Introduc)on to Fuel Cells

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2 Introduc)on to Fuel Cells Anode (oxida)on loss of electrons): 2H 2 à 4H + +4e - Cathode (reduc-on gain of electrons) O 2 +4H + +4e - à 2H 2 O Overall reac)on (redox): 2H 2 + O 2 à 2H 2 O We will par)cularly interested in the oxygen reduc)on reac)on (ORR) in this class O 2 +4H + +4e - à 2H 2 O

3 Explore mechanisms: ORR toy example Poten)al Energy Overall Fuel Cell Reac)on 2H 2 + O 2 à 2H 2 O The steps highlighted in blue tend to be rate limi3ng steps in ORR Reac)on Mechanism

4 Volcano Plot Previous research shows that binding energies of reac)on intermediates are good predictors of cataly)c ac)vity Cataly)c Ac)vity How can volcano plots be explained? B. Corona, M. Howard, L. Zhang, and G. Henkelman, Computa)onal Screening of Core- Shell Nanopar)cles for the Hydrogen Evolu)on and Oxygen Reduc)on Reac)onsComputa)onal, J. Chem. Phys. 145, (2016). DOI

5 Saba)er Principles Interac)on between a substrate and a catalyst needs to be just right. Too strong of binding means you can not remove the substrate from the material. Too weak means it is difficult to bind the substrate to the material strong binding difficult to activate Medford, Andrew J., et al. "From the Saba)er principle to a predic)ve theory of transi)on- metal heterogeneous catalysis." Journal of Catalysis 328 (2015):

6 Binding Energies Binding energy: energy required to separate a system into two parts E binding- oxygen = In our case, the two parts will be the material and the adsorbent. The reference of the adsorbent will always be the stable form of the species 1/2O 2 + M à MO What is the energy change in the chemical reac)on?

7 Binding Energies What does a posi)ve binding energy mean? It is energe)cally unfavorable for the substrate to bind to the material V r r

8 Explore mechanisms: ORR toy example Poten)al Energy Overall Fuel Cell Reac)on 2H 2 + O 2 à 2H 2 O It will be difficult to get oxygen to bind to the catalyst! Reac)on Mechanism

9 Binding Energies What does a posi)ve binding energy mean? It is energe)cally unfavorable for the substrate to bind to the material V r r What does a nega)ve binding energy mean? It is energe)cally favorable for the substrate to bind to the material V r

10 Explore mechanisms: ORR toy example Poten)al Energy Overall Fuel Cell Reac)on 2H 2 + O 2 à 2H 2 O It will be difficult to remove oxygen from the catalyst! Reac)on Mechanism

11 Cohesive Energies Cohesive Energy: Energy difference between the energy of a nanopar)cle or solid with the energy of the individual atoms not interac)ng (free atoms) E cohesive = - Another way to think about cohesive energy is how much energy are you gaining from crea)ng a molecular structure You can also think of it as a measure of stability

12 Cohesive Energies Cohesive Energy: Energy difference between the energy of a nanopar)cle or solid with the energy of the individual atoms not interac)ng (free atoms) E cohesive = - N where N is the number of atoms in the nanopar8cle Another way to think about cohesive energy is how much energy are you gaining from crea)ng a molecular structure You can also think of it as a measure of stability

13 Cohesive Energies Let s say I want to compare the stability of a 38 atom and a 55 atom nanopar)cle using the equa)on given. Can I directly compare cohesive energies? get a per atom cohesive energy E cohesive = - N N where N is the number of atoms in the nanopar8cle

14 Units We will be using the following units in this class: Energyà Electronvolts (ev) The energy in one photon of visible light is ev The energy to break a covalent bond in Silicon is around 1.1eV. Energies on an order of magnitude higher than this are too high! Lengthà Angstrom (Å) The bond lengths are typically around 1-3 Å

15 Overview of VASP command line tools

16 Required calcula)ons When calcula)ng binding and cohesive energies, you will need to localally op3mize or perform a geometry op3miza3on of each structure involved. E binding- oxygen = For an oxygen binding energy on material, M, you will need to perform three geometry op)miza)ons M- O, M and O 2. You will need to check that each op)miza)on successfully converges ( F < 0.005eV/Å). Next I will show you the tools required to check this with VASP.

17 Geometry Op)miza)on with VASP You will use a sosware package called VASP to run these calcula)ons; this sosware uses Density Func8onal Theory (our electronic structure method) to calculate proper)es of materials. These calcula)ons will be much slower than your previous lab; the will take several minutes to run or even longer if all of the computer is being used! Next I will show you the tools required to check this with VASP.

18 Command line for VASP oug FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS Make sure this force value reaches threshold (<0.005 ev/å); This parameter is specified in the INCAR file with the flag EDIFFG.

19 Command line for VASP oug FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS oute energy without entropy= energy(sigma- >0) = energy without entropy= energy(sigma- >0) = energy without entropy= energy(sigma- >0) = energy without entropy= energy(sigma- >0) = energy without entropy= energy(sigma- >0) = energy without entropy= energy(sigma- >0) =

20 Review: Algorithm for local op)miza)on while using an electronic structure method The general procedure for numerical geometry op)miza)on is as follows: 1. Calculate the force on all atoms for some configura)on of an atomic system. 1. To calculate the force on all the atoms (fixed nuclei fixed) we will need to op)mize the wave func)on for all the electrons in your chemical system 2. If the magnitude of the force is less than threshold, you have found a cri)cal point! STOP. 3. If not, move the atoms, or nuclei, such that they go towards a cri)cal points 4. Repeat.

21 Command line for VASP ou Itera)on 1( 41) Itera)on 1( 42) Itera)on 1( 43) Itera)on 1( 44) Itera)on 2( 1) Itera)on 2( 2) Itera)on 2( 3) Itera)on 2( 4) Itera)on 2( 5) Itera)on 2( 6) Itera)on 2( 7) Itera)on 2( 8) Itera)on 2( 9) Itera)on 3( 1) Op8miza8on Step number of nuclei loca8on Op8miza8on step number for the electrons at fixed nuclei

22 More VASP Info What does the script vfin.pl do? Moves all VASP output files to a directory you specify e.g vfin.pl min1 places these files in directory min1 It leaves all star)ng VASP files (POSCAR, INCAR,POTCAR,KPOINTS,frilab.sub) in your current directory The POSCAR file in you current directory, the new star)ng configura)on, becomes the final configura)on from the previous run or the CONTCAR file POSCAR CONTCAR The XDATCAR is a movie of all images in the op)miza)on

23 Common Issues on Lab 2 Calcula)ons are not converged oug FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS FORCES: max atom, RMS Make sure this force value reaches threshold (<0.005 ev) If not converged wrap up calcula8on and run the job again by running vfin.pl minx then qsub frilab2.sub