Fuel Cells 1 FUEL CELLS in energy technology (4) Werner Schindler Department of Physics Nonequilibrium Chemical Physics TU Munich summer term 213
Fuel Cells 2 Nernst equation and its application to fuel cells: Cell reaction: SOFC: ½ O 2 + H 2 H 2 O Overall cell voltage: E = φ (2) φ (1) T p 1/2 O2 p H2 a O 2- E = φ (2) φ (1) + ln 2F a O 2- p H2 O T p 1/2 O2 p H2 E = φ (2) φ (1) + ln 2F p H2 O T p 1/2 O2 p H2 E = 1.23 V + ln 2F p H2 O
Fuel Cells 3 The actual cell voltage of a fuel cell is lowered due to losses Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29
Fuel Cells 4 Overpotentials and Losses in Fuel cells η cath h < DE η anod h > fuel cell
Fuel Cells 5 Overpotentials Both electrode potentials change when there is current flux, but to a different extent The difference between the electrode potential at a certain current and the one at zero current (equilibrium potential) is called overpotential: η(j) = E(j) - E(j=) The overpotential is always negative at the cathode, and always positive at the anode.
Fuel Cells 6 Overpotentials Summary of electrochemical reactions at the positive pole: Electrolysis: O 2 + 4e - + 4 H + 2 H 2 O equilibrium: O 2 + 4e - + 4 H + 2 H 2 O fuel cell: O 2 + 4e - + 4 H + 2 H 2 O At the positive terminal both the reduction of oxygen to water and the oxidation of water to oxygen are taking place. In the fuel cell mode the reduction process outweighs the oxidation process, in the electrolysis mode it is the other way around. In the electrochemical equilibrium both processes are taking place at the same rate, so that there is no net reaction.
Fuel Cells 7 Overpotentials Schematic epresentation of the cell voltage in electrolysis mode : + h > DE E - h < fuel cell eq. electrolysis
Fuel Cells 8 Parameters that affect the rates of electrochemical reactions Electrode reaction Overpotentials Chemical reaction Charge (electron) transfer Steps preceding / following charge transfer Diffusion in electrolyte / electrode Cystallization processes Ohmic losses in electrolyte / electrode elevance of some parameters Charge transfer overpotential: catalyst material Diffusion overpotential: mass transport properties; in fuel cells, e.g., depending on the structure of the gas diffusion layer
Fuel Cells 9 The actual cell voltage of a fuel cell is lowered due to losses Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29
Fuel Cells 1 Voltage-current curve for a typical low temperature fuel cell Source: J. Larminie, A. Dicks: Fuel cell systems explained. 2nd ed., Wiley, 23
Fuel Cells 11 Voltage-current curve for a typical high temperature fuel cell Source: J. Larminie, A. Dicks: Fuel cell systems explained. 2nd ed., Wiley, 23
Fuel Cells 12 Electron transfer at electrodes: 1. Diffusion of the species to where the reaction occurs (mass transfer coefficient) 2. earrangement of the ionic atmosphere (1-8 s) 3. eorientation of the solvent dipoles (1-11 s) 4. Alterations in the distances between central ion and the ligands (1-14 s) 5. Electron transfer (1-16 s) 6. elaxation in the inverse sense Charge transfer process comprises steps 2-5, and is described by a charge transfer rate constant.
Fuel Cells 13 eaction rates at electrochemical interfaces are finite Chemical reactions proceed via an intermediate activated complex: Catalyst! Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29
Fuel Cells 14 The Butler-Volmer relation We consider the following one-step, one-electron process + e - j c, k j a, k ox Anodic current density (oxidation) Cathodic current density (reduction) j Fk a c j Fk c c Total current density j j j Fk c Fk c a c c () and c () are the concentrations of the electroactive species at the electrode surface (x = )
Fuel Cells 15 The Butler-Volmer relation (continued) Let us consider how the electrode potential affects the rate of an electron transfer reaction using expressions of the Arrhenius type: k k A A DG exp T # DG exp T # Gibbs Free Energy D + ne Activated complex at transition state G # e d DG ed eaction Coordinate
16 The energy profile shifts when the electrode potential is shifted from the standard value # DG, # DG E E nf( E E ) # DG # DG, Source: A.J. Bard, L.. Faulkner: Electrochemical Methods. Fundamentals and Applications, 2nd ed., Wiley, 21
Fuel Cells 17 An applied potential affects the activation energies for the reduction and the oxidation DG # DG #, nf( E E ) DG # DG #, (1 ) nf( E E ) Source: A.J. Bard, L.. Faulkner: Electrochemical Methods. Fundamentals and Applications, 2nd ed., Wiley, 21
18 The Butler-Volmer equation (continued) ate constant for the reduction k A DG exp T # A exp DG T #, nf( E exp T E ) k nf( E exp T E ) ate constant for the oxidation k A exp DG T # A exp DG T #, (1 ) nf( E exp T E ) k (1 ) nf( E exp T E )
19 The Butler-Volmer equation (continued) j c (1 ) nf( E E ) nf( E E ) nfk exp c nfk exp T T anodic current density j a cathodic current density j c For E = E the interface is at equilibrium and the concentrations are unity. Furthermore j = and we have k = k = k. The parameter k is called the standard rate constant and plays a key role in electrode kinetics.
2 The Butler-Volmer equation (continued) j nfk c (1 ) nf( E E exp T ) c exp nf( E T E ) For E = E eq we have j =, the interface is at equilibrium and the surface concentrations of and correspond to the bulk values c * and c *. Then j a = -j c = j where j is called exchange current density: j nfk c * (1 ) nf( E eq E ) nf( Eeq E ) * exp nfk c exp T T
The Butler-Volmer equation (continued) j j c c * (1 ) nf( E E exp T eq ) c c * nf( E exp T E eq ) Exponential dependence on overpotential: h E E eq 21 slope depends on j and α α=.5 results in a symmetric curve
The Butler-Volmer equation (continued) - Make sure that you understand the differences between E, E eq, and E - E is the actual potential of the electrode, i.e. under current flow. It depends on the current. - E eq is the equilibrium potential of the electrode. It depends on concentration and is given by the Nernst equation. - E is the standard potential of the electrode. It is a tabulated value. 22
The slope of the I-E curve depends on - the exchange current density j / rate constant k Overvoltage or overpotential h E E eq Source: A.J. Bard, L.. Faulkner: Electrochemical Methods. Fundamentals and Applications, 2nd ed., Wiley, 21 23
24 The symmetry of the I-E curve depends on - the charge transfer coefficient α Source: A.J. Bard, L.. Faulkner: Electrochemical Methods. Fundamentals and Applications, 2nd ed., Wiley, 21
25 Experimental determination of exchange current densities - the Tafel plot Source: A.J. Bard, L.. Faulkner: Electrochemical Methods. Fundamentals and Applications, 2nd ed., Wiley, 21
Exchange currents for the hydrogen reaction vary over a wide range Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29 26
27 Exchange currents for the oxygen reaction are rather small Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29
Fuel Cells 28 Concentration overpotential: j j c c * (1 ) nf( E exp T E eq ) c c * nf( E exp T E eq ) c * c c * c This is valid, when transport through the electrolyte is fast compared to the charge transfer process. In many cases, concentrations vary with proceeding electrochemical reaction:
Fuel Cells 29 Concentration overpotential: anodic current density: c j( h) j * c (1 ) nfh exp T cathodic current density: c j( h) j * c exp nfh T h * T j c ln ln ( 1) nf j c () T h nf ln j j * ln c c () at high anodic overpotentials: c * c h concentrat ion at high cathodic overpotentials: c * c h concentrat ion
Fuel Cells 3 j Fuel Cells: activation / charge transfer overpotentials anode (hydrogen oxidation) H 2 2H + + 2e - H 2 O 1/2O 2 + 2H + + 2e - (fuel cell voltage) E eq,1 E eq,2 cathode (oxygen reduction) (electrolyser voltage) E 2H + + 2e - H 2 1/2O 2 + 2H + + 2e - H 2 O (without mass transport limitations)
31 The activation overpotential (loss) increases with decreasing exchange current density Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29
32 The main activation loss is associated with the oxygen electrode due to the low exchange current density Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29
How can we increase the exchange current density? - Increase the reactant concentration - Decrease the activation barrier - Increase the temperature - Increase the number of reaction sites, i.e. increase the surface roughness of the reaction interface Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29 33 TPB: Triple phase boundary
Overpotentials / Losses in fuel cells: Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29 34
35 Losses in fuel cells / ohmic losses Ohmic drop: h h Electrolyte h Electrode h Contact ~ j Total losses: h V h Kin h Cell voltage DE cell / V h h kin P max (W cm -2 ) Current density j / (A cm -2 ) Voltage Efficiency voltage DE DE cell eq Major issues - Minimize ohmic losses - Optimize kinetics - Optimize fuel cell stacks
Fuel Cells 36 Mass transport, diffusion overpotential, and diffusion limited current: Charge transfer, as described by the Butler Volmer equation, coupled with a diffusion process: Without flow of current the concentration c is constant throughout the whole electrolyte; With flow of current, at a particular overvoltage, the concentration c drops down in front of the electrode to c S. The variation in concentration extends over a distance δ N, the Nernstian diffusion layer. Thickness of δ N is determined by hydrodynamics in front of the electrode surface.
Fuel Cells 37 Mass transport, diffusion overpotential, and diffusion limited current: At forced convection δ N is of the order of 1-4 cm, whereas it extends in an undisturbed solution to.5 mm. Times until such stationary conditions are reached are of the order of.1 1 s and 3 6 s, respectively. According to 1. Fick s Law: (j i = - D i grad c i ) Supposed the diffusion layer δ N is constant with time, j approaches a limit, the diffusion limited current density j lim :
Fuel Cells 38 Mass transport, diffusion overpotential, and diffusion limited current: Diffusion overpotential can be derived from the Nernstian equation: The diffusion overpotential is then: (η d < for c > c S )
Fuel Cells 39 Mass transport, diffusion overpotential, and diffusion limited current: Together with the expression for the current density j and the diffusion limited current density j lim :
Fuel Cells 4 Mass transport, diffusion overpotential, and diffusion limited current: Dependence of the normalized limiting current density on the diffusion overpotential η d : Diffusion limitation j lim proportional to c Charge transfer and diffusion limitation the smaller c, the smaller j lim
Fuel Cells 41 Overvoltages in Fuel Cells Interconnectors - conductivity Contacts Anode Cathode Electrolyte - diffusion Limitation of access to three phase boundary for reactants Limitation of product transport from three phase boundary - electrode porosity Kinetically hindered charge transfer - exchange current density - reaction rate - catalysts
E / V 42 The input power is converted to electrical power and heat E H E eq E H - E(I) D DE H H nf D DE G eq nf P heat DE H DE I E(I) P electric DE I Source:. O'Hayre et al.: Fuel cell fundamentals. 2nd ed., Wiley, 29
Fuel Cells 43 Electricity and heat generation in a Fuel Cell 1, 1,2,6,8 1, Power output @.8 V:,14 W el /,8 W th Heat h voltage,6,4,2, Cell voltage [V],8,6,4,2 Nominal power @.7 V:,26 W el /,2 W th Electricity Max. power @,44 V:,46 W el /,83 W th,,,,2,4,6,8 1, 1,2 1,4 1,6 Current density [A/cm 2 ],4,2 Power density [W/cm 2 ]
Electricity and heat generation in a Fuel Cell 4 1, 3 Tuning the operation mode for electricity or heat P el /P th 2 1 P el /P th P th P el,5 Power density [W/cm 2 ] 1,4 1,2 1,,8,6,4,2, Cell voltage [V] 13-5-17 Werner Schindler Fuel Cells 44,
45 Efficiency of a fuel cell real thermo voltage fuel H thermo thermodynamic efficiency voltage voltage efficiency fuel H faradaic efficiency heating value efficiency thermo voltage fuel H DG DH DE DE I nf v DH DH fuel r c cell eq [v fuel ] = mol/s DH r : heating value of the fuel component that is converted, e.g. H 2 DH C : heating value of all fuel components (z.b. CH 4 or CO)