Quantifying Confidence in Density Functional Theory
Quantifying Confidence in Density Functional Theory Predicted Surface Pourbaix Diagrams at Solid-Liquid Interfaces and its Implications for Electrochemical Processes Olga
a Vinogradova ,
Venkatasubramanian
a,b,* Viswanathan
aDepartment
of Chemical Engineering, Carnegie Mellon University bDepartment of Mechanical Engineering, Carnegie Mellon University
Motivation: Next-Generation Energy Conversion
Surface Pourbaix Diagram for Pt(111)
Results: Application to Other Metallic Surfaces
Global participation in the Paris Agreement of 2015 clearly shows there is a major push to mitigate the volume of greenhouse gases. A large component of these emissions comes from the transportation sector. Polymer Electrolyte Membrane (PEM) fuel cells provide an attractive alternative for powering vehicles since the reaction of hydrogen and oxygen simply releases water and heat. In addition to vehicles, fuel cells are used for human spaceflight missions, stationary power generation, and military equipment.
Limitation of Current PEM Fuel Cells Anode Reaction
pH=0
𝐻𝐻2 → 2𝐻𝐻 + + 2𝑒𝑒 −
+ − + 4𝐻𝐻 + 4𝑒𝑒 → 2𝐻𝐻2 𝑂𝑂 𝑂𝑂 Cathode Reaction 2
𝑂𝑂2 (𝑔𝑔) + ∗ +𝑒𝑒 − + 𝐻𝐻 + → 𝑂𝑂𝑂𝑂𝐻𝐻 ∗ 𝑂𝑂𝑂𝑂𝐻𝐻 ∗ + 𝑒𝑒 − + 𝐻𝐻+ → 𝑂𝑂∗ + 𝐻𝐻2 𝑂𝑂(𝑙𝑙) 𝑂𝑂∗ + 𝑒𝑒 − + 𝐻𝐻 + → 𝑂𝑂𝐻𝐻∗ 𝑂𝑂𝑂𝑂 ∗ + 𝑒𝑒 − + 𝐻𝐻 + → 𝐻𝐻2 𝑂𝑂 𝑙𝑙 + ∗ 𝐸𝐸 0 = 1.23𝑒𝑒𝑒𝑒
Pt(100)
∆𝐺𝐺1
∆𝐺𝐺2 ∆𝐺𝐺3 ∆𝐺𝐺4
−
Free Energy Diagram for 4 𝒆𝒆 Mechanism
Minimization of Gibbs free energy defines the most stable state at given pH. At finite pH: 𝐸𝐸 = 𝐸𝐸 0 − 2.303𝑘𝑘𝐵𝐵 𝑇𝑇(𝑝𝑝𝑝𝑝)
Methods: Uncertainty Quantification in DFT
Pd(111)
Ensemble of energies is computed from an ensemble of exchange-correlation functionals within BEEF-vdW.
Results: Predicting Multi-Phase Regions
∆𝐺𝐺 0 = −4𝐸𝐸 0 = −4.92𝑒𝑒𝑒𝑒
∆𝐺𝐺1
∆𝐺𝐺2
∆𝐺𝐺3
∆𝐺𝐺4
Scaling Relations Between Intermediates Limit Activity
∆𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = −4.92𝑒𝑒𝑒𝑒 + 3.2𝑒𝑒𝑒𝑒 = −1.72𝑒𝑒𝑒𝑒
Ir(111)
𝑈𝑈𝐿𝐿 = min(∆𝑮𝑮𝟏𝟏 , ∆𝐺𝐺2 , ∆𝐺𝐺3 , ∆𝑮𝑮𝟒𝟒 )
Maximum potential for ORR: 0.86 V
Volcano Relationship Showing Relative Activity
Acknowledgements I wish to thank my advisor Dr. Venkat Viswanathan for his guidance and mentoring as well as Dilip and Vikram for their indispensable contribution to this project. This work was supported financially by Volkswagen AG.
Methods: Surface Pourbaix Diagrams Surface Pourbaix diagrams capture the most stable state of the surface at varying reaction conditions of electrostatic potential and pH.
References 1. 2. 3. 4.
Vinogradova et al., arXiv:1710.08407 [cond-mat.mtrl-sci] Deshpande et al. ACS Catal. 2016, 6(8), 5251-5259. Hansen et al. Phys. Chem. Chem. Phys. 2008, 10(25), 3722-3730. Wellendorff et al. Phys. Rev. B. 2012, 85, 235149. *Corresponding Author: [email protected]
a Vinogradova ,
Venkatasubramanian
a,b,* Viswanathan
aDepartment
of Chemical Engineering, Carnegie Mellon University bDepartment of Mechanical Engineering, Carnegie Mellon University
Motivation: Next-Generation Energy Conversion
Surface Pourbaix Diagram for Pt(111)
Results: Application to Other Metallic Surfaces
Global participation in the Paris Agreement of 2015 clearly shows there is a major push to mitigate the volume of greenhouse gases. A large component of these emissions comes from the transportation sector. Polymer Electrolyte Membrane (PEM) fuel cells provide an attractive alternative for powering vehicles since the reaction of hydrogen and oxygen simply releases water and heat. In addition to vehicles, fuel cells are used for human spaceflight missions, stationary power generation, and military equipment.
Limitation of Current PEM Fuel Cells Anode Reaction
pH=0
𝐻𝐻2 → 2𝐻𝐻 + + 2𝑒𝑒 −
+ − + 4𝐻𝐻 + 4𝑒𝑒 → 2𝐻𝐻2 𝑂𝑂 𝑂𝑂 Cathode Reaction 2
𝑂𝑂2 (𝑔𝑔) + ∗ +𝑒𝑒 − + 𝐻𝐻 + → 𝑂𝑂𝑂𝑂𝐻𝐻 ∗ 𝑂𝑂𝑂𝑂𝐻𝐻 ∗ + 𝑒𝑒 − + 𝐻𝐻+ → 𝑂𝑂∗ + 𝐻𝐻2 𝑂𝑂(𝑙𝑙) 𝑂𝑂∗ + 𝑒𝑒 − + 𝐻𝐻 + → 𝑂𝑂𝐻𝐻∗ 𝑂𝑂𝑂𝑂 ∗ + 𝑒𝑒 − + 𝐻𝐻 + → 𝐻𝐻2 𝑂𝑂 𝑙𝑙 + ∗ 𝐸𝐸 0 = 1.23𝑒𝑒𝑒𝑒
Pt(100)
∆𝐺𝐺1
∆𝐺𝐺2 ∆𝐺𝐺3 ∆𝐺𝐺4
−
Free Energy Diagram for 4 𝒆𝒆 Mechanism
Minimization of Gibbs free energy defines the most stable state at given pH. At finite pH: 𝐸𝐸 = 𝐸𝐸 0 − 2.303𝑘𝑘𝐵𝐵 𝑇𝑇(𝑝𝑝𝑝𝑝)
Methods: Uncertainty Quantification in DFT
Pd(111)
Ensemble of energies is computed from an ensemble of exchange-correlation functionals within BEEF-vdW.
Results: Predicting Multi-Phase Regions
∆𝐺𝐺 0 = −4𝐸𝐸 0 = −4.92𝑒𝑒𝑒𝑒
∆𝐺𝐺1
∆𝐺𝐺2
∆𝐺𝐺3
∆𝐺𝐺4
Scaling Relations Between Intermediates Limit Activity
∆𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = −4.92𝑒𝑒𝑒𝑒 + 3.2𝑒𝑒𝑒𝑒 = −1.72𝑒𝑒𝑒𝑒
Ir(111)
𝑈𝑈𝐿𝐿 = min(∆𝑮𝑮𝟏𝟏 , ∆𝐺𝐺2 , ∆𝐺𝐺3 , ∆𝑮𝑮𝟒𝟒 )
Maximum potential for ORR: 0.86 V
Volcano Relationship Showing Relative Activity
Acknowledgements I wish to thank my advisor Dr. Venkat Viswanathan for his guidance and mentoring as well as Dilip and Vikram for their indispensable contribution to this project. This work was supported financially by Volkswagen AG.
Methods: Surface Pourbaix Diagrams Surface Pourbaix diagrams capture the most stable state of the surface at varying reaction conditions of electrostatic potential and pH.
References 1. 2. 3. 4.
Vinogradova et al., arXiv:1710.08407 [cond-mat.mtrl-sci] Deshpande et al. ACS Catal. 2016, 6(8), 5251-5259. Hansen et al. Phys. Chem. Chem. Phys. 2008, 10(25), 3722-3730. Wellendorff et al. Phys. Rev. B. 2012, 85, 235149. *Corresponding Author: [email protected]
