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Electrochemistry for Renewable Energy - Coggle Diagram
Electrochemistry for Renewable Energy
Electrode processes
Electrochemical cells and reactions
2 electrode processes
Reference electrode
Electrode where the half-reaction takes place that has a constant potential = Activities in nernst equation do not/little change because of constant composition
Types
One with silver/agcl in saturated cl-
Standard hydrogen electrode (SHE)
Is not commonly used due to hydrogen evolution
Is 4.5 V vs vacuum (absolute scale)
One with mercury (SCE)
Quasi-reference electrode
For example a Ag wire
When the potential is not known only via testing with an redox couple
Often used for non-aquous solutions
The RE to choose can depend on the medium
Working electrode
Electrode where the half-reaction takes place you want to study
Only this potential differs during the experiment
Only used to study half-reactions
Energy electron
E = -q*phi
Hence more positive potential = lower electron energy --> oxidation
Hence more negative potential = Higher electron energy --> reduction
3 electrode processes
Working electrode
Counter electrode
Supply's/takes electrons to/from working electrode
Much accurater for higher currrent and large internal resistance that leads to potential drop (IRs). Rs = electrolyte resistance
Reference electrode
High resistance between RE and WE
Placed close to WE, preferably to the side
Hence no current flows trough RE --> constant potential
Notation electrochemical cell
Left side = oxidation reaction
Right side = reduction reaction
/ = phase boundary, // = salt bridge
Use a noble (that is not oxidized itself) metal as electrode and place on the outsides
Write down all (counter) ions present
If pot cathode > anode = galvanic cell otherwise electrolytic cell
Type of processes
Non-faradaic processes (capacitance)
Ideal polarizable electrode
Small current leads to high potential in/decrease
Ideal working electrode
Does not really exist and can only be approached by an inert electrode in its potential window
No charge transfer occurs = only charge buildup on electrode and electron double layers forms (Pure capacitator)
Faradaic processes
Charge transfer process that occurs at the same potential, species must be present in the solution to take up/give electrons
Ideal non-polarizable electrode
Ideal reference electrode
High current will not lead to potential increase
Types and definitions
Electrolytic cell = external power source needed
Potentiostat (Vary E, measure I)
Works like an electron pump that changes the potential by sending electrons one way
Galvanic cell = spontanious
Galvanostat (vary I, measure E)
Factors affecting electrode reaction rate
2 electron transfer at electrode surface
3 Chemical reaction preceding/following electron transfer
1 Mass transfer
4 other surface reaction
Thermodynamics and Potentials
Basics
Reversibility
Electrochemical
Same chemical species are formed when the reaction has gone back and forth
Thermodynamic
Reaction can go in both directions with an infinitisimal change in potential
If reversible then in always in equilibrium --> nernst holds
Different potential oxidation/reduction in iv curve = diffusion overpotential/entropy effects but still reversible.
Reversibility is a matter of timescales
Half reactions
Determining solubility constants
Use two half reactions that gives same notation in the nernst equation as the solution formula of a compound
Then apply dE0 = RT/nf ln(K) to obtain solubility constant K
Half reaction can take place and leave charge on the electrons until the electrode has reached its equilibrium potential = Eeq that is given by the nernst equation. Eeq = E0 + RT/nF ln(a0/ar) for O+e- = R-. Almost no concentration difference to do that
Always work with the standard reduction potential in comparison with the reference potential
Change the potential of the half reaction = stabilising the reductant/oxidant with other species or change in solvent
Potentials types
Short circuit potential, potential = 0
Potential in between = alter external resistance
Open cell potential (Voc)
When no current flows,
Difference two equilibrium potentials
Cell potential Ecell = Eright - Eleft
Equilibrium potential = no nett current given by nernst equation
Overpotential = eta = E - Eeq
Positive/negative
potential = deficit electronic charge
potential = excess electronic charge
Formal potential E0'
If concentrations instead of activites are used
Acitvity = measure of the ''effective concentration''
Activity is 1 for solid phases or pure species
Activitys can change in certain electrolytes
Interfacial potential difference
Physics of phase potentials
Poisson equation
p = charge density (+ or -)
So no nett charge = no change in field = constant potential
dE = p/eps = -d2/dx2(pot)
Location charge
Space charge region
Electrolyte (few nm = double layer)
SC (1000 nm)
Metal (<nm)
In equilibrium there is no nett charge in the phase otherwise current will flow, charge situated on the outside
So the inner/galvani potential is altered with the charge distribution on the outside
Electrode in electrolyte
Double layer forms in electrolyte that cancels all charge
Potential difference electrode and electrolyte at the working electrode is the only potential that is altered.
Metal-metal interfaces cannot store charge so their IPD will be constant
Difference between potential in electrode and electrolyte solution that is cause of steering reactions
Electrochemical potential (energy)
mu^=mu + zFphi = mu0+RTlna+zFphi. Lowercase = specie, uppercase = phase. mu^= chemical + electrostatic potential
Properties
For electrons in metal (conc does not change) mu^ = mu0 -Fphi. mu0 is the fermi energy
For a pure phase at unit activity mu^=mu0
For uncharged species mu^=mu
For equi of species i in phase a and b = mu^a = mu^b
Determines the gibbs free energy, equal in equilibrium
Electrons will flow towards the lowest electrochemical potential
Change of potential = change of electrochemical potential of electrons
Work function/fermi level
If the fermi level of a metal is below the equilibrium potential, electrons will flow from the redox couple to the metal until it's potential is in equilibrium with the equilibrium potential
Does not alter if metal is nobel and is different than the reduction potential
Work function is in vacuum whereas redox pot is in solution
Electrochemistry
Chemical processes that include charge transport across interfaces between chemical phases
Goal
Limiting factors
Know how to set up an experiment
How does electrochemistry work
Kinetics
Electrode kinetics
Rate equations
Model rate constant
Arhenius equation
k = A*exp(-dG/RT)
A = attempt frequency
Transition state theory
Eyring equation
kf = transmission coefficient
rate of decay
activated complex
A barrier has to be overcome that depends for example on the reaction coordinate.
Current-overpotential equation
General
Can be derived from the butler-volmer equation
Two components = Mass transfer effects + electrode kinetics
Uses Eeq ipv E0'
At E = Eeq, vf=vb, v=0
Aproximate i-eta forms
Tafel equation
Approximations
Large overpotential
|eta|>100meV, so only one dominant reaction
No mass transfer limitations
C(0,t)=C*
Can be derived for the cathode and anode
Can be used to derive alpha and the exchange current
ln = 2.3 log
Can also be used for multi-electron transfer (slope is increases with n)
Lineair region
i/io = -feta
Hold for small overpotentials
Exchange current i0
Dependent on k0, concentrations and alpha
i0>>i
Very facile kinetics
Local equilibrium is ensured = reversible/nerstian reaction, because back reaction can still occurs at applied potential
Use nernst equation with surface concentrations (outside double layer)
So reaction is always mass transfer limited
Surface Concentrations are always known for certain E!!
Butler-volmer model
Overpotential increases/decreases activation energies oxidation/reduction reactions
dGc = dGc0 + aFeta
dGa = dGa0 - (1-a)Feta
a = transfer coefficient = symmetrie slopes
k0
Standard rate constant
k0 = large then dG0 is small and needed eta is small (simple reaction)
k0 = small then dG0 is large and needed eta also (complex)
Has units of cm / s mol
Relates the nett current with the applied overpotential (E-E0'). At E = E0 the two rate constants are equal
Only holds for single electron transfer and ss toch?
Multi-electron transfer
The key is to extend the theory of 1 e- transfer to multi-electron transfer
Determine the Rate determining step (RDS)
Fill in the values of that step into the BV model
No concentration buildup if all reactions are fast
Heterogeneous reaction
v = 0 and concentrations are at their bulk conc at Eeq
v = vf - vb = kf
Co(o,t) - kb
Cr(0,t) = i/nFA
Model electron transfer D + A --> D+ + A-
Marcus model
Energy donor and acceptor are quadratic in q(reaction coordinate) = hookes law
Energy at transition state dG(qts) = (dG0 + lam)^2/4lam
dG(qts) = (dG0 + lam)^2/4lam
Lambda = reorganisation energy
Energy donor/acceptor at coordinate acceptor/donor
At E=E0, dG = lam/4, value for k0
Contributions
Inner reorganisation energy
For example molecular vibrations
Solvent reorganisation energy
Dominates
Homogeneous
Heterogeneous
Eopt = refractive index^2
Is weaker for large molecules close to the electrode = higher kinetics
Hence determines the rate constant
Alpha = 0.5 + F(E-E0)/2lam
General
So Donor + acceptor must have same energies during transfer
So molecular rearrangement is needed to obtain same energy
ET reactions are radiationless
Type of reactions
Inner sphere reactions
Strong interactions between reactants
Difficult to model
Outer sphere reactions
D and A remain unaltered
Marcus model can be used
Reaction pathway
Reactant moves close to the surface
The solvent assume there transition state
The electron is transferred
System moves to new configuration
Reaction pathway
Mass transfer
Mechanisms
Migration
Cause ohmic resistance
Coupled with diffusion, can also balance
Movement of ions under electric field
Ability to migrate depends on conductivity solution
k = F|zi|
u
c
u = mobility ions
Larger if hydration radius ion is smaller
u = ziFDi/RT
lambda = molar conductivity ion
Per mol = Fziui
Per mol charge = Fui
transference number
Contribution ionic species i to overall conductivity
Convection
Usually small near surface
Diffusion
Cause nernstion overpotential
Electroneutrality must hold away from diff layer
Diffusion of ionic species is in same direction
limiting current density = nFADo*C0/delta
Nernst-plank equation
Contains diffussion and migration
Solve unsteady state problems using ficks second law + BC
Effect on potential
Nernstian overpotential
Non-linear
Causes the flattening of the curve
RT/nFln(ca/cr)
Ohmic resistance
Lineair
Is seen before the flattening --> skewing of figure
V=I*Rsol
It cost energy to move ions trough solution, depends on conductivity solution
Relec = d/k*A
Relec = d/k (cm2)
Mitigation
Low current density
Conducting electrolyte
High concentration
Convection
Smaller distance electrodes
Balance Sheet
Used to see what is limiting mass transfer and who is carrying the charge
Steps
3 Determine the number of electrons
4a Calculate the migration fluxes (watch zi!! and +- electrode)
2 Calculate the transference number of ionic species
5 Balance diffusion fluxes with migration
1 Write down the half reactions + sketch cell
4b Cations move to cathode and anions to anode
Note
Divide migration flux by charge ion
Supporting electrolytes do not participate in reaction and can help reduce ohmic resistance
Depending on the cell type and reaction, migration can increase/decrease diffusion
Electroneutrality must still hold, always check with diffusion!
Measurement methods
Step potential method
Experimental
Repeated steps
Repeat with increasing potentials until mass limitations reached
Measure current at specified step potential at time tau
Stirr to reach homogeneous concentration
Figure
2 Small current
3 Lineair increase in current (i/i0 = -feta)
1 No current, E<Eeq
4 Afflakking door mass limitations
Determination currents
Influence surface roughness
Geometric surface area
Microscopic surface area
Roughness = M/G
Use Geometric area if diffusion layer thickness > roughness
Assumptions
Boundary layer keeps growing
IC: Co(x,0) = Co*, Cr(x,0) = 0
Unsteady state mass transfer
Reversible process
BC: Co(inf,t) = Co*, Co(0,t) = 0 (t>0)
Transport equation
Ficks second law
Solve using IC/BC + laplace transformation
Cottrell equation
Gives the time dependent limiting current id = t^-1/2
Can be used to determine diffusion coefficient
If no convection occurs
Reversible reactions
Flux Co + flux Cr = 0
i(t) = id / (1 + eta*thetha)
Theta = Co(0,t)/Cr(0,t)
Given by nernst equation
If Co(0,t) = 0, original cottrell equation
So caused by assuming non-zero conc at surface
eta = (Do/Dr)^1/2
Half wave potential
Potential needed for half the limiting current
Close to E0, dependent on ration diffusion coefficient D0 and Dr
Obtained by substituting thetha and i(t) = 0.5 id
Quasireversible reaction
Half wave potential is far right from E0
Potential sweep methods
Cyclic voltammetry
Switching potential El
Potential at which the scan is reversed
Does influence reverse peak height, not peak position
Use correction for reverse peak height using mirroring
Demands Reversibility
The peak separation is close to 59 meV/n (from X(st))
The forward and backward peak current is constant (after correction)
Peak position is not altered by the scan rate
Area under the peaks must be the same (after corrections)
Only mass transfer limited
Differences with linear scan
Forward + backward sweep
Now the BC C(x,0) = Co* does not hold anymore
Quasireversible
Larger peak separation with decreasing k0
Assymmetry if alpha deviates from 0.5
Now also kinetically limited
Use nichelson method to determine relation
Overpotential
f(cr/co)
ETAbv(current dependent)
Zie schrift voor uitleg plot
Lineair scan voltammetry
Differences with step potential
Potential is function of time
v = scan rate (V/s)
E = Ei - v*t
BC is a function of time if reversibel
Current
Amplitude part
Depends on concentration, scan rate, diff constant
Shape part X(st)
Dimensionless
Use tabulated values
Decreases after peak due to mass limitations
Peak height
0.4463
(F^3/RT)
n^3/2
A
Do^1/2
Co
v^1/2
Depends on concentration, surface area, diff, scan rate, number of electrons
Are continious instead of repeated
Above i = 0, still same reaction
Real Life CV
Ohmic resistance
Makes the CV appear skewed
Correct always for the ohmic potential
Can be measured using certain method
Capacitative current Ic
Goes linear with scan rate = A Cd v
Dominant at high scan rates
Because of formation double layer
Irreversible reactions
Without backward reaction
No backward peak visible
With convection
Formation of gas species = no dip in peak
No backward peak
Multistep reaction
2 e- reaction
Shoulder peaks
Shape determined by difference E0
Electrochemical-chemical reaction
Chemical before
Use low scan rate to see forward peak
Chemical after
Use high scan rates to see backward peak
During measuring
2 Compensate for R and determine reversibility
3 Determine peak position, D,C
1 Identify number of reactions/peaks
4 Determine k0
Avoid side reactions, impurities
To measure
Constant potential
Reaction kinetics/reversibility
Diffusion coefficients and concentration
Redox potentials
Number of electrons in reaction
Surface area
Contant current
Production rate
Mass transfer rate
Product yield
FE efficiency
Other methods
Controlled current
Electrical impedance spectroscopy
Polarography
Are all unsteady state
Bulk electrolysis
Consumes so much during electolysis that it significantly changes the bulk (conc)
Theory
Stategies
Thin layer electrochemistry
Large area to volume ration
High current density
Extent of reaction
x = Nr/(Nr+N0)
Can be filled in into nernst equation
Effect
x < 0.5
Positive effect on potential
x > 0.5
Negative effect on potential
x = 1
Potential goes to inf
Reason why complete reaction is impossible
Can be related to the state of charge (SOC)
Current efficiency
Faradaic
How many of the electrons goes to the desired reaction
Coulombic
For ions
Experimental
Methods
Constant current
Know how much is produced
FE will be low, if current is set to high over time --> E increase that leads to side reactions
Constant potential
Limiting current = il(t) = i(t=0)*exp(-mAt/V)
V = volume reactor
m = mass transfer factor
A = electrode area
With i(t=0) = nFAm
C
Always know if side reactions occur
i(t) = nFAm
(C
-C(x)) always holds
Electrolysis designs
Electrolytic cell
Separators
Types
b knudsen diffusion
c molecular sieving
d solution diffusion (membranes)
a convective flow (Diapragm,same k as sol)
Smaller pore size a--> d
Separates the two compartments + physical stability
Cell resistances
Anode + cathode overpotential
Ohmic loss electrode
Ohmic loss electrolyte
Use zero gap cell
Porous electrode
Electrodes
Large Macrostructure
Increased area
Large microstructure
Increased area and activity
Flow electrolysis
Reactions out (Rout)
1-exp(-msAL/v)
v = vlowrate
s = reaction area per volume
1-exp(-mst)
t = residence time
Using limiting current
Continious production
Use large area to volume and use a favourable geometry, mass transfer coefficient is dependent on reynolds and sherwood number
Rotating disk electrode
Creates convection that increases limiting current
Applications
Industrial water electrolysis
Need
Towards electricity driven economy
Use in energy storage, synthesis, etc
Increase scale needed to compete with steam reforming
Theory
Kinetics
Good electrocatalyst
Principle of sabatier
Intermediate must not bind to strong or to weak
Steps HER half reaction
1 Volmer step: H+ e- --> Hads
2a heyrovsky step: Hads + H+ e- --> H2
2b Tafel step: Hads + Hads --> H2
Conditions determine wich step is rate limiting
Thermodynamics
Potential half reactions depend on pH
Use pourbaix diagram to observe behaviour
Alter pH to avoid side reactions (sea water)
-nFE=dG = dH - dTS
1.3-1.5V = endothermic region
1.5V = thermoneutral voltage (same amount of heat is produced as needed for the reaction)
Above 1.5V = exothermic region
So run electrolysis close to thermoneutral voltage
Steam electrolysis uses less energy input
Current electrolysers
Types
PEM
High current density and good at ittermitency
High CAPEX and uses rare metals
AEM
High efficiency and low CAPEX
Less mature and unknown lifetime
Alkaline
Mature and low CAPEX
But limited current density and poor at ittermitency
Solid oxide
High stack efficiency
Less mature and needs waste heat
Configuration
Monopolar(in parallel)
Bipolar(in series)
Challanges of water electrolysis
1 Overpotential OER (good catalyst needed)
3 Flow, heat and bubble modelling
5 Cost effective (low energy prices needed)
4 Intermittent production of hydrogen (offshore production)
2 Bulk resistances
Hyet
The make an AEM electrolyser/compressor that sends out hydrogen directly at 200 bar. Against low CAPEX
Membrane technology