Energy Storage in Batteries

Introduction to thermodynamics & electrochemistry

General concepts

Electrochemistry

Chemical potential is the driving force

Thermodynamics

dG = mu*dn = -nFEc

Intrinsic variable(size independent)

Path variable

Extrinsic variable(size dependent)

State variable

Nernst equation Eeq = Eo + RT/nF ln(1/Q)

dU = q + w

Use batteries

Performance quantities

To resolve the ittermittence energy problem

For mobility purposes

Everyday consumer goods

Energy

Volumetric energy density (Wh/L)

Stability

Gravimetric energy density (Wh/kg)

Cycle life

Charge

Number of cycles to reach 80%

Energy efficiency

Coulombic efficiency

Must be > 99.9% to have a proper cycle life

Specific capacity (Ah/g)

Power density (W/kg) (Higher P decreases the energy density)

Charge out / Charge in

Standard conditions = 1 molar, 293 K, 1 bar

Influence of current

Goal

To understand the basic principles of batteries and know the current developments

Charging speed

Current problems

Use of rare materials

CO2 intensive process

These quantities should be calculated for the final obtained product

Cobalt

Lithium is not nonexaustable

Cost

Stationary batteries must be cost effective

Mobile batteries may be more expensive for high performance

State of charge = C/Cmax * 100%

Otherwise Lithium goes away to fast

Overpotential eta = I*R (deviation Eeq)

Higher dischagre current means lower potential

XC rate = current that results in full capacity after 1/x hours

Dilute limit = concentration is activity

Does not describe solid electrochemical potential, for example li-ion batteries

Basis solid state materials

Structure

Diffraction

Solid state electrode reactions

Intersertion reaction

Reconstitution reaction

Formation (A + B = AB)

Displacement (A + BX = AX + B)

Phase diagrams

Structural changes in the electrodes determines capacity and voltage

Use the lever rule to determine the composition

(dis)advantages

Has good conductivity

Large volume changes lead to low cycle life

Have large specific capacity

Has poor lithium capacity and conductivity

Only small volume change (4%)

The reversible insertion of a guest species into a host structure

Conc will change during charge/discharge, V is time dependent

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

Alloying

Silicon battery for example that has an 300% volume increase

RuO2 for example

(Super)Capacitors

Battery properties (lithium-ion)

Thermodynamics

Approaches

Meso level

Nano level

DFT

Gibbs free energy

Basis

Theory double layer

Types

Hybrid capacitors

Pseudocapacitor

Double layer capacitors

Performance quantities

Capicitance

Entire cell (symmetric F/g)

C = Q/V = Idt/V = A(area) k0*eta / d (distance)

Single electrode (F/g)

C = Idt/mv

Ccell = 0.25Celec

Properties

Low energy density

High power density

Uses

Energy density

E = 0.5CV^2

In public transportation where chargers are available

Cheaper than batteries

Improving Capacitance

Higher dielectric constant

Have a co-ion desorption mechanism

Large surface area = Mesopores

Measurement methods

The capacitance is always measured for the discharge

Energy is stored in the electric double layer (adsorption ions)

Non-constant(linear) potential

Energy recovery during braking

C = Idt/(0.5m0.5V)

Cyclic voltammetry

Constant current (GCD)

Lineairly in/decreasing potential

Square like current

For symmetric cell(m1=m2)

Use inert polarisble electrodes (carbon)

Electrostatic potential

Driving force

phi = q/etax

eta = dielectric constant = k/k0

Models of double layers

So no chemical potential involved

Measure for how much charge can be stored under a certain potential

Gouy point charge model

Stern model

Hermholtz model

Single layer of countercharge

Ignores volume ions

Stern layer

Diffuse layer

Hence double layer

Power

Maximum = V^2/4R

Average = E/tau

Gibbs energy

G = q1q2/eta*r

Constant scan rate

Have electrolyte with good potential window (organic or ionic solvent)

Ions in electrolyte are used as countercharge

C = I / dv/dt for nonlinear potentials

Kinetics

Phase field modelling

Increased by

Many lithium vancencies = more difussion

Hence kinetics solid solutions > phase seperations

Porous electrode material

Small electrodes

Entropy component

Enthalpy compononent

Greatest when fraction x = 0.5

x = fraction lithium

If entropy>enthalpy = solid solution is formed

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

The structure will always follow the lowest energy profile!

Go from dal to dal

Slow kinetics will result in capacity losses with high C-rate, not enough time to lithuate al material before V cutoff

Solves for ground state by using electron density and solving the SE.

Ternary phase diagram

Will show the stable crystal structure for a given compostion

Shows phase route during charge-discharge

Only-nonfaradaic processes occur

Capacity (C/g)

Solid solution is fully discharged (E = 0) if in dal

Theory

Types

X-ray diffraction

Neutron diffraction

The diffraction pattern is unique for certain compound and can be used to observe the phase transitions during (dis)charge

Braggs law

Distance planes

When constructive interference occurs

nL=2dhklsin(thetha)

2thetha = diffraction angle

dhkl = a/root(h^2+k^2+l^2)

Gives higher intensity for higher atom numbers

Created using copper (b-radiation)

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

Phase diagrams are needed to describe electrodes and the reactions during charge and discharge

Both non-faradaic(double layer) and faradaic processes occur = pseudo

Subtypes

Only partial electron transfer occurs = different from battery

Redox

Insertion

Adsorption

Non-linear voltage profile

Theory Pseudo

Cycle life

Origin decrease

Influenced by

Depth of discharge

Temperature

Instability electrolyte

Structure failure electrode

Characterised by

Coulombic efficieny

Can chance during (dis)charging

Charge potential cutoff

Stability window

Stability

LUMO electrolyte > fermi level anode

Fermi level = electrochemical potential

Increasing stability window

HOMO electrolyte < fermi level cathode

Potential window where the electrolyte is not oxidized/reduced

Replace water with organic solvent

Adding salt ions to water

Expensive

High viscosity

Adsorbtion pseudocapacitance

Pseudomaterials

CV's

Redox

Intercalation

Adsorbtion

Peaks back/forward scan at same potential

Symmetrical but not square like shape

A bit square like

Constant capacitance at each potential

Peaks at same potential

Assymetrical cv

Langmuir isotherm

Depends on coverage surface (thetha)

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

Polymers

Metaloxides

Carbons

2D materials

Especially RuO2 has high capacitance

Large surface area/availability

Flexible and tunable

Better when adding carbon

p-type doping = + charged

n-type doping = - charged

Redox-pseudo

Redox with surface groups

Double layer

2d mxenes

Redox

Intercalation

Completely faradaic = peaks at different position

Both electrodes need same capacitance

Charge carrier kinetics

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

4 charge transfer processes

Influences

Storage efficiency (internal resistance)

Cycle life (less overpotential needed)

Charge speed, power density

3 Ionic conduction electrode material

4 Electronic conduction electrode

2 Charge transport over electrolyte-electrode interface

1 Ion conduction through 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

Organic polymers

So add enough salts, not to much

For stability and conductivity

Add flexibility

Use more salt (entropy) to favour solubility of good SEI salts

Depends on many properties and still the least understood

Chose of electrolyte

Good conductivity

Low melting point and low viscosity

Safety: high boiling/flash point

High permitivity

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

Charge cutoff is needed to protect the electrolyte

Artificial SEI

Expensive

Atomic layer deposition

Formation unwanted structures

Crack formation

NMC degradation

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

Nickel, manganese, cobalt battery: has capacity, stability and rate

But has surface degradation

Poor li/e conductivity

Large overpotential needed

Capacity losses

Overpotential eta = eta1 + eta2 +eta3+eta4

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

Step 2: electron transfer via BV model

Step 1: enter the double layer

Use formula k and use D = nl^2/t0

Often not limiting due to exponential term

Usually not so large

Less effect when nano particles are used

Can be increased by adding carbon

Creates pathways for the electrons

Advantages

Disadvantages

Can act as supercapacitor

Can host more strain

Higher charging rate

Lower packing density

Lower cycle life due to more surface area

Higher rate battery usually means lower capacity

Use straight channels to improve this

Solid State

Lead-acid

Redox-flow

Advantages

Current problems

General

Advantages

Problems

Thermodynamics

Half reations

Nernst equation

Does not have larger energy density --> only applicable when other electrode materials are possible

Conductivity SE

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

Safety

Immobile counterions

Trade-off stability and conductivity

Tortuosity

No polarisation

No kinetic limitation

No diffusion gradient

More zig-zagging of ions occurs when local SE concentration is low

Reactions

Chemical stabilisation

Chemical

Electrochemical

Redox

Inherently

Kineticly

Mechanical stability(flexible)

Dendrite formation using Li-metal

Non-toxic

Non-flammable

Non-volatile

Theoretical is not experimental capacity to protect cycle life

Sigma = nzmu

Large mobility needed

Many charge carriers via vac/int needed

ionic hopping

D = fL^2/2d

d = dimensionality

f = frequency succesfull jumps

General

Lead acid batteries are a mature technology

Types

Car batteries

Deep discharge battery

Breaks down when discharged below 50%

Gives a short/powerfull burst of 500A

Anode = Pb+HSO4- --> PbSO4 + H+ + 2e- (-0.356V)

Cathode = PbO2 + HSO4- + 3H+ + 2e- --> PbSO4 + 2H2O (1.685V)

Total reaction

Pb+PbO2 + 2 H2SO4 --> 2 PbSO4 + 2H2O (2.041V)

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)

Cheap

Mature

Water splitting at fast charging

Sulfation

Low energy efficiency (50%)

High internal resistance

Electrolyte resistance increases when consuming H2SO4

Occurs at low H2SO4 conc

PbSO4 falls down and cannot be used anymore

Self-discharging

Increases at higher T

Battery dies after few months

Increased by stratification (H2SO4 accumulation at bottum)

High overpotentials

Types

General

Charesteristics

Application

Can store large much energy + cheap

To use for grid stabilisation

Medium energy density

Large energy storage

Low power density

Safe if aquous solvent is used

Relatively cheap

Redox flow

Vanadium

Bromine

Hybrid

Dispersed systems

Lead acid flow battery

Li-metal

Only redox and lead acid are applicable for this application

Non-mature --> growthpotential

Construction

Thermodynamics vanadium

Total reaction

Half reactions

State of Charge

Two containers containing two redox couples

Liquid from containers is pumped towards the electrodes

Reaction method similar to that of a fuel cell

Containg Zn, Cu, etc

Aquous

Non-aquous

Most common

But vanadium is expensive

Unsafe, because solvent is flammable

Smaller stability window

H2SO4 is pumped around

Membrane is needed for counter ions that keep charge neutrality

Cathode: VO2+ e- + 2H+ -->VO2+ +H2O (1V)

Anode: v2+--> v3+ +e- (-0.26V)

VO2+ V2+ + 2H+--> VO2+ +H2O +V3+ (1.26V)

v2+/(v3+ v2+)

VO2+ /(VO2+ + VO2+)

Internal resistance

Ohmic resistance(bulk)

Mass transfer (diffusion layer)

Kinetic (absorbption layer)