface on potential? as function of the potential E(n,U RHE )=E(n,0)-E(0,0)-½nG(H 2 )-½neU RHE H + +e - +* H* U vs. RHE

14 Phase-diagrams G(n,U RHE ) Rossmeisl, Nørskov, Taylor, Janik, Neurock. J. Phys. Chem. B 110, (2006),

15 Cyclic voltammetry CV for Pt(111) 0 U RHE /V 1

16 H + +e - H* Markovic et al J. Phys. Chem. 101, 5405 (1997) G.S. Karlberg, T. Jaramillo, E.Skulason, J. Rossmeisl, T. Bligaard, J.K. Nørskov. PRL, 99, (2007)

17 ORR and OER intermediates H + H + H + H + e - -e - e- - e- -

18 Perfect catalyst G 1 G 2 G 3 G 4

19 U ORR and U OER U OER =max(δg 1, ΔG 2, ΔG 3, ΔG 4 )/e U ORR =min(δg 1, ΔG 2, ΔG 3, ΔG 4 )/e G 1 G 2 G 3 G 4

20 The role of the surface What is the role of the electrolyte?

21 Adding hydrogen to the electrolyte Rossmeisl, Skúlason, Björketun, Tripkovic, Nørskov. Chem. Phys. Lett (2008) 68-71

22 Challenge: Constant potential The potential is not the same in initial and final state

23 + + + n=1 Θ=n/N=1/ N=3 n=0 Θ=n/N=0 N=3

24 + + + n=3 Θ=n/N=1/ N= n=2 N=9 Θ=n/N=2/9

25 Enhedens navn The field is setup by the electrolyte Sted og dato Dias 26

26 Enhedens navn Salt bridge Sted og dato Dias 27

27 Enhedens navn The electrostatic potential is flat Potential differences Martin Hangaard Hansen, Chengjun Jin, Kristian S. Thygesen, Jan Rossmeisl, 2016 Sted og dato Dias 28

28 Enhedens navn Applying a bias Sted og dato Dias 29

29 How to use DFT 0 U RHE /V 1 <A>= i A i P i P i =e - Ei(pH,φ)/kT /Z Z= s e - Es(pH,φ)/kT /Z

30 Sted og dato Dias 31 Enhedens navn

31 Born-Haber-cycle

32 Born-Haber ΔG ½H 2 H + +e - From experiments ɸ e- ~ 4.4 ev at ph=0 Δɸ H+ = kt ln [a H+ ] = 0.059eV/pH Knowing μ H+ + e- and ɸ e- means that ph is known as well

33 Born-Haber ΔG H + +e - ½H 2 From experiments ɸ e- ~ 4.4 ev at ph=0 Δɸ H+ = kt ln [a H+ ] = 0.059eV/pH Knowing μ H+ + e- and ɸ e- means that ph is known as well

34 ph and potential μ (H + + e - ) ph=δɸ H+ /2.3kT ph=0 0 vs. RHE 0 vs. SHE (4.4 V) ɸ e-

35 The free energy of the interface E(n,U RHE )=E(n,0)-E(0,0)-½nE(H 2 )-½neU RHE E(n,φ e-,u RHE )=E(n,φ e-,0)-e(0,0)-½ne(h 2 )-½neU RHE ΔE int ɸ e- ph μ(h + +e - ) Rossmeisl, Chan, Ahmed, Tripkovic, Bjorketun, PCCP 2013

36 Projections ΔE int ɸ e- ph μ(h + +e - )

37 Projections ΔE int ɸ e- ph μ(h + +e - )

38 Projections ΔE int ɸ e- ph μ(h + +e - )

39 Sted og dato Dias 40 Enhedens navn

40 Enhedens navn Phasediagrams Sted og dato Dias 42

41 Enhedens navn Pt(111), Search with dynamics Sted og dato Dias 43

42 Enhedens navn Work function as order parameter Normal distribution Sted og dato Dias 44

43 Enhedens navn Potential of maximum entropy Climent, V.; Coles, B. A.; Compton, R. G. Laser-Induced Potential Transients on a Au(111) Single-Crystal Electrode. Determination of the Potential of Maximum Entropy of Double-Layer Formation. J. Phys. Chem. B 2002, 106, Sted og dato Dias 45

44 Enhedens navn Monte Carlo Sted og dato Dias 46

45 Enhedens navn Hydrogen on Au (111) H* Hollow Water down H* Ontop Sted og dato Dias 47

46 Enhedens navn Structure of water on Au (111) g O-O Kaya et al. Scientific Reports 2013 Soper & Ricci et al Sted og dato Dias 48

47 OH-coverage H 2 O OH*+H + +e - Langmuir isotherm Θ OH =1/3 1/(1+ exp((δg OH -eu)/kt)) Pt Pt 3 Ni Stamenkovic, Fowler, Mun, Wang, Ross, Lucas and Markovic, Science, 2007, 315, Rossmeisl, Karlberg, Jaramillo, Nørskov. Faraday Discussions 140, (2008)

48 Enhedens navn Structure of OH and H 2 O on Pt(111) Sted og dato Dias 50

49 Sted og dato Dias 52 Enhedens navn

50 The role of the electrolyte Why is proton transfer slow in alkaline? The donating molecule is different H 3 O + +e - H 2 O + H* H 2 O+e - HO - + H* But H 2 O H + +HO - is fast

51 Entropy and electrostatics

52 Low ph

53 Enhedens navn Entropic barrier is relevant for good catalysts Good catalyst -T S>eɳ - eu RHE Bad catalyst -T S<eɳ - eu RHE Rossmeisl, Chan, Skúlason, Björketun, Tripkovic, 2016 Sted og dato Dias 56

54 From experiments From Arrhenius the barrier is ~0.2 ev in both acid and alkaline The prefactor is 2-3 orders of magnitude smaller for alkaline Rate ~ exp(-g # /kt) =((-ΔH+TΔS)/kT) = exp(δs/k)exp(-δh/kt) Experiments is consistent with an entropic barrier 2-3 orders of magnitude ~ ev Durst, J.; Siebel, A.; Simon, C.; Hasche, F.; Herranz, J.; Gasteiger, H. A. Energ. Environ. Sci. 2014, 7, Sheng, Gasteiger, Shao-Horn; Jour. Electro.Chem Soc. 157 B1529-B1536 (2010)

55 Enhedens navn MH. Hansen, J. Rossmeisl 2016 Sted og dato Dias 58

56 Enhedens navn H -T S G Sted og dato Dias 59

57 Enhedens navn Summary A method for simulating the role of the interface. Features which have not been calculated before come out naturally. How will the electrostatic structure of the interface dependt on the electrolyte and anions? Vision: Theoretical CVs Sted og dato Dias 60