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Energy Storage in Batteries - Coggle Diagram
Energy Storage in Batteries
Introduction to thermodynamics & electrochemistry
Electrochemistry
Chemical potential is the driving force
dG = mu*dn = -nFEc
Nernst equation Eeq = Eo + RT/nF ln(1/Q)
Does not describe solid electrochemical potential, for example li-ion batteries
Conc will change during charge/discharge, V is time dependent
Standard conditions = 1 molar, 293 K, 1 bar
Dilute limit = concentration is activity
Influence of current
Overpotential eta = I*R (deviation Eeq)
Higher dischagre current means lower potential
Thermodynamics
Intrinsic variable(size independent)
Path variable
Extrinsic variable(size dependent)
State variable
dU = q + w
General concepts
Use batteries
To resolve the ittermittence energy problem
For mobility purposes
Everyday consumer goods
Performance quantities
Energy
Volumetric energy density (Wh/L)
Gravimetric energy density (Wh/kg)
Energy efficiency
Power density (W/kg) (Higher P decreases the energy density)
Stability
Cycle life
Number of cycles to reach 80%
Charge
Coulombic efficiency
Must be > 99.9% to have a proper cycle life
Charge out / Charge in
Otherwise Lithium goes away to fast
Specific capacity (Ah/g)
Charging speed
State of charge = C/Cmax * 100%
XC rate = current that results in full capacity after 1/x hours
These quantities should be calculated for the final obtained product
Cost
Stationary batteries must be cost effective
Mobile batteries may be more expensive for high performance
Current problems
Use of rare materials
Cobalt
Lithium is not nonexaustable
CO2 intensive process
Components battery
Current collectors
Electrolyte
Anode/Cathode
Battery packaging
Stages battery formation
Material level --> electrode level --> cell level --> battery level
Factor 4 difference in energy density between material and final battery
Goal
To understand the basic principles of batteries and know the current developments
Basis solid state materials
Structure
Diffraction
Theory
Braggs law
When constructive interference occurs
n
L=2dhkl
sin(thetha)
2thetha = diffraction angle
Distance planes
dhkl = a/root(h^2+k^2+l^2)
Can chance during (dis)charging
Types
X-ray diffraction
Gives higher intensity for higher atom numbers
Created using copper (b-radiation)
Neutron diffraction
Seperate on energy = same wavelength
Interacts very differently throughout the periodic table, most with H
Capture from nuclear plant
Is thus complementary with x-ray diffraction
The diffraction pattern is unique for certain compound and can be used to observe the phase transitions during (dis)charge
Phase diagrams
Structural changes in the electrodes determines capacity and voltage
Use the lever rule to determine the composition
Phase diagrams are needed to describe electrodes and the reactions during charge and discharge
Solid state electrode reactions
Intersertion reaction
(dis)advantages
Has poor lithium capacity and conductivity
Only small volume change (4%)
The reversible insertion of a guest species into a host structure
Reconstitution reaction
Formation (A + B = AB)
Alloying
Silicon battery for example that has an 300% volume increase
Displacement (A + BX = AX + B)
RuO2 for example
(dis)advantages
Has good conductivity
Large volume changes lead to low cycle life
Have large specific capacity
Battery properties (lithium-ion)
Thermodynamics
Approaches
Meso level
Phase field modelling
The structure will always follow the lowest energy profile!
Go from dal to dal
Ternary phase diagram
Will show the stable crystal structure for a given compostion
Shows phase route during charge-discharge
Nano level
DFT
Solves for ground state by using electron density and solving the SE.
Gibbs free energy
Entropy component
Greatest when fraction x = 0.5
x = fraction lithium
If entropy>enthalpy = solid solution is formed
Enthalpy compononent
omega = enthalpy of mixing
If omega>2kbt enthalpy dominates = phase separation
Cell potential
Resulting cell potential is constant for phase separation and decreasing for solid solution. Ecell = -1/f * dg/dx
Constant cell potential (voltage plateau)is preferred in batteries
Potential contains multiple plateaus if multiple phase transitions occur
Solid solution is fully discharged (E = 0) if in dal
Kinetics
Increased by
Many lithium vancencies = more difussion
Porous electrode material
Small electrodes
Hence kinetics solid solutions > phase seperations
Slow kinetics will result in capacity losses with high C-rate, not enough time to lithuate al material before V cutoff
(Super)Capacitors
Basis
Types
Hybrid capacitors
Pseudocapacitor
Both non-faradaic(double layer) and faradaic processes occur = pseudo
Subtypes
Redox
Insertion
Adsorption
Only partial electron transfer occurs = different from battery
Non-linear voltage profile
Double layer capacitors
Energy is stored in the electric double layer (adsorption ions)
Use inert polarisble electrodes (carbon)
Ions in electrolyte are used as countercharge
Only-nonfaradaic processes occur
Performance quantities
Capicitance
Entire cell (symmetric F/g)
C = Idt/mv
Ccell = 0.25Celec
C = Q/V = Idt/V = A(area) k0*eta / d (distance)
Single electrode (F/g)
C = Idt/(0.5
m
0.5V)
The capacitance is always measured for the discharge
Measure for how much charge can be stored under a certain potential
C = I / dv/dt for nonlinear potentials
Both electrodes need same capacitance
Energy density
E = 0.5
C
V^2
Power
Maximum = V^2/4R
Average = E/tau
Capacity (C/g)
Properties
Low energy density
High power density
Cheaper than batteries
Non-constant(linear) potential
Uses
In public transportation where chargers are available
Energy recovery during braking
Theory double layer
Improving Capacitance
Higher dielectric constant
Have a co-ion desorption mechanism
Large surface area = Mesopores
Have electrolyte with good potential window (organic or ionic solvent)
Measurement methods
Cyclic voltammetry
Square like current
Constant scan rate
Constant current (GCD)
Lineairly in/decreasing potential
For symmetric cell(m1=m2)
Electrostatic potential
Driving force
phi = q/etax
eta = dielectric constant = k/k0
So no chemical potential involved
Gibbs energy
G = q1q2/eta*r
Models of double layers
Gouy point charge model
Ignores volume ions
Stern model
Stern layer
Diffuse layer
Hence double layer
Hermholtz model
Single layer of countercharge
Theory Pseudo
Adsorbtion pseudocapacitance
Langmuir isotherm
If attraction g > 0 then it takes longer to reach full capacitance
How the surface coverage depends on the potential, rate constants and interaction between adsorbates
Depends on coverage surface (thetha)
Pseudomaterials
Polymers
Better when adding carbon
p-type doping = + charged
n-type doping = - charged
Redox-pseudo
Metaloxides
Especially RuO2 has high capacitance
Carbons
Redox with surface groups
Double layer
2D materials
Large surface area/availability
Flexible and tunable
2d mxenes
Redox
Intercalation
CV's
Redox
A bit square like
Constant capacitance at each potential
Intercalation
Peaks at same potential
Assymetrical cv
Adsorbtion
Peaks back/forward scan at same potential
Symmetrical but not square like shape
Completely faradaic = peaks at different position
Cycle life
Origin decrease
Instability electrolyte
Stability window
Stability
LUMO electrolyte > fermi level anode
Fermi level = electrochemical potential
HOMO electrolyte < fermi level cathode
Increasing stability window
Replace water with organic solvent
Adding salt ions to water
Expensive
High viscosity
Potential window where the electrolyte is not oxidized/reduced
Charge cutoff is needed to protect the electrolyte
Li-ion battery
Lithium is most reductive specie so there is no stable elecrolyte --> will always react wilth electrolyte --> creates solid electrolyte interface (SEI)
SEI
Effects
Limits Li-ion conductivity --> higher resistivity
Consumes lithium --> decrease in CE, great effect on cycle life
Favourable properties
Good Li-ion conductivity
Flexibile
Poor electrical conductivity
Less chance that more electrolyte gets reduced
Low solubility
Stable and good adhesion
Favourable composition
Inorganic salt
So add enough salts, not to much
For stability and conductivity
Use more salt (entropy) to favour solubility of good SEI salts
Organic polymers
Add flexibility
Depends on many properties and still the least understood
Artificial SEI
Expensive
Atomic layer deposition
Chose of electrolyte
Good conductivity
Low melting point and low viscosity
High permitivity
Safety: high boiling/flash point
High stability window
Usually a mixture is made to obtain all propeties
Forms good SEI
Li metal
Use high SEI Li conductivities to temper dendrite formation
Forms dendrites by large volume changes and can be encapsulated by SEI that results in dead Li
Structure failure electrode
Formation unwanted structures
Poor li/e conductivity
Large overpotential needed
Capacity losses
Crack formation
Can result in isolated islands --> capacity losses
Especially problem in Si-electrode
Due to large volume and structural changes
Some have almost no volume change --> no cracks and long cycle life
NMC degradation
Nickel, manganese, cobalt battery: has capacity, stability and rate
But has surface degradation
Influenced by
Depth of discharge
Temperature
Charge potential cutoff
Characterised by
Coulombic efficieny
Charge carrier kinetics
4 charge transfer processes
3 Ionic conduction electrode material
Use formula k and use D = nl^2/t0
Usually not so large
Less effect when nano particles are used
Advantages
Can act as supercapacitor
Can host more strain
Higher charging rate
Disadvantages
Lower packing density
Lower cycle life due to more surface area
4 Electronic conduction electrode
Can be increased by adding carbon
Creates pathways for the electrons
2 Charge transport over electrolyte-electrode interface
Step 2: electron transfer via BV model
Step 1: enter the double layer
Often not limiting due to exponential term
1 Ion conduction through electrolyte
R = l/kA
k = F^2/RT(zi^2DiCi)
Di gets lower when Ci is largely increases due to viscosity
Is often limiting due to large l/A values in narrow electrode channels
Use straight channels to improve this
Influences
Storage efficiency (internal resistance)
Cycle life (less overpotential needed)
Charge speed, power density
Overpotential eta = eta1 + eta2 +eta3+eta4
Higher rate battery usually means lower capacity
Battery types
Na-ion
Heavier and lower energy density (50%)
Easy to come by
Lower potential
Has favourable chemistrly, more can be done with Li
Solid State
Advantages
Safety
Non-toxic
Non-flammable
Non-volatile
Immobile counterions
No polarisation
No kinetic limitation
No diffusion gradient
Current problems
Trade-off stability and conductivity
Reactions
Chemical
Electrochemical
Redox
Chemical stabilisation
Inherently
Kineticly
Mechanical stability(flexible)
Tortuosity
More zig-zagging of ions occurs when local SE concentration is low
Dendrite formation using Li-metal
General
Does not have larger energy density --> only applicable when other electrode materials are possible
The liquid electrolyte is replaced by an solid electrolyte that has good ionic conductivity and poor electrical conductivity
The solid electrolyte sits in between the pores of the electrodes and in between
Theoretical is not experimental capacity to protect cycle life
Conductivity SE
Sigma = nzmu
Large mobility needed
Many charge carriers via vac/int needed
ionic hopping
D = fL^2/2d
d = dimensionality
f = frequency succesfull jumps
Lead-acid
Advantages
Cheap
Mature
Problems
Water splitting at fast charging
Sulfation
Occurs at low H2SO4 conc
PbSO4 falls down and cannot be used anymore
Increased by stratification (H2SO4 accumulation at bottum)
Low energy efficiency (50%)
High internal resistance
Electrolyte resistance increases when consuming H2SO4
High overpotentials
Self-discharging
Increases at higher T
Battery dies after few months
Thermodynamics
Half reations
Anode = Pb+HSO4- --> PbSO4 + H+ + 2e- (-0.356V)
Cathode = PbO2 + HSO4- + 3H+ + 2e- --> PbSO4 + 2H2O (1.685V)
Nernst equation
E = E0 + RT/2F ln(H+^2 * HSO4^2)
Molality is often used when electrolyte is consumed
m = moles of solute / mass of solvent (kg)
Total reaction
Pb+PbO2 + 2 H2SO4 --> 2 PbSO4 + 2H2O (2.041V)
General
Lead acid batteries are a mature technology
Types
Car batteries
Breaks down when discharged below 50%
Gives a short/powerfull burst of 500A
Deep discharge battery
Redox-flow
Types
Redox flow
Vanadium
Most common
But vanadium is expensive
Bromine
Aquous
Smaller stability window
Non-aquous
Unsafe, because solvent is flammable
Hybrid
Containg Zn, Cu, etc
Dispersed systems
Lead acid flow battery
H2SO4 is pumped around
Li-metal
General
Charesteristics
Medium energy density
Large energy storage
Low power density
Safe if aquous solvent is used
Relatively cheap
Non-mature --> growthpotential
Application
Can store large much energy + cheap
To use for grid stabilisation
Only redox and lead acid are applicable for this application
Construction
Two containers containing two redox couples
Liquid from containers is pumped towards the electrodes
Reaction method similar to that of a fuel cell
Membrane is needed for counter ions that keep charge neutrality
Thermodynamics vanadium
Total reaction
VO2+ V2+ + 2H+--> VO2+ +H2O +V3+ (1.26V)
Half reactions
Cathode: VO2+ e- + 2H+ -->VO2+ +H2O (1V)
Anode: v2+--> v3+ +e- (-0.26V)
State of Charge
v2+/(v3+ v2+)
VO2+ /(VO2+ + VO2+)
Internal resistance
Ohmic resistance(bulk)
Mass transfer (diffusion layer)
Kinetic (absorbption layer)