First-principles simulation of electrochemical reactions at solid- - PowerPoint PPT Presentation

First-principles simulation of electrochemical reactions at solid- liquid interface National Institute of Advanced Industrial Science and Technology (AIST), Japan Minoru Otani 07/03/2018 ISS2018@ISSP 1

Outline • Introduction • Simulation platform for electrochemical interface - Effective screening medium (ESM) method - Constant bias potential (constant- μ e ) method - Hybrid simulation method: DFT+liquid theory 
 (ESM-RISM) • Applications - Lithium Insertion/Desorption Reaction in Li-ion battery • Summary • Appendix (How to define the electrode potential from DFT) 2


 
 
 Electrochemical devices/engineering photoelectrochemical 
 hydrogen production Sensor Battery pH meter Manganese dry cell ion selective concentration meter Lead battery glucose, etc. (using enzyme) NiCd, NiH secondary battery gas (oxygen, etc.) Fuel cell Electroplating Lithium secondary battery Cathodic protection Capacitor Fe → Fe 2 O 3 Electrolytic condenser Electrolysis Double layer condenser Aluminum, Copper, etc. Supercapacitor Water, salt, etc. Photovoltaic cell Organic chemicals c-Si, a-Si solar cell tetraethyl lead Dye sensitized solar cell 3

Target systems Energy generation Energy storage Energy harvesting (Fuel cell) (Secondary battery) (PV, PEC) H 2 out O 2 out Load e – e – Li Li sunlight in Li + ex) graphite anode electrolyte cathode water-based electrolyte Electrolyte � � � Electrolyte � � SEI Pt � � � � � � Si �� Si anode 24 �� � 24 hour Carbon support • corrosion mechanism 500 nm • surface modification • overpotential • formation mechanism • a cheaper alternative to Pt of SEI • interface resistance 4

Electrochemical interface 25 ℃ , 1.0M NaCl, Electrode: Pt electrode 4 nm 2 surface area + - + + 1 NaCl / 50 H 2 O 3-layer Pt(111): + + - - 460Pt atoms V ε f Length scale of EDL: µ EDL Electric field: 0.1~0.5 V/Å nm ~ μ m Diffuse layer V ∞ Helmholtz layer: ~Å z Depth 2 nm: 800 atoms ( 264 H 2 O, 5 NaCl) 10 nm: 5000 atoms ( 1320 H 2 O, 25 NaCl) 0.1 μ m: 50000 atoms (13200 H 2 O, 250 NaCl) 5

4 Challenges in modeling an electrochemical reaction for DFT-MD Electrochemical interface electrode + - + + 2.Bias potential + + - - control 1.Strong electric V Electrostatic potential field in Helmholtz ε f layer µ EDL V ∞ z 3.Screening in diffuse 4.Origin of electrostatic layer potential 6

4 Challenges in modeling an electrochemical reaction for DFT-MD 1.Strong electric ESM method field in Helmholtz Effective Screening Medium method layer Phys. Rev. B 73 , 115407 (2006) Constant- μ e method 2.Bias potential control Phys. Rev. Lett. 109 , 266101 (2012) 3.Screening in diffuse ESM-RISM method layer Reference Interaction Site Model 4.Origin of electrostatic Phys. Rev. B 96 ,115429 (2017) potential 6

J. Haruyama, et. al., MO, J. Phys. Chem. C, 122, 9804(2018) Solvation process of Li-ion constant- μ µ ext V 0 e − e − Li + Li + e − e − Li + Li + EC, LiPF 6 (1ML) Graphite, LCO DFT RISM Calculation cell 7

Electrochemical impedance spectroscopy (EIS) measurements Typical EIS of Conventional LIB cell LiCoO2|EC3:EMC7 LiPF6 1M|Graphite In the fully charged and discharged states as well as at the low temperatures ( ≤ 20 ◦ C), the R cell of the Li- ion cells is predominated by the R ct . S. S. Zhang, K. Xu, and T. R. Jow, Electrochemica Acta 49 , 1057 (2004). Temperature-dependence of R ct @0.2 V vs. Li/Li + The activation energies were evaluated to be around 50-60 kJ/mol (0.5-0.6 eV). These values are very large compared to lithium ion conduction in active materials. T. Abe, H. Fukuda, Y. Iriyama, and Z. Ogumi, J. Electrochem. Soc. 151 , A1120 (2004). 8

Outline • Introduction • Simulation platform for electrochemical interface - Effective screening medium (ESM) method - Constant bias potential (constant- μ e ) method - Hybrid simulation method: DFT+liquid theory 
 (ESM-RISM) • Applications - Lithium Insertion/Desorption Reaction in Li-ion battery • Summary • Appendix (How to define the electrode potential from DFT) 9

Total energy functional in conventional method Total energy functional E [ ρ e ] = T [ ρ e ] + E xc [ ρ e ] + 1 d r d r 0 ρ e ( r ) ρ e ( r 0 ) ZZ Z + d r v ext ( r ) ρ e ( r ) + E II 2 | r − r 0 | δ E = 0 Kohn-Sham equation δρ e INPUT { R } , ρ in � � 1 ⇥ 2 ⇥ 2 + V ( r ) + ˆ V NL + V xc ( r ) ψ i ( r ) = ε i ψ i ( r ) E II , v ext ( r ) Poisson equation is solved with SCF periodic boundary condition in Kohn-Sham eq. advance and use the following expression V ( r ) d r 0 ρ tot ( r 0 ) Z Z d r 0 G PBC ( r , r 0 ) ρ tot ( r 0 ) V ( r ) = | r − r 0 | = OUTPUT E, F I Need to solve Poisson eq. with different BC. 10

Boundary condition at the interface y 2D periodic boundary Open boundary condition x condition (2D PBC) (OBC) 11 z

Boundary condition at the interface •In the density functional theory (DFT), we need to solve two equations. Kohn-Sham equation � � 1 ⇥ 2 ⇥ 2 + V ( r ) + ˆ V NL + V xc ( r ) ψ i ( r ) = ε i ψ i ( r ) ρ ( r ) → 3D PBC Poisson equation ⇥ [ � ( r ) ⇥ ] V ( r ) = � 4 ⇥⇤ tot ( r ) → 2D PBC + OBC V ( r ) y + + Mixed boundary condition (MBC) + x + 12 z

Effective screening medium (ESM) M.O. and O. Sugino, PRB 73, 115407 (2006) How to solve the poisson equation under MBC? ⇥ [ � ( r ) ⇥ ] V ( r ) = � 4 ⇥⇤ tot ( r ) Laue representation [ ⇧ z { � ( z ) ⇧ } − � ( z ) g 2 || ] V ( g || , z ) = − 4 ⇥⇤ ( g || , z ) [ ⇧ z { ⇥ ( z ) ⇧ } − ⇥ ( z ) g 2 || ] G ( g || , z, z � ) = − 4 ⇤� ( g || , z − z � ) We can get Green’s function analytically with each boundary conditions. 13

electrode electrode electrode Effective screening medium (ESM) M.O. and O. Sugino, PRB 73, 115407 (2006) (i) slab � ⇤ z V ( g ⇤ , z ) z = ± ⇥ = 0 , � ( z ) = 1 � neutral surface, polarized surface... (ii) ⇥ V ( g ⇤ , z 1 ) = 0 � ∂ z V ( g ⇤ , z ) z = �⇥ = 0 � slab � 1 if z ≥ z 1 � ( z ) = if ∞ z ≤ z 1 STM, gate electrode... (iii) � V ( g � , z 1 ) = 0 V ( g � , − z 1 ) = V 0 slab � ( z ) = ∞ if | z | ≥ z 1 nano-structure in capacitor, zigzag pot. 14

electrode electrode electrode Effective screening medium (ESM) M.O. and O. Sugino, PRB 73, 115407 (2006) G (i) ( g ⌅ , z, z ⇥ ) = 4 π e � g ⇥ | z � z � | 2 g ⌅ slab G (ii) ( g ⌅ , z, z ⇥ ) = 4 π e � g ⇥ | z � z � | − 4 π e � g ⇥ (2 z 1 � z � z � ) 2 g ⌅ 2 g ⌅ slab G (iii) ( g ⌅ , z, z ⇥ ) = 4 π e � g ⇥ | z � z � | 2 g ⌅ e � 2 g ⇥ z 1 cosh { g ⌅ ( z − z ⇥ ) } − cosh { g ⌅ ( z + z ⇥ ) } + 4 π 2 g ⌅ sinh(2 g ⌅ z 1 ) 15

Total energy functional of the ESM method Total energy functional E [ ρ ] = T [ ρ ] + E xc [ ρ ] + 1 d r d r � ρ ( r ) ρ ( r � ) �� � | r − r � | + d r v ext ( r ) ρ ( r ) + E ion 2 V ➠ variable � ⇥ � � ( r ) ⇤ 8 ⇥ | ⇤ V ( r ) | 2 + ⇤ tot ( r ) V ( r ) E [ ⇤ e , V ] = T [ ⇤ e ] + E xc [ ⇤ e ] + d r conventional δ E � ( r ) = 1 δ V = 0 Generalized Poisson equation d r ρ tot ( r � ) � V ( r ) = | r − r � | ⇥ [ � ( r ) ⇥ ] V ( r ) = � 4 ⇥⇤ tot ( r ) δ E ESM = 0 δρ e � ( r ) : model dependent Kohn-Sham equation � d r G ( r , r � ) ρ tot ( r � ) V ( r ) = � ⇥ � 1 2 ⇥ 2 + V ( r ) + ˆ V NL + V xc ( r ) ψ i ( r ) = ε i ψ i ( r ) 16

Schematic animation of electrochemical interface simulation ESM J. Phys. Soc. Jpn 77 , 024802 (2008) 17

Electrochemical reaction Hydrogen adsorption reaction H 3 O + + e − → H 2 O + H ad e - Pt Pt J. Phys. Soc. Jpn 77 , 024802 (2008) Q=-0.95 (e/cell) 18

Outline • Introduction • Simulation platform for electrochemical interface - Effective screening medium (ESM) method - Constant bias potential (constant- μ e ) method - Hybrid simulation method: DFT+liquid theory 
 (ESM-RISM) • Applications - Lithium Insertion/Desorption Reaction in Li-ion battery • Summary • Appendix (How to define the electrode potential from DFT) 19

Why we need a bias control? Hydrogen adsorption reaction e - Pt Pt Electron transfer 8 − 0.2 − 0.3 6 − 0.4 Excess charge Q( e ) Fermi energy (eV) 4 − 0.5 − 0.6 2 − 0.7 0 − 0.8 − 0.9 − 2 − 1 0 1 2 3 4 5 6 7 Q=-0.95 (e/cell) Time (ps) 20

Limitation of the original conventional DFT-MD conventional simulation experimental simulation A. Lozovoi et al., JCP 115, 1661 (2001) 21